Management Science : Current Researches and Developments - Part II 9781846634819, 9781846634802

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06/06/2007

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ISSN 0368-492X

Volume 36 Number 5/6 2007

Kybernetes The international journal of cybernetics, systems and management sciences Management science: current researches and developments – part II

Selected as the official journal of the World Organisation of Systems and Cybernetics

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Kybernetes

ISSN 0368-492X

The International Journal of Systems, Cybernetics and Management Science

Volume 36 Number 5/6 2007

Management science: current researches and developments – part II Editor Brian H. Rudall

Access this journal online _________________________

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Editorial advisory board __________________________

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Preface __________________________________________

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INVITED PAPERS Symbiosis and the viable system model Allenna Leonard _______________________________________________

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Managing sustainable service improvements in manufacturing companies Heiko Gebauer and Elgar Fleisch __________________________________

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Cybernetics of culture James Rowe ___________________________________________________

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Knowledge management: modeling the knowledge diffusion in community of practice Nen-Ting Huang, Chiu-Chi Wei and Wei-Kou Chang _________________

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CONTENTS

CONTENTS

Service-oriented architecture is a driver for daily decision support

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Annika Granebring and Pe´ter Re´vay _______________________________

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A viable systems perspective to knowledge management Chyan Yang and Hsueh-Chuan Yen _______________________________

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A flexible platform for mixed-integer non-linear programming problems ¨ stermark ________________________________________________ Ralf O

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INDEX TO PART I Index to contributions published in Part I of the series: Management Science: Current researches and developments_____________________________________

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REGULAR JOURNAL SECTIONS CONTEMPORARY CYBERNETICS, SYSTEMS AND MANAGEMENT SCIENCE Emerging innovative systems Brian H. Rudall and C.J.H. Mann _________________________________

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CYBERNETICS AND SYSTEMS ON THE WEB Newlook ASC, new WOSC address, machine translation Alex M. Andrew _______________________________________________

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A stability theory for model systems Y. Villacampa, F. Verdu´ and A. Pe´rez _____________________________

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A reliable technique for solving third-order dispersion equations D. Lesnic _____________________________________________________

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Reconciliation of perception of information granules and granular mappings W. Pedrycz ___________________________________________________

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Numerical solution of the Burgers’ equation over geometrically graded mesh ˙Idris Dag˘ and Ali S¸ahin _________________________________________

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Hierarchical system of natural grammars and the process of innovations exchange in polylingual fields Svetlana Novikava and Kanstantsin Miatliuk ________________________

CONTENTS 736

Covering properties in intuitionistic fuzzy topological spaces Francisco Gallego Lupia´n˜ez ______________________________________

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A new look at the Heisenberg’s uncertainty principle: a cybernetics and general dynamical systems approach Dwijesh K. Dutta Majumder and Swapan K. Dutta ___________________

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Homomorphisms of fuzzy recognizers S.R. Chaudhari ________________________________________________

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Systems view, emergence and complexity J. Korn_______________________________________________________

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Time-splitting procedures for the solution of the two-dimensional transport equation Mehdi Dehghan________________________________________________

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A simulation study of a new family of test statistics for the Behrens-Fisher problem Julio Angel Pardo and Marı´a del Carmen Pardo _____________________

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Communications and forum _______________________

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News, conferences and technical reports ___________

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Book reviews_____________________________________

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Book reports _____________________________________

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Announcements __________________________________

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Special announcements ___________________________

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continued

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EDITORIAL ADVISORY BOARD A. Bensoussan President of INRIA, France V. Chavchanidze Institute of Cybernetics, Tbilisi University, Georgia A.B. Engel IMECC-Unicamp, Universidad Estadual de Campinas, Brazil R. Espejo Syncho Ltd, UK R.L. Flood Hull University, UK F. Geyer The Netherlands Universities Institute for Co-ordination of Research in Social Sciences, Amsterdam, The Netherlands A. Ghosal Honorary Fellow, World Organisation of Systems and Cybernetics, New Delhi, India R. Glanville CybernEthics Research, UK R.W. Grubbstro¨m Linko¨ping University, Sweden Chen Hanfu Institute of Systems Science, Academia Sinica, People’s Republic of China G.J. Klir State University of New York, USA A. Leonard Independant Consultant, Toronto, Canada Yi Lin International Institute for General Systems Studies Inc., USA

K.E. McKee IIT Research Institute, Chicago, IL, USA M. Ma˘nescu Academician Professor, Bucharest, Romania M. Mansour Swiss Federal Institute of Technology, Switzerland K.S. Narendra Yale University, New Haven, CT, USA C.V. Negoita City University of New York, USA W. Pearlman Technion Haifa, Israel A. Raouf Pro-Rector, Ghulam Ishaq Khan (GIK) Institute of Engineering Sciences & Technology, Topi, Pakistan Y. Sawaragi Kyoto University, Japan B. Scott Cranfield University, Royal Military College of Science, Swindon, UK M. Schwaninger University of St. Gallen, Switzerland D.J. Stewart Human Factors Research, UK I.A. Ushakov Moscow, Russia J. van der Zouwen Free University, Amsterdam, The Netherlands

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Preface Management Science: Current researches and Developments – Part II This special double issue of the journal is the second part in a series that contributes to our increased involvement with management science. Part I was published earlier this year (Kybernetes, Volume 36, Nos 3/4). We are pleased to publish these contributions and in particular the invited paper of Dr Allenna Leonard, who is a former President of the American Society for Cybernetics, and a Research Fellow of Liverpool John Moores University, UK. As a newly appointed member of this journal’s Editorial Advisory Board (EAB), with a special interest in Management Science, she joins Professors Raul Espejo and Marcus Schwaninger in furthering our commitment to the field. As is our practice we have also included our regular journal sections and a selection of papers that will confirm our aim to publish a wide range of contributions that cover the many facets of the interdisciplinary areas of Systems and Cybernetics. Brian H. Rudall Editor-in-Chief

The current issue and full text archive of this journal is available at www.emeraldinsight.com/0368-492X.htm

INVITED PAPER

Symbiosis and the viable system model Allenna Leonard

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The Complementary Set, Toronto, Canada Abstract Purpose – The purpose of this paper is to suggest symbiosis could be a metaphor for finding ways to help countries that are challenged to become economically and socially viable. Beer’s viable system model (VSM), which also has biological roots could be applied to look for gaps in the conditions for viability and to seek to fill them through collaborative arrangements. Design/methodology/approach – This is a conceptual paper suggesting various symbiotic processes in biology could inform actions in the social environment. Findings – Concepts from biological and environmental sciences can be applied to social conditions. The viable system model provides a framework for such applications. Research limitations/implications – This paper presents general ideas and some examples of possibilities for symbiotic collaboration. Opportunities for symbiosis to be applied to the social arena would emerge through exploration of local conditions. Practical implications – Much could be accomplished at various scales through imaginative collaboration. The natural world provides models and metaphors to stimulate thinking about collaboration. Originality/value – The author suggests that the phenomenon of symbiosis in the natural world could provide useful concepts to apply to situations where countries and regions that are not viable or viable enough in the global marketplace. The VSM is discussed regarding a framework to integrate opportunities for collaboration. Keywords Cybernetics, Control systems, International cooperation Paper type Conceptual paper

Introduction Applications of Stafford Beer’s viable system model (VSM) usually proceed under the assumption that the entity being modeled is viable, or could in principle be viable. When the diagnosis shows an entity to be non-viable, suggestions are made to either redesign it to make it viable or to abandon the project. In the world, however, there are entities that a conventional diagnosis would show to be non-viable that do not (and should not) “die.” The list includes complex entities such as failed states, conflict-ridden states and states that are simply not able to compete under the current global marketplace constraints. It may also include cultures, regions and major cities that find themselves unable to participate effectively enough in the world marketplace to access the resources they need. The costs of their lack of viability are unacceptable to them and, connected as we are, unacceptable to the rest of the world. In nature, some organisms are particularly interdependent although the rest are all connected within a web of life. Predator/prey relationships abound; other animals eat vegetation; many plants depend on birds, bees and other insects for pollination and

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helpful bacteria live inside and enable larger organisms. Human beings, who are learning about the load their activities place on the environment, are becoming reacquainted with the facts of their dependency on the natural world. We are, in short, becoming aware of our ecological footprints and coming to realize that we must learn to live off the “income” of the natural world rather than continuing to draw on its “capital” if we are to survive. There is considerably less awareness of the social footprints left by our collective actions. Colonialism and the demand in the west for natural resources and inexpensive products has led to conflict, exploitation, human rights abuses, poverty and disease in parts of the world less effective in defending their own interests or less responsive to the interests of their populations. Although this has not been intentional, it has been too easy not to know. The result is that many people live in conditions where their own efforts are not suffficient to sustain them because their countries lack the social and technological infrastructure to support competitive economic activities. In the natural world, some organisms that are not viable, or as viable on their own, increase their capability to meet environmental challenges through symbiosis. Could symbiosis offer a metaphor or a model for social sustainability in regions of the world where viability is a challenge? Symbiosis has the advantage of spanning scale. The relations could be country to country, but they could also be NGO or university to region or community, business to city or village or between communities. Many such relationships exist already but they could be seen as part of a larger pattern, expanded and integrated. Could the viable system model offer a way of looking at these situations that would link existing situations and uncover potential beneficial relationships? It is an idea worth exploring. Symbiosis Symbiosis has been defined as “living together” where one organism or type of organism lives in close proximity to, touching or, in the case of bacteria, inside another. One or more species provides, to another or others, some function that they do not possess or that they cannot perform as efficiently. There are three main types of symbiosis: (1) Mutualism. Where both organisms benefit. (2) Commenserability. Where one organism benefits but there is no effect on the other. (3) Parasitism. Where one organism prospers at the expense of the other (although the expense cannot be too great or neither will survive). A visit this summer to the coral reef exhibit in San Francisco’s Steinhart Aquarium showed me a number of examples of symbiosis. The cleaner wrasse eats the parasites and dead skin from other fish that would otherwise make them less viable. Sometimes “cleaning stations” are established where larger fish come to be rid of their parasites. The Goby fish and the pistol shrimp have a mutual defense alliance. The shrimp cannot see predators but can dig a tunnel or burrow into the sand that has room for both. The Goby fish can see and moves its tail when predators appear. The shrimp has learned to interpret this as a warning and disappears, followed closely by the Goby. The imperial shrimp enlarges its food gathering range by hitching a ride on a sea

cucumber to a new feeding ground, moving with little energy expenditure of its own without adversely affecting the sea cucumber. Perhaps the most colorful sight was that of the clownfish and sea anemone that have a very complex relationship. The clownfish has a covering of mucous that protects it from the sting of the anemone. The colorful clownfish darts around and attracts predators to the stinging tentacles of the stationery anemone. The anemone makes a meal of the would-be predator and the clownfish gets enough to eat from the leavings of the anemone and keeps the water circulating and the anemone’s area clean. Nutrition, shelter, defense, transportation and camouflage are among the services provided or exchanged by symbiotic partners. They are not unlike services that human beings provide for another through cooperation. Like symbiosis, cooperation typically flourishes among individuals who are usually in close contact with one another. With communications technology, this close contact need not be geographical proximity. Some comparative examples among human societies will be familiar. Trade has taken place since before the introduction of currency. Mutual defense pacts are common; coastal regions and mountain passes often serve as outposts for the traffic of goods and people; and crops that grow in one climate are in demand in others. Other examples are newer. Photographer Edward Burtynsky has documented ship-breaking industry in Bangladesh and the salvaging of e-waste in China. (Buchwald, 2006). A combination of willing workers (however, dangerous the occupation) market niches and economies of scale make such specializations advantageous. Challenges to viability In human communities there have always been individuals or groups that were less able than others to provide for their own needs. Some are too young, too old or too sick to be independent. Others suffer no condition of age or disability but are simply not a good enough fit with the opportunities at hand. This is becoming an increasing problem even in western countries. In Ontario, in May 2006, the Task Force on Modernizing Income Security for Working Age Adults issued its report and recommendations (Lewington, 2006). The report addressed the situation of the working poor – people who do not earn enough, even working full time, to pay for the basic necessities of life. Their situation reflects changes in the labor market where there is more competition for places in the ranks of the professions and skilled trades and less potential for unskilled or semi-skilled workers to find a secure job that pays a living wage. Many of the jobs that are available to such people pay minimum wage or are sort term, part time or insecure. Coupled with this is a shortage of low-cost housing – a result of increasing population and a reduction in the construction of social housing by recent Ontario governments. The report cited the danger of developing a permanent economic under-class who would have little hope of advancing beyond subsistence living in the midst of the prosperity of their more fortunate peers. The report’s recommendations included a number of improvements to the social safety net as well as further grants to bring income to just over the official poverty line. Western countries, some more willingly than others, can and do redistribute income from the better off to those less fortunate through a combination of public support and charitable work so that people seldom are required to go without food and shelter. Western countries too have to find ways to engage all of their citizens in meaningful activities.

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To some extent redistribution happens at the international level too, with the United Nations, governmental foreign aid agencies and NGO’s making efforts to improve conditions in less developed parts of the world. Their work, while not insignificant, cannot keep up with the need and the growing disparity between haves and have-nots. Some countries and regions simply cannot survive as functioning societies without outside resources. Of course, it is necessary to establish what counts as survival. Human settlements evolved, after all, from small hunter-gatherer groups and agricultural communities that survived without much considered necessary today. Resource poor countries and cultures have differing ideas about what they need and want. For example, some rural aboriginal and pastoral communities who wish to continue their traditional ways of life should be able to pick and choose from what is on offer from the wider world. Their needs include security of their persons and physical and intellectual property, protection of their natural environment and its flora and fauna and some access to education, health care and materials. They may also require sporadic assistance in special circumstances such as drought or natural disaster. In denser human settlements, the variety people must cope with explodes and the needs are commensurably greater. A truly humane solution, such as the institution of a Global Marshall Plan will require a higher level of enlightenment and infrastructure than currently exists. Stopgap measures could play a part, both in alleviating suffering and in laying the groundwork for appreciating the level of our common connections. There is some urgency here because the most vulnerable regions, which are disproportionately in the less developed regions of the world, will feel the effects of predicted climate change more keenly. Global market forces do not provide a level playing field. It is difficult for smaller or more sparsely populated countries, if they have not already achieved a high standard of development, to do so now. The barriers to entry are high. They include many factors that are taken for granted in the west. Small countries and their communities suffer other disadvantages too. They may lack even rudimentary infrastructure in all but their major cities. They may be located far from transportation hubs both domestic and international. They may not be able to take advantage of economies of scale that are enjoyed by larger countries, even those in the developing world. Getting started Beck (1992) talked about a change in perception whereby the exchange of “bads” joined the exchange of “goods.” This provides one opening for symbiotic exchange such as that occurring between cleaner fish and their “clients.” Canada, in common with the USA and much of Europe, consumes a great deal of energy and is producing well over its share of CO2 emissions. Since, the effects of rising CO2 levels will be felt all over the globe, it has been suggested that some form of carbon credit arrangements should be introduced. If a country uses more than its agreed allotment, it must “buy” carbon credits to make up the difference from countries that have used less than their share and hence have credits to “sell.” This option can also be scaled down within countries to the individual household or company. In developed countries, families would have a domestic tradable quota (DTO) in which their carbon purchases would be recorded on a smart card. Where such recordkeeping facilities do not exist, coupons could take their place (Bruges, 2004). The same form of exchange

could be applied at the country level. The result would provide a flow of money from those who used more than their share to those who used less. All would benefit from the expected result – a gradual lowering of the rate of emissions and its associated risk of climate catastrophe. The viable system model Beer’s (1979, 1981, 1985) viable system model describes five management functions that every viable system performs, whether consciously or not, from an individual organism to its largest collectives. In the VSM, the role of the five management functions is to manage the available variety to assist the relationship between operations of the system and its environment, whether that is a natural environment or an organizational one. It does so with a collection of homeostats that join higher variety blocks with lower variety blocks, with the variable(s) to be coped with, influenced or controlled monitored by a comparator. Similar homeostats work for organisms in symbiosis, the main difference being that some of their survival needs are outsourced to others. These homeostats work on feedback, often rapid, to make small adjustments to either correct error or continue what is working well. One of the most helpful features of the VSM is its scalability. This model can be repeated for any viable system from the individual to the small group to the organization and so on. The only criterion is that each level has the potential to support itself as an independent entity. Entities are nested or embedded within other entities, usually according to a number of different criteria. Beer calls this embedment recursion. Each viable unit performs in a manner appropriate to its scale, with attention to the requirements of both its environment and of the larger entities, if any, in which they are embedded. Of course, higher levels of recursion vary greatly in the amount of authority, if any, they exert over their component members. To preserve autonomy and efficiency, the most effective level for a decision to be made is the lowest that does not require more comprehensive input. A chain of restaurant franchises, for example, will specify in great detail what will be served and any changes are made at corporate headquarters. The city health department, which has the authority to close a restaurant down, demands only that health and safety regulations are obeyed; while the area’s restaurant association may have no demands at all except, possibly, modest annual dues. Any viable system needs to manage the activities it performs in its environment to obtain the resources needed to survive. It must keep these activities working smoothly together with minimal additional expenditure. It must have a means of making decisions in the here and now to optimize its different activities. It must anticipate and act to provide for its future. Finally, it must bring all these efforts together in a coherent fashion, consistent with its identity and level of autonomy. As well it monitors the balance between concentration on the day-to-day operations and preparing for the future; judging when circumstances call for a shift in emphasis. The environment of the viable system All viable systems, including symbiotic ones, operate in the context of their environment. One of the services a symbiot may perform is to change the external environment of its partner. For example, when fungi and algae combine to form the lichen, the fungi protects the algae inside from the harsh soil and weather conditions

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on the rocks where lichens form which enables the algae to use photosynthesis to nourish both (Margulis, 1998). In the same fashion, international entities or neighbors might act to protect or improve the environments of particular regions so that they could fulfill their potential to benefit others. Or, conversely, purchase and maintenance of property containing fragile ecosystems such as rainforests by NGO’s in the west could be expanded and supported as a planetary resource. If we consider a small developing country, what are its environments and which characteristics influence these relationships? First, it shares in the natural environment of its region including its topology, climate and weather, its lakes, rivers and wetlands, its soil, forests and fish stocks and its natural beauty. Second, it has a cultural environment, (profoundly influenced by its natural environment) which includes its values and traditions and its institutions, both secular and religious. Third, it has a political environment, which includes its history and both its internal stability and its relations with neighboring states and the international community. Fourth, it has a commercial environment where its external transactions occur and its trade partnerships are formed. These and other environments overlap each other. A country’s near neighbors or its former colonial rulers may share, to varying extents, a common language or culture. They may compete or collaborate in the marketplace. Regrettably, they may also share a history of conflict with one another or among ethnic groups within their borders. All these factors influence their ability to benefit from collaborative relationships with one another or with western entities. There is a growing body of knowledge about what is required to bring an ailing natural environment back to health but methods to restore the health of cultural, political and commercial environments are not as well developed although they may hamper efforts to restore a damaged natural environment. The first requirement is that countries have or acquire the sort of peaceful relations that would make positive interactions with various environments possible. The lucky ones have a history of contacts that are either positive or neutral and enjoy many formal and informal exchanges. The tighter their communication networks, the more likely it is that they will be able to identify common threats and opportunities. To take a common example, one might have access to a seaport, while the other had products that traveled down a long river. There is nothing new about such arrangements; they have been made for millennia. What has not often happened is for such arrangements, and many others, to be examined from different perspectives as a whole system, so that gaps may be identified and filled. A neutral start is not possible for countries that carry heavy historical baggage. Some borders have been disputed for many years. Colonial powers sometimes drew borders around antagonistic groups to avoid the perceived greater difficulty of managing ethnically homogenous populations that could have mounted more effective resistance. Some privileged one group (often a minority) over another; leaving a residue of resentment. Finally, a number of countries, especially those who gained independence recently, were left poorly prepared to meet the challenges of the twentieth century, never mind the twenty-first. Many conflicts of today have their roots in this history. Under colonization, decisions affecting these countries and their internal conflicts were completed from without by the “mother country.” This suggests the first order of business for intervention from the wider world. Since, the possibilities for other

countries to provide “completion from without” are limited (and carry additional risks), the job must be done by international collectives – the larger the better. There are things that individual countries can do, provided they are not too closely associated with one side or another. Emphasis might be placed on providing safe places for discussions and negotiations. Conferences and meetings are dismissed by some as frills, but it is inescapable that individuals who travel to them return with a wider range of information, some acquaintances if not friends from elsewhere and a sense of post-conflict possibilities. Group processes, including the team syntegrity process invented by Beer (1994) as well as others can be invaluable here. It should be possible for the international community to begin to engage before a situation degenerates into armed conflict. It is questionable whether notions of national sovereignty appropriate for well established states should continue to apply when no national government is in control. Both world opinion and international organizations have not yet evolved to be able to implement broad-based intentions to prevent genocide and gross human rights violations. Recent history in the former Yugoslavia and Rwanda has shown that earlier and stronger intervention could have prevented much bloodshed. Completion from without is necessary to deal with leftover issues but many can be addressed in an expanded international court system. This service should be provided by the international community and backed by commitments to assist the disputants to solve their problems and overcome barriers to enter the world economy. In a sense, this is not so different from what happens in spousal abuse cases that may be affected by history that predates that of the individuals. Police officers lay complaints without the consent of either spouse. Early intervention including such services as counseling, anger management and job training can often avoid an escalation of violence and return the members of the family to productive lives. Once the environment for cooperation has been restored, possibilities will emerge. Bordering countries might collaborate in a free trade agreement or perhaps work together to develop common processing or transportation facilities. What emerges will depend the specifics and intentions of the parties. Characteristics of location, climate, population density and dispersal and the strengths and capabilities of the cultures may suggest possibilities for symbiosis or other common efforts. System one In the viable system model, activities at the system one level make the organism or organization viable. A system one operation must do something that will provide it with nutrients of whatever sort it requires. For a business, it will be a product or service that customers want to buy. The environment of a business system one operation includes its customers and their preferences; but also its suppliers, its competitors, its regulators and so on. Typically, several system one operations are contained in a business, and there are a number of ways in which it might be useful to distinguish them. A small operation probably finds its most useful distinctions to be by product or geographical location. A large company may find others useful at different levels of recursion including, but not limited to, market, time zone, jurisdiction and regulatory authority. Country or regional potential system one distinctions might be by language or culture, by the type of agriculture of aquaculture they practiced or by proximity to shipping routes.

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A country also offers something in exchange for resources. It could be “goods” such as raw materials or finished products or services such as reprocessing, tourism and call centers. These are goods that a country must compete on the world market to sell. It can be quite hard for small countries to find ways to produce and distribute their goods cheaply enough to compete with large low-wage countries that enjoy economies of scale. A more effective strategy would be to look for and develop those areas that are unique to a country. Neighboring small countries could join together to achieve obtain some economies of scale such as collectively deciding to build processing facilities that both could use economically. Many small developing countries or sparsely settled regions of larger countries have unique ecosystems with unusual flora, fauna and geological characteristics. They are, literally, repositories of resources that the wider world has a strong interest in recording and maintaining for its own survival. Here is a case where there can be significant mutual benefit if there is mutual respect and if a relationship of trust is established. Many universities and research stations already exist and are doing excellent work, adding to the world’s knowledge and contributing to the local economy. Their funding is often insecure and it seems that every week there is a story of a research facility laying off staff and reducing or ceasing operations. This is wasteful of knowledge, good will, and even money. It would be an excellent investment for the international community to guarantee support for such projects and expand them with respect to both their number and the extent to which local people are involved and employed in them. Even less respected are the repositories of social knowledge. This includes languages and dialects at risk, cultural knowledge that may be forgotten and the knowledge and skill to survive without modern conveniences. This information could make a significant contribution in the future to the well being of many outside their borders. Educational institutions and NGO’s might take the lead here, offering experiences to researchers, students and volunteers, and contributing money and a means of earning a livelihood to residents. Some such experiences are already offered as special varieties of tourism. For example, volunteers at archaeological digs typically pay their own way and make a contribution to the project. NGO work groups, and university field courses make similar arrangements. These too could be expanded and put on a secure financial footing. Surely one of the most common reports of people who volunteered is to say that they received more than they gave. The possibility of offering exchange opportunities to young people from both the west and the underdeveloped would also has great promise as both would gain some understanding of the other. Symbiotic relationships could also be in the nature of preventing or absorbing “bads”; as the cleaner fish do. In a domestic public health context, no one now thinks twice about providing vaccinations or sanitary water supplies to all, regardless of ability to pay. If most people are vaccinated against a disease, the population as a whole gains a level of herd immunity so that the disease does not spread as easily among the unvaccinated. Some western cities attempt to achieve a degree of immunization against social ills as well. Programs such as Head Start in the United States and Sure Start in the UK provide experiences to improve the chances for young children at school. Mentoring and arts programs for secondary school students at risk

and job placement for unemployed youth provide access to teenagers and young adults. Would it be that much of a stretch to see that disadvantaged children and young people around the world had access to comparable services? It is well known that desperation and unrest thrive in an atmosphere of poverty and a lack of opportunity. Poverty and disease force many into suboptimal choices. Furthermore, some will turn to crime if no legitimate means of obtaining their desires is available. If this occurs, it makes it more difficult for other legitimate businesses to succeed, especially those, like tourism, that depend on people coming from elsewhere. System two Different operations in an organization can get into each other’s way or reinvent the wheel on a regular basis. System two provides a lot of the internal infrastructure to make sure that operations run smoothly. In technical terms, this is referred to as damping oscillation. A company would use compatible IT software and recordkeeping protocols; it would schedule the use of common facilities such as meeting rooms and loading docks and it would follow common procedures for safety and security measures. For countries, such system two concerns might focus on compatibility of standards for rail gauges, electrical connections and emergency communications protocols. A lot of infrastructure is a given in the developed world and the organization’s system two functions just plug into it. Someone who wants to start a business in Toronto will find waiting electric utilities, telephone, water supply, extensive transport connections, an educated potential workforce, media to advertise their presence and potential customers with money to spend. They will find streamlined and inexpensive processes to establish their business, a reliable body of contract law, relative security from crime, a banking and credit infrastructure and a host of business services to provide almost anything they might need. Less formal advantages abound as well. It would be difficult to quantify the value of business clubs and networks and good restaurants in which to entertain clients, but they add considerably to the ease and enjoyment of doing business. Enterprises in smaller countries, especially in remote areas may find themselves having to provide much of this on a one-off basis. This makes it difficult to develop routines and to have confidence in the delivery capability of different aspects of the business. Symbiotic possibilities with respect to infrastructure might involve collaborating on low-technology ways to provide for communication, transportation and energy. Certainly it could create a market for products that would not require the extensive investment in infrastructure that has happened in the west. The proliferation of cell phones is one example. Stringing wire in areas with low-population density is not feasible but putting up transmission towers is. The same could be said of alternative energy sources. Even today you can see the windmills that once provided power in The Netherlands. The huge wind farms that can be seen for miles are not the only option for a modern version. Contiguous countries could collaborate on building roads, bridges and ports. Some opportunities for small hydroelectric plants exist where a river forms the boundary. One difficulty that affects people in some developing countries is that of language translation. Sometimes only a minority of the population is fluent in any widely spoken language. This is an issue that is eventually amenable to a technological fix. Video demonstrations of hand held translation machines developed for the US military and

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being used in Iraq seem to be effective, at least with respect to translating relatively conventional words and phrases. Such technology, when it comes down in price, could make it possible for the cost of translation to be much less of a burden on countries where many do not speak or write a major language and to facilitate commerce between speakers of different major languages. Likewise, current computer voice recognition systems like Dragon Naturally Speaking offer help to those who are not good typists. These technologies could make it practical for groups to retain their languages in common use and create a demand for people who could provide translations and local institutions where such work could be done. System three In the viable system model, system three exists to provide completion from without for the component system one units. This is needed because what is optimum for one may be sub-optimum for all of them together and because the operations can achieve positive effects of synergy together that they could not achieve separately. system three engages in both one way and two-way communications with the system one units and with system two’s support. Efficient organizations make limited use of the one way channel, using it predominantly to convey legal requirements or decisions that have been made after due deliberation. The two-way channel allows for considerable autonomy as it focuses on resource bargains between the parts and the whole. Quite often a system three decision is needed because one of several alternative choices needs to be made. What works to achieve synergy between parts of a single organization can also be employed at least partially to achieve symbiosis between different organizations or countries that decide to distribute the construction of resources to be used in common or who see advantages in the facts of their “living together.” For larger entities than companies, completion from without gives competing interests a forum to decide on common paths. The European Union has been working in this mode. Although countries have differing preferences, it is more beneficial to all to distribute projects and aid according to a common formula. It also provides a bureaucracy to buffer disagreements so they do not blow up into crises. System three Star is a special audit function of system three that conducts enquiries concerning matters that arise and are not already covered by systems two and three. Its role, according to Beer, is to mop up excess variety. It could be used to evaluate symbiotic relationships from time to time to make sure that benefits are flowing as they should or that none of the parties is overly stressed. System four System four is the facility to consider the outside and future and take steps to adapt to changing conditions in the environment. System four is connected to the expected environment of the future, as system one is connected to the present environment. If system four is acting for a country, it will be looking for new alliances and opportunities to prosper. If it is acting for an industry, it will be looking for new technologies, training and advancement opportunities, new customers and new products. In a company, planning, marketing, research and development, succession and attempts to influence the future through public relations and lobbying are typical functions. Similar efforts may be made on behalf of any collective group, although succession questions would remain the responsibility of the sovereign entities.

System four works by having an evolving internal model of its organization and monitoring its fit with the pictures of the world they see developing that will eventually coalesce to become its present environment. Another of its functions is to warn of approaching threats. Changes in the marketplace may increase the demands for the output some system one units and decrease the demand for others. Internal threats may arise if catastrophes are poorly handled or if it becomes obvious that the current capabilities will not match future needs. External threats, possibly from far away, are a worry too. Like the Goby fish that can see the approach of a predator and signal the shrimp to start tunneling, collaborative nets of communities, NGO’s businesses and countries could divide up the work of monitoring a host of natural and social variables and provide earlier warning of incipient instability. System five The final function described in the viable system model brings closure to the other four, providing a reference point for identity and strengthening coherence in its view of itself and others. A strong and communicable identity is very important to a country and to subgroups within it. The stronger this identity is, the less likely it is to be threatened by change and the easier it is to decide what is vital and worth keeping and what is ephemeral and can be let go. If there is a widespread awareness of identity, it is easier to determine what is necessary to promote healing if that is required, or to move away from feelings of being tossed on the winds of circumstance. Identity can be scaled up many levels although it may become more diffuse. To some extent certain criteria will remain local while others pervade all levels. Identity can expand to include participation in a variety of symbiotic relationships. System five also monitors the balance between concentrating resources on present activities and investing in the future. This balance is not the same for every community or industry or for the same one at different times. It is also probable that, within a country or other good size agglomeration, there will be system one activities that are more volatile or less volatile at any given time. With a strong system five, they will not have to rely on a one size fits all formula. The same set of functions can be repeated at as many levels of recursion as desired. When Beer (1981) did his work in Chile, 11 levels of recursion were identified from the shop floor to the social economy. Like the criteria selected to distinguish among system one units, the ones that best handle variety will be different from situation to situation. Conclusion The phenomenon of symbiosis suggests opportunities to explore ways in which small countries, remote regions and communities could work together to create conditions for viability in the international economy and to offset to some extent the difficulties associated with untrammeled market forces. The viable system model is a useful frame within which to consider these possibilities and to build capacity for concerted action. Our common survival may well depend on our ability “live together” and to find local ways to collaborate in the face of potential risks and to work together to prevent them or to blunt their effect. If this does not happen, some of the potential “bads” will be worse. If there is no route to

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viability for whole countries and large population groups within countries, conflict is predictable. Technology enables even a small group of people to do a great deal of damage and it is not a happy alternative to let increasing security become the only answer to problem situations. Climate change will affect us all. It could be that currently less developed portions of the world will have what is needed to make the difference between massive collapse and bearable adjustments. Human beings could take a lesson from the fungi and the algae. They took a “lichen” to each other and thrive in conditions that neither could survive alone. References Beck, U. (1992), Risk Society, Sage, London. Beer, S. (1979), The Heart of Enterprise, Wiley, Chichester. Beer, S. (1981), Brain of the Firm, 2nd ed., Wiley, Chichester. Beer, S. (1985), Diagnosing the System for Organizations, Wiley, Chichester. Beer, S. (1994), Beyond Dispute: The Invention of Team Syntegrity, Wiley, Chichester. Bruges, J. (2004), The Little Earth Book, Sawday Publications, Bristol. Buchwald, J. (2006), Manufactured Landscapes, Mongrel Media, Toronto. Lewington, J. (2006), “More than an issue of ‘social justice’”, The Globe and Mail, May, p. 16. Margulis, L. (1998), Symbiotic Planet, Basic Books, New York, NY. About the author Allenna Leonard earned her PhD from the University of Maryland with a dissertation on broadcast regulation. She is an Independent Consultant, a Licensee and Facilitator of the team syntegrity process and sometime adjunct and Visiting Professor. She continues to focus primarily on the application of Stafford Beer’s organizational cybernetics. Her research interests include accountability, governance and the integration of environmental and social thinking. She was President of the American Society for Cybernetics from 2002 to 2005. Allenna Leonard can be contacted at: [email protected] or via her web site at: www.allennaleonard.com

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INVITED PAPER

Managing sustainable service improvements in manufacturing companies

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Heiko Gebauer and Elgar Fleisch Institute of Technology Management, University of St. Gallen, St. Gallen, Switzerland Abstract Purpose – The paper aims to provide a better understanding of how cognitive processes limit service improvements in typical product manufacturing companies. Design/methodology/approach – Case studies are the main tool for theory development. All investigated manufacturing companies have been seeking possibilities to enhance their profitability through services, because their products were mainly in the maturity stage with decreasing margins and profitability. Findings – The objective was to show how companies can overcome the typical “cultural” habits and cognitive processes by offering some guidelines to managers seeking to establish sustainable service improvement programs. Research limitations/implications – The remarks are limited to product manufacturing firms. Practical implications – The key managerial implication is a method to overcome cognitive processes, which limit service improvements. Originality/value – The paper establishes that cognitive processes form several feedback structures that all play a critical role in determining the success of service improvements. Keywords Decision making, Services, Cognition Paper type Research paper

Introduction In order to meet more complex customer needs and to respond to increasing challenges from competitors, manufacturing companies have developed a growing interest in services as a source of competitive advantage. A rich body of literature has explored the numerous opportunities an extended service business can provide: financial, marketing and strategic opportunities. The substantial potential revenue, higher margins and the fact that services are a more stable source of revenue, represent the financial benefit (VDMA, 1998). Marketing opportunities can be understood in this context as the use of services for selling more products (Mathe and Shapiro, 1993). Finally, there are strategic arguments such as competitive strategy which is based on services (Anderson and Narus, 1995; Oliva and Kallenberg, 2003). Lay and Erceg (2002) found that, compared to several strategic options including fostering innovation and technology, product quality, suitability for customer needs, cost leadership and delivery time, competing through services enables manufacturers to earn the potential highest margins.

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Most companies initiate service improvement programs so as to use the opportunities outlined above. These programs focus on new service innovations, enhanced service quality, extended service offering, improved service marketing or initiating a service culture. However, effective service management cannot be easily achieved and integration into a company is often fraught with difficulties. Sustainable and ongoing service improvement programs are, in a sense, processes that must grown organically. To do so, manufacturing companies must grapple with several issues relating to improvement programs. The literature is surprisingly sparse on describing how the typical “cultural” habits and, sometimes counterproductive behavioural patterns of manufacturers limit sustainable service improvements. The following paper adds a complementary perspective to existing literature on enhancing services in manufacturing companies. We attempt to provide a better understanding of necessary changes in behavioural processes and to demonstrate their impact on service improvements. The paper is organised as follows: the next section describes our research methodology. In the third section, we explain the main characteristics of service improvements. We identify several cognitive processes which influence the success of service improvements. In conclusion, we summarise the results and discuss both the managerial implications and those for further research. Research methodology By investigating the behavioural dimension of sustainable service improvements, we use the most recent studies of improvement programs (Repenning and Sterman, 2002), characteristics as presented in the literature of service management in manufacturing companies (Lay and Erceg, 2002) and of service management in general (Mills, 1986; Oliva and Sterman, 2001) and on the behavioural side of judgement under uncertainty (Kahneman et al., 1982), aspiration theory (Lant, 1992) and the “teleological” theory (Van de Ven and Poole, 1995), etc. Case studies are the main tool for theory development. We focus mainly on German and Swiss manufacturers whose products represent a high level of investment for customers. All investigated manufacturing companies have been seeking possibilities to enhance their profitability through services, because their products were mainly in the maturity stage with decreasing margins and profitability. Thus, these companies have become increasingly interested in using services as a source of competitive advantage. The research process was implemented in two phases. In the first phase, we used more or less polar-typed case studies (Eisenhardt, 1989). We identified five companies that were highly successful in initiating sustainable service improvements and five companies that struggled to sustain service improvements successfully. The primary data collection methods were semi-structured interviews (for the successful companies) and action research for companies that struggled to achieve sustainable service improvements. Our analysis captures both managerial and employee levels (service workers). The interviews with each of the five successful companies lasted one day. The companies were asked to give a detailed account of their experience with service improvements. The subjects assessed the behavioural processes and successive hurdles encountered during the implementation of service improvements and suggested hypotheses as to their causes. Based on the interview transcripts, we wrote

five detailed case studies describing the history of each service-improvement program. Both participants and the research team reviewed the cases. The reviews often led interviewees, of their own accord, to volunteer more detailed background information. By allowing all the participants to review their own cases, we could offset some of the bias normally associated with retrospective interviews. By reviewing our first finding in action research with companies struggling to initiate sustainable service improvements, we could gain additional insight into how improvements are influenced by the day-to-day work. The action research lasted between six months and one year. In the second phase, we developed a theory to explain the evolution of service improvements in manufacturing companies. We used causal loop diagrams (Forrester, 1961) to provide an understanding of the multiple feedback mechanisms among the mental models of organisational actors which guide their behaviour. We first identied the patterns of interest. Then we continued with an iterative development of categories, variables and casual links. The two key categories into which our observations can be coded, were successful and unsuccessful service improvement programs. The variables and casual links form the feedback processes that generate the dynamics of service improvements. At the end of the process, we integrated our findings into an unified framework which explained the nature of both the successful and unsuccessful service improvements. The result is a single set of feedback processes capable of generating patterns for the phenomena that we observed. As our model emerged, we reviewed each link in the causal maps to assess whether the relationship was supported by existing theory. The combination of the two phases helped us to ensure that our emerging theory is grounded in the field data and consistent with existing principles in service management, management of improvements, and the literature on decision making. Cognitive processes and service improvements The following sections describe different coginitive processes and their impact on the management of sustainable service improvements: (1) We discuss the differences between improving services and improving products. (2) We identify two different managerial options to enhance service improvements. (3) We show how employees decide to invest resources in service improvements and discuss unanticipated side effects. (4) We explain how an employee-pull effect can arise. This employee-pull effect is influenced by the objectives set by managers. (5) We discuss appropriate objectives. (6) We conclude with the description of differences between first and second-order improvements and show how second-order improvements overcome the unanticipated side effects of investing resources in service improvements. Improving services versus improving products The first positive feedback loops arise from the ability of firms to invest in resources in improving a company’s products or services (R1 and R2). Because both improvements to products or services boost a firm’s competitive position in terms of higher

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differentiation, which in turn leads to higher profits. This enables them to invest more resources in improving products or services. Most products or services can be improved through enhanced features, functionality, reliability and suitability with respect to the current and latent needs of the customers. Entirely new products and services are other means of improving either services or products and of enhancing differentiation. Additionally, companies offering clearly superior products or services leading to higher differentiation, can often charge a (price) premium (R3). As long as charging a premium does not choke growth, the resulting higher margins enable firms to invest even further in improved products or services. The feedback loops R1, R2 and R3 are shown in Figure 1. Creating a competitive advantage through the physical product is becoming increasingly difficult and product margins are decreasing (VDMA, 1998). Therefore, theorists in production and service management, assert that differentiation through services and sustainable service improvements are the only way to escape the trap of decreasing product margins (Frambach et al., 1997). However, investing resources in services and overcoming decreasing product margins is limited by two cognitive processes at the managerial level. The first refers to the risk aversion of managers in manufacturing companies. We found out that in most companies that were unable to achieve sustainable service improvements, managers believed providing services to be beyond the scope of their competencies and that it was too risky to invest resources in an area that does not use the traditional core competencies of manufacturing companies. Risk aversion is a basic characteristic of human decision making (Einhorn and Hogarth, 1986). It explains why managers prefer the risk-free outcomes of

+ Profits

+ R3

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Price Premium Differentiation +

R1 +

Improving Products

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Figure 1. Achieving differentiation and price premium through improving services or products

Arrows indicate the directions of causality. The signs (‘‘+‘ or ‘-‘) at the arrow heads indicate the polarity of relationships: a ‘+‘ denotes that an increase in the independent variable causes the dependent variable to increase, ceteris paribus (and vice versa). That is, X +Y⇔ θY/θX > 0. Similarly, ‘-‘ indicates that an increase in the independent variable causes the dependent variable to decrease; that is, X -Y ⇔ θY/ θX < 0. The loop identifiers (e.g. B1) indicate whether a loop exerts a negative (balancing) feedback or a positive (self-reinforcing) feedback (e.g. R1). See Richardson and Pugh 1981.

investing resources in improving products, to the uncertain outcome of investing in improving services. The economic potential of improving services is the second cognitive process which limits investment in improving services. Managers may not believe in the economic potential of extended service business. Most of the unsuccessful companies argued that they sell multi-million Euro pieces of equipment. It was therefore difficult for them to be enthusiastic about a maintenance contract worth e50.000. Both risk aversion and economic potential, explain managerial bias against investing resources in improving services initiating feedback-loops R2 and R3. These loops explain how the typical and in some respects, counterproductive cultural habits of managers in manufacturing companies, limit service improvements. Successful companies are able to overcome these two cognitive processes. Managers change their service awareness from regarding services as an add-on, to regarding them as “value-added”. Changing managerial service awareness means that managers become aware of the economic potential of improving the service aspect of their firm. Furthermore, they are willing to take the risks inherent in service improvements and invest resources, even in areas beyond their traditional core competencies. Managerial options for service improvements According to the “teleological” theory (Van de Ven and Poole, 1995), if managers believe in the economic potential of services and are willing to take the associated risks, they set goals for the level of service improvements. Combining this with aspiration theory (Lant, 1992), managers assess the adequacy of the current level of service improvements and compare it to the desired level. Since, most manufacturing companies are reluctant to hire more staff, managers hoping to close a performance gap, have only two basic options. Extending the level of service improvement implies encouraging employees to improve services (B1) and giving employees the freedom to set up structures and processes that exploit the economic potential of services (B2), (for example, to establish a separate service organisation with profit-and-loss responsibility, to define a new market-oriented service development process, etc.). Both are necessary for sustainable service improvements in manufacturing companies. Figure 2 shows both options, which form two balancing feedback loops, the (employee) push loop B1 or the (setting up) structures and processes loop B2. B1 and B2 form balancing feedback loops that are able to close the gap between desired and existing levels of service improvement. Unfortunately, setting up the necessary structures and processes for sustainable service improvements are limited by Ross’ (1977) “fundamental attribution error”. Ross (1977) established that people attribute undesirable outcomes to people rather than to system structures. Managers push employees to improve the service business, but do not focus sufficiently on setting up the necessary structures and processes that are necessary for sustainable service improvements. The management of the five companies that achieve low levels of service improvement, focussed mainly on pushing service workers to sell more service, thereby initiating only loop B1. Management succumbed to the “fundamental attribution error” leading to a lack of necessary structural changes, which then limited service improvements. Management has to overcome the “fundamental attribution error” by initiating a balanced change in both employee behaviour and structural settings. The five companies which sustained service improvements, initiated both

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Figure 2. Feedback structures resulting from a performance gap

First-order improvements

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B1 and B2. They set up new structures and processes, and motivated employees to improve services. New managerial tasks such as establishing structures and processes, require a change in the traditional role understanding of service managers within manufacturing companies. Service managers traditionally think and act as “customer support”. They merely manage customer complaints, but do not extend the service business by defining new service innovation processes and, for example, actively setting up a profit-centre with profit and loss responsibility. Overcoming the “fundamental attribution error” requires a new role understanding in terms of business managers. Employee resources for service improvements If the management believes that the lack of structural change is the reason for the gap between current and desired levels of service improvement, then the rational response

is to invest human resources (services workers) in structural changes. Service workers are located at the employee level. Service workers have limited time which must be allocated between routine daily business and structural changes (March and Simon, 1993). Most theorists assert that employees doing a job, are the best-informed “experts” and should be responsible for structural changes. This strategy has two advantages. On the one hand, employees already understand the structures and processes. That reduces the time needed for data collection and for the implementation of service improvements. On the other hand, employees have a strong interest in implementing service improvements that they developed themselves (Deming, 1986). Structural changes are linked to the service delivery, because they interrupt the creation of services. This link stems from the following argument. In order to address the issue of the inseparability of service delivery and quality (Oliva and Sterman, 2001), service quality has been defined as a function of the allocated time per order – a proxy for the degree of attention and care that service workers provide. According to Mill’s equation of service quality to service productivity (Mills, 1986), we assume that increased work effort leads to less time per order, thus decreasing the service quality. By combining the issue of inseparability with the interaction arising from service workers’ finite resources, there is a short-term effect of structural changes. The short-term effect which erodes service quality is shown in Figure 2. For example, increasing resources for structural changes, constrains the resources available for daily business activities, leading to more work effort and less time per service order, thus eroding service quality and limiting service improvements. The short-term effect would overcome the balancing effect of B2. This suggests that any service improvement is quite difficult to sustain, because of the lack of resources. Ours is not the first article to identify the trade-off between improvement activities and daily business and to explain the resource bottleneck. This problem is discussed in several studies and has been the subject of rational actor models (Repenning and Sterman, 2000, 2002). The key question in terms of the theory, is why many service workers do not “push” such service impand Ercegand Ercegrovements. The answer is determined in large measure by the mental models of service workers with respect to the optimal ways of allocating their resources. Yet, there are several reasons as to why service improvements are not sustained, that are related to risk aversion and to the economic potential of services, rooted mainly in cognitive processes. In choosing whether to pursue improvement or daily business, services workers must evaluate or judge the value of investing resources in service improvements. Employee-pull effect Freeing employees to establish new structures and processes can be understood as a managerial “push” or normative pressure to initiate service improvement programs. Management push often creates temporary excitement, but must, over time, be replaced by other sources of motivation such as an employee pull effect (Shiba et al., 1993). Employee pull arises when service workers come to understand the benefits of service improvements and commit themselves to improvements and increased effort. Figure 3 shows the employee pull effect (R5). In this situation, improvement efforts are independent of managerial attitudes and support. The management push boosts the “value-added” service awareness from the managerial to the employee level, thus

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Figure 3. Employee-pull effect and credibility gap

R5

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Perceived feasability of objectves

eradicating typical cultural habits of service workers in manufacturing companies. Usually, services workers think about services as add-ons to the product, and initial services (installation, commissioning and so on, etc.) are often “given for free” during negotiations to sell products in manufacturing firms. Under these conditions, service workers are not willing to invest resources in service improvements. The employee-pull enforces the cultural transformation from product-oriented to a service culture. Service workers learn to improve the services (for example, how to estimate the value of their services, how to sell the service offerings, how to convince customers as to the benefits offered by the services, how to deliver superior service quality and how to bill services). The employee-pull effect explains the evolution of a “value-added” service awareness at the employee level. All five companies that achieved high levels of service improvements, were able to initiate the employee-pull effect, establishing a “value-added” service awareness at the employee level. In contrast, the five companies that achieved a low level of service awareness, were not able to initiate the employee-pull effect. Appropriate objectives The employee-pull effect (R5) has the same property as a re-investment cycle. It can function as a virtuous (structural changes boosts service improvements, stimulating efforts, leading to still more structural changes and higher level of service improvement) or vicious cycle (poor results from service improvements leading to less effort, ensuring even poorer results). As shown in Figure 3, the expectations and aspirations of service workers interfere with the employee-pull effect, raising the odds of a vicious cycle. In evaluating how much effort to devote to service improvements, service workers compare the results of service improvements which they observe, to their expectations

(Cyert and March, 1992). The employee perception of service improvements rises, if progress is high relative to aspirations and falls when progress is disappointing. As shown in Figure 3, expectations are influenced by the objectives set by managers. The dependence of employee perception on observed progress, means that aggressive objectives can adversely effect the success of service improvements. Aggressive goals can undermine the development of the employee-pull effect. When objectives are set too high, expectations outstrip the observed benefits of service improvements, weakening the employee pull-effect. The “overstretched” objectives create a credibility gap, confirming service workers’ belief that the goal was not feasible from the start. A vicious cycle of goal erosion and cynicism about service improvements can set in. In most case studies in which manufacturing companies achieve low levels of service improvement, the overambitious objectives were not well received, thus initiating R6. For example, management announces a dramatic increase in the share of services revenue (from 5 to 50 per cent within five years). Service workers respond to that rather aggressive goal in a cycle of goal erosion and cynicism about service improvements, initiating R6. Defining appropriate objectives for service improvements requires a greater role understanding in terms of business managers. That means the managerial role understanding changes from a customer support emphasis to that of a business manager. Managers running the service business as professional business managers, are able to set appropriate goals, avoiding the credibility gap. Both the employee-pull effect and appropriate objectives explain why service workers are willing to invest resources in service improvements. However, it does not explain how manufacturing companies overcome the short-term effect shown in Figure 2. In order to understand how manufacturing companies can overcome the short-term effect (eroding service quality), one has to distinguish between first and second-order improvements. First and second-order improvements The most recent research on improvement programs (Repenning and Sterman, 2000), demonstrates that it is possible to focus on first or second- order improvement. According to the service or quality movement (Deming, 1986; Heskett et al., 1994), first-order improvement deals only with symptoms (B4). Conversely, second-order improvements treat structural problems and thus reduce the severity of or eliminate problems or symptoms, in turn increasing efficiency and productivity. This equates to “working smarter”. The causal loop structure is shown in Figure 2. By concentrating the improvement effort on the second-order aspect, one can increase the current level of service improvements (B3b) as well as efficiency and productivity, making more resources available for day-to-day business activities (B3a). B4a compensates for the negative impact of service improvements on service quality (R4), by operating as a “virtuous” cycle, leading to a sustainable improvement of services (Schlesinger and Heskett, 1991; Heskett et al., 1994). In other words, first-order improvements are insufficient and second-order improvements are necessary for sustainable service improvement. However, what determines the feedback loop (B3a/b or B5) that we have described and how does it operate? The answer is that it is influenced substantially by employee

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role understanding. First-order changes which eradicate symptoms only, are simply more obvious and tangible than second-order causes. In a service setting, for example, the number of customer complaints is visible to all. By contrast, service-quality problems leading to customer complaints are less visible, harder to observe and usually take more time to resolve. Improving service quality can be a laborious process: documenting the existing service delivery process, diagnosing causes of poor service quality, implementing solutions and training participants. All are painstaking procedures. Service workers have repeatedly been shown to pay undue attention to conspicuous and tangible aspects of the environment. First-order improvements are simply more obvious than second-order changes (Kahneman et al., 1982). Service workers would, therefore, normally favour first order changes. The overemphasis on obvious and tangible characteristics explains why service workers favor first-order changes. First-order changes do not reduce the resource bottleneck, so that it remains difficult for any service improvements to be sustained. Concentrating on second-order changes helps companies to increase their productivity, compensating for the short-term effect of eroding service quality, that has been discussed above. This means that second order-changes are necessary, because they help to reduce the resource bottleneck. In the case of concentrating on second-order improvements, one can initiate feedback loop B2, leading to sustainable service improvements and a strengthening of a company’s competitive position. In order to do so, eemployee role understanding must change from that related to selling products to that of providing services. Service provision overcomes the bias against second-order changes. Second-order changes or providing service solutions, enhances productivity in the service organization, compensating for the short-term effect of improving services. Conclusions Our study has some significant implications for both researchers and managers. For production and service management theorists, it suggests that the design and implementation of sustainable service improvements in manufacturing companies is influenced strongly by several behavioural dimensions. A complete theory of sustainable service improvements, requires an interdisciplinary theory which integrates service management and human decision making. We have established that cognitive processes form several feedback structures that all play a critical role in determining the success of service improvements. Our analysis suggests that future studies and research should consider explicitly, those factors which influence service improvements. The challenges discussed, result from several cognitive processes: risk aversion, the economic potential of services, “fundamental attribution error” an overweighing of obvious and tangible features of the environment, etc. These cognitive processes function as a series of barriers or hurdles, which limit service improvements. Companies achieving sustainable service improvements, are able to overcome barriers by: . reducing risk aversion and increasing awareness of the economic potential of services by changing — non-value-added into value-added managerial service awareness;

.

.

.

initiating a balanced combination of encouraging employees and establishing structures and processes as well as setting appropriate goals by changing managerial role understanding - from traditional customer support to business manager; initiating the employee pull effect by changing non-value-added into a value-added employee service awareness; and focusing on second order changes by changing employee role understanding from selling products to providing services.

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These four changes seem to be the appropriate triggers for overcoming typical, and in some respect, counterproductive “cultural” habits of manufacturing companies. As shown in Figure 4, manufacturing companies achieving sustainable service improvement, overcome the cognitive processes mentioned earlier, by using these four triggers and initiating feedback loops R2, R3, a balanced combination of B1 and B2, B3a/b overcoming R4 and avoiding B4 and R6 leading to an increased employee-pull effect. Figure 4 also shows that companies achieving low levels of service improvement, do not overcome these cognitive processes. They focus mainly on feedback loop R1, B1, B4 and R6. Our ideas presented in this paper, offer a complementary perspective to many existing theories advocated by practitioners. Establishing a “value-added” service awareness at the employee and managerial levels, the managerial role understanding and employee’s role understanding in terms of providing services, can be understood as the key managerial implications and recommendations for achieving sustainable

Configuration of cognitive processes and triggers

Initiated feedback loops

Five companies achieving sustainable service improvements

Five companies achieving no sustainable service improvements

Reducing risk aversion and increasing awareness of the economic potential of services by changing - non ‘value added’ into ‘value added’ managerial service awareness

Risk aversion and no awareness of economic potential of services, because of non ‘value added’ service awareness

Initiating a balanced combination of encouraging employees and setting up structures and processes, as well as appropriate goals, by changing managerial role understanding - from traditional customer support to business manager

Focus on encouraging employees and aggressive goals because of traditional role understanding in term of customer support

Initiating the employee-pull effect by changing non ‘value added’ into ‘value added’ employee service awareness

Failure to initiate employee-pull effect because of non ‘value added’ service awareness

Focusing on second-order changes by changing employee role understanding from selling products to providing services.

Focusing on first order changes because of traditional employee role understanding in terms of selling products.

Feedback loops R2, R3

Feedback loop R1 instead of R2

Balanced combination of B1 and B2

No balanced combination of B1and B2

Feedback loops B3a/b avoiding B4

B4 instead of B3a/b not overcoming R4

Feedback loop R5

Feedback loop R6 limiting R5

Figure 4. Cognitive processes, triggers and feedback loops among companies achieving sustainable and no service improvements

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service improvements in manufacturing companies. Monitoring these factors and gaining an understanding of the impact of behavioural processes, provides some guidance for managers seeking to design sustainable service improvements. Sustainable service improvements lead to an increased service contribution in terms of service revenue and service profits, enabling manufacturing companies to avoid the trap of decreasing product margins. Sustainable service improvements constitute a successful extension of the service business in manufacturing companies. Over the long-term, they even support the transition from a product manufacturer to a service provider. A product manufacturer uses services as one of the main differentiating factors in its product marketing strategy. Profits and revenue are generated mainly through the company’s products and the contribution of services is quite low. A service provider whose products are merely an add-on to the services creates the main share of total value creation through an extended service business. Products represent only a small part of total value creation.

References Anderson, J.C. and Narus, J.A. (1995), “Capturing the value of supplementary services”, Harvard Business Review, Vol. 73 No. 3, pp. 75-83. Cyert, R. and March, J. (1992), A Behavioral Theory of the Firm, MIT Press, Cambridge, MA. Deming, W.E. (1986), Out of the Crisis, MIT Press, Cambridge, MA. Einhorn, H.J. and Hogarth, R.M. (1986), “Behavioral decision theory: process of judgement and choice”, Annual Review of Psychology, Vol. 32, pp. 53-88. Eisenhardt, K.M. (1989), “Building theories from case study research”, Academy of Management Review, Vol. 14 No. 4, pp. 532-50. Forrester, J.W. (1961), Industrial Dynamics, MIT Press, Cambridge, MA. Frambach, R.T., Wels-Lips, I. and Gu¨ndlach, A. (1997), “Proactive product service strategies – an application in the European health market”, Industrial Marketing Management, Vol. 26 No. 4, pp. 341-52. Heskett, J.L., Jones, T.O., Loveman, G.W., Sasser, W.E. and Schlesinger, L.A. (1994), “Putting the service-profit chain to work”, Harvard Business Review, Vol. 72 No. 2, pp. 164-74. Kahneman, D., Slovic, P. and Tversky, A. (1982), Judgement Under Uncertainty: Heuristics and Biases, Cambridge University Press, Cambridge, MA. Lant, T. (1992), “Aspiration level adaption: an empirical exploration”, Management Science, Vol. 38 No. 5, pp. 623-44. Lay, G. and Erceg, J. (2002), Produktbegleitende Dienstleistungen: Konzepte und Beispiele erfolgreicher Strategieentwicklung, Springer-Verlag, Berlin. March, J.G. and Simon, H. (1993), Organizations, Blackwell, Oxford. Mathe, H. and Shapiro, R.D. (1993), Integrating Service Strategy in the Manufacturing Company, Chapman & Hall, London. Mills, P.K. (1986), Managing Service Industries, Ballinger Publishing Company, Cambridge, MA. Oliva, R. and Kallenberg, R. (2003), “Managing the transition from products to services”, International Journal of Service Industry Management, Vol. 14 No. 2, pp. 160-72. Oliva, R. and Sterman, J. D. (2001), “Cutting corners and working overtime: quality erosion in the service industry”, Management Science, Vol. 47 No. 7, pp. 894-914.

Repenning, N. and Sterman, J. (2000), “Getting quality the old fashion: self-confirming attributions in the dynamics of process improvement”, in Cole, R.B. and Scott, R. (Eds), Improving Theory and Research on Quality Enhancement in Organizations, Sage, Thousand Oaks, CA. Repenning, N. and Sterman, J. (2002), “Capability traps and self-confirming attribution errors in the dynamics of process improvement”, Administrative Science Quarterly, Vol. 47 No. 2, pp. 265-95. Richardson, G. and Pugh, A. (1981), Introduction to System Dynamics Modelling with DYNAMO, MIT Press, Camnbridge. Ross, L. (1977), “The intuitive psychologist and his shortcomings: distortions in the attribution proces”, in Berkowitz, E. (Ed.), Advances in Experimental Social Psychology,Vol. 10, Academic Press, New York, NY. Schlesinger, L.A. and Heskett, J.L. (1991), “Breaking the cycle of failure in services”, Sloan Management Review, Vol. 32 No. 3, pp. 17-29. Shiba, S., Graham, A. and Walden, D. (1993), A New American TQM: Four Practical Revolutions in Management, Productivity Press and the Center for Quality Management, Cambridge MA. Van de Ven, A. and Poole, M.S. (1995), “Explaining development and change and organizations”, Academy of Management Review, Vol. 20 No. 3, pp. 510-40. VDMA (1998), Dienen und Verdienen, VDMA Verlag, Frankfurt. Corresponding author Heiko Gebauer can be contacted at: [email protected]

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Sunderland Business School, University Of Sunderland, Sunderland, UK Abstract Purpose – The purpose of this paper is to argue that culture is our primeval management that has its roots the same desire for control that management does. The paper explores the fundamental cognitive systems that allow us to create culture. Design/methodology/approach – The paper applies basic systems concepts to the notion of culture and draws parallels with other cybernetic processes in order to consider the means of developing culture as a systemic possibility and/or inevitability. Findings – Where management is reductive relying on cause and effect to apply its models to organising, culture is emergent and relies on correspondence to develop mutual models of organising. Research limitations/implications – The paper explores the creation of culture from a systems perspective and so further work could be devised to consider the demise of specific cultures such as the entropy of culture and its radical change in crisis. Practical implications – The paper is attempting to demonstrate that organisations may need to see culture along with structure and management as a control issue. That culture is at the heart of the individual and in the ether of the organisation and so the cybernetics of culture should not be considered as an adjunct to the management of the organisation but seminal to it. Originality/value – The paper attempts to consider culture as a cybernetic process of development. Keywords Culture, Cybernetics, Control, Management theory Paper type Conceptual paper

Kybernetes Vol. 36 No. 5/6, 2007 pp. 596-606 q Emerald Group Publishing Limited 0368-492X DOI 10.1108/03684920710749695

Prologue Most management literature, teaching and training is concerned with the operation of management, the competence of managers and the hegemony of management within the organisation domain. So much so Grey (1999) informed us that “We Are All Managers Now”. In some economies we have tried more management and more managers but still other economies with less management (and less management education) out perform the “developed” economies. In crisis, management often looks out to economics for new models; we see this in “globalisation” with Dunning’s (1980, 1995, 2000) eclectic paradigm and Porter’s (1990, 1998) diamond model for example. Management may look out to other cultures such as Japanese production techniques. This paper considers that we might also look into culture as a controlling dynamic where management and managers have been lacking. Culture and leadership often arise as higher order supra-areas of management or as an appendage to mainstream management. This could lead us to think that managers and management predate or precede leadership and culture as organising dynamics – but the archaeology of social systems would point out the obvious. The existence of Many thanks to Dr Robin Asby whose conversation started this paper and many thanks to Dr Lieselotte van Leeuwen whose conversation brought the paper to a conclusion.

cultural systems predates what we might call management and leaders predate managers. The modern monarchy is a relic of leadership rather than management. We have a need to order our world, we do this to cope with complexity and make more precise our responses to it. If culture is a controlling social system or primeval management, then how does the culture of the social interact and develop with the individual? It is clear that management controls through the imposition of its models – roles, job descriptions, methods, etc. but how do cultural models evolve in order for order to emerge. As organisations oscillate between stability and change the notion that an organisation is “in control” may or may not be the same construct as managers “having control”. The culture process of the organisation that connects the individual with the social, at a deeper emotional level, acts as the second-order system in which the job descriptions, etc. Sit sometimes having control and sometimes not. Culture operates at an emotional level; we speak of a warm or friendly culture. We love our leaders. We empathise with the organisation. We rarely love our managers or talk of friendly decisions or discuss how we would walk barefoot over broken glass for the MRP system. Because culture of the organisation is often tied into “soft” issues of human emotions, folklore and superstition, culture or indeed “the” culture of an organisation is problematic in management literature. Whilst bureaucracy and general management can align itself with positivism, applied maths and cause and effect – culture is much more in flux. Beer (1981, 1985) in system 5 of the viable system’s model cites culture in relation to ethics – the shifting correspondence between individual and social behaviour. Culture includes but management deals with specifics and so excludes, Beer’s (1981, 1985) system 5 is an including variety sponge that mops up aberrant behaviour. This paper attempts to explore the mutual development of culture control of the individual and the social in organisations. The paper considers in systemic terms (modelling, control and system pathology) how cultures come about and develop from a processual perspective. The paper is not attempting to consider what might be a “good” or “bad” culture but rather “culturing” – considering culture as emergent or “becoming”. The question being reflected on here is how or why does culturing occur, i.e. what are the cybernetics of culture? Desire for order and control: why culture? We might find a partial answer to this question if we consider the pathology of systems. Culture (like management) is concerned with the avoidance of chaos disorder and death – we are scared of death. As Woody Allen put it “I don’t want to live on in my work, I want to live on in my apartment.” Whilst management deals with tangible (or perceived tangible) organisational artefacts such as resources, culture is concerned with softer issues such as fear, desire, uneasiness, joy – the symbols or totems of the organisation or its emotions. Culture is more concerned with the non-explainable dimensions of organisation. It is clear that all systems are pathological – the company will fold, the sun will die, etc. To consider a culture we need to consider its attitude towards the unexplained – life (change) and death (obsolescence). The illustrious Marvin Gaye suggested, “There’s three thing that’s for sure; taxes, death and trouble.” Bataille (1988, p. XXXII) narrowing this down suggested that the only two universal certainties are “that we are

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not everything and that we will die”. Linstead and Chan (1994) suggest that the fear of the death sentence permeates all organisational directives. Whittington (2001), in his model of generic strategies, suggests that the unitary goal of classical strategy is profit maximisation a goal that evolutionary strategy accepts. Whilst the unitary nature of the strategic goal is not questioned here, it is survival the organisation seeks through profit and not profit itself. The organisation, like the individual, is attempting to survive and part of survival is encapsulated in the avoidance of death. Death, as with love and hate, etc. is difficult to rationalise and so it becomes much more apparent in our culture than our management. To bring this notion closer, try the following experiment; take a piece of paper and write on the paper the name of someone you love – wife, husband, mother, father, lover. Human would be best but pets are acceptable. Look at the name of your chosen person for a moment and think about them; then next to their name write “is dead”. You probably could not bring yourself to write “is dead” or had some difficulty in doing so; such is the emotional concern to avoid death and difficulty in seeing this exercise as insignificant. By writing “is dead” you may cause their death or should they die you could be responsible. One way to avoid death is not to consider it or not move towards it. Of course we cannot stay still as stasis is in fact death, but we can attempt to arrest and control the rate we travel towards death. In organisational management, bureaucracy acts to maintain the stillness as the procedures, routine and order holds steady our lives Binns (1994). Culture offers a shared perspective of the organisation whose interpretation of reality gains efficacy from the depth of agreement in the individual and breadth of agreement in the social. Culture offers the safety of the herd rather than the safety of the rule. Culture offers us knowing without having necessarily to understand – we know about death but we have tacitly agreed not to discuss it. Developing culture “culturing” When the French Philosopher Henri Bergson proclaimed “Je n’ai pas de syste`me” (cited in Mullarkey, 1999, p. 5) he was possibly (ironically) opening up a dichotomy he might otherwise have sought, given the tendency of his work to dichotomise. Through the refutation of system in some senses Bergson acknowledges its puissance. The idea that the universe, organisations and individuals are incomplete and fragmented is attestable as well as open to refute, though there is evidence to suggest that we are structured or able or inclined to think systemically. We may not be systems but that is how we think. From the temperature of our bodies to the profitability of our organisations we seek control through the accommodation of error. More fundamentally we model in order to seek our goals – we are predisposed to order, to make sense of our worlds and ourselves. How might we understand the modelling of our more fragmented and incomplete organisational dimensions such as culture? In discussing culture, the social dimension of organisations, it might be helpful (perversely) to think about us as individuals. Anything that attempts to control something needs to have a model of what it controls within it. If we consider the thermostat containing a bi-metallic strip controlling a domestic central heating system we can find a simple control mechanism that uses a model. As the temperature of the bi-metallic strip heats up one side of the strip expands and bends the strip breaking a contact that stops the flow of gas or electricity, etc. The temperature of the strip falls

and the expanding half starts to contract, which closes the contact and restarts the heating process. The movement of the strip models the temperature change of the strip, which models the temperature change in the room the strip is in, which models the temperature of the house the room is in. Modelling is a necessary process for our existence; because we can model we can experience control. When talking to a friend we might think about the model we are using to have our conversation – this person is my friend so their behaviour is “X” where “X” may mean a number of simple and complex assumptions about their behaviour – they will tend to be kind to you and forgiving of your mistakes. We check that our models still work from time to time when our friend does something that does not fit with our model, and then we may have to re-jig our model of “friend”. There are a number of possible reasons why we might use models but the ones taken up here are that we have to or that we can. If when talking to someone we had to absorb their every word, gesture, thought, physicality, sexuality, etc. then we would have to hold the perfect model of them. This perfect model would in fact take most, if not all, of our brain and body to hold and consequently we would be them. Baudrillard (1983) explores the idea that if you could make a perfect model of the Mona Lisa using electron microscopes, laser technology and leading edge science, who could tell the difference? This then is a limit of the model, i.e. the model is so perfect it is the thing itself. This degree of knowledge would obviously be unbearable. In practice we have to have a simplified model because we cannot hold the whole thing in our heads. Greenfield (2000) cites the work of V.S. Ramachandran who has shown that our brain even holds a model of our own body. Such that an amputee who experienced pain in his missing hand whenever he shaved his face, did so because his brain’s “body model” had the hand next to the cheek. When the hand was amputated the space where the hand was mapped was taken over by the model of the cheek, so pain in the cheek was perceived as occurring in the hand. This in a sense suggests that we even have to model our own bodies because we cannot continually manage the information our own body generates – what chance of managing other people then? Modelling is our short cut to knowing, ordering and control given the unbearable nature of full knowledge. Management causes, culture corresponds One of our key human models is an ability/desire to see cause and effect (Hume, 1992). Michotte (1963) shows a propensity in adults to perceive cause and effect even when they know it is not present. Leslie and Keeble (1987) demonstrate that as early as 27 weeks old infants perceive and expect cause and effect before weight of experience or theory building might explain the perception. If as you read this paper a 10 pound haddock suddenly falls on your lap, your first reflective reaction will be to look up to see which nutty prankster dropped it on you – the cause – we see cause and effect because we can – just as we plan because we can. Cause and effect is problematic. Management needs cause and effect in order to control, so if it cannot be relied upon de facto or de jure to explain or maintain control we need to consider an alternative model. When dealing with social systems cause and effect becomes difficult to quantify though our desire for it remains. The more qualitative model of correspondence allows us to consider a relationship between systems not of “actor” and “acted on” but “mutual acting”. We see with correspondence a parallel development of feed-forward

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creativity as with the conductor and the orchestra or the music and the dancer. In some instances the mutual relationship is more apparent – jazz music or improvisation comedy or theatre – but nothing is ever truly the cause or the effect. Anyone who has been to a modern English wedding party can bear testament to the fact that there is a correspondence between “disco” music and dancing. Though a causal relationship would be difficult to prove. Especially, given the inevitable uncle George whose feedback sample indicates a John Travoltaesque physical poetry whilst second-order observation reveals an excited gibbon on a pogo stick. The observing of cause and effect are facilitated by the desire for correspondence rather than inherent deterministic relationships. This is exemplified in cybernetic learning. If we consider the development of the brain and the thumb we see that an opposable thumb enables complex manipulation. Complex manipulation requires complex thought and so a complex brain. A complex brain then facilitates more complex thinking that requires an outlet in further complex manipulation, etc. – thus to be viable, humans had to develop thumb and brain separately and together. If we consider Wittgenstein’s (1978, p. 7) assertion that “What we cannot speak about we must pass over in silence.” Then the counterview that – what can happen, will happen – may partly explain the cybernetics of learning – and culture. We can model, we can communicate and we have a desire for order so culture then management will evolve. Our human models (cause and effect, friend, body) allow us to forget about huge lumps of information. Human infants can distinguish between ten or so chimpanzees as being different individuals, something adults are unable or have forgotten how to do. A parallel may be drawn here in that our culture could be considered to be our forgotten model of the organisation. Culture is a shared meaning that has been forgotten but culture can also be a strategic response. Culture then flips; it is the social emotional system that corresponds to the individual emotional system and vice versa. Thus, our individual actions based on instinct or intuition (our half remembered history) may parallel our actions premised on our organisation’s culture. As the interaction of the emotional nature of culture swings from the social to the individual we can see parallels with human cybernetic learning. Complex emotions facilitate complex social relationships and complex social relationships require complex emotional responses in the individual. We see from Wittgenstein (1978) that because learning can happen it does but from O’Shea (2001, 2002) and Gheradi (2003) we see a desire of learning driving (or dragging) the ability to do so. The “mutual acting” of the brain and the thumb and the individual and the social requires a meta-systemic desire to act. Modelling culture Repeatable processes become forgotten – the professional golfer does not need to think about the grip of the golf bat in the way a novice does. Once forgotten of course some things are difficult to remember – so culture can be difficult to change. Scho¨n (1983) with reflective practice and Churchman (1968) both consider the human dimension of systems showing that the model of our understanding is deeply internal to us rather than externally given. That change requires us to re-surface our model and usually this can only be done when our model has failed us. Even then our model is robust – we can absorb a lot of failure before we recognise the need to change. This may be a positive in making our culture tolerant but it may be a negative in making our culture intransigent.

If we now move on from the individual to consider the social and so cultural we see that models and forgetting are useful but also complex and problematic. Language as a human and cultural system offers a useful model for the discussion (or even understanding) of culture. As with language culture is genetically possible but socially developed, so error and difference are inevitable and necessary. Pinker (1994) suggests that all human languages are based on “subject” “object” and “verb” and that at around 11 months babies around the world begin to understand the order their parent language has them in. The idea here is that language is an instinct we are born with, we “just” need to learn how to translate from the language of our brain to the language of our society (culture). We are born with language ability but we need to learn English, French, German, Spanish and Japanese, etc. depending on our home culture. We have the potential for language as individuals but learning it requires other people, it is a social cultural activity – we cannot learn to speak a language on our own. Once we have learned (say) English we can simply talk and communicate without having to concentrate on the language itself – we can forget it – not absolutely of course but relatively[1]. Similarly, we are born as individuals with emotions but they are socially validated and developed. Within our culture we have no problem in our daily existence because we have all forgotten pretty much the same stuff. If we accept this view of language development as a primitive model of culture then we can see two obvious problems – most of it is forgotten and so you cannot isolate it to analyse it – take a piece of paper and write down every word you know. On average you will have written about 10 per cent of the words you actually know – you just cannot remember them out of context. Another problem is when one culture meets another, what each has forgotten is similar but different. With language the differences are relatively apparent. An extreme example to make a point is outlined by Wittgenstein (1978) who posited, “If a lion could talk, we could not understand him.” Sadly Dr Doolittle would find the phrase “please don’t eat me” to have no available response in a lion. Its language (of the brain and culture) has been created so differently that we cannot even rely on miming “Je ne me mange pas, s’il vous plait” to avoid the quite culturally accepted eating of people if the chance arises. For communication to occur we must construct our worlds similarly and have similar life experience. We can have partial communication with dogs, better communication with primates, better communication with other human beings, better communication with people who speak our language, etc. But we can never achieve perfect communication – perhaps not even with ourselves. This may seem a very solipsistic approach in that we may feel that we are not communicating with our friends or other people in our organisations but with our models of them. So how can we be sure of anything we have learned or understood to be “true” – how can we know that we really do agree or disagree on something. Foucault (1970, p. 29) in thinking about how we order our world suggests that: Every resemblance receives a signature; but this signature is no more than an intermediate form of the same resemblance. As a result, the totality of these marks, sliding over the great circle of similitudes, forms a second circle which would be an exact duplication of the first, point by point, were it not for that tiny degree of displacement . . . The signature and what it denotes are of exactly the same nature; [but] they obey a different law of distribution; [however] the pattern from which they are cut is the same.

Here we see the mutuality or correspondence of what is created separately. For example, you read this text and build up an idea (or counter idea) of culture or rethink

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your own – so is your idea the interpretation of culture as written here or is it your own view? Our understanding is both individual but social. To explain this further, in writing about culture a writer is attempting to explore, explain, describe and analyse some ideas about culture. The text is a representation of the writer’s ideas at a given moment in time. The reader reads the text and understands the writer’s ideas – or does she/he? The reality is that we have no way of knowing or accepting that the writer’s ideas are now the reader’s ideas – even if the reader has a desire to agree. We have correspondence but not causation. If we ignore disagreement for a moment and accept that in our organisations we have a need to agree on some (most) things, then the reader and the writer will largely see the same things but with variations in understanding and interpretation. The agreement will be forgotten into our mutual psyche, our culture. For example, – how often in our transactions with people do we say “OK so we agree on X and Y, so forget about them and let’s just concentrate on Z because Z seems to be where we have a problem (a disagreement).” Further, how often are we upset to find that the aforementioned X and Y are going to be changed when we “thought we’d agreed on them ages ago” or when “we always do X and Y like this” – and we have to change our forgotten models. We have difficulty changing our history, which may explain why the original Mona Lisa is the original Mona Lisa – it has a history. This might also explain why we find metaphors so important in discussing culture. Morgan (1986) explores the use of machine or brain (etc.) metaphors to explain organisation. By tapping into our forgetting, metaphor allows us to understand enough of something in order that we can communicate, discuss, analyse or synthesise when (counter to management practice), exactitude might not be able to. Bataille’s (1988, p. XXXII) second dimension “that we are not everything” may explain why culture uses metaphor to cope with not knowing – or accommodate the lack of exactitude. The metaphor carries enough general detail to facilitate correspondence but also jettisons enough of the detail that might prohibit wider understanding or application. This allows us to create Foucault’s (1970) error or “. . . tiny degree of displacement . . . ” to hold our misunderstandings with impunity. Management’s reliance on cause and effect and autonomy must seek or assume exactitude to be right first time and eradicate misunderstanding. In a sense Foucault (1970) may be suggesting that because the way we construct models of other people is inevitably similar to the way we construct ourselves. We end up with, not the truth, but a viable model of our organisation that we can use in our everyday organisational existence. So, for example we see other people as being like ourselves unless we have reason not to, in which case we need to revise our model. Thus, when we are dealing with people who are our age, gender, intelligence, nationality, etc. we have to do less work, have less risk and need to do less changing (learning). This is in general another excellent reason to dislike racists – they are in fact giving perfectly respectable lazy people a bad name. Because we cannot see culture as an exact objective “thing” from a detached perspective or from beyond a boundary we have to “be in touch” with it or intuit culture. Culture as a subject evokes many arcane ideas such as mysticism, fable, folklore and superstition. Superstition is in some sense a systematic dealing with the unexplained. Stories are ways in which ideas are communicated so there is no surprise they exist in organisations. Johnson and Scholes (2002) explore stories that exemplify the best and worst of the organisation – the heroes and villains, etc. We can reflect

on the process of using story in leadership, culture and strategy in order to include people in the process. Porter’s (1980, 1985) notion of value adding can be considered in this way, as the organisation can have a “value adding” culture. Here stories of adding value and the language of value act to include people in the organisation in its culture and strategy – to socialise individual ideas of conduct. Stories mop up the detached and the dislocated to bring them into the strategy. We see white-coated scientists in labs hover over Bunsen burners discussing how favourable results of the experiment could potentially “add value” to the product and the organisation. Ebb and flow Bate (1994) suggests that strategy emerges within a cultural context and culture emerges in a strategic context. Bate (1994) explores the idea that the issues of strategy, culture and the organisation are in fact interchangeable if not the same thing from a different angle, i.e. culture is strategy and strategy is culture. These interrelations can operate at a shallow visible level or deep invisible semiotic level. Bate (1994) sees culture as a creation (a fiction) of the organisation where many fictions might exist and be held together. Consequently, leaders are like writers of fiction as they are creating the “story” of the organisation, as it would like to be presented internally and externally. Boje (1995) uses the Tamara[2] metaphor for organisations where people in organisations are never aware of the entire plot. As individuals we operate in, a state of partial knowledge. Boje (1995) suggests that the fullest story of an organisation is the story of the development of the organisation’s strategy. Again, the use of Porter’s (1980, 1985) notions of value emerge from the leader’s toolkit, to act as a proto-story to include people throughout the organisation in the strategy story without making the story explicit. The use of “value” and other metaphors such as “machine” or “organism”, etc. allow us access to understanding when we do not have all of the facts. Metaphor offers us the possibility to take more appropriate actions when all of the details of a situation are unknown or too difficult to fully comprehend – they allow us to cope with incomplete knowledge. This may add to our understanding of the cybernetics of culture, in that if the development of language shows us how culturing might occur – then storytelling is one of its observable processes. The telling and listening to and re-telling and recollection of and re-interpretation of stories link the individual with the social and explore the complication of organisation, as well as contribute to its culture. Social worlds (specifically our organisations) are held together amidst infinite possibility through their metaphors, transactions, relationships and behaviours. We generate models of the world that are similar to other people’s models because we are people (and not lions). We generate models more similar to the people in our organisation because we have more similar starting points from which to generate. We build up models in similar ways so our culture emerges from our natural propensity to be similar. This similarity can be at once forgotten and at the same time celebrated as a fulfilment of ritual desire for reciprocal mirroring (Orr, 1993). We see people as similar to us because we build up models of ourselves as we build up models of them but we must be aware of the slippage, outlined by Foucault (1970) above – the degree of displacement that necessitates constant learning and paradigm shifts, to accommodate new perceptions and creations. Again this model of the situation may appear to be a little solipsistic – that the world is just a figment of our

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individual imagination and that other people are roles being played out in our heads. This is not so, we do get information and some of it we process to modify our models. May be this can be explained in terms of Foucault’s similitudes – when we talk with another person we mediate with our model of them. If they use a word such as “poetic” we may not be sure that their exact definition of this word is exactly the same as ours. The commonality of our brain and body and emotions and experience of this word, etc. will ensure that our models have been developed in a similar way giving a degree of correspondence. Though the “truth” may only exist in our own minds as individuals, our relationship with each other can be at least viable, because although we are different we are also the same and so our derivations will be similar enough to allow us to organise but different enough to allow us to create. Epilogue Culture is apparent in the relationship between the individual and the social and as such cannot be separated from the group or the individual. The coincidence of meaning must be emergent in the relationship of the individual and the group and not in one or the other. Culturing is the process of developing individual social emotional activity that both learns from and creates group social emotional activity. Culture corresponds the individual with the social, as does management, though culture operates at a much deeper personal level and at the same time a second-order social level. Correspondence in culture is a reciprocal relation, cause and effect unidirectional. Correspondence allows for or accommodates error that could be our new creation – uncle George may in fact be the new dance sensation regardless of the right-first-time total quality management metric that finds him lacking. This may resonate with our (especially initial) rejection of ideas or arguments, that are not rationally unsound but at loggerheads with our relevant model. They are aesthetically displeasing and so we require time to get used to them or reconfigure our model. Management cannot deal with (have control of) the big issues of the organisation such as its death or its radical changes. Culture deals with the dramatic/symbolic points of inflection to substitute order with a sense of safety or well being in the face of disorder. Culture copes – is in control. Culture facilitates organisational control on the basis of the mutuality of development of models and a shared desire for order that might help us to abate the death of the organisation. In relation to management, culture is the inherently more democratic system of building individual and group understanding of the organisation and its control. Culture mops up and includes through holding where management might boundary to exclude. Culture emerges from the individual and the individual emerges from culture. Culture was offered to us when we arrived and it is what we leave behind. Culture acts as the complex shifting control of the organisation, where management regulates, culture accommodates though both stem from a desire to order. Where management imposes external regulation culture “becomes” from internal emotion. As the thumb and the brain develop separately and together the emotions of the individual and the emotions of the social also develop pari passu. Culture and management emerge form the ability to order and control as well as a desire to do so. The cybernetics of culture evolves from a desire to order the complex realities and unknowables of social interaction and cope with the limitations of

“not being everything”. The process of culturing stems from an intuitive ability to model emotional social interaction referenced to individual emotional action. The cybernetics of culture is seen in the correspondence and mutuality of models created separately. Models are created similarly and separately but validated socially such that individuals model the social organisation and the social organisation offers reference points and guidance in the model’s development. Culture develops because it can and because there is a desire to order and be in control. Notes 1. How many of us still remember how to conjugate verbs or can wax lyrically about nouns, pronouns, indefinite articles, past participles, infinitives, idiom. . .? We tend only to do these things when we learn a foreign language. 2. Tamara is a play played out by actors in different rooms constructed on stage. In an attempt to gain an understanding of the story, the audience is invited to follow particular characters from room to room or stay in one room while actors come and go. What emerges is that members of the audience see part of the story unfold and have to rely on discussions with, and interpretations of, other audience members (and actors) to gain a wider but not necessarily complete understanding of what transpires. The audience become part of the play. References Bataille, G. (1988), Inner Experience (translated by Leslie Anne Boldt), State University of New York Press, New York, NY. Bate, P. (1994), Strategies For Cultural Change, Butterworth-Heinemann, London. Baudrillard, J. (1983), Simulations, Semiotext(e), New York, NY. Beer, S. (1981), Brain of the Firm, 2nd ed., Wiley, Chichester. Beer, S. (1985), Diagnosing The System for Organisations, Wiley, Chichester. Binns, P. (1994), “Organisations, values and learning”, in Burgoyne, J., Pedler, M. and Boydell, T. (Eds), Towards The Learning Company: Concepts and Practices, McGraw-Hill, London. Boje, D.M. (1995), “Stories of the storytelling organisation: a postmodern analysis of Disney as ‘Tamara-Land’”, Academy Of Management Journal, Vol. 38 No. 4, pp. 997-1036. Churchman, C.W. (1968), The Systems Approach, Dell Publishing, New York, NY. Dunning, J.H. (1980), “Towards an eclectic theory of international production: some empirical tests”, Journal Of International Business Studies, Vol. 11 No. 1, pp. 9-31. Dunning, J.H. (1995), “Reappraising the eclectic paradigm in the age of alliance capitalism”, Journal of International Business Studies, Vol. 26, pp. 461-91. Dunning, J.H. (2000), “The eclectic paradigm as an envelope for economic and business theories of MNE activity”, International Business Review, Vol. 9, pp. 163-90. Foucault, M. (1970), The Order of Things, Routledge, London. Gheradi, S. (2003), “Knowing as desiring. Mythic knowledge and the knowledge journey in communities of practitioners”, Journal of Workplace Learning, Vol. 15 Nos 7/8, pp. 352-8. Greenfield, S.A. (2000), The Private Life Of The Brain, Allen Lane The Penguin Press, London. Grey, C. (1999), “‘We are all managers now’ ‘we always were’: on the development and demise of management”, Journal of Management Studies, Vol. 36 No. 5, pp. 562-85. Hume, D. (1992), A Treatise of Human Nature, 2nd ed., Oxford University Press, Oxford.

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Johnson, G. and Scholes, K. (2002), Exploring Corporate Strategy: Text and Cases, 6th ed., Pearson Education, Harlow. Linstead, S. and Chan, A. (1994), “The sting of organization: command, reciprocity and change management”, Journal of Organizational Change Management, Vol. 7 No. 5, pp. 4-19. Leslie, A.M. and Keeble, S. (1987), “Do six-month-old infants perceive causality?”, Cognition, Vol. 25, pp. 265-88. Michotte, A. (1963), The Perception Of Causality, Methuen, London. Morgan, G. (1986), Images Of Organisation, Sage, Thousand Oaks, CA. Mullarkey, J. (1999), Bergson and Philosophy, Edinburgh University Press, Edinburgh. Orr, J. (1993), “Sharing knowledge, celebrating identity: war stories and community memory amongst service technicians”, in Middleton, D.S. and Edwards, D. (Eds), Collective Remembering: Memory in Society, Sage, Beverly Hills, CA, pp. 169-89. O’Shea, A. (2001), “The eternal return of organizing. Or why is there organization rather than nothing?”, working Paper. O’Shea, A. (2002), “Desiring desire: how desire makes us human, all too human”, Sociology, Vol. 36 No. 4, pp. 925-40. Pinker, S. (1994), The Language Instinct, Penguin, London. Porter, M.E. (1980), Competitive Strategy: Techniques for Analysing Industries and Competitors, The Free Press, New York, NY. Porter, M.E. (1985), Competitive Advantage: Creating and Sustaining Superior Performance, The Free Press, New York, NY. Porter, M.E. (1990), The Competitive Advantage of Nations, Macmillan. Porter, M.E. (1998), “Clusters and the new economics of competition”, Harvard Business Review, November-December, pp. 77-90. Scho¨n, D.A. (1983), The Reflective Practitioner How Professionals Think in Action, Basic Books, London. Whittington, R. (2001), What is Strategy and Does it Matter?, Routledge, London. Wittgenstein, L. (1978), Philosophical Investigations, 3rd ed., Basil Blackwell, Oxford. Further reading Schein, E. (1997), Organisation Culture and Leadership, Jossey-Bass, San Francisco, CA. Corresponding author James Rowe can be contacted at: [email protected]

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INVITED PAPER

Knowledge management: modeling the knowledge diffusion in community of practice

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Nen-Ting Huang, Chiu-Chi Wei and Wei-Kou Chang School of Technology Management, Chung-Hua University, Taiwan, Republic of China Abstract Purpose – To propose a model which can demonstrate the knowledge diffusion phenomenon in the community of practice. Design/methodology/approach – An algorithm has been developed to illustrate the processes of knowledge diffusion between knowledge workers, and factor the coefficients of distance, willingness, motivation, and ability of comprehension and expression. Besides, two types of knowledge diffusion are proposed, i.e. the knowledge sharing and the knowledge discussion. Findings – Change of knowledge worker will affect the knowledge diffusion within community of practice. The knowledge level of knowledge workers will be increased if more members join the community of practice, and vice versa. Besides, the development of knowledge workers will be constrained by the budget allocated and time available. Research limitations/implications – The model developed is one of the few research papers that can quantify the knowledge diffusion within community of practice. Practical implications – The development of knowledge workers can be tangibly measured and linked to the budget and time constraints, as a result, the enterprises can plan, predict and improve the knowledge management initiate. Originality/value – Previous papers are mostly descriptive in nature, and they are too abstract to be tangibly understood. The model proposed eliminates the drawbacks and expand the research areas by using a mathematical model. Keywords Knowledge management, Modelling, Programming, Knowledge transfer Paper type Research paper

1. Introduction Information technology has changed the nature of enterprises whose ability were assessed based on traditional values such as real estate, capital, and so on. In other words, the competitive advantage of future enterprises will rely heavily on knowledge, and enterprise capabilities in knowledge extraction, knowledge utilization and knowledge creation. All depend on effective deployment of knowledge management. Drucker (2002a, b) has noted that knowledge should not be equally viewed as materials, money, and real estate in the new economic world, but rather is the only meaningful resource. He predicted that knowledge workers will become the major source of power in the future society. Technology brings a new type of economy in which knowledge plays a prominent role, and this is known as the “Knowledge-based economy.” In this era, knowledge becomes the main source that drives the economic growth, and the means through which enterprises develop and sustain competitiveness.

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The Oxford Dictionary defines knowledge as “knowing,” the sum of individual understanding, discovery, and learning from experience. Generally, knowledge comprises four different levels: data, information, knowledge and wisdom (Hong and Wang, 2002). “Data” is something that has not been organized but has been observed and collated. Examples of data include sales volume, scale of population, and records of quality control. “Information” is data being analyzed for a specific purpose, and expressed more widely or systematically. “Knowledge” is information that has been practically verified to effectively solve real problems. Therefore, it is quite common that a group of people receiving same information, but each of them may induce different knowledge. “Wisdom” is the competence that, based on personal analysis, judgment and evaluation of decision environments, useful and valuable decisions can always be developed. Wisdom is the key in determining individual and organizational strategy that can produce valuable and powerful competitive advantage. The Oxford English Concise Dictionary divides knowledge into four categories: (1) know-what; (2) know-why; (3) know-how; and (4) know-who. Know-what and know-why can be found from books, articles, and database; know-how derives primarily from efficient practical executions and experiences; know-who is obtained from the same industry, vertical industries and experts and research units (Wu and Chen, 2001). Hedlund (1994) further divided knowledge into explicit knowledge, including descriptions, verbal, formulae, patents, charts, and so on, and tacit knowledge, such as non-verbal experiences or other non-expressional actions. Explicit knowledge must use systematic transformation methods for knowledge flow, sharing, and extension, and becomes a useful tacit knowledge for corporations or staff. Based on the analysis of Hedlund, the concept of knowledge is ambiguous and multi-faceted. It cannot be explained or understood based on verbal description (Peng and Tung, 2003). In numerous cases, creativities are derived from technical skills that are included in invisible knowledge. Knowledge diffusion is the key to delivering staff invisible knowledge to others, and transferring this knowledge into visible knowledge and therefore, leading to valuable production. Following staff sharing and digesting of corporate knowledge, the knowledge is explored, extended, and refined Finally, knowledge accumulation creates advantages in building core competitive abilities (Drucker 2002a, b). A key question raised is how the invisible knowledge of staff can be transferred into useful corporate knowledge. Thomas Stewart (Chuang and Chang, 2000), the Editor of American Fortune Magazine, produced a book called Intellectual Capital: The New Wealth of Organizations in 1997. In this book, Stewart emphasized the value of staff knowledge to organizations. Staff Knowledge can include techniques, experiences, habits, instincts, perspectives and so on. The most important task of knowledge management is to increase the value of the invisible knowledge of staff through creativity. Secondly, management should seek to increase the value of staff intelligence, and provide employees with an environment that encourages free exchange of ideas, in which they are not afraid of reprisals from others. The final goal

is to establish community of practice, which enables knowledge workers to flow and share knowledge and thus, stimulate creativity. The organization should support essential resources such as the internet, meeting rooms, activity expenses, and awards. The effect of group creativity is absolutely higher than the summation of each individual, and most importantly, the capability of group creation belongs to the organization, and cannot be taken away by any individual.

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609 2. Literature review Knowledge interchange among group members is the most direct and effective means of elevating the knowledge level of the entire group. Being part of knowledge diffusion activities, new members can rapidly become acquainted with skills and techniques through discussion and sharing of knowledge among members. They do not have to learn by making mistakes from the beginning again and can accumulate work knowledge naturally and rapidly (Chuang and Chang, 2000). Cutler (1989) pointed out that the transfer and diffusion of higher level knowledge primarily relies on individual communication and cooperation. Allen (1973) also noted that inter-group communication should be people focused. Cutler (1989) and Smilor et al. (1991), and some other scholars argued that interaction and communication among skilled workers is the most effective means of knowledge transfer, diffusion, and interflow. If the members of a certain project interact or contact with other colleagues more frequently, the successful achievement of the project will be higher (Allen, 1988). Therefore, the critical point of having successful knowledge management is to promote and enhance organization member’s intercommunication. The serial researches of Allen (Allen, 1973, 1988; Allen and Fusfeld, 1976) showed an inverse relationship between the distance among people and the likelihood of knowledge flow. Distance can influence the probability of communication and the most effective maximum distance is 30 m, thus, the proportion of interaction decreases with increasing distance (Allen and Fusfeld, 1976). Smilor et al. (1991) also proposed that the rate of success of skill transfer increases with decreasing distance. Consequently, the design of the office building, space decoration, and seating arrangement will influence the communication among organization members. In a work place, characteristics such as work station and layout planning can be adjusted to suit workers needs, thus improving knowledge flow. Summarily, the environment can affect individual knowledge flow. Knowledge flow is important for organization members to regularly improve their proficiency, therefore, management must optimize the distance between individuals via proper space management to prevent knowledge sharing from being failure (Allen and Fusfeld, 1976). The distance can be further divided into four categories: (1) geographical distance, such as vertical and horizontal straight-line distance; (2) cultural distance, such as languages, values, and the likes; (3) technology distance, such as technological level, and technological field; and (4) social distance, such as social status and strength of power (Tseng, 1994). Brown (1981) indicated that technology flow is related to time, distance, and peripheral structure transportation, market, facilities. Smilor et al. (1991) both concluded that the success rate of technology transfer increases with decreasing distance.

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Short distance implies that the differences between individual values, attitudes, methods and points of view are minimized. Staying closer to technology, one can benefit more from diffuses. For example, in urban areas, more technology is required and the diffusion rate is also higher (Davelaar and Nijkamp, 1990). Wu and Chen (2001) discovered that enterprise development and creativity, and academic research institutions can be closely related to better transfer knowledge. In short, reducing the distance among members or organizations can improve mutual interaction, and therefore, enrich the improve knowledge diffusion. It is important to identify factors hindering the implementation of the community of practice to increase the possibility of successful knowledge sharing. The factors that affect the knowledge sharing can be individual and cultural. The individual factor can be further divided into the one that influences the tutor, and the one that influences the learner. The tutor may not be willing to share what he or she knows because of fear of being replaced. The learner may not have the desire to learn because of lack of motivation. Besides, knowledge sharing depends primarily on the individual communication ability, social pattern, and self-esteem to ones professional knowledge. The existence of such factors stops individuals to transfer their knowledge willingly or automatically. Employee tends to avoid sharing some specific knowledge to protect their power or status of being seen as an expert. Additionally, Employees cannot be possibly forced to share individual knowledge with others; therefore, monetary means should be tactically utilized to gain the trust of knowledge owners. Szulanski found that participants may lack learning motivation during the process of the knowledge sharing activity, because of resistance to change (Probst et al., 2003). Organizational forgetting is another natural phenomenon that represents a crisis in maintaining individual knowledge, because losing essential knowledge can reduce competitiveness (Holan and Martin, 2004). Two causes of organizational forgetting exist, firstly, erasing of memories causes unredeemable losses. For instance, employees quit or commission their jobs to others. Secondly, memory is either temporarily or permanently kept. The same mechanism occurs when an individual learns a new skill or knowledge; one will gradually forget or become unfamiliar with that knowledge if they cannot apply their learning to the work. Therefore, natural forgetting is also a negative factor that cannot be neglected. It is obvious that employees must be given the chance to practice their knowledge if they are expected to preserve or maintain the knowledge (Probst et al., 2003). As a result, enterprises should establish internal knowledge system that provides employees with opportunities to learning and practice knowledge to stop natural forgetting. Some enterprises deploy the system that senior workers guide junior workers to rapidly adapt to the work environment, and members share and learn knowledge to improve the knowledge level of the members. The knowledge management researches that are related to the community of practice and knowledge diffusion are mostly descriptive in nature, and they are too abstract to be tangibly understood. Therefore, this study intends to propose a mathematical model to vividly demonstrate the process of knowledge diffusion activities in the community of practice by considering various factors such as distance, knowledge gap, learning ability and willingness to share. Besides, since knowledge diffusion activities certainly consume cost and time, thus, a resource constraint knowledge sharing is introduced to the model to practically explore the knowledge diffusion within the community of practice.

3. Model formulation The main objective of establishing a community of practice is to share essential knowledge and upgrade the knowledge levels of group members. However, several concerns need to be clarified. Firstly, what knowledge members have to learn, which member lacks this knowledge, and which member owns this knowledge. Besides, knowledge owners may be unwilling to share due to fear of being replaced, or intentionally to maintain their supremacy. While members who lack this essential knowledge or skills may regard learning new knowledge as a difficult task owing to lack of learning motivation. Furthermore, if the distance between two members is too far, for example, if they are on different floors or in different buildings, it will be quite inconvenient to have a face-to-face discussion, and, the possibility of knowledge sharing will be reduced. As stated above, whether knowledge can be exchanged within community of practice depends on if sufficient knowledge flow exists, and the knowledge flow is in inverse proportion to the distance among members, and in direct proportion to knowledge gap. Therefore, the best performance of knowledge diffusion exists if members can conduct face-to-face sharing, because the distance is minimized in this situation. However, knowledge flow is inversely related to the willingness of members (tutors) to share, the learning motivation of members (learners) to learn, and the knowledge gap between these two. Let Fij represents knowledge flow between any two members, and Dij represent the distance, and (Ki 2 Kj), Wi, and Mj represent knowledge gap, sharing willingness, and learning motivation coefficients. The following equation can be derived: F ij ¼

M jW i ðK i 2 K j Þ Dij

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ð1Þ

This model assumes that knowledge diffusion will occur between tutor and learner when the knowledge flow exceeds a threshold level F. This is called knowledge sharing activities (Figure 1). If the knowledge flow is smaller than F, only discussion activities can occur (Figure 2). Generally, the amount of knowledge diffuses in knowledge sharing activities exceeds that in discussion activities. Both knowledge sharing and discussion activities are termed as knowledge diffusion activities in this study. Secondly, learners frequently cannot fully absorb all of the knowledge and skills that tutors have taught during knowledge sharing. Even learners have strong learning Share Knowledge

Learner 2

1

Sharing Learn Knowledge

Tutor

Figure 1. Learner learns and tutor shares

Partner

Learn and Share Knowledge 2 1 Partner

Discussion Learn and Share Knowledge

Figure 2. Discussion between learner and tutor

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motivation, because knowledge diffusion is limited by individual learning ability, such as ability of comprehension and memorization. Generally, learner comprehension and knowledge absorption increases with their learning abilities. Besides, tutor’s ability of expressions also influences knowledge sharing. Some people are knowledgeable but not eloquent, which reduces the effectiveness of teaching and learning. Therefore, for efficient knowledge diffusion, enterprises must realize the relevant factors, overcome obstacles, and specify methods of assessment and reward, such as providing bonuses to increase tutor willingness and learner motivation, designing methods of measuring the knowledge levels of all members, and so on. Essentially, in addition to monetary means and evaluations, systematic feedback can also promotes tutor willingness to share, such a sense of fulfillment and interacting with learners. This paper proposes a mathematical model for knowledge diffusion based on the related factors discussed above to quantitatively measure the knowledge diffusion activities. 3.1 Problem statement A community of practice is composed of N members each with different knowledge level, and it is assumed that knowledge sharing and learning activities can occur between any two members if their knowledge gap is higher than a threshold value. However, if the knowledge gap between two members is less than the threshold value, then only discussions can be expected to occur between those two. Furthermore, for human nature, one with higher knowledge level may not be willing to share, and one with lower knowledge level may not be motivated to learn. Therefore, all members are characterized by different coefficients of knowledge sharing willingness and knowledge learning motivation. Besides, one who is willing to share knowledge may not be able to fully transfer his knowledge to those who lack, because of inability of teaching. By the same token, one who is motivated to learn may not be able to completely absorb knowledge form the tutor, because of poor comprehension. In addition, distance between two members play a significant role in the transformation of knowledge, because possibility of either knowledge sharing and learning or discussion is in reverse proportional to the distance in between. Nevertheless, reward system can lead to better tutor’s sharing willingness and learner’s learning motivation. Finally, owning to the fact that resources are always limited in nature, thus, it is supposed that each knowledge sharing and learning or discussion activity consumes certain amount of cost and time. It is therefore expected that, given a budget and time constraint, the overall knowledge level of the community of practice can be maximized. To reveal how community of practice conducts knowledge diffusion activities, this study develops an algorithm measuring the knowledge gap, knowledge flow, knowledge growth and knowledge level among members. The proposed algorithm is as follows. 3.2 Algorithm . Step 1. Examine member’s knowledge level. Ki ¼ knowledge level of member i, where i; ¼ 1; 2; . . . ; n: The knowledge level depends on member’s educational background, seniority, and licenses. Large Ki indicates high knowledge level. . Step 2. Determine knowledge sharing willingness coefficient Wi, teaching ability coefficient Ei, learning motivation coefficient Mi, distance coefficient Dij, learning ability coefficient Li, and learning by discussion coefficient f:

.

.

Step 3: Calculate the knowledge flow Fij between any two members based on equation (1). When F ij $ F; knowledge sharing occurs, and when F ij , F; discussion occurs. Knowledge flow may simultaneously exceed F in multiple groups, but each individual member can only share knowledge with one member at a given time. Step 4: Compute the knowledge growth Kij. It involves tutor willingness to share, tutor teaching ability, and learner motivation and learning ability, namely: K ij ¼ ðK i 2 K j ÞW i E i M j Lj

ð2Þ

If two members engage in discussion, then knowledge growth is expressed as: K dij ¼ MaxðfK i ; fK j Þ where f is a constant .

ð3Þ

Step 5: Calculate the new knowledge level of learner j following the knowledge sharing. It is the summation of the original level plus the knowledge growth from sharing: K 0j ¼ K j þ K ij

ð4Þ

If it is discussion, then the new knowledge level K 0i ; K 0j of learner i, j is:

.

K 0i ¼ K i þ K dij

ð5Þ

K 0j

ð6Þ

¼ Kj þ

K dij

Step 6: Compute cost and time consumption from knowledge sharing. Let Cij represents the cost associated with sharing, and is directly proportional to Kij, and let: C ij ¼ 3K 2ij þ 4K ij þ 1

ð7Þ

Let Tij represents the time associated with sharing, and is directly proportional to Kij, and let: T ij ¼ K ij þ 2K ij þ 1

.

ð8Þ

The cost and time expenditure associated with discussion is assumed to be smaller than sharing, and both C ij ; T ij are set as constant. Step 7: Verify if the cost and time expenditure on knowledge sharing and discussion exceeds the budget and time limit, i.e.: C¼

n X

C ij þ

i¼1

and: T¼

n X i¼1

n X

C dij

ð9Þ

T dij

ð10Þ

i¼1

T ij þ

n X i¼1

If C $budget or T $time limit, then stop knowledge diffusion activities. If C , budget and T , time limit, then return to Step 3.

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Step 8: Let K m i represents the final knowledge level of members following the most recent knowledge sharing or discussion. Where i ¼ 1; 2 . . . ; n; m ¼ frequency of sharing, the knowledge level of all members within that community of practice can be obtained as follows: n X

614

m m Ki ¼ Km 1 þ K2 þ · · · þ Kn

ð11Þ

i¼1

4. Application example To demonstrate the applicability of the proposed model, the above algorithm is experimented using a real world example. The product development department of a technology company consists of six engineers, and due to the stiff market competition, the management decides to enhance their capability by increasing the knowledge level of all engineers. Therefore, a community of practice (Figure 3) is formed in expectation of, under limited cost and time, upgrading the knowledge level of all members by promoting the knowledge sharing activities. Based on the algorithm, the computations of the knowledge sharing and discussion activities are detailed in following steps: (1) Identify knowledge level Ki, it is assumed that a scale of 1-30 is used. K 1 ¼ 20; K 2 ¼ 18; K 3 ¼ 8; K 4 ¼ 12; K 5 ¼ 3; K 6 ¼ 5 (2) Determine the coefficients of sharing willingness, teaching ability, learning motivation, learning ability, the discussion coefficient, and the distance coefficient of members i and j. Table I lists the various coefficients. Table II shows the distance coefficient. The distance is assumed to be as follow: K1 is at the same floor but different offices with K4, and works in a same city to K2, K3, K5, and K6. Moreover, K2,

1

3 4

5 6

Figure 3. Community of practice

Table I. Various coefficients of members

2

K workers

Ki

Wi

Ei

Mi

Li

C

1 2 3 4 5 6

20 18 8 12 3 5

0.90 0.95 0.75 0.70 0.60 0.60

0.9 0.9 0.7 0.8 0.5 0.6

0.80 0.85 0.90 0.70 0.90 0.75

0.9 0.85 0.7 0.8 0.6 0.65

0.05 0.05 0.05 0.05 0.05 0.05

K3, K5, and K6 all work in the same building, K2 and K6 are in the same office, but are on different floors to K3 and K5, and K3 and K5 share the same office. Table III illustrates the distance coefficient among the various organizational members. (3) Compute the knowledge flow Fij, when F ij $ F, knowledge occurs, and let F ¼ 3. Table IV lists the knowledge flow among members. The knowledge flow is 9.26 between member 2 and 6, and 6.89 between members 1 and 5, thus the knowledge sharing activity is to be performed between 2 and 6, and 1 and 5. However, the knowledge flow is only 1.26 between member 3 and 4, thus only discussion occurs.

Same office

Same floor

Same building

Same city

1

1.2

1.5

2

Distance coefficient

Dij

Distance coefficient

Dij

Distance coefficient

D12 D13 D14 D15 D16 D23 D24 D25

2 2 1.2 2 2 1.5 2 1.5

D26 D34 D35 D36 D45 D46 D56

1 2 1 1.5 2 2 1.5

Pairs

Ki 2 Kj

Dij

MjWi(Ki 2 Kj)

Fij ¼ MjWi(Ki 2 Kj)/Dij

K12 K13 K14 K15 K16 K23 K24 K25 K26 K43 K35 K36 K45 K46 K65

2 12 8 17 15 10 6 15 13 4 5 3 9 7 2

2 2 1.2 2 2 1.5 2 1.5 1 2 1 1.5 2 2 1.5

1.53 9.72 5.04 13.77 10.125 8.55 3.99 12.825 9.2625 2.52 3.375 1.6875 5.67 3.675 1.08

0.77 4.86 4.20 6.89 5.06 5.70 2.00 8.55 9.26 1.26 3.38 1.13 2.84 1.84 0.72

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Table II. Distance coefficients

Table III. Distance coefficients among members

Knowledge diffusion

Sharing

Sharing Discussion Table IV. Knowledge flow between two members

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(4) Calculate the knowledge growth Kij following the knowledge sharing activity and K i following the discussion activity (Table V). (5) Obtain the knowledge level K 0j of learner j and K 0i of discussion joiner i following the knowledge diffusion. Table VI lists the details. (6) Compute the time and cost consumption as shown in Table VII. It is assumed that discussion requires two units of cost and four units of time.

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(7) Examine if the cost and time consumption exceed the limitation following the first knowledge diffusion activity. Table VIII lists the details. This study assumes that the budget and time allocated are 1,000 and 500 units, respectively. (8) Step 8: List the new knowledge level of members and find the total group knowledge level following the first knowledge diffusion. See Table IX.

Table V. Knowledge growth

Table VI. New knowledge level of individual members

Member

Ki

2 6 1 5 4 3

18 5 20 3 12 8

Member

Ki (1)

2 6 1 5 4 3

18 5 20 3 12 8

Group

Table VII. The cost and time consumed of the first knowledge diffusion

2 6 1 5 4 3

Ki ¼ (Ki 2 Kj)WiEiMjLj

Kdi ¼ Max(cKi,cKj) c =0.05

7.44 5.42 Discussion Discussion

Kij ¼ (Ki 2 Kj)WiEiMjLj (2)

Kj0 (1) þ (2)

7.44

10.44

5.42 Discussion Discussion

10.42

0.60 0.40

Kdi ¼ Max(cKi,cKj) c =0.05 (3)

Ki0 (1) þ (3)

0.60 0.60

12.60 8.60

C ij ¼ 3K 2ij þ 4K ij þ 1

T ij ¼ K 2ij þ 2K ij þ 1

369.46

130.78

368.31

130.38

Cdij ¼ 2 units

Tdij ¼ 4 units

2.00

4.00

C¼ Group 2 6 1 5 4 3 Total Budget Balance

Member 1 2 3 4 5 6 Total

n X i¼1

C ij þ

n X

C dij

i¼1

T¼

n X i¼1

T ij þ

n X

T dij

i¼1

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369.46

130.78

368.31

130.38

617

2.00 739.77 1,000 þ 260.23

4.00 265.16 500 þ 234.84

Table VIII. Comparison of the budget and time constraint after first knowledge diffusion

Original Ki

K 0i

20 18 8 12 3 5 66

20 18 8.6 12.6 10.44 10.42 80.06

It is noted that members of the community of practice can vary, therefore, three situations may occur when conducting the second knowledge diffusion activities: (1) members of community remain the same; (2) member K1 leaves the community; and (3) new member K7 joins the community. Applying the algorithm to the above three situations, Table X can be obtained. It can be seen that after one knowledge worker leaves, the overall knowledge level of the community of practice suffers by less knowledge improvement than the other two cases. On the other hand, when one knowledge worker joins the community of practice, the total knowledge level of the community of practice increases more than other two cases. This phenomenon verifies the fact that human resource must be treated as the most important asset for enterprises. 5. Discussions The number of members in a community of practice is always difficult to control in this competitive environment, especially the most skillful knowledge workers. Those workers are frequently lured elsewhere by offering high salary and better package. The example demonstrated in the previous section shows that when the number of members in the community of practice changes, the transformation of the knowledge within the community is also greatly affected. Figures 4-7 show the knowledge growth of the community for the three situations described above. Since, the knowledge level of K1 and K2 are the highest and act as tutors, thus, this section only compares the knowledge growth of members of K3, K4, K5, K6, K7.

Table IX. The new knowledge level of members following first knowledge diffusion

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Step

Situation (1)

Knowledge flow Fij

Fij $ 3

Knowledge growth

Fij , 3 K 0ij

618

K di Resources consumption

Table X. Results of three situations after second knowledge diffusion

Exceeds resources constraints Knowledge Level after second knowledge diffusion

K1 and K3 (4.62) K2 and K6 (5.40) K4 and K5 K3 increases 5.82 K6 increases 2.61 K4 and K5 increase 0.63 1,246.54 438.48 Yes

0

Cost Time Increased knowledge level Total knowledge level

Situation (2)

Situation (3)

K2 and K6 (5.40) K1 and K3 (4.62) K2 and K6 (5.40) K3, K4 and K5 K4, K5 and K7 K6 increases 3.61 K3 increases 5.82 K6 increases 3.61 K3, K4 and K5 increase 0.63 611.57 218.58 Yes

K4, K5 and K7 increase 0.63 1,293.71 456.23 Yes

9.69

5.05

10.87

89.75

65.11

101.93

16 14

K level

12

Figure 4. Knowledge growth if members remain unchanged

K3

10

K4

8

K5

6

K6

4 2 0 K

K'

K"

16 14

K level

12 K3

10

K4

8

K5

6

K6

4

Figure 5. Knowledge growth if one member leaves

2 0 K

K'

K"

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16

K level

14 12

K3

10

K4

8

K5

6

K6

4

K7

2

Figure 6. Knowledge growth if one member joins

0 K

K'

619

K"

120 100

K level

80

remains one leaves

60

one joins 40 20 0 K

.

.

.

K'

K"

Figure 4 shows the knowledge growth of members after second knowledge diffusion if all of them remain working in that community of practice. Since, members K3, K5, and K6 participated in the knowledge sharing activities, their knowledge levels grows significantly. Whereas member K4 only joined the discussions, the knowledge level is improved slightly. Besides, it is apparent that the knowledge level of the four members becomes closer after being part of the knowledge diffusion activities; and the rank of knowledge level are members 3, 4, 6 and then member 5. The knowledge level of all members is escalated to be above 10. This explains the importance of deploying the community of practice in enterprises. Figure 5 shows the knowledge growth of members in the community of practice after second knowledge diffusion if member 1 leaves the community of practice. Compared to the results of situation 1, it can be seen that the rank of the knowledge level has now become members 6, 4, 5 and 3, meaning that the knowledge sharing and discussion activities are related to the composition of the group members. Figure 6 shows the knowledge growth of members in the community of practice after second knowledge diffusion if new member 7 joins the community

Figure 7. Knowledge growth of the entire community of practice

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of practice. It is obvious that the knowledge level of all members has been even greatly improved by the new member, and the rank of the knowledge level has now changed to members 3, 6, 4 and 5. Figure 7 shows the overall knowledge growth of the entire community of practice for the three situations. It matches the argument that the knowledge level of the community will suffer and benefit if one leaves and another joins, respectively.

6. Conclusion To maintain competitive and creative, and to accumulate advanced knowledge better than the competitors, organizations need to deploy knowledge management and to establish the community of practice to encourage employees to share knowledge in order to upgrade the knowledge level of the entire organization. The purposes of the knowledge diffusion activities are primarily to transfer the tangible or intangible knowledge that are preserved by members to the one who lacks. Successfully implementing the knowledge diffusion activities requires members’ willingness to share and motivation to learn, which can be stimulated by means such as reward and performance evaluation system. This paper proposed a mathematical model to measure the knowledge sharing and discussion among members of community of practice. The factors considered include the knowledge gap, the distance between members, the tutor’s willingness to share and learner’s motivation to learn. Knowledge sharing occurs when knowledge flow is sufficiently strong, and discussion occurs when it is weak. The knowledge growth of members is expected to be more in sharing activities than that of discussion, and it is influenced not only by the tutor’s willingness to share and learner’s motivation to learn, but also by tutor’s communication capabilities and learner’s comprehension competency. This study utilized an application example to clearly explain the knowledge diffusion activity within the community of practice. Results demonstrate that members of community can gain more knowledge if more staffs join the knowledge sharing or discussion activities. Besides, if the frequency of conducting the knowledge diffusion activities increases, the knowledge level of members can also be escalated significantly. Based on the results of this study, it is recommended that organizations should strive to create an environment that promotes sharing and discussion of knowledge if competitive advantage is to be expected. It is concluded that the model proposed can be a useful technique to vividly demonstrate and quantify the knowledge diffusion phenomenon in the community of practice. References Allen, T.J. (1973), “Institutional roles in technology transfer: a diagnosis of the situation in one small country”, R&D Management, Vol. 4 No. 1, pp. 41-51. Allen, T.J. (1988), Managing the Flow of Technology, MIT Press, Cambridge, MA. Allen, T.J. and Fusfeld, A.R. (1976), “Design for communication in the research and development lab”, Technology Review, Vol. 78 No. 6, pp. 1-8. Brown, L.A. (1981), Innovation Diffusion: A New Perspective, Methuen Co., London. Chuang, S.Y. and Chang, Y.W. (2000), CEO & Management Theory, Commonwealth Publishing Group, Taipei.

Cutler, R.S. (1989), “Survey of high-technology transfer practices in Japan and in the United States”, Interfaces, Vol. 19 No. 6, pp. 67-77. Davelaar, E.J. and Nijkamp, P. (1990), “Technological innovation and spatial transformation”, Technological Forecasting and Social Change, Vol. 37, pp. 181-202. Drucker, P.F. (2002a), Harvard Business Review: Knowledge Management, Commonwealth Publishing Group, Taipei. Drucker, P.F. (2002b), Management in the Next Society: Beyond the Information Revolution, Business Weekly Publications Inc., Taipei. Hedlund, G. (1994), “A model of knowledge management and the N-Form corporation”, Strategic Management Journal, Vol. 15, pp. 73-90. Holan, D. and Martin, P. (2004), “Managing organizational forgetting”, MIT Sloan Management Review, Vol. 45 No. 2, p. 45. Hong, M.Z. and Wang, E.R. (2002), Knowledge Management, Hwa Tai Publisher, Taipei. Peng, Ya-Hui and Tung, Cheng-Mei (2003), “The expansion of knowledge management in hospitals of Taiwan”, Journal of Healthcare Management, Vol. 4 No. 1, pp. 72-84. Probst, G., Raub, S. and Romhardt, K. (2003), Knowledge Management, BestWise Publishing Co., Taipei. Smilor, A., Raymond, W. and Gibson, D.V. (1991), “Accelerating technology transfer in R&D consortia”, Research Technology Management, Vol. 34 No. 1, pp. 44-9. Tseng, H.C. (1994), “Technology transfer, diffusion and communication: a conceptual clarification”, Sun Yat-Sen Management Review, Vol. 2 No. 4, pp. 111-33. Wu, J.H. and Chen, H.S. (2001), “A study on innovation diffusion and spatial interaction of firms in the industrial zones of Taiwan”, Sun Yat-Sen Management Review, Vol. 9 No. 2, pp. 179-200. Further reading Knudsen, D. (1983), “An analysis of temporary evolution in a spatial interaction system: a new look at: US commodity flow”, unpublished paper, Annual Meetings of the Association of American Geographers, Denver, CO. Pittfield, D.E. (1978), “Freight distribution model predictions compared: a test of hypotheses”, Environment and Planning, Vol. 10, pp. 813-36. Corresponding author Chiu-Chi Wei can be contacted at: [email protected]

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INVITED PAPER

Service-oriented architecture is a driver for daily decision support

622

Annika Granebring and Pe´ter Re´vay School of Business, Ma¨lardalen University, Va¨stera˚s, Sweden Abstract Purpose – This paper aims to explain why service-oriented business intelligence (SOBI) happened, the new development and how to make a strategy to introduce daily decision support in the retail trade. Design/methodology/approach – The diffusion of business intelligence (BI) tools is operationalized on Rogers’ innovation theory. Findings – The article answered the question: How to draft a BI strategy for all parts of the retail enterprise? By excellent data warehouse quality; choosing an area for common decision support; starting simply, with metrics (sale, gross margin, number of customers) to get users started and then continue the iterative process of practicing more comparing and personalized BI. Practical implications – Retailers meet a changeable world around where business decisions must be taken daily. In the retail industry, the customer’s current demands control the supply of commodities, inventories and crew. Retailers have enterprise applications designed for their business processes, but also daily want to measure the performance. It is a question of from existing enterprise applications and databases design new decision processes and business flows that currently request BI data to be presented directly to operative responsible staff. Originality/value – Explains why there are attempts to combine the two broad architectural paradigms BI and service orientation. Service-oriented architecture, BI, on line analytical processing, extract, transform and load, SOBI are discussed in detail. Keywords Business improvement, Cybernetics, Management theory Paper type Case study

Kybernetes Vol. 36 No. 5/6, 2007 pp. 622-635 q Emerald Group Publishing Limited 0368-492X DOI 10.1108/03684920710749712

1. Introduction Why should retailers invest in analyzing tools for business intelligence (BI)? Gather materials for reporting from various systems and let the report generator operate on different data sources, is difficult and expensive. Separate excel sheets with their own formulas are the “walk-around” solution bringing person dependencies and expensive maintenance over time. Inadequate or biased aggregated information silos turns decision-making for pricing goods, launching a new product or service, etc. into gambling. The principles and practice of service-oriented architecture (SOA) is to break through the barriers of business integration and help enterprises get their information resources in better order. SOA facilitates the design, the implementation, and re-use of multi-dimensional on line analytical processing (OLAP) databases, but above all SOA increases the availability by presentating services to new categories of BI users. According to the BI managers interviewed in this case study most retailers conduct some sort of customer survey to find out, how customers say they act. In the consumer market surveys can be problematic because customers are unable to articulate their future needs (Tidd et al., 2005, p. 279). BI gives customer relationship management (CRM) information on how customers really act and forecasts how they will act in

the future. The BI manager from the case company experiences how customers demand for BI assistance increases. The BI market is among the fastest growing worldwide. This is confirmed by IDC, Gartner Group, the Standish Group and other analysis institute’s reports of market intelligence for the information and technology markets (IDC: “Worldwide Business Intelligence Tools 2005 Vendor Shares,” July 2006, Appendix 2). Some reasons for this are that the BI tools have improved, the costs for disc storage decreased, and in addition new large user categories are joining. BI systems ease the understanding of enterprises and markets by mirroring the reality with tools for operative and directive purposes. The common failure of enterprise applications to support business agility (Strohmaier and Rollett, 2005; Verstraete, 2004), the dead-end integration situation experienced by the case company, and the fact that major software vendors like IBM, SAP, Oracle, and Microsoft are fundamentally re-developing their monolithic products into autonomous services accessible over the internet, all this indicates that enterprises will – to various extents – take advantage of SOA to fulfill customers’ changing demands of goods and services. It is not enough to cover the capabilities of business processes like enterprise resource planning (ERP) systems do. ERP systems are not fit to give basic data for decision-making. Business needs to evaluate each activity in terms of how important it is to the organization’s results, how well it needs to perform versus how well it actually does perform, and if differentiating or outsourcing help. The focus in this paper is on SOA being a decision support driver due to the increasing importance of the data warehouse (DW). First, we define BI, then SOA and finally the reasons why SOA is an OLAP driver are presented. 2. Method and theoretical background This case is a study of the diffusion of the innovative BI support in the retail industry. The case company AB Retail Business System is a retail software provider that offers consulting in customized BI and DW. The empiric in our recent research and for this paper (especially Chapter 5) comes from the documentation that was made available for the researchers by the case company, interviews with one of the BI managers at the case company, and participating observations in customer projects of the retail system vendor. The case company is introducing their new service oriented store solution: RetailCenter (RC) (Figure 1). The new RC concept is run on a communication platform which opens for integration with any point of sale system, local or central back office systems, central RP systems BI products and BI services with regard to finance management and analysis, etc. This paper is based upon a case study. The use of case studies is preferable in situations where processes and changes are in focus. It is common to gather information in different ways when using case studies (Patel and Davidsson, 2003). Yin (2003) recommends three principles to be followed to maximize the benefit of data collection. The first principle is that multiple sources of evidence should be used. This case study uses participant-observation, semi-structured interviews conducted with BI managers, study of documentation created during customer projects (business documents, project plans, evaluation reports, audits, specifications, mail correspondence) ranging from 2004 to 2007. The second principle is to create a case study database. We have done this by collecting information in binders. The third principle is to maintain a chain of evidence to ensure quality control. Here the information is sorted in chronological order. The study contains elements of action research where the role of the researcher lies between the role of researcher and

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EIS Business Performance Dashboard Executive Support Systems INTERFACE

Business Process Dashboard Workflow Automation INTERFACE

B2B, Supply Chain Management INTERFACE

RC BI MS Reporting Service

Financial Performance

624

Collaborative Dashboard

QIS

RC Data Warehouse RC CRM

Figure 1. The RC solution with the DW supporting BI to be the potential nerve center of managing the enterprise. DW with OLAP cubes, SQL, views, queries from BI tools vendors like Cognos, SAS, and Business Objects

Central Back Office (CBO) INTERFACE

RC Market INTERFACE

ERP/ Logistics

RC Gift Certificates INTERFACE

RC StorePOS / Point-of-Sale INTERFACE

Customer Card loyalty systems

Raw data feed stransaction systems

Source: Case Company (2006)

consultant (Avison et al., 2001; Gummesson, 1998). By performing a case study, a theory can be both developed and tested. The selection of units that are to be investigated can be made in different ways and both qualitative and quantitative information can be used. Deductive researchers hope to find data to match a theory, and inductive researchers hope to find a theory that explains their data (Merriam, 1998). The issue of objectivity is important like the choice regarding selection of information (Holme and Solvang, 1997). In management control systems theory, the concept of diffusion is relevant, e.g. Ax and Bjornenak (2000), Xu and Quaddus (2005), and Rogers (2003). For this paper, primary and secondary data are operationalised on Rogers’ (2003, p. 207) innovation theory with five adoption characteristics applied on the long-term process of establishing BI. Innovation is here defined as the difference between having a DW and BI compared to not using BI in the retail industry. The Relative advantage is expressed as economic profitability in establishing BI to increase business value at a reasonable cost. The Compatibility issues, i.e. consistent with existing values (customers integrity, culture), past experience (of retail industry) and needs (knowing the customer’s businesses). Strategies to manage BI Complexity according tools and methods. Trialability is defined as all potential users possibility to try the retailers’ BI efforts. Observability of if BI results are generally accessible. 3. Knowledge management and business intelligence Herbert A. Simon (1916-2001) in 1978 won the Nobel Prize in Economics for his research on decision making in organizations. Simon was Professor at Carnegie Mellon,

Pittsburg University, USA, and one of the founders of Artificial Intelligence (AI). Simon (1965, 1969) identifies threes stages in a sequential decision-making process: (1) intelligence finding occasions for making a decision; (2) design finding, inventing, developing, and analyzing alternative courses of action; and (3) choice – selecting a course of action. The most known contribution of Professor Simon (1965) is probably the data chess. In 1956, Simon and Newell produced the AI program – The Logic Theorist – proving many of the theorems of symbolic logic in Whitehead and Russell’s Principia Mathematica (Russell and Norvig, 1995; Whitehead and Russell, 1910). Can the IS theory approach BI help management in making better business decisions? Models/theories are useful and can automate knowledge to be operationalized down in the hierarchy/organization. The term BI is less fantasy oriented but with substance when it comes to decision making. Automated decision-making systems are becoming increasingly more common. Researchers are discussing and studying whether expert systems achieve better results than human experts (Davenport and Harris, 2005). Corporate performance management aims to provide different scorecards (dashboards, scorecard, balanced scorecard). Automated decision making and guarding the enterprise with vigilant systems, e.g. “health check” of the factory performance or of the entire enterprise, come of use with not only support of decisions but also decision making with automated alerts to initiate actions. At Western Digital a dozen dashboards with their own OLAP cube that includes metrics and ratios, help staff accelerate their Observe-Orient-Decide-Act loops of the processes monitored (Houghton et al., 2004). Sveiby (2001) argues that there are two separate tracks in KM; the IT-track where knowledge is viewed as objects and the people-track where knowledge is equivalent to processes. Dividing activities according to “urgent” and “important” in a four field figure presuppose that focusing on the urgent but sacrificing the important have unwanted consequences (Covey and Merrill, 1994). Quadrant I which is urgent-important is generally rewarded by organizations. Quadrant II is not urgent-important and needs reflection and dealing with, to avoid future crisis; e.g. planning and managing relations. Not important-urgent (Q III) and not important-not urgent (Q IV) are what we should avoid doing. The metrics and ratios should bring business value to the retailers and benefit the individual customer. Storing more and more information is not the key, but discovering patterns and making templates. Discover what is important by shrinking and reduction helps to create clarity in our information overloaded world. Data warehousing support BI by gathering, consolidating, and storing data. The components of successful DW can be summarized as data collection, cleansing, consolidation, and data storage. BI is the delivery of information to support the decision-making needs of the business. It can be described as the process of enhancing data into information and then into knowledge (Gordon et al., 2005). BI is granular information about the business and its supply chain that line-of-business managers seek when they are analyzing key performance metrics of their enterprise (Houghton et al., 2004). Having valuable data in a DW has no value at all if it is not accessible. Powerful report- and analysis software (like Claudia Win 2005, SAP NetWeaver BI (Appendix 1), MS BI) are flexible and versatile reporting and

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data analysis tools that combine powerful OLAP functionality (data cubes for BI presentation) with ease of use and user-friendliness. 4. Service Oriented Architecture SOA is a way of thinking and making it possible to use existing IT/IS investment for new demands. Business people are realizing that SOA provide potential for their companies. SOA views everything as a service provider, from applications, to databases, companies, and devices. Microsoft, Apple, Google, SAP, and IBM all have the strategy to both open and offer their applications as services delivered by the internet and paid for by advertisement and subscriptions. The change to loosely coupled, standards-based integration opens up the opportunity for using many pre-built services and being able to integrate with professional business applications on the market (e.g. ERP systems, CRM systems, accounts systems, billing systems, web systems). SOA’s possibility to bridge between modern service-oriented solutions (see case company’s RC communication platform) and integrate existing component-oriented ERP system like SAP or Axapta, and in-house main frame systems. The idea of SOA is to create a palette of these different business services from different enterprise applications that can then be orchestrated back together again into a logical order and managed using. This degree of independent components (services) protects the flexibility. To meet the needs of the agile enterprise, the practice of SOA has following core principles: . The business drives the services, and the services drive the technology. In essence, services act as layer of abstraction between the business and the technology. . Business agility is a fundamental business requirement. The requirements from business must reach the next level of abstraction “meta-requirement.” (Granebring and Re´vay, 2007). 5. BI at case company Retailers have indicated that knowledge of the individual customer is needed in key business segments of retail (Granebring et al., 2006). Case company realizes the need to support personalized customer offers and support following-up on promotional activities to build competitive advantages for retailers. Two people work with BI at case company. Case company’s store systems are today in use in more than 2,500 stores. About 17 of the 20 biggest grocery stores in Sweden use the whole or parts of case company’s store solutions. Most of those customers analyze and make decisions with the help of case company’s customized RC BI products for analysis and finance management. 5.1 RC business intelligence analysis RBI and RetailCenter Business Intelligence (RC BI) are the case company’s solutions for BI management and DW. DW is central storage of data from numerous sources. Relevant information areas within retailing are customers, suppliers, articles, and stores. Data warehousing demands powerful servers and large storage capacity. BI analysis – put together and organizing data to metric data and ratios serving as basic data used to identify bottlenecks in the enterprise and provide the business with data to support strategic business initiatives. BI analysis demands advanced reports, high

level of visualization, and powerful analysis tools. Case company’s platform is Microsoft SQL Server e.g.: . MS SQL Server 2005 ¼ RDMS, Report Builder, Business Scorecard Manager. . Microsoft Data Transformation Services (DTS) ¼ Microsoft’s ETL tool. . Analysis Services ¼ OLAP database. . MS Reporting Services. Several retailers have installed case company’s analysis support RC BI. RC BI is case company’s solution for presenting statistics, business information and renders possible analysis of primary the store operation. The solution is based on that the collection of sales data from case company’s back office products StoreOffice (local) or RC CBO (central) is daily transformed to a central database (data layer). From the stores there are information collected each day concerning article statistics, category statistics, frequency, recycling statistics, cash discount, receipts, assortment data, and sales representatives. The presentation is preference in ProClarity or Excel but also other presentation tools are used. Information can be collected from other systems like central ERP, customer card loyalty systems, etc. as well as from local store systems (Figure 1). Multi dimensional OLAP-cubes are used to optimize basic data for reports and analysis’s. RC BI is used among others to analyze sales-, frequencies-, discount-, and wastage data. RC BI gives each store access to a clear picture of the own customers and their buying patterns. The information can be used for actions to increase the turnover, analysis of different marketing efforts, and also increased precision concerning optimal purchase volumes. As these type of business information and analysis demand changeability and development to conform to the enterprise and its changes this RC BI solution underlie in close and continuing cooperation with the customer to develop and change data content as well as information in the shape of reports, ratios, and investigations. (Interviews with BI Manager at case company). In the central back-office there are a server, databases, monitors for supervision and control, DTS package for “cleaning” of source date, OLAP-cubes for multi-dimensional compilation of data, report generators and analysis applications. The case company’s way of working with business information is characterized by: . pre-study to identify the customers requirements and needs; . the assignments are performed as consultancy project; . customer unique database design of data layer; . customer unique ETL-process; . customer unique OLAP-cubes; and . customer unique reports and analysis are developed in cooperation with the customer. 5.2 Analysis – an innovation theory perspective on the BI building process According to Rogers (2003) the perceived attributes of innovations consist of five different characteristics that have systematic effect of diffusion and assimilation: Relative advantages, compatibility, complexity, trialability, and observability. 5.2.1 Relative advantage. A more effective handling of customers, suppliers, articles, and stores combined with increased quality regarding the information due to formal

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logging of errors, which opens up for statistics over incoming complaints which makes them more noticeable. Professional handling increases efficiency, availability, flexibility, and quality. It was impossible to get this BI information earlier – it took hours to put together. Decision supports for market departments by campaign following-ups, like double points, buy three for two. Evaluate ad items and campaigns items. Bench marketing between similar stores located in similar residential areas (LPA ¼ lokal prisanpassning), etc. regarding pricing, exposure of commodities. ICA[1] do not bench mark (individual retailers own the shops) but Coop do. Support in the negotiations for a contract (prices, new articles) with suppliers by presenting business information like margins, prices, demands. BI get away from the criticized “smearing same offers like cheep ketchup to all.” More precise marketing with improved customer clustering. For grocery commodities personalization is not a practical viability yet. The case company’s customer mobile phone network provider TRE, being sale oriented, uses RC BI to manage commission to sellers. 5.2.2 Compatibility. RC Central back office (CBO) makes BI easier compared to local back office (StoreOffice) since data is already centrally collected. Industry experience and BI knowledge are required to interpret and understand BI. Drowning in BI information is a disease that has struck also retailers. Most users are at head office in marketing and purchasing areas. The collaboration with BI manager support from case company is the basis of authority when starting with BI at customer site. 5.2.3 Complexibility. Common solutions on the market offer different kinds of OLAP cubes, a tool for following-up, analysis and decision support. An OLAP-user is obliged to be familiar with common data and underlying structures, making BI difficult to decentralize. The BI working method to accomplish “one-version-of-the-truth” from various data sources increases complexity. Data is redundantly stored in many systems under separate concepts. The BI managers have awareness of that some data is biased, needing correction to produce a correct data base for decision support. What is important for the customer is always the starting point. Customer unique designs complicate re-use of ratios, affordance in interfaces, etc. 5.2.4 Triability. Increased availability and flexibility for all users and not the traditional target group CEO and controllers is one of the introductory goals of the new common BI. BI do not act real time and is therefore not operational critical. BI for all presupposes resources for a large operative mass of end-users with BI tools, methods and skills. Users at customer sites expect support from skilled BI managers. BI management consultants at case company have technical skills, social skills, and retail business process experienced. The user-friendly BI tools in Office 2007 open for BI for an increasing amount of end-users. Excel 2007 and excel services in the browser makes it possible to build advanced analysis solutions and publish in SharePoint 2007 and visualize in dashboards. One of Bill Gates early mottos for the goals of Microsoft is “IAYF” (Information At Your Fingertips) and their new enabling BI tools are a way to achieve that. 5.2.5 Observability. Web interfaces simplify distribution and accessibility of BI. Stores get better margins and profits with BI support. Customers and the public are now familiar with the fact that different actors collect data about them.

6. Service-oriented business intelligence The concept of synergy in this case means the combined action of discrete entities or conditions such that the total effect is greater than the sum of their individual effects (Gordon et al., 2005). As shown in Table I SOBI Synergy is the idea of SOA þ BI ¼ business improvement. In any complex environment, there are a number of data sources which contain information which must be consumed by the solution. Some data sources are likely to be held in semi-structured or unstructured formats, such as spreadsheets (mostly excel), Google, home pages, and document management systems. With these kinds of systems it is important to structure the information prior to integration into the DW. This will be achieved in one of the following ways: . Apply structure to the data store. Available structured and change controlled templates for spreadsheets and documents, such that the information can be accurately and reliably extracted from the document. This will involve business process change. . Impose structure on the data read from the store. This is inherently difficult as it relies on making assumptions about the semantics of the existing structure of the data source and relying on this never changing. If this assumption holds, programmatic extraction can be achieved (Gordon et al., 2005). The number and variety of data sources interested for BI purpose increases with the adoption of SOA and SOA associated enabling technologies. SOA apply application-to-application integration with low volume and high frequency. SOA encapsulation, high abstract formality, and re-use of components are helpful also in the business decision support and data transformation world of BI. BI solutions are tightly coupled to the data sources that feed the DW. SOA exhibit loose coupling between their services. Real enough time vs online. SO: s event driven integration might even improve traditional ETL (Extract, Transform and Load) mechanism. All data do not have to be physically moved to the BI platform. Operational data can be accessed from the SOBI framework platform. There are advantages like: . brings interface abstract patterns to BI; . aggregation as a service (i.e. known queries re-useable at month level); and . calculations (i.e. business logic for sales and forecast, etc. available for the whole organization). There are business and organizational issues that need to be solved like: . governance: . enterprise data and SOA strategy; and . operational versus management reporting 7. Conclusions and future work SOBI is the mixing of approaches from SOA and BI. A SOBI architectural framework attempts to solve problems of integration in an enterprise of disparate “stove piped” systems. It attempts to provide a common data transformation mechanism for operational

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Separation of interface and implementation by 1) Boundaries are explicit 2) Services are autonomous 3) Services share schema and contract – not classes 4) Policy-based service compatibility with consumers Entity services owns record data. A cornerstone of SOA internal vs external Event-driven loose coupling between services Application-to-application integration subscribe to a service Support operational reporting

Tenets of architecture

Availability reporting/ information

Delivers data event-driven þ better foundation for the future þ easy to update/change þ standard þ platform independent still traditional ETL techniques for large-scale data transfer Publications collective information to be shared

Handling analytical capabilities Batch-driven ETL during business downtime Current data quality improvement Specific set of data-manipulation tools, e.g. expensive client licences DW is not the data owner. DW owns BI and reference data One version of the truth Tightly coupled to the data sources that feed the DW. Data-to-data-integration with large data volumes, e.g. traditional ETL mechanism OLAP databases with MIS data. An OLAP-user is obliged to be familiar with common data and underlying structures, making BI difficult to decentralize. Gather materials for reporting from various systems and let the report generator operate on different data sources is difficult and expensive

(continued)

SOBI provide presentation services for operational and MIS data

þ data-to data ETL and SOA loose coupling

SOBI

BI

630

Strategic information analysis and data ownership Integration

SOA

Table I. SOA and BI are separate but they also overlap and can support each other

Dimension

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Sources: Gordon et al. (2005), interviews with BI Manager at Case Company (2006) and Granebring et al. (2006)

Questions

Tools

Data sources

Users

Metrics (sale, gross margin, number of Mapping, e.g. transformation logic customers) are of interest for several where ever possible customers (in same trade). Ratios (sales/customer, changes compared to previous period, efficiency measurements, etc.) must be defined customer unique Operational staff Executives Wider audience Right solution for each user Opens for unstructured data; excel, In orderly manner. Accessed by SOA Difficult to manage various data associated techniques. Non-record data sources It is not unusual with hundreds Google, home pages; presupposes Content Management (CM-software) of systems having for instance their is solved with the concept of publications and subscriptions in SOA own customer data OLAP applications – powerful but not Cheaper and more user-friendly clients (like MS excel 2007) user-friendly MIS questions EIS-dashboards Operative question: What packagings Has the article been sold the last three Identify profitable customers and products. Buying patterns for are available for article X? months and what is the forecast for improved forecasts next month? Re-use of generic capabilities. Re-use of object oriented components. Re-use of services trough information analysis, e.g. Identify System of Record Re-use of business rules

SOBI

Re-use

BI

SOA

Dimension

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and management information both. It sets out guidance in the form of principles and patterns. Publications are the SOA term for data warehousing data. Information areas like orders, catalogs, web sites, and price lists have different demands for versioning schemas, internal vs external use, reference data vs operative data, etc. At what periodicity is updating required? At the event when change or new data is available or batch wise each night, for instance. There is a price to pay for online data and often older data can be accepted. By deciding the level of current interest a strategy can be made. The responsibility for the publications should be on the enterprise architect/enterprise information area manager. Orderliness is important and less volatile data is more suitable to manage as publications. Consumer and provider have specific roles. Providers must know their consumers and be sure to send publications to them. In point-to-point links the layers are one-way directed. With SOBI there is no rank between the organizational levels – they are all equal. More and more end-users will demand access to relevant BI information and flexible BI tools in the future. Business systems and non-enterprise data sources will be refined with orderliness among all information sources to meet constantly growing needs to support all kinds of offered services, including SOBI services. Access to relevant and dispose of irrelevant BI information are key issues. And above all – after knowing comes deciding and acting – otherwise the knowledge industry is of no value. There are new driving forces making companies having to make business decisions each day. Every BI system has a specific business goal. By improved reporting and data analysis processes retailers can gain new insights about customers, suppliers and the market, e.g. explain and discover long-term methods for strategic purposes like fusions or which products are to be provided in ten years. SOBI can accomplish daily decision support. The case company gives some clues for right solution for each receiver. Introducing continuous decision support in a big chain of stores is a process. Experience of the retail industry is a condition for success. How to draft a BI strategy for all parts of the enterprise? . excellent DW quality; . choose an area for daily decision support; and . start simple with metrics (sale, gross margin, number of customers) to get users started and then continue the iterative process of practicing more comparing and personalized BI. Note 1. ICA, Coop and Axfood are the three dominating Swedish grocery wholesaling and retailing organizations: These three accounted for approximately 72 percent of Swedish grocery sales in 2004. References Avison, D., Baskerville, R. and Myers, M. (2001), “Controlling action research projects”, Information Technology & People, Vol. 14 No. 1, pp. 28-45. Ax, C. and Bjornenak, T. (2000), “The bundling and diffusion of management accounting innovations – the case of the balances scorecard in Scandinavia”, paper presented at the 23rd Annual Congress of the European Accounting Association (EAA), Munich, Germany. Case Company (2006), Homepage of AB Retail Business System – available at: www.rbs.se (accessed December 17, 2006, 13:04).

Covey, S. and Merrill, R. (1994), First Things First, Simon & Schuster, New York, NY. Davenport, T.H. and Harris, J.G. (2005), “Automated decision making comes of age”, Research Report, Accenture Institute for High Performance Business, January. Gordon, S., Grigg, R., Horne, M. and Thurman, S. (2005), “Service-oriented business intelligence”, The Architecture Journal, Vol. 6, available at: www.architecturejournal.net (accessed December 7, 2006). Granebring, A. and Re´vay, P. (2007), “Maturity stages in SOA”, paper presented at the microCAD-2007 International Scientific Conference, University of Miskolc, Hungary. Granebring, A., Thile´nius, P. and Re´vay, P. (2006), “SOA is a driver for personalization”, paper presented at the ECITE-2006 conference 28-29 September 2006, Genua, Italy. Gummesson, E. (1998), Qualitative Methods in Management Research, Sage, Thousand Oaks, CA. Holme, I.M. and Solvang, B.K. (1997), Forskningsmetodik – om kvalitativa och kvantitativa metoder, Studentlitteratur, Lund. Houghton, R., El Sawy, O., Gray, P., Donegan, C. and Joshi, A. (2004), “Vigilant information systems for managing enterprises in dynamic supply chains: real-time dashboards at western digital”, MIS Quarterly Executive, Vol. 3 No. 1. Merriam, S.B. (1998), Fallstudien som forskningsmetod, Studentlitteratur, Lund. Patel, R. and Davidsson, B. (2003), Forskningsmetodikens grunder – Att planera, genomfo¨ra och rapportera en underso¨kning, Studentlitteratur, Lund. Rogers, E.M. (2003), Diffusion of Innovations, 5th ed., The Free Press, New York, NY. Russell, S. and Norvig, P. (1995), Artificial Intelligence – A Modern Approach, Prentice-Hall, Englewood Cliffs, NJ. Simon, H. (1965), The Shape of Automation for Men and Management, Harper & Row, New York, NY. Simon, H. (1969), The Sciences of the Artificial, MIT Press, Cambridge, MA. Strohmaier, M. and Rollett, H. (2005), “Future research challenges in business agility – time, control and information systems”, E-Commerce Technology Workshops, IEEE Computer Society, pp. 109-15. Sveiby, K-E. (2001), “What is knowledge management? A KM library containing articles that describes the history of KM and also shows status quo in the research of KM”, available at: www.sveiby.com/TheLibrary/KnowledgeManagement/tabid/78/Default.aspx Tidd, J., Bessant, J. and Pavitt, K. (2005), Managing Innovation: Integrating Technological, Market and Organizational Change, 3rd ed., Wiley, Chichester. Verstraete, C. (2004), “Planning for the unexpected (business agility)”, IEEE Manufacturing Engineer, Vol. 83 No. 3, pp. 18-21. Whitehead, A.N. and Russell, B. (1910), Principia Mathematica, Cambridge University Press, Cambridge. Xu, J. and Quaddus, M. (2005), “Adoption and diffusion of knowledge management systems: field studies of factors and variables”, Knowledge-Based Systems, Vol. 18 Nos 2/3, pp. 107-15. Yin, R.K. (2003), Case study research: Design and Methods, 3rd ed., Sage, Thousand Oaks, CA.

Further reading Alvesson, M. and Deetz, S. (2000), Kritisk samha¨llsvetenskaplig metod, Studentlitteratur, Lund. Litterer, J.A. (1973), The Analysis of an Organisation, Wiley, New York, NY.

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Prahalad, C.K. and Hamel, G. (1990), “The core competence of the corporation”, Harvard Business Review, Vol. 68, pp. 79-91. Walls, J., Widemeyer, G. and El Sawy, O. (2004), “Addressing information system design theory in perspective: how useful was our 1992 initial rendition?”, Journal of Information Technology Theory and Application (JITTA), Vol. 6 No. 2. Electronic sources IDC, a global provider of market intelligence – available at http://idc.com (accessed December 17, 2006, 13:07). Interviews Interviews with Mats Ba¨cklund, BI Manager at RBS AB, July 7, 2006, October 10, 2006.

Appendix 1. Description of the SAP NetWeaver BI Source: SAP Netweaver BI, available at: www.sap.com/platform/netweaver/components/bi/ index.epx (accessed December 19, 2006). SAP NetWeaver BI offers tools and processes of bringing and refining business information for: . Data warehousing. DW management, business modeling, and extraction, transformation, and loading (ETL) enable you to build DWs, model information architecture according to business structure, and manage data from multiple sources. . Business intelligence. OLAP, data mining, and alerts provide a foundation for accessing and presenting data, searching for patterns, and identifying exceptions. . Business insights. Query design, reporting and analysis, and web application design allow you to create analysis reports, support decisions at every level, and present BI applications on the web. . Measurement and management. Business-content management, metadata management, and collaborative BI monitor progress, provide reporting templates, ensure consistent data, and help decision-makers work together. . Open hub services. Open hub services features enable the delivery of high-quality, audited enterprise information through web services to applications. Bulk data exchange, change data capture, and modeling features streamline deployment and enable cost-effective operations. . Information broadcasting. Information broadcasting features support the distribution of mass information to large audiences in a personalized and secure manner, e.g. as an offline document, live report through personalized e-mail, according to a schedule or based on key events. . High performance analytics. Based on compressions, parallel in-memory processing, and search technologies, the SAP NetWeaver BI accelerator functionality improves the performance of queries, reduces administration tasks, and shortens batch processes. Developed jointly with Intel Corporation, the accelerator runs on state-of-the-art chips, such as the Intel Xeon 64-bit chip, and can be deployed on affordable blade server technology.

Appendix 2. Magic Quadrant for BI Platforms, 1Q06 The analyst firm Gartner expects the BI market to experience sustained growth as the technology includes more users within an organization. Business Objects, Cognos, Information Builders, and SAS Institute are setting the standards in BI, according to Gartner’s “Magic Quadrant for Business Intelligence Platforms, 1Q06.” The companies are listed as leaders, with

all four offering a range of capabilities across reporting, analysis, performance management, and data integration, according to the report. Microsoft, Oracle, and SAP are listed as close challengers, while Hyperion, MicroStrategy, QlikTech, and Siebel Systems are listed as visionaries, or those companies with potential to become leaders (Figure A1). challengers

leaders

SAP

635

Information Builders

Microsoft ability to execute

Service-oriented architecture

Cognos Business Objects SAS Institute Hyperion Solutions MicroStrategy

Oracle

Actuate

Siebel Systems QlikTech Applix ProClarity Panorama Software arcplan

niche players

visionaries

Completeness of vision As of December 2005 Source: Gartner

Corresponding author Pe´ter Re´vay can be contacted at: [email protected]

To purchase reprints of this article please e-mail: [email protected] Or visit our web site for further details: www.emeraldinsight.com/reprints

Figure A1. Magic Quadrant for BI Platforms, 1Q06

The current issue and full text archive of this journal is available at www.emeraldinsight.com/0368-492X.htm

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INVITED PAPER

A viable systems perspective to knowledge management

636

Chyan Yang National Chiao-Tung University, Taipei, Taiwan, Republic of China, and

Hsueh-Chuan Yen National Chiao-Tung University, Taipei, Taiwan, Republic of China and Chienkuo Technology University, Changhua City, Taiwan, Republic of China Abstract Purpose – To provide the knowledge structure for an effective knowledge-based organization which integrates knowledge into organizational goals. Design/methodology/approach – The structure, function, and process of a viable organization were discussed which provided a basis to construct a knowledge management (KM) framework and demonstrate knowledge structure in a knowledge-based organization. Based on systems view and viable systems model (VSM), a range of recently published KM practices were reviewed to position various knowledge content. Findings – This study proposed a viable systems framework for organizational KM based on the VSM of Beer. Using the viable systems framework, organizational knowledge can be classified into four categories. Knowledge content was articulated based on the systems view. Thus, knowledge structure of various management hierarchies can be captured. Originality/value – The result contributes to the practice of knowledge executive by supporting the diagnosis and design of an effective knowledge-based organization. The framework also provides a basis for future empirical studies on the relationships between KM strategies and organizational effectiveness. A specific KM strategy exists that can maximize the effectiveness of each of the four types of knowledge. Keywords Knowledge management, Organizations, Systems analysis Paper type Research paper

Kybernetes Vol. 36 No. 5/6, 2007 pp. 636-651 q Emerald Group Publishing Limited 0368-492X DOI 10.1108/03684920710749721

Introduction The strategic use of knowledge management (KM) for retaining competitive advantage is well recognized (Senge, 1990; Nonaka and Takeuchi, 1995; Bollouju et al., 2002; Hlupic et al., 2002; Nemati et al., 2002). It is generally believed that most of intellectual assets of a firm exist as knowledge in the minds of its employees (Horvath, 1999; Stenmark, 2001). Various practices, tools, and methodologies have been developed for promoting knowledge creation and sharing (Martensson, 2000; Binney, 2001; Gray, 2001; Achterbergh and Vriens, 2002; Hlupic et al., 2002; Desouza, 2003). The wide application of information technology (IT) is the most important force to improve the transition of society (Drucker, 1968). According to IT progress in organization, management information systems (MIS) focused on efficient transaction processing and providing decision-relevant information (Davis and Olson, 1985). MIS provides the infrastructure necessary for organizational daily operations. To raise the IT applications at the organizational level, the concept of decision support systems

(DSS) emerged. DSS attempts to support semi-structured or non-structured decision tasks. Two main types of DSS have been developed: data oriented or model oriented (Alter, 1977). Early MIS and DSS successfully integrated organizational tasks and helped firm to achieve competitive advantage. While MIS and DSS capture the majority of explicit organizational knowledge (Beveren, 2002), the tacit nature of skilled experience, insight, and vision, which are the building blocks of KM, is critical to gain competitive advantage when organization confronting the more turbulent environment (Nonaka and Takeuchi, 1995). Knowledge has multiple properties (Horvath, 1999). Knowledge is a resource that can help in problem-solving. Knowledge can also be an output that is embedded in products or services. There one success companies that integrate KM, information system, and core capabilities to facilitate competitive advantage (Parise and Henderson, 2001; MacSweeney, 2003). Nonaka provided the theoretical base about KM. There are two-dimensions of knowledge creation, four modes of knowledge conversion, and five-phase model of the organizational knowledge-creation process (Nonaka and Takeuchi, 1995). Based on the effort of Nonaka, numerous authors have investigated the relationship between KM dimensions and organizational effectiveness. Choi indicated that different KM styles are related to different performance. Moreover, performance can be improved by focusing on both tacit-oriented and explicit-oriented KM styles (Choi and Lee, 2003). Becerra-Fernandez and Sabherwal (2001) proposed that the context influences the suitability of a KM process. More specifically, the task characteristic is the moderating effects of the effectiveness of one specific KM process (Becerra-Fernandez and Sabherwal, 2001). Gray developed a categorization system for KM practices. The role of KM practices varies according to the problem-solving process and the type of problem being addressed (Gray, 2001). Apparently, due to the intricate characteristics of knowledge, only depend on IT cannot share knowledge effectively (Mcdermott, 1999; Lang, 2001a, b). KM processes, tools, and methodologies are not universally appropriate relating to various organizational contexts. There is no guarantee that KM project will be equally effective. Organizational supporting capabilities and a stimulus context are required (Gold et al., 2001). KM should align with organizational goals for developing an advantage over competitors. Organizational goals were accomplished through tasks design (Drucker, 1955). Organizational design is a complex process in integrating knowledge capabilities. To clarify the required knowledge capabilities, focus on individual function or department is inadequate. We need a macro framework to investigate the role and mission among various organizational components as a whole. While the traditional orthodox organizational structure is inadequate for knowledge-based organization (Nonaka and Takeuchi, 1995), a new organic organization structure that encourages effective and efficient communication is required to foster knowledge creation and sharing. Systems thinking provides a new sight to design a new organic organization. In the systems approach that satisfies the tenets of systems thinking, cybernetics is related to organizational effectiveness. Wiener defined cybernetics as the science of control and communication involving animals and the machines (Weiner, 1948). The universal principles of cybernetics apply not only to engineering systems but also to living systems, which Beer called the science of effective organization. Beer integrated cybernetics in relation to the principles governing the human nervous system, with a particular emphasis on its application to organizational management (Beer, 1979, 1981, 1985). Beer indicated organization behavior is conducted to survive,

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that is, competitive advantage (Porter, 1985). Human nervous system is a rich and flexible control system – a viable system. Viable means “Able to maintain a separate existence.” The central thesis of the viable systems model (VSM) is self-organization and self-regulation, actualized by autonomous management and consciousness adaptation ability. The regulatory mechanism of VSM provided a theoretical basis for designing the structure, process, and function of organizational tasks that integrate knowledge into organization value, thus improving organizational viability. This study proposed a viable systems framework for organizational KM. Using the viable systems framework, organizational knowledge can be classified into four categories: constructive, bureaucratic, entrepreneurial, and transactive. Knowledge content was articulated based on the systems view. Thus, knowledge structure of various management hierarchies can be captured. This framework provides a basis for future empirical studies on the relationships between KM strategies and organizational effectiveness. A specific KM strategy exists that can maximize the effectiveness of each of the four knowledge types. Conceptual foundations of knowledge management KM is about leveraging knowledge into organizational value. This study reviews this subject from two angles. First, this study discusses the concept of knowledge from the organizational perspective. Second, this study reviews the theory of organizational knowledge creation. The KM related thesis below is the conceptual foundations of the proposed framework that is discussed in the latter sections of this paper. Knowledge and organization Some studies have considered knowledge from an IT perspective. A hierarchical relationship exists among data, information, and knowledge (Van der Spek and Spijkervet, 1997; Arthur Andersen Business Consulting, 2000; Rouse, 2002). Data are still uninterpreted symbols. Data are records of events or structured transaction records. Moreover, information is data that has been assigned a meaning. Methods of contextualizing, categorizing, calculating, correcting, and condensing are used to invest data with meaning. Information is generally transferred via documents or other media that aims to influence the perception of receiver and to alter their decisions and behavior. Knowledge enables people to assign meaning to data and thus generate information. Knowledge is the whole set of insights, experiences, and procedures which are considered correct and true, and which consequently guide human thoughts, behavior, and communication. The existence of a hierarchy is assumed from data to information to knowledge. However, the hierarchical view of knowledge cannot effectively capture the essence of leveraging organizational knowledge. McDermott outlines six characteristics of knowledge that differentiate it from information (Mcdermott, 1999): (1) Knowledge always involves a person who knows; knowing is a human act. (2) Knowledge is the residue of thinking. (3) Knowledge is created in the present moment. (4) Knowledge belongs to communities. (5) Knowledge circulates through communities in many ways. (6) New knowledge is created at the boundaries of old.

Lang elaborated these six characteristics of knowledge and discussed each in detail (Lang, 2001a, b). Furthermore, Lang indicated that organizational knowledge has a social character. From the organization perspective, valuable knowledge is context-dependent. Human dimensions of organizing are central to effective knowledge work. Important functions of KM were to connect people and enable them to think together and share mental information, which they know will be useful to their community. However, knowledge representation has limits, IT inspired but only depend on IT cannot deliver knowledge effectively. Consequently, KM must breakthrough the barriers regarding creation, archiving and recovery of knowledge in relation to actual fuzzy contextualized activities.

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Theory of organizational knowledge creation From the organization perspective, knowledge as a resource aims to improve organizational effectiveness and efficiency. Simply stated, the objective of KM is to build, organize, and make good use of knowledge assets to make the enterprise act as intelligently as possible and thus secure its viability and overall success (Wiig, 1997). Authors have been advocated numerous prescriptive or descriptive frameworks to facilitate the sharing and integration of knowledge in organizational activities (Rubenstein-Montano et al., 2001; Satyadas et al., 2001). Since, organizational knowledge is derived from individual knowledge, knowledge creation process plays a key role in integrating all another KM practice. Nonaka develops a framework of knowledge creation that integrates both traditional and nontraditional views of knowledge (Nonaka and Takeuchi, 1995). The framework contains two dimensions, epistemological and ontological, as shown in Figure 1. The ontological dimension involves knowledge level. Knowledge is created by individuals, and then spreads to intra-organization, ultimately to inter-organization. As for the epistemological, Nonaka draw on Michael Polanyi’s distinction between tacit knowledge and explicit knowledge. Tacit knowledge is personal, context-specific, and consequently difficult Epistemological dimension Explicit knowledge

Tacit knowledge Ontological dimension Individual

Group

Organization Knowledge level

Inter-organization

Figure 1. Knowledge creation plane

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to formalize and communicate. Tacit knowledge contains cognitive and technical elements. The cognitive elements center on the “mental model” of individual, which consist the schemata, paradigms, perspectives, beliefs, and viewpoints. Meanwhile, the technical elements of tacit knowledge include concrete know-how, crafts, and skills. On the other hand, explicit knowledge refers to knowledge that can be transmitted using formal, systematic language. The tacit and explicit dimensions are not mutually exclusive. Instead, these two dimensions are simply different to various degrees and constitute knowledge spectrum. In fact, Figure 1 shows the knowledge creation plane that will be used in fourth section to position various knowledge contents in an organization. Both Nonaka and others emphasize the importance of tacit knowledge (Nonaka and Takeuchi, 1995; Beveren, 2002). Nonaka considers tacit knowledge to be more valuable than explicit knowledge. However, Alavi and Leidner indicated that these two types of knowledge are not dichotomous knowledge states; but rather are mutually dependent and reinforcing knowledge qualities. Focus excessively on one or the other may lead to the point being missed (Alavi and Leidner, 2001). Assuming that knowledge is created via the interaction between tacit and explicit knowledge, Nonaka devised four modes of knowledge conversion, as shown in Figure 2 (Nonaka and Takeuchi, 1995): (1) Socialization: from tacit to tacit. Socialization is a process of sharing experiences and thereby creating tacit knowledge, such as shared mental models and technical skills. (2) Externalization: from tacit to explicit. Externalization is a process of articulating tacit knowledge into explicit concepts. It is a quintessential knowledge-creation process in that tacit knowledge becomes explicit, taking the shapes of metaphors, analogies, concepts, hypotheses, or models. (3) Combination: from explicit to explicit. Combination is a process of systemizing concepts into a knowledge system. This mode of knowledge conversion involves combining different bodies of explicit knowledge. Tacit Knowledge To Explicit Knowledge

Tacit Knowledge

Socialization

Externalization

Internalization

Combination

From

Figure 2. Four modes of knowledge conversion

Explicit Knowledge

(4) Internalization: from explicit to tacit. Internalization is a process of embodying explicit knowledge into tacit knowledge. It is closely related to “learning by doing.” When experiences through socialization, externalization, and combination are internalized into individuals’ tacit knowledge bases in the form of shared mental models or technical know-how, they become valuable assets.

Knowledge management

641 The viable systems model To identify the relationship between organizational goals and KM that supports organizational viability, this study first elaborates the concept of the VSM. Beer indicated that the human nervous system is a rich and flexible control system. The control essence of the human nervous system was integrated into the VSM. If organization can be designed similarly to the human nervous system, the regulating relationship of the two isomorphic systems can be obtained. Thus, the concept of human nervous system is important when discussing the thesis of VSM. According to physiology, organs and function systems constitute the body organization (Best and Tayler, 1948; Martin, 1881). Human body exchanges energy between inside and outside environment continually. Each component uses various negative feedback systems to avoid huge status change and to maintain their homeostasis. The human nervous system composes two regulating mechanisms to maintain the internal stability and to direct consciousness movement of human body. First, the components of human body rely on mutual interaction to detect external change and self-regulated to maintain the internal stability. Secondly, human brain and sensory organs detect environment oscillation, handling crisis, direct the movement of body, and integrate local activity into an organic balance. Self-regulation and consciousness adaptation abilities are the essence of human nervous systems for designing an effective organization. Figure 3 shows the structure similarity between organizational architecture and nervous system. The functions and processes of each subsystem in a VSM-based organization and analogy to human nervous system are shown in Tables I and II. The term “viable organization” means that the organization has the characteristics or capabilities of a VSM. A viable organization that bases on nervous system’s regulating mechanism also comprises five subsystems. For simplification, this study labels the five subsystems as S1, S2, S3, S4, and S5, respectively. Similarly to nervous system, the regulating mechanisms of a viable organization also involves two dimensions: the subsystems S1-S3 perform autonomic management to achieve predefined objectives. The subsystems S3-S5 perform consciousness adaptation to environment. In terms of management, subsystems S3-S5 are the strategic function. S3 is the gateway between two regulation mechanisms. The difference of a viable organization from human nervous system is that the total system contains two subsystems, which are identical with it (Figure 3). The labeled subsystem one (S1) likes organ’s function. Usually S1 is a division or department and is producer of the organization. But S1 has the full function of a whole viable system. In management vocabulary, this means a division not only take orders from superior. A division has the autonomous and ability to determine which means to attain its goals. Thus, the VSM is a recursive model. To be a viable system, organization must comprise a collection of viable systems. Therefore, a viable

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VSM based organization structure Nervous control echelons Input

S5 Control Echelon V Cerebral Cortex

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Control Echelon IV S4

Diencephalon Basal Ganglia 3rd ventricle

Eyes Ears . . .

Control Echelon III Mesencephalon Pons Medulla Cerebellum

S3

S3* S2 S5

S1

S2 S3

S4

Control Echelon II Spinal cord

S2

S1 S2 S1

S2

Synapse S1

S5 Control Echelon I

S3

S4

S2

Figure 3. VSM-based organization structure and isomorphic relationships to human nervous system

Spinal vertebral level S2

Organ (heart, stomach, ..) Hands, Legs, Skin, ... Input: affective (sensory) Output: effective (motor)

S1 S2 S1 S2

organization has hierarchical relationship between subsystems. But hierarchical principle in VSM is different from traditional orthodox concept. Hierarchy is thesis of general systems theory (GST) when big systems are becoming organized (Von Bertalanffy, 1973). “Variety” is a key concept in the VSM. Organization is an extreme complex system. Effective organization concerned with management complexity. Variety is a cybernetic term that can be used to measure of the complexity deal with by management (Beer, 1959, 1966, 1975, 1976). Variety is the number of possible system states. The problems come from environment are called variety. Moreover, the alternatives that a viable organization possessed in dealing with outside environment are also called variety. The variety of alternatives must lager than the variety of problems to achieve effective management. The law of requisite variety describes that only variety can

Subsystem S5 S4

S3

S2

S1

Function Policy

Define the future development of organization Intelligence Define the status in competitive industry Alignment with environment development Environment scanning Control Govern the stability of the internal environment of the organization Responsible for the internal resource allocation Communication gateway between S4 and S1’s Coordinate Local regulatory between divisions Anti-oscillation between divisions Implementation Producer of the organization Self-regulation Pursue the predefined objectives to maintain internal environment’s steady state

Knowledge level Consciousness adaptation

Knowledge management

Inter-organization organization Inter-organization organization

643 Organization Autonomous management Group

Individual

absorb variety (Ashby, 1956; Beer, 1976, 1979). Subsequently, the viable organization design is based upon the concept of requisite variety to accomplish the homeostasis regulation. Clearly, environmental variety significantly exceeds the operation centers’. Operation center’s variety also significantly exceeds the management centre that regulates or controls it. High variety thus must be attenuated to the number of possible states that the receiving entity can handle. Additionally, low variety must be amplified to the number of possible states that the receiving entity requires to remain regulated. Hierarchical relationships among viable organization contributes to amplify alternative variety and to attenuate problem variety. Viable organization also called variety engineer. Integrating knowledge capability into task means organization possess more variety to handle management complexity (Leonard, 2000; Yolles, 2000; Achterbergh and Vriens, 2002). The form of variety is information. Therefore, in addition to structural consideration, the effectiveness of information flow must also be considered. In the two dimensions of KM framework, Nonaka indicated that knowledge is created only by individuals (Nonaka and Takeuchi, 1995). Organization provides a “knowledge network” to amplify the knowledge creation from individuals to group, organization, and ultimately, inter-organization. From the viable systems perspective, knowledge ontology can be mapped onto the VSM hierarchical structure. In a viable organization, S1 generally comprises divisions. But “division” is a concept. Division cannot perform organizational tasks. Employee is proxy of division to perform required activity which to pursue organizational viability. Consequently, the knowledge created and retained in S1 is individual knowledge. However, from the organizational perspective, the activities performed by individual employees are part

Table I. Functions of a viable organization

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Subsystem

Process/mechanism

Human nervous system

S5

Thinking centre of the organization Define and conscious direct the function of divisions into an organic whole Crisis handling Catch outside environment information and internal operational performance to determine the competitive status and behavior of the total organization Translate organizational goals into goals of each S1’s Define the framework of S1’s via three ways: legal and corporate requirements, resource bargain, and . . . Crisis information sent upward to S4 Define the framework of S1’s via accountability Routine auditing to S1 Handles interdivisional interaction Formal communication systems between divisions, such as information system Informal communication systems between divisions Building operation protocol between S1’s Error-controlled (negative) feedback systems Operation within the intention of the whole organization Operation within the coordinating framework of S2 Submit to the automatic control of S3

Brain (cerebral) cortex Brain store and recall memory, think and learning

S4

S3

S2

S1 Table II. Processes/mechanism of viable organization and analogy to human nervous system

Use eyes, ears, nose, tongue, and body to perceive outside environment Equilibriums the outside and inside environment’s needs Sympathetic nervous system regulates organ’s function when body suffers from pressure

Parasympathetic nervous system relaxes organ’s function Peripheral nervous system Nerve that bring message between each organs Hormone secreted Autonomic reflex arc

of the whole. Individual employees are fragment and sterile. Effective knowledge worker must consider who is going to use their output and what these others need to know about their works. Therefore, the knowledge of S2 about the interface between individuals that aims for anti-oscillation is group knowledge. While specialist knowledge is spread from individuals throughout organization, the scope of knowledge vision changed. The knowledge in “organization” level comprises the whole set of vision, experience, or insight that investigates the organization as a whole. The “organization” level knowledge includes: . governs internal stability of organization (S3 knowledge); . alignment with environment competitiveness (S4 knowledge); and . pursing future organizational development (S5 knowledge). Organization pursues increased competitive advantage through continuous interactions with its environment. The general environment organization face includes economic, political, social, and cultural factors. These environmental factors would influence organization’s competitiveness. Facing increasingly complex environment, organization

are pursuing a new business strategy of strategic alignment with industrial partner or competitors to pursue common goals, such as through developing industrial protocols to standardize product specifications (Porter, 1985; Lang, 2001a, b). These synergistic advantages cannot achieve by individual organization. Therefore, knowledge of S4 and S5 must include inter-organization knowledge.

Knowledge management

A viable systems framework to knowledge management This section develops a systematic framework that used to further analyze and discuss the potential role of KM for organization pursuing viability. From the VSM perspective, knowledge content can be classified into four categories: constructive, bureaucratic, entrepreneurial, and transactive (Figure 4). Table III summarized the systematic considerations regarding viable organization as a whole. The key knowledge players in performing the consciousness adaptation function by viable organization are top managers and middle managers. Drucker (1955) described the task of top managers as follows:

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The chief executive (that is the top manager) thinks through the business the company is in. He develops and sets over-all objectives. He makes the basic decisions needed to reach these objectives. He communicates the objectives and the decisions to his management people. He educates these managers in seeing the business as a whole and helps them to develop their own objectives from those of the business. He measures performance and results against the objectives. He reviews and revises objectives as conditions demand.

According to GST, top manager can: . . . direct the organizational growth by changing organizational goals, terminating certain activities, initiating new activities, engaging in research, continually searching its memory for vital information, modifying the value systems of its personnel, or changing the firm’s operating patterns (Schoderbek et al., 1975).

Essentially, top managers use positive feedbacks as regulation mechanism, a growth-prompting device, to enhance organizational competitiveness. Organizational Epistemological dimension Explicit knowledge

Tacit knowledge

Transactive

Bureaucratic

Entrepreneurial

Constructive

Ontological dimension (Viable Organization) S1

S2 Autonomous Management

S3

S4 Consciousness Adaptation

S5

Figure 4. A viable systems framework for KM

Table III. A viable systems consideration for KM

Tacit knowledge

Explicit knowledge

Front-line employees

Top managers Middle managers Front-line employees

S1 þ S2

S4 þ S5

S3

S1 þ S2

S3

Top managers Middle managers

S4 þ S5

Negative feedback

Negative feedback

Positive feedback

Negative feedback

Positive feedback Negative feedback

1. Experience-based bodily knowledge 2. Know-how 3. Congitive knowledge

1. Cognitive model

1. Professional, scientific, and head analysis 2. Quantifiable knowledge 3. Codiable knowledge 1. Grand concept 2. Knowledge vision

1. Grand concept 2. knowledge vision 1. Cognitive model

1. Key knowledge 2. Regulation 3. Input (knowledge players mechanism base)

1. Technological skill 2. Human skill 3. Analytical skill

1. Integration skill

1. Conceptual skill

1. Technological skill 2. Human skill 3. Analytical skill

1. Integration skill

1. Conceptual skill

1. Best practices

1. Product/service innovation 2. Mental data base 1. Management practice

1. Menu 2. Standard operating procedure

1. Writing data base 1. Decision rules

Intention Consciousness Interaction Coordination Communication Building operation protocol

1. 2. 3. 1.

Interaction Coordination Communication Autonomy

1. Intention 2. Consciousness

1. 2. 1. 2. 3. 1.

4. Process (skill for 5. Output (form of 6. Environment (factors affect KM knowledge knowledge effectiveness) created) creation)

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Functions of viable Knowledge characteristics organization

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intention and consciousness ability help top managers to create knowledge. Top managers based on grand concept and knowledge vision to create knowledge using conceptual skill. Meanwhile, middle managers physically implement strategic plans. Middle managers acquire and allocate resources, establishment and monitoring of budgets (Anthony, 1965). Negative feedbacks are used for control in that they are designed to minimize deviations between set standards and actual performance. As channels linking top managers and frontline employees, interaction, coordination, and communication affect the effectiveness of knowledge creation by middle managers. Middle managers based upon cognitive model to create knowledge using integration skill. Environment and task complexity influence the explicitness of knowledge in the knowledge spectrum. Knowledge is more tacit in nature when there is more environment and task complexity. Tacit knowledge that aims to organizational consciousness adaptation is “constructive” knowledge. Such knowledge comprises two parts. The first part created by top managers is the form of product/service innovation, as well as human experience recorded in the mental database (Forrester, 1980). Meanwhile, the second part is created by middle managers and comprises management practice. Explicit knowledge that aims to improve organizational consciousness adaptation is “bureaucratic” knowledge. This knowledge is “bureaucratic” in the sense that a definite procedure exists for handling repetitive and routine tasks. The explicit knowledge created by top managers is stored in writing database (Forrester, 1980). This data base records the history of decisions, and the rationale governing decisions. The explicit knowledge created by middle managers takes the form of decision rules. For autonomous management function of a viable organization, the key knowledge players are middle managers and frontline employees. The systematic consideration of KM relating middle managers was discussed above. For frontline employees, they worked under predefined objectives, effectively and efficiently used existing facilities and resources to carry out activities within budget constraints (Anthony, 1965). Negative feedbacks served as regulation mechanism, just as middle managers. Task content can be used to classify the frontline employees into two types: physical-flow incentive or information-flow incentive. The tacit knowledge that supports autonomous management is “entrepreneurial” knowledge. Relying on experience-based bodily knowledge and know-how, the physical-flow incentive employees use technological skill to create knowledge. Meanwhile, the information-flow incentive employees use human skill and analytical skill to create knowledge that based on cognitive knowledge. Autonomy is critical for facilitating the creation of “entrepreneurial” knowledge. Output knowledge takes the form of “best practices.” On the other hand, the explicit knowledge that supports autonomous management is “transactive” knowledge. Operation protocol is the critical success factor. Frontline employees Using professional, scientific, and head analysis, quantifiable and codiable knowledge to create “describable” knowledge. Output knowledge takes the form of menu or standard operation procedure. Discussion While IT facilitates the internationalization trend, organization faces more complex and dynamic environment. Knowledge must integrate into routine operation to

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improve competitiveness. From the proposed VSM-based KM framework, one can recognize that there exist different knowledge contents in an organization. Tacit and explicit knowledge spread out each functions and management hierarchies simultaneously. For an organization wish to leverage knowledge advantage, a total function of KM system may be inadequate. Various knowledge management systems (KMS) are needed, Such as operation-oriented KMS or strategic-oriented KMS. Knowledge creation and sharing must across function and management hierarchy to accommodate competitive strategy. Based upon environment’s opportunity and risk, top management evaluates organization’s strength and weakness to determine the competitive strategy. Knowledge vision of top management directs the integration of cross-functional knowledge to develop core competence. Therefore, knowledge spreading in the same organization function indicates sharing professional knowledge to enhance individual capability. Knowledge spreading across organization functions and management hierarchies indicate communicating professional knowledge to enhance organizational competitive advantage. Consequently, knowledge creation and knowledge sharing do not limit in the same function or management level. The viable systems framework for KM provides managerial connotation to Nonaka’s theory of knowledge creation. That is, knowledge creation and sharing that across function and management hierarchy are requisite. In the knowledge conversion process, individual recognizes his role and mission that takes organization as a whole. Internet technology promotes knowledge sharing and strengthens KM. Based upon IT, MIS and DSS successfully integrate computerization activities and support management decision. MIS, DSS and KMS are three IT-based systems that progressed for helping different management practices. These systems are interdependent activities. Data and information processing methodology can integrate into KMS to enhance KM performance. For example, using file management methodology to manage “best practice” document, each employee whenever can access these knowledge resource via internet or intranet. Thus, a synergy can be created via holistic use of these three systems. Conclusion To leverage knowledge resource, one must catch the whole picture about organizational knowledge to facilitate viability. Environment complexity affects knowledge explicitness. Some knowledge can easily be articulated and stored by electronic media, while some tacit knowledge cannot. However, tacit knowledge can be transferred and learned through efficient communication networks. This study proposed a viable systems framework for organizational KM based on the VSM of Beer. The proposed framework classifies organizational knowledge into four categories: constructive, bureaucratic, entrepreneurial, and transactive. Knowledge content was articulated by key knowledge players, regulation mechanism, input (knowledge base), process (skill for knowledge creation), output (form of knowledge created), and environment (factors affect KM effectiveness). In other words, a KM system can be viewed as a framework of knowledge taxonomy. This taxonomy can be used to systematically explore the key components and environmental factors for various KMS. By exploring the structure, functions, and processes of a viable organization, one can affirm that KM plays a key role in facilitating an organization to pursue its viability. Consequently, knowledge structure of various organizational

function domains can be captured. The framework also provides a basis for future empirical studies on the relationships between KM strategies and organizational effectiveness. A specific KM strategy exists that can maximize the effectiveness of each of the four knowledge types.

Knowledge management

References Achterbergh, J. and Vriens, D. (2002), “Managing viable knowledge”, Systems Research and Behavioral Science, Vol. 19 No. 3, pp. 223-41. Alavi, M. and Leidner, D.E. (2001), “Review: knowledge management and knowledge management systems: conceptual foundations and research issues”, MIS Quarterly, Vol. 25 No. 1, pp. 107-36. Alter, S. (1977), “A taxonomy of decision support systems”, Sloan Management Review, Vol. 19 No. 1, pp. 39-58. Anthony, R.N. (1965), Planning and Control Systems: A Framework for Analysis, Harvard University Press, Cambridge, MA. Arthur Andersen Business Consulting (2000), Zukai Knowledge Management, Toyo Kenizai Inc., Tokyo. Ashby, W.R. (1956), An Introduction to Cybernetics, Methuen, London. Becerra-Fernandez, I. and Sabherwal, R. (2001), “Organizational knowledge management: a contingency perspective”, Journal of Management Information Systems, Vol. 18 No. 1, pp. 23-55. Beer, S. (1959), Cybernetics and Management, English Universities Press, London. Beer, S. (1966), Decision and Control, Wiley, New York, NY. Beer, S. (1975), Platform for Change, Wiley, New York, NY. Beer, S. (1976), Design Freedom, Wiley, New York, NY. Beer, S. (1979), The Heart of Enterprise, Wiley, New York, NY. Beer, S. (1981), Brain of the Firm, Wiley, New York, NY. Beer, S. (1985), Diagnosing the System for Organization, Wiley, New York, NY. Best, C.H. and Tayler, N.B. (1948), Human Body and its Functions: An Elementary Textbook of Physiology, H. Holt, New York, NY. Beveren, J.V. (2002), “A model of knowledge acquisition that refocuses knowledge management”, Journal of Knowledge Management, Vol. 6 No. 1, pp. 18-22. Binney, D. (2001), “The knowledge management spectrum – understanding the KM landscape”, Journal of Knowledge Management, Vol. 5 No. 1, pp. 33-42. Bollouju, N., Khalifa, M. and Turban, E. (2002), “Integrating knowledge management into enterprise environments for the next generation decision support”, Decision Support Systems, Vol. 33, pp. 163-76. Choi, B. and Lee, H. (2003), “An empirical investigation of KM styles and their effect on corporate performance”, Information & Management, Vol. 40, pp. 403-17. Davis, G.B. and Olson, M.H. (1985), Management Information Systems: Conceptual Foundation, Structure, and Development, McGraw-Hill, New York, NY. Desouza, K.C. (2003), “Strategic contributions of game rooms to knowledge management: some preliminary insights”, Information & Management, Vol. 41, pp. 63-74. Drucker, P.F. (1955), The Practice of Management, Billing & Sons Ltd, Oxford.

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Drucker, P.F. (1968), The Age of Discontinuity: Guidelines to our Changing Society, Harper & Row, Publishers, New York, NY. Forrester, J.W. (1980), System Dynamics, North-Holland Publishing Company, New York, NY. Gold, A.H., Malhorta, A. and Segars, A.H. (2001), “Knowledge management: an organizational capabilities perspective”, Journal of Management Information Systems, Vol. 18 No. 1, pp. 185-214. Gray, P.H. (2001), “A problem-solving perspective on knowledge management practices”, Decision Support Systems, Vol. 31, pp. 87-102. Hlupic, V., Pouloudi, A. and Rzevski, G. (2002), “Towards an integrated approach to knowledge management: ‘hard’, ‘soft’ and ‘abstract’ issues”, Knowledge and Process Management, Vol. 9 No. 2, pp. 90-102. Horvath, J.A. (1999), “Working with tacit knowledge”, in Cortada, J.W. and Woods, J.A. (Eds), Knowledge Management Yearbook, Butterworth-Heinemann, Boston, MA, pp. 34-51. Lang, J.C. (2001a), “Managerial concerns in knowledge management”, Journal of Knowledge Management, Vol. 5 No. 1, pp. 43-57. Lang, J.C. (2001b), “Managing in knowledge-based competition”, Journal of Organizational Change Management, Vol. 14 No. 6, pp. 539-53. Leonard, A. (2000), “The viable system model and knowledge management”, Kybernetes, Vol. 29 Nos 5/6, pp. 710-5. Mcdermott, R. (1999), “Why information technology inspired but cannot deliver knowledge management”, California Management Review, Vol. 41 No. 4, pp. 103-17. MacSweeney, G. (2003), “Knowledge is power”, Insurance & Technology, Vol. 28 No. 9, pp. 41-2. Martensson, M. (2000), “A critical review of knowledge management as a management tool”, Journal of Knowledge Management, Vol. 4 No. 3, pp. 204-16. Martin, H. (1881), The Human Body: An Account of its Structure and Activities and the Conditions of its Healthy Working, H. Holt, New York, NY. Nemati, H.R., Steiger, D.M., Iyer, L.S. and Herschel, R.T. (2002), “Knowledge warehouse: an architectural integration of knowledge management, decisions support, artificial intelligence and data warehousing”, Decision Support Systems, Vol. 33, pp. 143-61. Nonaka, I. and Takeuchi, H. (1995), The Knowledge-Creating Company: How Japanese Companies Create the Dynamics of Innovation, Oxford University Press, New York, NY. Parise, S. and Henderson, J.C. (2001), “Knowledge resource exchange in strategic alliances”, IBM Systems Journal, Vol. 40 No. 4, pp. 908-24. Porter, M.E. (1985), Competitive Advantage: Creating and Sustaining Superior Performance, Collier Macmillan, London. Rouse, W.B. (2002), “Need to know-information, knowledge, and decision making”, IEEE Transactions on Systems, Man and Cybernetics-Part C: Applications and Reviews, Vol. 32 No. 4, pp. 282-92. Rubenstein-Montano, B., Liebowitz, J., Buchwalter, J., McCaw, D., Newman, B. and Rebeck, K. (2001), “A systems thinking framework for knowledge management”, Decision Support Systems, Vol. 31 No. 1, pp. 5-16. Satyadas, A., Harigopal, U. and Cassaigne, N.P. (2001), “Knowledge management tutorial: an editorial overview”, IEEE Transactions on Systems, Man and Cybernetics-Part C: Applications and Reviews, Vol. 31 No. 4, pp. 429-37. Schoderbek, C.G., Schoderbek, P.P. and Kefalas, A.G. (1975), Management Systems, Business Publications, Inc., New York, NY.

Senge, P. (1990), The Fifth Discipline, Doubleday, New York, NY. Stenmark, D. (2001), “Leveraging tacit organizational knowledge”, Journal of Management Information Systems, Vol. 17 No. 3, pp. 9-24. Van der Spek, R. and Spijkervet, A. (1997), “Knowledge management: dealing intelligently with knowledge”, in Liebowitz, J. and Wilcox, L.C. (Eds), Knowledge Management and its Integrative Elements, CRC Press, Boca Raton, FL. Von Bertalanffy, L. (1973), General System Theory, Penguin Books, New York, NY. Weiner, N. (1948), Cybernetics, or Control and Communication in the Animal and the Machine, Wiley, New York, NY. Wiig, K.M. (1997), “Roles of knowledge-based systems in support knowledge management”, in Liebowitz, J. and Wilcox, L.C. (Eds), Knowledge Management and its Integrative Elements, CRC Press, Boca Raton, FL, pp. 69-87. Yolles, M. (2000), “Organisations, complexity and viable knowledge management”, Kybernetes, Vol. 29 Nos 9/10, pp. 1202-22. Corresponding author Chyan Yang can be contacted at: [email protected]

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INVITED PAPER

A flexible platform for mixed-integer non-linear programming problems Ralf O¨stermark

˚ bo Akademi University, Department of Business Administration, A ˚Abo, Finland Abstract Purpose – To propose a new algorithmic platform (minlp_machine) for complex mixed-integer non-linear programming (MINLP) problems. Design/methodology/approach – The platform combines features from classical non-linear optimization methodology with novel innovations in computational techniques. The system constructs discrete search zones around non-integer discrete-valued variables of local solutions, which reduces the search process significantly. In complicated problems fast feasibility restoration is achieved through concentrated Hessians. The system is programmed in strict ANSI C and can be run either stand alone or as a support library for other programs. File I/O is designed to recognize possible usage in both single and parallel processor environments. Findings – The system has been tested on Alpha and Sun mainframes and – as a support library for a Genetic Hybrid Algorithm (GHA()) – in Linux and IBM parallel supercomputer environments. The constrained problem can, for example, be solved through a sequence of first order Taylor approximations of the non-linear constraints and occasional feasibility restoration through Hessian information of the Lagrangian of the MINLP problem, or by invoking a nonlinear solver like SQP directly in the branch and bound tree. The system has been successfully tested on a small sample of representative continuous-valued non-linear programming problems. Originality/value – It is demonstrated that – through zone-constrained search – minlp_machine() outperforms some recent competing approaches with respect to the number of nodes in the branch and bound tree. Keywords Programming, Information, Cybernetics, Management theory Paper type Technical paper

Kybernetes Vol. 36 No 5/6, 2007 pp. 652-670 q Emerald Group Publishing Limited 0368-492X DOI 10.1108/03684920710749730

1. Introduction Mixed-integer non-linear programming (MINLP) methods can be classified according to their use of specific NLP relaxations and mixed integer linear programming (MILP) specializations. Grossmann and Kravanja (1997) present a unified representation of MINLP methods, where it is shown that the currently known classical MINLP methods fall into one of three categories. Firstly, MINLP-problems can be solved through tree enumeration, where a relaxed NLP-problem is solved in each node of the branch and bound tree. Secondly, some algorithms produce a sequence of MILP problems ultimately converging to the optimal solution (Westerlund et al., 1998). Finally, a sequence of LP/NLP-based branch and bound search with relaxed non-linear programming NLP-problems can be used, where additional upper and lower bounds are added for the discrete variables yj during the branching process

(Quesada and Grossmann, 1992). Alternative approaches to discrete and continuous problem solving are provided by logic-based methods and artificial intelligence-based techniques applying sophisticated methods of logical inference (Grossmann and Biegler, 2004). The choice of any particular algorithm naturally is intimately connected to the characteristics of the MINLP problem at issue. In this study, we discuss a new powerful algorithmic platform – minlp_machine()-for MINLP problems, where different categories of algorithms can be entertained. The standard MINLP is usually formulated as follows: minimize f ðx; yÞ s:t: gi ðx ; yÞ # 0;


i ¼ 1; . . . ; m

x [ X; y [ Y ; nx

L

U



ð1:1Þ

X ¼ x [ R jx # x # x
 Y ¼ y [ Zny jy L # y # y U

f(x,y) and gi(x,y), i ¼ 1, . . . ,m are non-linear continuously differentiable functions defined on the set X < Y: X is real-valued and Y is discrete. Minlp_machine() is a platform where alternative approaches can be combined for integrated monitoring of geno-mathematical programming algorithms. The zone search idea discussed below is novel and has not been tested elsewhere. We present a unifying framework enabling the use of MILP-sequences or relaxed NLP-sequences in the branch and bound tree as specified by the user. The framework supports user-specific algorithms to be incorporated in the system if desired. Minlp_machine() can be executed standalone or as a support library for the Genetic Hybrid Algorithm (GHA(), O¨stermark, 2003). The main components of GHA are shown in Figure 1. Some encouraging evidence on the performance of GHA on larger problems as well as on non-convex problems is provided in O¨stermark (1999a, b, 2000) and O¨stermark et al. (2000). 2. The MINLP platform (minlp_machine) Minlp_machine() solves the MINLP-problem iteratively. If the problem has linear parts, they are entered separately. A system file is loaded with the parametric changes (number of new rows, new columns and new discrete variables) needed in order to augment the linear problem with non-linear elements. If desired, a Taylor approximation of the non-linear model may be defined in a separate user level function (add_minlp()) utilizing the information on the original problem size as well as the non-linear amendments. Since, add_minlp() is invoked at each major iteration of minlp_machine(), the user function itself can contain a tailor-made mathematical programming algorithm (cf. the process flow chart in Figure 2). The original non-linear model can be defined in separate user level functions for the objective and the constraint set. Either numerical (Dennis and Schnabel, 1983) or analytical gradient and sparse Hessian information can be utilized. Calculation of the Hessian is concentrated to those dimensions for which second order information exists. The MINLP-problem can be solved either using the linearized model in ordinary MILP-search – improved by occasional second order Lagrangian conjugate steps – or using sequential quadratic programming solvers in the branch and bound tree with the original non-linear specification. The branch and bound algorithm has been tested using the FSQP algorithm of Lawrence et al. (1997) and DNCONG() of IMSL (1987)

Flexible platform MINLP problems

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CATSM(1)-support libraries QuasiNewton

SPMX

MINOS

LAPACK & IMSL

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GQOPT

FSQP

VMX Numerical Recipes

MINLPMACHINE(2)

GHA

NEURAL

PROJECT KNN

RLS

ACCELERATOR

EVALUATOR

GRADIENT

HESSIAN

PREPROCESSOR

POSTPROCESSOR

MACHINEDEPENDENT LIBRARIES

Figure 1. The computational support engines of GHA

PROJECTDEPENDENT SUPPORT FUNCTIONS

Notes: All computational engines are linked to gha depending on the current computational task. The libraries are separately operational stand alone systems; (1) CATSM = Computer-aided time series modelling algorithms implemented by the author SPMX = Vector-valued State Space Modelling With Exogenous Variables, based on the algorithm of Masanao Aoki (1987) VMX = Vector-valued VARMAX-search algorithm based on Höglund & Östermark (1991) NEURAL = the backpropagation 1-3 layer algorithm refined from Östermark (1994) KNN = The K-nearest neigbours algorithm of J. Farmer and J. Sidorowich (1987) RLS = The Recursive Least Squares algorithm for vector processes by L. Ljung (1987); (2) MINLP_MACHINE is a flexible computational tool for MINLP-problems. The system uses the branch-and bound method in MILP-problems, where the local LPs are solved by the powerful dual simplex algorithm of Maros (2003). In MINLP-problems the nodes of the branch and bound tree can be solved by the FSQP-algorithm of Lawrence et al. (1997)

Flexible platform MINLP problems

milp_caller(): Load linear section (if present)

nonlinear constraints?

no

solve (MI)LP-problem using zone constrained (Gomory/other) cuts

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yes construct_system(): Add nonlinear constraints/ variables conformant with the solver being used.

convergence reached?

add_minlp(): use taylor approximating algorithms?

yes

augment linear problem by taylor approximations of the nonlinear constraints at (x*,y*)

no

yes

terminate and generate output

no solve (MI)NLP-problem using zone constrained (Gomory/other) cuts

as non-linear node level solvers. Other commercial or noncommercial solvers can be incorporated in the platform if needed. The MILP-solver of minlp_machine() works basically as a branch and bound depth first algorithm, using any available LP-solver. Currently, three LLP-solvers have been connected to the algorithm: the DDLPRS()-routine of IMSL (1987), the LP_SOLVE-package and – in order to implement zone-constrained cuts in the MILP-search – a sparse bound flipping dual (BFD) algorithm lpr() based on the ideas in Taha (1982), Bradley et al. (1977) and Maros (2003). Lpr() was programmed in strict ˚ bo Akademi ANSI C and compiled on the Sun and Alpha main frame computers at A University and the IBM SP supercomputer at the Centre of Scientific Computing in Helsinki. The distinguishing features of the BFD algorithm of Maros (2003) are: . in one iteration it can make progress equivalent to many traditional dual iterations; . using proper data structures it can be implemented efficiently so that an iteration requires hardly more work than the traditional pivot method; . its effectiveness increases with the number of bounded variables present – a typical situation occurring down in the branch and bound tree; . it has inherently better numerical stability because it can create a large flexibility in finding a pivot element; and . it can cope with degeneracy as it can bypass dual degenerate vertices more easily than the traditional pivot procedures. The BFD algorithm lpr() can be executed standalone or as a support library to minlp_machine() and/or GHA(). lpr(), minlp_machine() and supergha() are compiled as

Figure 2. Flowchart of minlp_machine

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separate libraries and can be used as a powerful joint resource kit for user defined problems on sequential and parallel computers. Minlp_machine() is a highly flexible platform for difficult programming problems. The most important new ideas are the discrete search zones and the zone constrained cuts (ZCC) included in the MILP-search. We illustrate ZCC by mixed Gomory cuts below. The discrete search zones can be imposed at a predetermined depth of the branch and bound tree. From that level on, a search zone is formed from the discrete elements of a non-terminal node i as follows: LBi ¼ floor(y *), UBi ¼ ceil(y *), where y * is the discrete subvector of the optimal solution at the current node. In lower levels of the tree, the search zone is further reduced until convergence. In practice, if the search zone is imposed prematurely, the true optimal solution may be cut off from the search tree. The empirical tests presented subsequently indicate, however, that in many problems the depth at which the search zone is imposed is non-critical. Furthermore, as shown below, prematurely imposed search zones frequently yield near-optimal approximations, which is sufficient in many real-world problems where processing time is a critical factor. The usage of minlp_machine() in linear/non-linear mathematical programming problems is illustrated below. 2.1 Solving MILP-problems with minlp_machine() The first example is a small MILP-problem of the form: min c0 w Aw # b; A [ Rm£n ; b [ Rm  0 w ¼ y0 ; x0 [ Rn ni

y [ Z ;x [ R

ð2:1Þ

nx

n ¼ ni þ nx The size of the problem is {m,n} ¼ {2,4}, with the first variable discrete and the others real-valued. The MILP-problem is entered in an ASCII-file having the following components (the most important parameters are explained below) (Table I). The input file contains a header and seven parameter rows before the actual data-section. On each row, the parameters are followed by definitions for ease of reference. In the current problem, we have no separate deviational variables (nd ¼ 0). The size of the tree is set to 50 nodes. TREE_LIMIT ¼ 21 means that the branch and bound tree is unlimited. The precision is set to EPS ¼ 1.0 £ 102 7. EPS_FACTOR is used to control the optimality of the current solution at the precision level EPS £ EPS_FACTOR. For example, if EPS_FACTOR . 1, then the branch and bound algorithm will terminate faster but usually with a suboptimal solution. The parameter L_FEASIBILITY can be used to screen acceptable solutions in cases where the problem contains deviational variables (nd . 0). From a practical point of view, the parameters for controlling the zone search are the most interesting. ROOT_SEARCH is a binary flag for imposing a discrete zone already at the root level, i.e, around the relaxed LP-solution. ZONE_SEARCH controls whether or not a discrete zone is to be imposed at a specified depth of the tree and if it should be imposed immediately at the specified depth (abs(ZONE_DEPTH) ¼ 2) or conditional on whether a feasible MILP-solution has already been found (abs(ZONE_DEPTH) ¼ 1). If ZONE_DEPTH . 0, then the zone will be imposed over

Taha (1982, p. 307) 24130 50 1.0 £ 102 7 1.0 0 0 0 0 0.0 10100 0002

m;n;ni;nx,nd TREE_LIMIT;EPS;EPS_FACTOR L_FEASIBILITY(0/1) ROOT_SEARCH(0/1);ZONE_SEARCH(-2/-1/0/1/2);ZONE_DEPTH;ALPHA SGC;CUT(0 ¼ FIRST;1 ¼ MAX;2 ¼ MIN),print_flip(-1/0/1/2); debug(0/1); scale(0/1) GET_RCOND;RCOND_LIMIT;RCOND_ITERS;LP(2 ¼ LPR;3 ¼ LPS;4 ¼ DDLP) IS_DATA(0/1)

1 b: 6.0 35.0 c: 7.0 9.0 0.0 0.0 LB: 0.0 0.0 0.0 0.0 UB: 15.0 15.0 15.0 15.0 IRTYPE(0 ¼ EQ_rh,1 ¼ LE_rh;2 ¼ GE_rh): 0 0 A: -1.0 3.0 1.0 0.0 7.0 1.0 0.0 1.0

all discrete-valued dimensions. If ZONE_DEPTH , 0, then the zone is imposed on nonzero discrete-valued dimensions only. In the current example these parameters are deactive, but they will be used heavily in the test cases below. ALPHA is a measure of imprecision that can be used for identifying near discrete-valued solutions. All discrete-valued variables satisfying the condition max(ceil( yj) 2 yj, yj –floor( yj)) # ALPHA will be considered acceptable ALPHA-level approximators of the true MILP-solution. SGC ¼ (2 1/0/1) indicates whether simultaneous Gomory cuts should be imposed at the current node. SGC , 0 signals that a single Gomory cut will be added to the LP-problem of the current node, selected from the first non-integer discrete variable encountered in the solution of the parent to this node. SGC . 0 signals that separate Gomory cuts will be imposed for each non-integer discrete variable encountered. CUT determines the type of rule used to select the cutting variable in the branch and bound algorithm. In the present example, we use the first fraction encountered among the discrete-valued variables. The RCOND-parameters can be used in non-linear problems to control and possibly improve the condition number of matrices before inversion by slight perturbation. Slight perturbation of, for example, the Hessian may render invertibility without too much distorting the solution process in numerically unstable systems. IS_DATA, finally, is used to signal whether system data is provided in the problem file. In non-linear optimization problems the complete system data may sometimes be provided more suitably in the user level function add_minlp(). The solution to the MILP-problem ( f * ¼ 58, y * ¼ 4, x * ¼ [3.33 0.00 3.67]) is obtained by minlp_machine() with a single node when SGC ¼ 1. With only one discrete variable, SGC ¼ þ 1 or 2 1 gives the same result. In comparison, if SGC is deactivated, the same solution requires three nodes. 2.2 Solving linearized MINLP-problems with minlp_machine() The second example is a small quadratic problem with discrete variables – two circles in a plane and two linear constraints:

Flexible platform MINLP problems

657

Table I. MILP-problem data input for minlp_machine()

K 36,5/6

658

min c0 w Aw # b; A [ Rm£n ; b [ Rm 0 w ¼ ½y0 ; x0
[ Rn y [ Z ni ; x [ Rnx n ¼ ni þ nx J X g k ðwÞ ¼ ðwj 2 w
j Þ2 2 r k # 0; k ¼ {1; 2; . . . ; K}

ð2:2Þ

j¼1

The size of the test problem is {m þ mg ; ni ; nx ; K} ¼ {4; 1; 1; 2} The data pertaining to the linear and non-linear sections of the problem is given in two separate files (minlp_test.in, minlp_test.sys) (Tables II and III). Minlp_machine() entertains three alternative schemes for introducing non-linear constraints to the system: simultaneous, sequential and maximal constraint violation. In the present case, the simultaneous scheme is selected. In the other schemes, a user function add_row() must be loaded with the exact increase in different variables each time a new constraint is selected. For example, the maximal constraint violation scheme can speedup computations significantly in systems with a large number of non-linear constraints. The non-linear constraints are loaded in a user

Table II. Linear section of MINLP-problem data input (minlp_test.in)

MINLP-test: linear components of MINLP-problem 22110 m;n;ni;nx,nd 10 1.0 £ 102 7 0.0 TREE_LIMIT;EPS;EPS_FACTOR 0 L_FEASIBILITY(0/1) 0 1 3 0.0 ROOT_SEARCH(0/1);ZONE_SEARCH(-2/-1/0/1/2); ZONE_DEPTH;ALPHA 11000 SGC;CUT(0 ¼ FIRST;1 ¼ MAX;2 ¼ MIN),print_flip(-1/0/1/2); debug(0/1); scale(0/1) 0002 GET_RCOND;RCOND_LIMIT;RCOND_ITERS;ALGORITHM: (2 ¼ LPR;3 ¼ LPS; 4 ¼ DDLPRS; 5 ¼ DNCONG; 6 ¼ FSQP) 1 IS_DATA(0/1) b: 35.0 36.0 c: 2.0 3.0 LB: 0.0 0.0 UB: 9.0 3.0 IRTYPE(0 ¼ EQ_rh,1 ¼ LE_rh;2 ¼ GE_rh): 1 1 A: 5.0 7.0 4.0 9.0

Table III. Non-linear section of MINLP-problem data input (minlp_test.sys)

MINLP-test: parametric changes in non-linear stage of MINLP-problem 020000 mf; mg; ni,g; nx,g; nd,g; g-inclusion(0 ¼ simultaneous; 1 ¼ sequential; 21 ¼ maximal g) 0511 nlp-it; minlp-it; g-feasibility(0/1); termination(2 1/1 ¼ g-feasib, 2 ¼ improvement) 01 restore_g; keep LCC 12 stable gradient (0/1); h_type(1 ¼ fixed; 2 ¼ variable) 0000 Linemethod (1-4); calculate Hessian(0/1); nlp-grad(0 ¼ num/1 ¼ anal);use Taylor(0/1)

function g_function(). If analytical derivatives are provided, they may be defined in the user level functions g_gradient() and g_hessian(). The MINLP-solution ( f * ¼ 14.1428571, y * ¼ 6, x * ¼ 0.714286) is obtained by minlp_machine() with three nodes with SGC ¼ 1. In comparison, if SGC is deactivated, the same solution is obtained with nine nodes. The linear constraints can be eliminated from the above MINLP-problem by setting m ¼ 0 in minlp_test.in. The parameters relating to n are still loaded. This leads to the following quadratic MINLP: min c0 w s:t: gk ðwÞ ¼

J X

ðwj 2 w
j Þ2 2 r k # 0;

k ¼ {1; 2; . . . ; K}

j¼1 0

w ¼ ½y0 ; x0
[ Rn

ð2:3Þ

y [ Z ni ; x [ Rnx n ¼ ni þ nx In this case, the size of the test problem is {mg ; ni ; nx ; K} ¼ {2; 1; 1; 2} The MINLP-solution ( f * ¼ 22.1961524, y * ¼ 7, x * ¼ 2.732051) is obtained with ten nodes when SGC ¼ 1. If SGC is deactivated, the solution ( f * ¼ 22.1964286, y * ¼ 7, x * ¼ 2.732143) is obtained with ten nodes both using lpr() and ddlprs() as node solvers. This solution is superoptimal, since it deviates from the feasible space by 0.0003189. The problem turns, finally, into an NLP by defining ni ¼ 0, nx ¼ 2 in the file minlp_test.in. The optimal solution ( f * ¼ 22.4529404, x * ¼ [6.75, 2.984313]) is obtained in 6 iterations involving the same amount of first order Taylor linearizations. 2.3 Solving MINLP-problems with minlp_machine() Systems (2.2) and (2.3) may be solved directly as MINP-problems by invoking an SQP-solver in the nodes of the branch and bound tree. We have connected the FSQP-algorithm of Lawrence et al. (1997) as a support library to minlp_machine(). Systems (2.2) and (2.3) are readily solved. The only change needed is to select the node solver FSQP in minlp_test.in. If the MINLP-problem has one or more non-linear objectives, then the parameter mf in minlp_test.sys is set and a user function f_function() and – if analytical derivatives are provided – the user functions f_gradient() and f_hessian() are loaded correspondingly. Systems (2.2) and (2.3) are solved to their optima with minlp_machine() using FSQP as the node solver with three nodes in both cases. The pure NLP-problem {ni,nx} ¼ {0,2} is solved by one call to FSQP. 3. Empirical tests 3.1 Comparison between competing algorithms We chose ten problems from the literature. Seven of them – cases {1,2,6-10} – were used in testing the SQP-algorithm of Still and Westerlund (2006). Four test cases are solved below as linearized MINLP-problems, both with and without zone constrained Gomory cuts. The remaining six cases are solved directly as MINLP-problems using the FSQP-solver in the branch and bound algorithm of minlp_machine(). The problem characteristics are

Flexible platform MINLP problems

659

K 36,5/6

660

summarized in Table IV. The best results are summarized in Table V. Corresponding results obtained with some competing algorithms are presented in Table VI. Of the problems, only OPTPRLOC (optimal product location, Duran and Grossmann, 1986; Gavish et al., 1983) contains a large number of non-linear constraints. Being quadratic, however, the problem is suitable for first order Case

m

Node solver: LP 1. Optprloc 30 2. Trimloss2 24 3. Sharexs 27 4. Sharexm 126 5. Sharexb 462 Node solver: FSQP 6. Alan 7 7. Batch 73 8. GBD 4 9. Synthesis1 6 10. Synthesis3 24 Table IV. Characteristics of the test problems

n

mi

me

30 37 48 336 1,232

5 16 9 12 33

6 18 114 429

8 46 4 6 17

5 60 4 4 16

ni

nx

Objective

25 2

25 31 24 216 720

5 6 24 120 512

Non-linear Linear Linear Linear Linear

4 24 3 3 31

4 22 1 3 6

Non-linear Non-linear Non-linear Non-linear Non-linear

2 12

1

6

2 2

Notes: (m, n) ¼ number of (rows, columns) in the problem. (ni, nx) ¼ number of (discrete, continuous) valued variables, (mi, me, mn) ¼ number of linear inequalities, linear equalities and non-linear inequalities

Case

f*

1. Optprloc (linearized) 8.064142 Optprloc (MINLP) 8.064142 2. Trimlosse2 5.3 3. Sharexfs 1.99228 4. Sharexm 2.50239 5. Sharexb 1.3690 6. Alan 2.925 7. Batchg 285506.5 8. GBD 2.2 9. Synthesis1 6.009759 10. Synthesis3 68.00974

Table V. Summary of test results obtained with minlp_machine()

mn

No. of nodes Node solvera Zone searchb Zone depthc SGCd 23 80 72 37 56 85 27 25 2 4 12

LP SQP LP LP LP LP SQP SQP SQP SQP SQP

2 2 2 2 2 2 2 2

3 3 14 5 5 5 5 10

1

3

21 21 1

Notes: aThe given solver is invoked once for each node of the branch and bound tree. When the LP-solver is used, the non-linear constraints are approximated by first-order Taylor-expansion and occasional conjugate gradient projections onto the feasible space; bzone search is an urgency indicator: if ZS ¼ 1 then the discrete zone will be imposed at the specified zone depth but not before a feasible MINLP-solution has been obtained. ZS ¼ 2 indicates that the search zone will always be imposed, beginning at the specified depth; czone depth is the level down a path from the root of the branch and bound tree at which the discrete search zone is activated. The zone is imposed at the current node and all its off springs; dSGC indicates whether the simultaneous (possibly zone constrained) Gomory cut will be added for one (SGC ¼ 21) or all (SGC ¼ 1) discrete-valued variables that are non-integer in the current node; eThe trimloss problem was solved as a pure MILP problem; fSharex is a multiperiod portfolio management problem stated as a MILP (O¨stermark, 1992); gThe same objective value is reported by Leyffer (www-unix.mcs.anl.gov/,leyffer/MacMINLP/)

8.064142 5.3 1.99228 2.50290 1.37010 2.925 285506 2.2 6.009759 68.00974

f*

106 32 1357

Cplex No. of nds

7 17 3 5 15

79 107

15 56 1 16 34

139 169

15 15 3 5 15

77 93

7 144 1 24 68

251 246

SCP-BB No. of nds/LPs

5 162 3 26 147

1072 302

5 24 3 10 27

38 10

a-ECP No. of nds/MILPs

5 85 3 9 91

309 312

5 12 3 5 16

7 9

a-ECP (g . s) No. of nds/MILPs

632 1420

20 151 6 15 70

103 479

13 35 3 5 25

MINLP-BB No. of nds/QPs

Note: aThe trimloss problem was solved as a non-linear problem by Still and Westerlund (2006), whereas we solved it as a pure MILP-problem using minlp_machine()

1. Optprloc 2. Trimlossa2 3. Sharexs 4. Sharexm 5. Sharexb 6. Alan 7. Batch 8. GBD 9. Synthesis1 10. Synthesis3

Algorithm: case

SCP No. of nds/LPs

Flexible platform MINLP problems

661

Table VI. Summary of test results obtained with some competing algorithms

K 36,5/6

662

Taylor approximation. Second order improvement is achieved via the Lagrangian conjugacy condition (Grossmann and Kravanja, 1997) using concentrated Hessian information, enforcing feasibility in the original non-linear solution space. The linearized problem is solved iteratively by minlp_machine() using 29-84 nodes (Table VII). The number of nodes needed depends on the specified zone depth and whether or not Gomory cuts are being used. For example, the solution was obtained with 44 nodes using four concentrated Hessians for the Lagrangian conjugacy condition, absorbing 0.83 CPU-seconds on a Sun Ultra 2 main frame computer and 0.196 seconds on an Alpha XT 1000 main frame computer. When solving the problem in its non-linear form with FSQP as node solver, the solution was obtained with 80 nodes (Table V). The results compare favorably with the competing algorithms. Table VI reports the corresponding results for some competing algorithms (Table VII). Compared to the competing algorithms, minlp_machine() produces the optimal result with a smaller number of nodes in cases 1-3, 8-10. In cases 1-3, the difference is significant. In the portfolio problems 3-5, the optimal or a near-optimal solution is produced with a considerably smaller number of nodes than required by Cplex. In problems 6-7, minlp_machine() needs more nodes than the other algorithms. These problems frequently produce ill-conditioned nodes for FSQP. (In fact, about 50 per cent of the nodes cannot be solved by FSQP due to numerical instability). A more robust node solver would probably prove valuable in these cases, as suggested by the creators of FSQP (Lawrence et al., 1997). Figures 3(a) – (c) show the tradeoff between the objective value and number of nodes needed in the three portfolio problems (Table VIII for some numerical tests). Case: optprloc (Leyffer, 2003) Problem size: {m,n,n_i,n_x} ¼ {32 30 25 5}

Table VII. Total number of LP-solutions (tree size) and optimal solution in the MINLP-machine of GHA in the optprloc-problem

Milp_machine: Pure depth first Pure depth first þ SGC(20.1) Zone1 Zone1 þ SGC(2 0.1) Zone2 Zone2 þ SGC(2 0.1) Zone2 þ SGC(2 0.05) Zone2 þ SGC(0.1) Zone2 þ SGC(0.01) Zone3 Zone3 þ SGC(2 0.1) Zone3 þ SGC(0.1) Zone3 þ SGC(0.01)

Nodes Hessians

F

Dev

{R_SRCH,Z_SRCH,Z_DEPTH} ¼ {0,0,0}

70

4

2 8.0641415 0.000000

{R_SRCH,Z_SRCH,Z_DEPTH} ¼ {0,0,0} {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {1,2,3}a {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {1,2,3}a {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {0,2,3} {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {0,2,3}a {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {0,2,3}a {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {0,2,3}a {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {0,2,3}a {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {0,2,5} {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {0,2,5} {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {0,2,5} {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {0,2,5}

67 120 106 70 58 57 19 18 70 58 19 18

4 4 4 4 4 4 4 4 4 4 4 4

2 8.0641415 2 8.0641415 2 8.0641415 2 8.0641415 2 8.0641415 2 8.0641415 2 8.0641415 2 8.0641415 2 8.0641415 2 8.0641415 2 8.0641415 2 8.0641415

0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

Notes: aThe parameters {R_SRCH,Z_SRCH,Z_DEPTH} refer, respectively, to the 0/1 switches ROOT_SEARCH & ZONE_SEARCH and the depth of the tree (ZONE_DEPTH) at which a discrete search zone is imposed by the milp solver. For example, {R_SRCH,Z_SRCH,Z_DEPTH} ¼ [1,1,5} imposes a discrete zone around the relaxed LP-solution at the root of the tree, followed by a discrete zone at depth 5 of the tree. If the parameters are zero, a pure depth first search is carried out

4000 3500 3000 2500 2000 1500 1000 500 0

Flexible platform MINLP problems

–1.94000 –1.95000 –1.96000 –1.97000 –1.98000

tree size optimal F

663

Depth first D.first + SGC(0.1) D. first + SGC(0.05) D.first + SGC(–0.05) Zone1+SGC(0.05) Zone1+SGC(0.1) Zone2+SGC(0.1) Zone3+SGC(0.1) Zone3+SGC(0.1) Zone6+SGC(0.1) Zone6+SGC(-0.1) Zone3+SGC(-0.1) Zone4+SGC(0.1) Zone5+SGC(0.1) Zone2 Zone3 Zone4' Zone6 Zone5

–1.99000 –2.00000

(a)

60

–2.43000 –2.44000

50

–2.45000 40

tree size optimal F

–2.46000

30

–2.47000 –2.48000

20

–2.49000 10

–2.50000 Zone5

Zone4

Zone3

Zone2

–2.51000 Zone1

0

(b) 90 80 70 60 50 40 30 20 10 0

–1.34000 –1.34500 –1.35000 –1.35500 –1.36000 –1.36500

tree size optimal F

–1.37000 –1.37500 Zone1

Zone2

Zone3 (c)

The tradeoff curves were produced by systematic increases of the zone depth under conditional (ZC ¼ 1) and unconditional (ZC ¼ 2) zone search, respectively. We find that considerable computational savings can be achieved with a suitable zone depth at the cost of only a minor deterioration. A zone depth between 3-5 reduces the number of nodes needed in the different portfolio problems {small, medium, big}, respectively, by

Figure 3. (a) Tradeoff between number of LP-solutions and optimal solution in the small problem; (b) Tradeoff between number of LP-solutions and optimal solution in the medium problem; (c) Tradeoff between number of LP-solutions and optimal solution in the big problem

Cplex Minlp_machine: Zone2 Depth first D.first þ SGC(0.1) D. first þ SGC(0. 05) D.f\rsl þ SGC(2 0.05) Zone1 þ SGC(0.05) Zone1 þ SGC(0. 1) Zone2 þ SGC(0.1) Zone3 þ SGC(0.1) Zone3 þ SGC(0.1) Zone6 þ SGC(0.1) Zone6þ SGC(2 0.1) Zone3 þ SGC(2 0.1) Zone4 þ SGC(0.1) Zone 5 þ SGC(0.1) Zone 2 Zone3 Zone4 Zone 6 Zone 5 Medium –

20 5 3 37 32 18 17 7

} ¼ {1,2,5} } ¼ {0,2,3} } ¼ {0,2,2} } ¼ {0,2,7} } ¼ {1,2,5} } ¼ {1,2,3} } ¼ {0,2,5} } ¼ {0,2,2} 2 2.50568

2 1.98737 2 1.98506 2 1.98506 2 1.96036 2 1.96036 2 1.96036 2 1.96036 2 1.96036

2 1.99228 2 1.99228 2 1.99228 2 1.99228 2 1.99228 2 1.98895 2 1.98895 2 1.98737

1,821 2 1.99228

3,872 2 1.99228 3,869 2 1.99228 2,217 2 1.99228

1,561 64 58 49 30 17 17 13

{R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {m,n,n_i,n_x,n_d} ¼ {126 336 216 120 0} Relaxed LP 2 solution

Optimal F

– 2 1.99376 106 2 1.99228

{R_SRCH,Z_SRCH,Z_DEPTH} ¼ {1,2,7} {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {1,2,7} {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {0,2,7}a {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {1,2,5} {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {0,2,5} {R_SRCH,Z_SRCH,Z_DEPTH} ¼ {0,2,5} {R_SRCH,Z_SRCH,Z_DEPTH } ¼ {0,2,5}

{R_SRCH,Z_SRCH,Z_DEPTH } ¼ {1,0,0} Pure depth first using maximum fraction

{m,n,n_i,n_x,n_d} ¼ {27 48 24 24 0} Relaxed LP-solution Cplex-solution

Table VIII. Total number of LP-solutions (tree size) and optimal solution in the MINLP-machine of GHA vs Cplex in three SHAREX-portfolio problems

Small

Tree size

36

4

Assets (N)

2

2

3

2

126

27

336

48

120

24

(continued)

126

24

Horizon m ¼ (N þ G þ 3) n ¼ (3 *N þ 4) Integers Floats *(H þ 1) *(H þ 1) nx (H) G n1

664

Case

K 36,5/6

Depth first Cplex Minlp_machine: Zone1 Zone2 Zone3

Zone3 Zone4 Zone5 Big

Zone2

Depth first Cplex Minlp_machine: Zone1

Case

2 2.50239 2 2.45722 2 2.45722 2 2.45722

85 2 1.36920 25 2 1.36851 7 2 1.35306

54 18 12 7

{R_SRCH,Z_SRCH,Z_DEPTH } ¼ {1,2,5} {R_SRCH,Z_SRCH,Z_DEPTH } ¼ {1,2,4} {R_SRCH,Z_SRCH,Z_DEPTH } ¼ {0,2,0}

(lp_so

(lp_so (lp_so

48 2 2.50239

– 2 1.37743 64,978 2 1.37012 1,357 2 1.37010

(lp_so

1,133 2 2.50322 32 2 2.50290

Optimal F

{R_SRCH,Z_SRCH,Z_DEPTH } ¼ {1,2,5}8 {R_SRCH,Z_SRCH,Z_DEPTH } ¼ {1,1,5}a {R_SRCH,Z_SRCH,Z_DEPTH } ¼ {1,2,3} {R_SRCH,Z_SRCH,Z_DEPTH } ¼ {1,2,2} {R_SRCH,Z_SRCH,Z_DEPTH } ¼ {0,2,2} {m,n,n_i,n_x,n_d} ¼ {451 1232 720 512 0} Relaxed LP-solution Pure depth first using maximum fraction Cplex-solution

Pure depth first using maximum fraction Cplex 2 solution

Tree size

36

Assets (N)

10

3

462

1,232

720

512

Horizon m ¼ (N þ G þ 3) n ¼ (3 *N þ 4) Integers Floats *(H þ 1) *(H þ 1) nx (H) G n1

Flexible platform MINLP problems

665

Table VIII.

K 36,5/6

666

{31, 65, 94 per cent}. At the same time, the objective value deteriorates by no more than {1.6, 0.02, 0.066 per cent}, respectively. 3.2 Simulation results for the trim loss problem In the previous section, the trim loss problem was tested with only one of an infinite number of possible instances (Table IX). Parametric changes – concerning, for example, the zone depth or simultaneous Gomory cuts – affect the size of the branch and bound tree noticeably (Tables X– XII). Therefore, a more detailed analysis of the sensitivity of the trim loss problem to different parametric changes is motivated. In this study, we focus on the effect of changing the numerical characteristics of the trim loss problem in small Monte Carlo tests (500 iterations) on the size of the branch and bound tree and the optimal objective value. The tests are carried out separately for some suitable settings of zone depth and Gomory cuts. Other conceivable sensitivity studies are left for future research. Table X presents the simulation settings for the sensitivity analysis. In the first test case, the trim loss problem is fixed as in Still and Westerlund (2006) (Table X), whereas the linearization parameters {K1, K2, L1, L2} (defined in Still and Westerlund, 2006) are varied within small intervals. In the second test case, both the trim loss problem and the linearization settings are varied through the parameters Bmax and Delta (Table X). The key results are summarized in Tables XI-XII. In both cases, a significant variability of the tree size is noticed. The results reveal the need for extensive simulation studies of different mathematical programming problems, in order to capture the range of variability of competing algorithms in practice.

Milp machine

Table IX. Total number of LP-solutions (tree size) and optimal solution in the MINLP-machine of GHA in the trimloss(2)-problem

Depth first Depth first þ SGC(2 0.1) Zone4 Zone4 Zone1 þ SGC(20.05) Zone1 þ SGC(0.1) Zone1 Zone 2 Zone2 þ SGC(20.1) Zone2 þ SGC(20.1) Zone 2 Zone3 Zone3 þ SGC(20.1)

{m,n,n_i,n_x,n_d} ¼ {27 48 24 24 0} Cplex-solution solver Pure depth first using maximum fraction {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH {R_SRCH,Z_SRCH,Z_DEPTH

} ¼ {0,1,20} } ¼ {0,2,20} } ¼ {0,1,19}a } ¼ {0,1,19}a } ¼ {0,1,19}a } ¼ {0,1,15} } ¼ {0,1,15} } ¼ {1,1,15} } ¼ {1,1,15} } ¼ {0,1,17} } ¼ {0,1,17}

Ipr Tree size 89 79 89 89 67 175 87 79 57 68 92 85 63

f* 2 5.30 2 5.30 2 5.30 2 5.30 2 5.30 2 5.30 2 5.30 2 5.30 2 5.30 2 5.30 2 5.30 2 5.30 2 5.30

Notes: aThe parameters {R_SRCH,Z_SRCH,Z_DEPTH} refer, respectively, to the 0/1 switches ROOT_SEARCH & ZONE_SEARCH and the depth of the tree (ZONE_DEPTH) at which a discrete search zone is imposed by the milp solver. For example, {R_SRCH,Z_SRCH,Z_DEPTH} ¼ [1,1,5} imposes a discrete zone around the relaxed LP-solution at the root of the tree, followed by a discrete zone at depth 5 of the tree. If the parameters are zero, a pure depth first search is carried out

Flexible platform MINLP problems

Case 1: fixed trim loss problem, variable linearizations Fixed problem parameters Bmax 1,900 Delta 200 Nmax 5 PT

2

b norder

Product 1 460 8

The width of a raw paper roll Width tolerance Total number of product paper rolls Number of types of product rolls to be cut Product 2 570 7

Simulation parameters No of simulations TREE_LIMIT ¼ 21

500 EPS ¼ 1.O £ 102 7 SGC ¼ 0 CUT ¼ 1 Simulation intervals for the linearization parameters Lower Upper K1, K2 3 5 L1, L2 5 7 Case 2: variable trim loss problem, variable linearizations Problem parameter simulation intervals Lower Upper Bmax 1,890 1,910 Delta 190 210

Objective and tree size problem size F TREE_SIZE Mean 5.3605 144.44 (0,1,15) 2 0.10 (st. dev) (0.2467) (43.35) Mean 5.3000 339.43 (0,0,0) 0.00 (st. dev) (0.00) (70.44) Distribution of objective value ZONE SGC 5.3 6.3 (0,1,15) 2 0.10 No. 467 28 Per cent 93.40 5.60 (0,0,0) 0.00 No. 500 Per cent 100.00 ZONE

SGC

667

Width of the product rolls Total number of product roll to be cut LP_solver: BFD (Maros, 2003)

Table X. Simulation results for Trimloss2

m 61.39 (5.82) 61.83 (5.90)

n 31.69 (2.91) 31.92 (2.95)

K1 3.96 (0.70) 3.99 (0.71)

7.3 1 0.20

8.3

10.3

Linearization K2 L1 3.94 5.98 (0.70) (0.71) 3.98 6.02 (0.68) (0.69) 12.3

L2 6.02 (0.69) 6.01 (0.68)

Failed 4 0.80 0 0.00

4. Conclusions We present a new powerful algorithm for convex MINLP-problems. Minlp_machine() is a flexible tool that, e.g. can be used as a support engine for GHA. Minlp_machine() has ˚ bo been compiled and tested on the Sun and Alpha single processor main frames at A Akademi University and on the IBM parallel supercomputer at the Centre of Scientific Computing in Helsinki. The system can be linked as a support engine for high performance computing on these platforms. Extensive simulation studies of different mathematical programming problems represent an important avenue for future research efforts, where genetic and classical solution techniques can be combined to overcome the difficulties (for example, nonconvexities) encountered in practice.

Table XI. Simulation results for case 1 (failures ignored in mean and spread figures)

20.10

0.00

SGC 20.10

0.00

(0,1,19)

(0,1,19)

ZONE (0,1,19)

(0,1,19)

Table XII. Simulation results for case 2 (failures ignored in mean and spread figures)

SGC

No. Per cent No. Per cent

Mean (st.dev) Mean (st.dev) 5.3 437 87.40 445 89.00

5.3180 (0.1329) 5.3000 (0.0000)

F 202.45 61.63 31.81 (58.83) (5.98) (2.99) 259.42 61.48 31.74 (44.46) (5.98) (2.99) Distribution of objective value 6.3 7.3 8.3 8 1.60

Objective and tree size problem size TREE_SIZI m n

9.3

1900.05 (5.81) 1899.81 (5.66)

Bmax

10.3

200.07 (5.66) 199.79 (5.88)

Failed 55 11.00 55 11.00

3.92 (0.71) 3.96 (0.71)

4.01 (0.69) 3.95 (0.73)

5.99 (0.70) 5.99 (0.74)

Width parameters Linearization Delta K1 K2 L1

668

ZONE

5.99 (0.69) 5.99 (0.69)

L2

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References Aoki, M. (1987), State Space Modeling of Time Series, Springer-Verlag, Heidelberg, NY.

Flexible platform MINLP problems

Bradley, S., Hax, A. and Magnanti, T. (1977), Applied Mathematical Programming, Addison-Wesley Publishing Company, Reading, MA. Dennis, J.E. and Schnabel, R.B. (1983), Numerical Methods for Unconstrained Optimization and Non-linear Equations, Prentice-Hall Inc., Englewood Cliffs, NJ. Duran, M.A. and Grossmann, I.E. (1986), “An outer-approximation algorithm for a class of mixed-integer non-linear programs”, Mathematical Programming, Vol. 36, pp. 307-39. Farmer, J.D. and Sidorowich, J.J. (1987), “Predicting chaotic time series”, Physical Review Letters, Vol. 24, pp. 1277-97. Gavish, B., Horsky, D. and Srikanth, K. (1983), “An approach to the optimal positioning of a new product”, Management Science, Vol. 29, pp. 1277-97. Grossmann, I.E. and Biegler, L.T. (2004), “Future perspective on optimization”, Computers & Chemical Engineering, Vol. 28, pp. 1193-218. Grossmann, I.E. and Kravanja, Z. (1997), “Mixed-integer non-linear programming: a survey of algorithms and applications”, in Conn, A.R., Biegler, L.T., Coleman, T.F. and Santosa, F.N. (Eds), Large-scale Optimization with Applications, Part II: Optimal Design and Control, Springer-Verlag, New York, NY. Ho¨glund, R. and O¨stermark, R. (1991), “Automatic ARIMA modelling by the cartesian search algorithm”, Journal of Forecasting, Vol. 10, pp. 465-76. IMSL (1987), IMSL STAT/Library. FORTRAN Subroutines for Statistical Analysis, IMSL Inc., Houston, TX. Lawrence, C., Zhou, J. and Tits, A. (1997), User’s Guide for CFSQP Version 2.5: A Code for Solving (Large-scale) Constrained Non-linear (Minimal) Optimization Problems, Generating Iterations Satisfying All Inequality Constraints, University of Maryland, College Park, MD, 20472. Institute for Systems Research TR-94-16rl. Copyright q by Craig T. Lawrence, Jian L. Zhou and Andre´ L. Tits. Leyffer, S. (2003), “MacMINLP:AMPL collection of MINLP test problems”, available at: www-unix.mcs.anl.gov/leyffer/MacMINLP/ Ljung, L. (1987), System Identification. Theory for the User, Prentice-Hall, Inc., Englewood Cliffs, NJ. Maros, I. (2003), “A generalized dual phase-2 simplex algorithm”, European Journal of Operational Research, Vol. 149 No. 1, pp. 1-16. ¨ stermark, R. (1992), “Solving a linear multiperiod portfolio problem by interior point O methodology”, Computer Science in Economics and Management, Vol. 5, pp. 283-302. ¨ stermark, R. (1994), “Using neural nets in modelling vector time series”, Kybernetes, Vol. 23 O No. 9, pp. 12-22, Studies in Systems and Cybernetics. ¨ stermark, R. (1999a), “Solving irregular econometric and mathematical optimization problems O with a genetic hybrid algorithm”, Computational Economics, Vol. 13 No. 2, pp. 103-15. ¨ Ostermark, R. (1999b), “Solving a non-linear non-convex trim loss problem with a genetic hybrid algorithm”, Computers & Operations Research, Vol. 26, pp. 623-35. ¨ Ostermark, R. (2000), “A hybrid genetic fuzzy neural network algorithm designed for classification problems involving several groups”, Fuzzy Sets and Systems, Vol. 114 No. 2, pp. 311-24.

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¨ stermark, R. (2003), “A multipurpose parallel genetic hybrid algorithm for non-linear O nonconvex programming problems”, European Journal of Operational Research, Vol. 152, pp. 195-214. O¨stermark, R., Westerlund, T. and Skrifvars, H. (2000), “A non-linear mixed-integer multi-period firm model”, International Journal of Production Economics, Vol. 67, pp. 183-99. Quesada, I. and Grossmann, I.E. (1992), “An LP/NLP based branch-and-bound algorithm for convex MINLP optimization problems”, Computers & Chemical Engineering, Vol. 16, pp. 937-47. Still, C. and Westerlund, T. (2006), “Solving convex MINLP optimization problems using a sequential cutting plane algorithm”, Computational Optimization and Applications, Vol. 34, pp. 63-83. Taha, H. (1982), Operations Research. An Introduction, Macmillan, New York, NY. Westerlund, T., Skrifvars, H., Harjunkoski, I. and Po¨rn, R. (1998), “An extended cutting plane method for a class of non-convex MINLP problems”, Computers & Chemical Engineering, Vol. 22, pp. 357-65. Further reading ¨ stermark, R. and Saarinen, M. (1996), “A multiprocessor interior point algorithm”, Kybernetes, O Vol. 25 No. 4, pp. 84-100, Anniversary Issue. Studies in Systems and Cybernetics. Westerlund, T., Pettersson, F. and Grossmann, I.E. (1994), “Optimization of pump configurations as a MINLP problem”, Computers & Chemical Engineering, Vol. 18 No. 9, pp. 845-58. Corresponding author Ralf O¨stermark can be contacted at: [email protected]

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Index to part I

INDEX TO PART I Index to the contributions published in Part I of the series: Management Science: Current researches and developments

671

(Published in Kybernetes Volume 36 Nos. 3/4 2007) The RISCOM model: dialogues and requisite organisation Raul Espejo

291

Optimal structures for social systems Markus Schwaninger

307

Requisite holism – precondition of reliable business information Matjaz Mulej and Vojko Potocan

319

Beyond hierarchy: a complexity management perspective A. Espinosa, R. Harnden and J. Walker

333

Technology learning systems as non-trivial machines Clas-Otto Wene

348

Rethinking research management in Colombia Roberto Zarama, Alfonso Reyes, Eduardo Aldana, Jorge Villalobos, Juan C. Bohorquez, Juan P. Caldero´n, Alonso Botero, Nelson L. Lammoglia, Jose´ L. Villaveces, Luis Pinzo´n, Ricardo Bonilla, Andre´s Mejı´a, Jose´ Bermeo, Isaac Dyner, Neil F. Johnson and Juan A. Valdivia

364

From sociohistory to psychohistory M.I. Yolles

378

Fostering innovation by unlearning tacit knowledge Miroslav Rebernik and Karin Sˇirec

406

From management science to sociology: cybernetics, finalization and the possibility of a social science Paul A. Stokes

420

Stafford Beer’s contribution to management science – renewal and development Denis Adams and Doug Haynes

437

COMMUNICATIONS AND FORUM On management science: an informal communication Werner Schuhmann

451

Cyber profiles Raul Espejo and Marcus Schwaninger

453

Kybernetes Vol. 36 No. 5/6, 2007 p. 671 q Emerald Group Publishing Limited 0368-492X

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REGULAR JOURNAL SECTIONS CONTEMPORARY CYBERNETICS, SYSTEMS AND MANAGEMENT SCIENCE

Emerging innovative systems Brian H. Rudall Norbert Wiener Institute of Systems and Cybernetics, University of Wales, UK, and

C.J.H. Mann University of Wales, UK Abstract Purpose – This paper aims to review current research and developments with particular reference to emerging innovative management and information systems. Design/methodology/approach – A general review and survey of selected research and development topics. Findings – Illustrates the multi- and trans-disciplinary natures of studies in cybernetics, systems and management science with a view to further research and development activity. Practical implications – The choice of reviews provides the awareness of current trends in these areas of endeavour. Originality/value – The reviews are selected from a global database and give a studied assessment of current research and development initiatives. Keywords Computer applications, Cybernetics, Information systems Paper type Technical paper

1. Rail traffic management system 1.1 Introduction The European rail traffic management system (ERTMS) is designed as a safety system for high-speed and conventional trains. It aims to allow these trains to operate in all European countries. It is claimed that it provides extra safety in that trains will not be able overrun red warning lights. In addition it will increase the capacity of the railways because it will allow an extra five trains an hour or more on many railway lines. ERTMS uses the currently proven technology of digital sensors and computer systems. The question cyberneticians and systemists have asked is why has it taken so long to adapt this existing technology to this particular application. The system is already operating on the Rome-Naples rail route providing a maximum capacity of 24 trains an hour at speeds up to 186 mph. This route is 125 miles long and journey times have already decreased from 65 min in 2006 to a target time of 55 min in 2008. Kybernetes Vol. 36 No. 5/6, 2007 pp. 672-679 q Emerald Group Publishing Limited 0368-492X DOI 10.1108/03684920710749749

1.2 System functions The system functions in the following way: . A track that is fitted with a “balise” – this is a positioning device-every three quarters of a mile apart.

.

.

.

.

The train has onboard antenna which makes contact with a “balise” – identifying its position as it passes over it. The radio antenna communicates using the GSM-R radio frequency. The train is equipped with its own computer which constantly monitors speed, braking capability and proximity to the train in front. Driver has a cab display to provide exact instructions. A control centre that processes information about the position of trains and gives permission for their movement. Should a train become too close to another one in front brakes will be automatically applied.

1.3 Future developments This system can be utilised to develop the completely automated train. Already ERTMS will allow high-speed trains to operate without drivers. The railway industry says that at present it believes that it will be many years before this option can be utilised because it is not yet acceptable to the public. Automation also brings the benefit of increased capacity and safety. In addition we are told because the existing traditional signal system is dismantled a cost saving in maintenance is made. In the UK a pilot scheme has been instigated in a North Wales region of the rail system which will become operational in 2008. The new system is to be installed in other regions of the network and in some instances this system will provide an alternative to building new railway lines. In this instance this new system appears to confirm that automation can reduce costs and also offer not only a better service but also reduce the impact of the network on the environment. ERTMS has the advantage of being an European standard and as such will surely enhance the whole European rail network as it is implemented across the whole community. 2. Warehouse management systems 2.1 Innovative system A new generation of warehouse management systems services (WMS) is the subject of a new research initiative. Net-WMS is a new generation of warehouse management systems network services which aims at integrating virtual reality and optimisation techniques in a new generation of networked businesses in WMS under constraints. This is a new project that is working to develop interactive optimisation tools and prototype software that will form the basis for a new generation of networked services for WMS. Net-WMS commenced on 1 September 2006 and will be active for some three years. Full details of the project are given by the coordinators (Fages and Aggoun, 2007a). They write that: Net-WMS will handle networked communication and co-operation processes through the integration of decision-making technologies, generic 2D, 3D and higher-dimensional placement constraint solvers, visualisation and interaction with the solvers in virtual reality, packing models and knowledge modelling with business rules. Its scientific outcome will be relevant to the whole domain of combinatorial optimisation and will have direct technological impact on supply chain management at both the WMS and Transportation Management Software (TMS) levels, especially in the areas of packing, vehicle loading, space management, planning and scheduling, inventory control and packed item visualisation.

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2.2 The prototype applications We are told that Net-WMS prototype applications will be operational in an environment of networked Warehouses. This has been made possible because of their interoperability and to the user-friendly interface designed for plant-level technicians. Our attention has been drawn to some of the innovative tools and to the plug-ins which include: . a packing modeller of items based on optimisation techniques and interactions in virtual reality; . a palletizer tool using optimisation techniques; . a dispatcher – this includes the virtualisation of a truckload; and . a set of interfaces enabling communications between several planning components across a network. 2.3 Project’s goals Fages and Aggoun (2007b) outline the project’s goals as: (1) From a scientific standpoint-significant advances are expected on: . the algorithmic treatment of global placement constraints for objects of higher dimensions including space and time; . the expression of constraint optimisation problems with a language of business rules; and . the control of an optimisation tool with interactions in virtual reality. (2) On the technological side, the project will pave the way for next generation WMS software by applying innovative technology to enhance operations in industrial warehouse environment. This includes: . a set of JAVA Platform Enterprise Edition interfaces for interoperability and mobile services; . a mobility interface-allows remote users; . new interactive modules combining constraint programming and virtual reality; . a set of high-level modelling libraries – for Choco (constraint programming system); . extensions to rule programming tools such as constraint handling rules (CHR) and Drools (3) On the commercial side: . aims to improve European competitiveness in the area of warehouse management by significantly reducing costs related to packing manpower and transportation. 2.4 Targeted research This project is a Specific Targeted Research Project which is co-funded by the European Commission’s initiative for networking, it therefore focuses on future-generation technology in which computers and networks will be integrated into everyday environments. This consequence will allow easy access to a multitude of applications and services through user-friendly interfaces. We are informed that

Net-WMS has a consortium with combined expertise and field knowledge with members from both academia and industry. 3. New global logistics information system 3.1 Demand for the system A new comprehensive global logistics information platform called the – secure trade lane (STL) has now been developed by IBM. The IBM STL gives global supply chain stakeholders access to information on demand, allowing real-time access and response to physical cargo monitoring data as well as the related logistics transaction data. In effect this means for what is claimed to be the first time, shipments can be monitored from the manufacturer to the store and related activities such as port operations optimized. The world’s shipping industry carries some 90 per cent of world trade using 50,000 merchant ships that annually transport over six billion tons of goods in some 20 million maritime containers. These are the statistics that convinced IBM researchers that a new STL solution should be urgently found. The importance of international shipping industry to the global economy cannot be underestimated, but the challenges of security, reliability, liability, visibility and efficiency of the shipments and in particular container shipments must be met. 3.2 Description of the IBM STL Dolivo (2007) of the IBM Research Laboratory, Switzerland describes the IBM STL as: The IBM Secure Trade Lane (STL) is a new comprehensive global logistics information platform that addresses all these challenges by providing unprecedented levels of supply chain efficiency and security. It gives global supply-chain stakeholders access to information on demand, allowing real-time access and response to physical cargo monitoring data, and related logistics transaction data such as order information, invoices, financial data, bills of lading and manifests.

Details of the STL architecture (IBM, 2007) include a detailed overview of the whole system. At its heart, we are told, is a tamper-resistant embedded controller (TREC) which is an intelligent wireless monitoring device that is mounted on the container. The information provided by TRECs is made available to supply chain participants through the shipment information systems (SIS). The SIS is a distributed network based on service-oriented architecture (SOA) which enables an end-to end data collection and reporting system to function. The aim is to share the information across authorized parties using the proven techniques and tools. We are told that TREC has two main functions: The first is to create an audit trail of container movements and events from the point of origin to the destination. The second is to make this information available to authorized entities, allowing them to perform risk analyses, to assess the container’s security and integrity and to optimize the efficiency of container shipments. The TREC device automatically collects information on container events, including its physical location (based on GPS) and state (e.g. temperature, humidity, ambient light, acceleration and door status). It can communicate with the backend server via a satellite network, a cellular system (GSM/GPRS), or a Wireless Personal Area Network (WPAN) based on ZigBee/IEEE 802.15.4 radio. A handheld can also be used to communicate with the TREC over a WPAN.

TREC has sufficient processing power to enable it to analyse events and to take appropriate actions. Interference with the doors of the container in an unauthorised way is logged and an alert can be sent to the monitoring station.

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3.3 STL’s controlling services These controlling services are summed as: . complete monitoring service; . information – sharing services – trading parties can exchange data more easily; . efficiency services – helps users to optimise their supply chains; . security services – helps traders balance efficiency and security in the context of their specific industry. 4. Automatic translator system 4.1 Background to the developments Translator systems have been developed for computer systems since the early 1950s. The first systems were virtually dictionaries stored in the computer memory which were accessed by a program that was able to recognise words and then attempt to match them to the stored word data bank. As technology advanced they became more sophisticated and were able to attempt translation of phrases and later sentences sometimes with rather comic results. About a decade ago hand-held systems were marketed that allowed their user to type in a common phrase in one language and the translation would appear in a viewing window or small screen. Some of these systems boasted translations from English to a number of the commonly used European languages. Tourists were particularly pleased with the results which once again were not always acceptable translations. More intense researches have now produced systems which very nearly pass the Turing test in that translated conversations can be held between the translating computer and the user. A great deal more research is of course, required before such systems will become versatile enough to allow us to use them with confidence. A sign of the enormous progress in such developments came recently when we were informed by researchers that we will now no longer need to take a phrase-book on our foreign holidays. Instead a software package had been developed that will automatically translate for us. 4.2 Developing the instant electronic translator In essence the innovative system uses electrodes attached to the users face and neck to interpret what is a uniques pattern of electrical signals sent to the facial muscles and the tongue which occurs when someone is speaking. These are sent to an attached computer system which has the software program that translates what is being spoken into the required language so that it is output simultaneously by a synthesised voice box. The researchers from Carnegie Mellon University in Pennsylvania, USA and from the Nasa Research Centre in California have great hopes for the system. In 2005 the researchers demonstrated an automatic translator system that was limited to a 100 words of Mandarin Chinese which translated into English or Spanish. More recently they have developed a system that is based on understanding the phonetics of words with the possibility of translating each word. The research team say that: The computer program recognises which word sounds are most likely to be uttered next to each other and is able to translate them into a foreign language on the basis of probability.

They do admit, however, that the system is certainly not perfect yet. Since, when asked to translate a sequence of words not previously encountered it translates with an

accuracy of some 62 per cent. Commenting on this performance the research team say that: This is showing that the technology is really within reach. English, German and Spanish are the languages that are being tested for the prototype translators but eventually every language could be within the capabilities of the machinery.

Dealing with language idioms has presented the translator with some real problems and the software has to be programmed specially to deal with them to provide their equivalent sense in another language. 4.3 Future prospects Future prospects are good and the initial problems of developing an instant electronic translator have been overcome. The aim of the research is to be in a position where the system can be used for conversational purposes. The potential uses of such a system are of course enormous. 5. System to model humans 5.1 Project discussions It seems to have been a long time coming after the great advance in modelling using computer systems but now medical experts are intent on a project to produce the virtual physiological human being (VPH). At a meeting in the Universite´ Libre de Bruxcelles discussions took place which aimed at integrating the efforts to produce a VPH. This project aims at developing systems that can model the workings of organs of the human body in a computer and to create a virtual human body. The computer model would be a VPH which would: . bleed as we do showing the same clotting actions; . a virtual wound would see immune cells rushing to it; . biochemical stress reactions will mimic those of our bodies; and . be capable of being dissected revealing the minute detail of all body activities. In other words, the model would be dynamic and the aim would be to simulate all actions and reactions that can take place in the human body. Experimentation would be possible with the virtual-reality software displaying any part that we wish to see. 5.2 Support for the project There is a great deal of interest and enthusiasm for the project and a consortium has been setup after the meeting in Bruxelles of several hundred experts in the field. In the UK some universities are already involved Oxford, Nottingham, Sheffield, Bedfordshire, London (UCL) are amongst them. It has been estimated that some £350 million would be required to fund a ten year European VPH programme, with some £50 million to start it off. Initially it would appear to be too ambitious but even partial systems would assist research and indeed the medical services. 5.3 Some current computer modelling systems Modern computer systems are already being used to model the organs of the body and to simulate many processes. Some scientists believe that we should aim to produce a virtual human being from the genes and proteins within cells following nature’s path of

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forming substructures of cells to organs and onto the whole body. This is discounted by many scientists, of course. Many important pioneering researches have been carried out. For example, the first mathematical models of cardiac cells by Professor Dennis Noble of the University of Oxford. With Dr Dario Di Francisco in Milan, Professor Noble wrote a program based on a mathematical model which reduced the cell’s activity to around 30 equations, that captured the main chemical processes that take place in the cell. Later in 1993 Professor Noble with colleagues from the John Hopkins University and from the University of Auckland developed a true virtual heart. Now we are told that billions of cells in a real heart can be mimicked by several million grid points in a silicon chip. The researchers do, however, say that they have modelled only about 2 per cent of the genes and proteins involved in reconstructing, for example a heart attack. A number of papers on the subject have been published by Professor Noble and his colleagues in the journal Nature. Other scientists are developing virtual kidneys and modelling, for example, the action s of the gut (Highfield, 2006). Dr Marco Viceconti of the Rizzoli Orthopaedic Institute, Bologna, Italy, initiated the “Living Human Project” which is simulating the muscles and skeleton needed to animate the virtual body. In the United States Entelos, a Californian Company is designing a simple “virtual patient” so that they can screen the effects of candidate drugs on a range of life support systems from liver to bladder and on to circulation. Attempts to simulate the brain are ongoing. A consortium called Aneurist in Spain is modelling the brain to find out which aneurisms are worth trying to treat with surgery. 5.4 Future system development These projects are limited by the computer power currently available and obviously when new super-computers become available computer models of the body will become a more attainable goal. Biocyberneticians will be the first to recall that the power of our computers just two decades ago limited so much of the research that they wished to carry out. Two decades on may well see significant changes in the systems that we use and indeed in the way that we use them. Raw power is, of course, a necessity for so many applications but the design of the systems we use may well be even more important, particularly in building systems that can model human beings in the way which is being planned. 6. Software system for a “Chatbot” 6.1 New interactive virtual system Robots have been programmed to respond in an interactive manner whilst also being able to perform real tasks, now a software “robot” system has been devised. It is called a “chatbox”. It was developed by Rollo Carpenter, an Artificial Intelligence Programmer who is also Managing Director of Icogno Ltd, and Tim Child the founder of Televirtual Ltd 6.2 The “George” system Called George the software chatbox is said to be able to hold some 1,000 conversations at the same time. George appears as a thin balding androgynous 40-year old who is sufficiently animated to be able to blink, figet and carry out a conversation speaking

what is described as a peculiar, languid accent. This virtual character has a conversational capacity that is based on an encyclopaedia of responses which he has collected in previous interactions. Rollo Carpenter says that: . . . the kind of machine intelligence used in George will one day-enable robotic “pets” to chat to their owners. These could hold conversations based on the owners’ typical discussions with friends, or assume roles of Hollywood stars, or even “a dead spouse”. George’s AI learns emotions and employs gesture and expression as well as language, helping it to “form relationships”.

What makes this innovative development interesting to those who work in the AI area is that unlike some other chatbox systems which are usually limited by the builtin program and are consequently not as versatile as they might be, George uses an ever expanding data base. This is a data base of responses that George has learnt form all of its interactions over the web. This in effect can be described as an encyclopaedia which has an ever increasing number of pages. What the AI programmer has done is to refine the conversation so that George is able to give mainly, highly appropriate responses. George can be found on www.jabberwacky.com and is currently available for a “chat” in text. 6.3 The future is with AI? The developers see this as a cost-effective way of offering presenters in a media that is increasingly in need of providing such interactive facilities. The prospects of using such AI techniques that combine expert programming with a data base builtup from previous interactions has been used before but obviously, the degree of sophistication of the software chatbox in improving at an encouraging rate. References Dolivo, F. (2007), IBM Research GmbH, Zurich Research Laboratory, Ruschlikon, available at: [email protected] Fages, F. and Aggoun, A. (2007a), available at: http:net-wms.ercitn.org/ Fages, F. and Aggoun, A. (2007b), “NetWMS – a new generation of warehouse management systems networked services”, paper presented at European Research Consortium for Informatics and Mathematics No. 68, pp. 44-5. Highfield, R. (2006), “The virtual medical man”, Science, UK Daily Telegraph, p. 31. IBM (2007), available at: www-306.ibm.com/software/solutions/LE/LG04-01/solutions_overview. html Corresponding author Brian H. Rudall is the corresponding author.

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Alex M. Andrew

Newlook ASC, new WOSC address, machine translation Reading, UK Abstract Purpose – To discuss the announcement of plans for invigoration of the American Society for Cybernetics, with reference to that society’s web site for details. Design/methodology/approach – The aim is to review developments on the internet, especially those of general cybernetic interest. New arrangements for the WOSC web site and associated internet items are explained. Illustrations are given of limitations of simple machine translation. Findings – The ASC is alive and well. The WOSC web site is accessible despite the discontinuation of the British Library facility. Simple machine translation can produce bizarre results. Practical implications – Developments in the ASC will be worth watching, new WOSC details should be noted, and results of simple machine translation need to be used with care. Originality/value – It is hoped this is a valuable periodic review. Keywords Cybernetics, Search engines Paper type General review

Kybernetes Vol. 36 No. 5/6, 2007 pp. 680-682 q Emerald Group Publishing Limited 0368-492X DOI 10.1108/03684920710749758

American Society for Cybernetics In a letter sent in mid-January and addressed to “members, former members, future members and friends” of the ASC, Ranulph Glanville, now Vice-President, discusses benefits of membership and announces plans to invigorate the society. His comments come under the six headings of benefits, membership, awards, conferences, publications and nominations. Details under any heading can be found on the Society’s web site at: www.asc-cybernetics.org. Benefits of membership at one time included receiving the Society’s Newsletter, but this has not been published for some time and its place has been taken by another small but valuable journal entitled Patterns. Other benefits include greatly reduced subscriptions to certain journals. A nice feature of the membership arrangements is that the fee can be paid by credit card. This must be welcomed by British members, for whom other methods of transferring moderate amounts of money internationally (other than by the frowned-upon method of sending cash) incur punitive bank charges. The ASC has three grades of membership, associate/student, member and fellow, with specific recognition of the status of Emeritus of each of the last two. The grades allow the letters after a name of ASCA, ASCM or ASCF, the last two corresponding to the MCybS and FCybS of the UK Society. Election as a Fellow is considered following nomination, where self-nomination is mentioned as acceptable. (Fellowships are also awarded by WOSC though on a somewhat different basis). Conferences are an important activity of the ASC and there is mention of the 2007 Annual Conference on: Constructivism, Design, Cybernetics: Radical, Social, Second-order, which will be over when this is read, and others in which the ASC is

involved. The matter of awards is interesting as there are both Wiener and McCulloch medals. There is no clash between the two since the Wiener medal is given in recognition of past achievements while the McCulloch one is given as encouragement to promising young workers, a criterion that would certainly have pleased Warren McCulloch.

ASC, WOSC and machine translation

Change of address For a good many years, I have taken advantage of the British Library’s kind offer of free internet access, and have used the e-mail address: [email protected], and have also taken advantage of their webspace for a personal page with links to a variety of items including a section that has comprised the web site of WOSC, with address: http://pages.britishlibrary.net/alexandrew/wosc.htm. By courtesy of the UK Cybernetics Society, access has also been possible using the more easily-remembered address of: www.cybsoc.org/wosc. The British Library has decided to discontinue its function as an ISP, from the end of March 2007. The function was in fact run by a company called Easynet, and the library administration investigated, along with Easynet, the possibility of upgrading to a broadband-based service, but decided that this seemed unlikely to prove cost-effective particularly since broadband access provision is now so ubiquitous. The service would soon have begun to draw unfairly on public funds. A new personal page, including the WOSC site, has been set up with the Tiscali company, and for the time being the WOSC site can be accessed at: http://myweb. tiscali.co.uk/alexandrew/wosc.htm. The link provided by the Cybernetics Society has been updated accordingly. Other, perhaps more appropriate, possibilities for the WOSC site, probably with a domain name, are under consideration. A number of items that are relevant to cybernetics, though not included in the WOSC web site, have also been moved to the Tiscali webspace. JavaScript programs that have been made available at: http://pages.britishlibrary.net/alexandrew/simpprog. htm, and similarly for simpnewprog and riffleprog, can now be found at addresses that are similar except in having pages.britishlibrary.net replaced by myweb.tiscali.co.uk. The program simpprog is associated with a short paper in Kybernetes 31/2, 2002: “Homogenising Simpson’s Rule” and the others with one in 35/5, 2006: “Two mathematical notes.”

681

Deficiencies of machine translation The Google search engine has a facility for translation of material into languages other than that of its source. This is, however, done by rather primitive means, and Prof. Robert Valle´e discovered some amusing “translations” into French of material on the WOSC site, and was able to verify that the same errors were carried into German and Italian and Spanish. The word “Wiener” was recognised only as referring to a kind of sausage, so that the Norbert Wiener Institute became: “Institut de saucisse de Norbert des syste`mes et de la cyberne´tique.” Similarly the word “Beer” was recognised as a common noun, so that Stafford Beer was shown as: “Bie`re de Stafford.” A slightly more elaborate example was the translation of my address, 95 Finch Road, Earley, Reading, as: “Route des 95 pinsons, Earley, lisant” or “Road of the 95 Finches,” followed by recognition of “Reading” as a form of the verb “to read” rather than as a place name.

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Obviously the method used is well short of the state of the art in machine translation, but despite these bizarre examples the results can be useful if some imagination is brought to bear. They undoubtedly illustrate the shortcomings of a simplistic approach to translation, but that is not to deny their usefulness as part of the Google facility, where users can refer to original versions for names and addresses. Possibly a simple algorithm could be devised for identifying parts of an entry that constitute such items and that should not be converted. Corresponding author Alex M. Andrew can be contacted at: [email protected]

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A stability theory for model systems

Stability theory for model systems

Y. Villacampa, F. Verdu´ and A. Pe´rez Department of Applied Mathematics, University of Alicante, Alicante, Spain

683

Abstract Purpose – The purpose of this paper is to carry out a theoretical study of the stability of the mathematical models defined in a class of systems. Furthermore, it will be supposed that the models have been obtained from experimental data and by means of the application of a methodology. The studies carried out in this paper are, on one hand, the theoretical framework for an analysis of the sensitivity and stability of a type of systems; on the other hand, they supplement the studies carried out by the authors, in which, using a computational program, the sensitivity of the mathematical models is analyzed with respect to a type of perturbation. Design/methodology/approach – Initially, a class of systems is considered that are denominated quantifiable systems, in which model systems are defined that are determined by a set and a family of relationships. An initial study of the sensitivity of the mathematical models to perturbations in the experimental data lead to a concept of sensitive and stable models that forms the basis of the theory of stability developed in this paper. Furthermore, this permits a definition of the stability function for the set of the perturbations and, consequently, a determination of stable models according to the defined theoretical structure. Findings – An analysis of the sensitivity and stability of mathematical models in quantifiable systems from a systems theory perspective will be fundamental for the determination of mathematical model stability in environmental systems. Originality/value – The studies carried out in this paper supposes an advance in the study and modeling of a type of systems that the authors have denominated as quantifiable systems, applicable to the study of environmental systems and supplementing the numeric studies carried out by the authors. Keywords Cybernetics, Systems theory, Mathematical modelling, Stability (control theory) Paper type Conceptual paper

Introduction The various system definitions to be found in scientific literature are used as the basis for several theories. The authors commence with the studies carried out by Mesarovic and Takahara (1975), Lin (1987), Lin and Ma (1987), Yang (1989) and Villacampa et al. (1995). In a general sense, the system can be considered as an interrelated group of components (interconnected sets of components or interactions), where the components represent objects or processes. In the study and modeling of environmental systems it is primordial to determine mathematical models for the measurable processes or attributes that reflect their behavior, a fact which will rebound directly on the knowledge and evolution of the system. In this respect, the authors consider it necessary to define theoretical structure from the point of view of a systems theory, for systems whose mathematical modeling The authors wish to acknowledge the funding of this work by Project GV04B-563 of the Generalitat Valenciana (Department of Culture, Education and Sports) and the University of Alicante (Spain).

Kybernetes Vol. 36 No. 5/6, 2007 pp. 683-696 q Emerald Group Publishing Limited 0368-492X DOI 10.1108/03684920710749767

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684

requires analysis and also to generate a theory of the stability of the models. This paper makes special reference to models that have been obtained from experimental data. The study of systems and their mathematical models also leads us to consider their analysis in the context of a theory of mathematical model linguistics, such as that developed in the studies carried out (Villacampa and Uso´-Domenech, 1999; Villacampa-Esteve et al., 1999), in which mainly linguistic relationships are analyzed for a language of models. This also allows mathematical models to be studied from the perspective of text theory (Villacampa and Uso´-Domenech, 1999; Villacampa-Esteve et al., 1999). Moreover, in any study of a system the knowledge of the behavior of its elements is important, also defined by the behavior of certain associated characteristics or attributes. Consequently, a knowledge of the behavior of a system frequently implies the study of a group of relationships; moreover, it would be desirable to express this relationship using mathematical models. It is important for the study of systems and their models to have available methodologies that permit mathematical equations to be built from experimental data that reflect the evolution of a certain real variable in line with those that affect its behavior. There is a range of methodologies for mathematically modeling said relationships in the scientific literature (Splus, 1999; Spss, 1999; Corte´s et al., 2000). Once the mathematical models are determined, one can determine which models are more stable in relation to small variations in the initial data from which they were obtained. Previous articles written by the authors have led to the development of an initial theoretical study of sensitivity as well as the generation of a computational tool to determine, both numerically and graphically, the effects caused by a type of perturbation where the Monte Carlo method is applied (Verdu´ and Villacampa, 2002). We propose a theoretical structure that analyzes the behavior of mathematical models from the point of view of their sensitivity to the realized perturbations; this permits a study of the stability of the mathematical representations of the systems. As in other studies, the authors commence with the definition of a stable system given by Mesarovic and Takahara (1975) namely, that a system is generally considered to be stable if small changes in the conditions correspond to small changes in the behavior of the system. Stability depending on the notion of small change and on the system’s behavior is evaluated. The theoretical context of an analysis of systems theory has been to consider a class of systems that are called quantifiable systems and that are characteristically formed of a set X of real variables and a set R of relationships among the elements. The definition of a quantifiable system permits it to be considered as a system according to the definition by Yang (1989), in the sense that every quantifiable system is also a system according to this definition. In quantifiable systems, model systems are defined as well as their representations, so that the languages defined (here) and their relationships permit the construction of mathematical models in which stability is analyzed. Quantifiable system Definition of quantifiable system A quantifiable system, SC, is defined as a 2-tuple (orderly couple) SC ¼ ðX; RÞ, where X is a set of real variables and R a set of relationships, so that:


 R [ R > > > : j 3:

ð20Þ

The set of those B-splines ðQ21 ; Q0 ; . . . ; QN þ1 Þ forms a basis over the problem domain ½a; b
. Therefore, a numerical approximation U N to the analytical solution U ðx; tÞ can be constructed in terms of the cubic B-splines: N þ1 X dm ðtÞQm ðxÞ ð21Þ U N ðx; tÞ ¼ m¼21

where the time dependent parameters dm are to be found from the boundary conditions and collocation form of the equation (1). The graded cubic B-splines are continuous up to the second order so that approximate function is continuous of order 2 in space parameter x of the solution U ðx; tÞ. The values of U ; U 0 ; U 00 at the mesh points have an expression in terms of the element parameters dm by: U m ¼ s 3 dm21 þ 2sðs þ 1Þdm þ dmþ1 hm U 0m ¼ 3s½dmþ1 þ ðs 2 2 1Þdm 2 s 2 dm21
h2m U 00m

ð22Þ

2

¼ 6s ½sdm21 2 ðs þ 1Þdm þ dmþ1


where 0 , 00 denote the first and the second differentiations with respect to x, respectively. To apply the collocation method at the defined mesh points, substituting U m ; U 0m ; U 00m in the equation (1) gives us the following matrix system of the first order ordinary differential equations: +

+

+

s 3 dm21 þ 2sðs þ 1Þdm þ dmþ1 þ 2

6s 2 h2m

3s zm ðdmþ1 þ ðs 2 2 1Þdm 2 s 2 dm21 Þ hm

ð23Þ

nðsdm21 2 ðs þ 1Þdm þ dmþ1 Þ ¼ 0

where “+” denotes derivative with respect to time and: zm ¼ s 3 dm21 þ 2sðs þ 1Þdm þ dmþ1 is the non-linear term of the equation (23). Assume that the vector of parameters dm and their time derivatives are interpolated between two time levels n and n þ 1 by using equation (15). Putting expressions (15) into the system of equation (23) yields the following relation between the element parameters: nþ1 nþ1 n n n am1 dnþ1 m21 þ am2 dm þ am3 dmþ1 ¼ am4 dm21 þ am5 dm þ am6 dmþ1 ¼ 0

m ¼ 0; 1; . . . ; N : where:

ð24Þ

3

3

Burgers’ equation

3

s n am1 ¼ sDt 2 3s2hmzm 2 62h 2 ; m 2

sþ1Þ am2 ¼ 2sðDt þ 3szm2hðsm 21Þ þ 6s

2

ðsþ1Þn ; 2h2m

2

szm s n am3 ¼ Dt1 þ 32h 2 62h 2 ; m m

am4 ¼

s3 Dt

þ

3s 3 z m 2hm

þ

727

6s 3 n ; 2h2m 2

sþ1Þ am5 ¼ 2sðDt 2 3szm2hðsm 21Þ 2 6s

2

ðsþ1Þn ; 2h2m

2

szm s n am6 ¼ Dt1 2 32h þ 62h 2 : m m

The above system consists of N þ 1 equations in N þ 3 unknown parameters ðd21 ; d0 ; . . . ; dNþ1 Þ Using the boundary conditions U ða; tÞ ¼ a1 and U ðb; tÞ ¼ a2 enables us to eliminate the boundary parameters d21 ; dN þ1 from the equation (24) so that we obtain a solvable tridiagonal band matrix system in dimension ðN þ 1Þ £ ðN þ 1Þ. This matrix system can be solved by using Thomas algorithm with an inner iteration described in equation (17). The parameters d21 and dN þ1 can be determined from the boundary conditions at each time step using the equation U m ¼ s 3 dm21 þ 2sðs þ 1Þdm þ dmþ1 at the end boundaries. To carry on obtaining solution parameters, it is necessary to find the initial parameters d0m : To do this, initial condition: U N ðxm ; t 0 Þ ¼ s 3 dm21 þ 2sðs þ 1Þdm þ dmþ1 ¼ U ðxm ; 0Þ; m ¼ 0; 1; . . . ; N :

ð25Þ

and boundary conditions:  3s  0 d1 þ ðs 2 2 1Þd0 2 s 2 d21 ¼ U ðx0 ; 0Þ; h0  0 3s  0 U N ðxN ; 0Þ ¼ dNþ1 þ ðs 2 2 1ÞdN 2 s 2 dN21 ¼ U ðxN ; 0Þ: hN21 0

U N ðx0 ; 0Þ ¼

ð26Þ

are used. The equations (25) and (26) give a tridiagonal band matrix system. The solution of this system can also be calculated by using Thomas algorithm. After obtaining initial parameters d0m , at next time steps the time parameters dnm are computed from the recurrence relationship (24). Before proceeding the each time step dnþ1 m , the iteration (17) should be apply two or three times for getting better solution from the non-linear algebraic equation system (24). 3. Numerical examples The errors in the numerical solutions are measured using L1 -error norm defined by: L1 ¼ jU 2 U N j1 ¼ maxjU j 2 ðU nN Þj j: j

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(1) Shock-like solution of the Burgers’ equation has analytic solution of the form: U ðx; tÞ ¼

728

x=t pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; 1 þ ðt=T 0 Þexpðx 2 =4ntÞ

t $ 1; 0 # x # 1

ð27Þ

where T 0 ¼ expð1=8nÞ. Initial condition that computed from equation (27) at time t0 ¼ 1 is taken and boundary conditions U ð0; tÞ ¼ U ð1; tÞ ¼ 0 are used. We run the program with earlier used-data sets over the uniform mesh. According to distribution of the error over the problem domain, if large error exists near the right-hand boundary, we have chosen graded mesh parameter s , 1, which results in concentration of mesh points near the right end and similarly selection of s . 1 result in the concentration of mesh points near the left-hand end where large error has detected. The problem is solved with parameters Dt ¼ 0:01; n ¼ 0:005 and N ¼ 200 over the interval ½0; 1
. Program is run up to time t ¼ 3:25: According to observation of the error over the problem domain during the run of the algorithms, concentration of the largest error happens at about the left hand boundary. To reduce the error, investigation of the parameters  s are carried out to search in the interval 1; 1:1 with increment of value 0:001: Best parameter s at different time steps are found and results are tabulated in Table I. The results of the some other methods are also given in the same table for purpose of the comparison. Numerical solutions of the methods GQBG and GCBC are graphed at times t ¼ 1:7; t ¼ 2:5; t ¼ 3:25 in Figure 1. Errors of the schemes are visualized at some times in Figures 2-4 when the uniform mesh and best selection of the graded mesh are used. Considerable reduction in error at early times are obtained. As time goes, the effect of the graded mesh on the solution of the Burgers’ equation diminishes for the proposed algorithms. We can also conclude that GQBG method provided less error than the GCBC method generally. Similar simulation is carried out by using the smaller viscosity constant v ¼ 0:0005. Thus, sharpness of the shock-wave is very much increased. The proposed numerical schemes are rerun with using the uniform mesh. The perspective views of the numerical solutions are shown in Figure 5. After the error concentration have been determined over the problem domain, selection of the mesh parameter s , 1 is done over the interval ½0:9; 1
with the increment 0:0001 to find the least error. Comparison of results with the case of s ¼ 1, the best parameter of s in the domain interval and those referenced in the paper (Dag et al. (2005) and Ali et al. (1992)) are presented in Table II. In Figures 6-8 error distributions of the both schemes at times t ¼ 1:7; t ¼ 2:5 and t ¼ 3:25 are plotted for both uniform and graded meshes together. Even though results are acceptable for the uniform mesh, graded schemes provide a little better accuracy. (2) For our second test problem we consider the exact solution of the Burgers’ equation:

t ¼ 1.7 1 1.77619 0.31153 27.5770 t ¼ 1.7 2.576 t ¼ 1.7 1 2.72298 0.31153 27.5770 t ¼ 1.7 2.576

s GQBG QBCM (Dag et al., 2005) CBCM (Dag et al., 2005) Ali et al. (1992)

s GCBC QBCM (Dag et al., 2005) CBCM (Dag et al., 2005) Ali et al. (1992)

t ¼ 2.5

1.026 0.05197

1.016 0.43406

1 1.23401 0.18902 25.1517 t ¼ 2.4 1.242 t ¼ 2.5 1 2.76426 0.18902 25.1517 t ¼ 2.4 1.242

0.50 t=0

1 0.95663 8.98390 21.0489 t ¼ 3.1 0.688 t ¼ 3.25 1 9.25009 8.98390 21.0489 t ¼ 3.1 0.688

1.017 0.39872

1.004 0.68244

729 For all 9.25009 Table I. At different times, L1 £ 103 errors for n ¼ 0:005 and Dt ¼ 0:01

t=1.7

0.30

t=0

0.40

t=2.5 t=3.25

0.20

U(x,t)

U(x,t)

1.025 0.04015

0.50

0.40

0.10 0.00 0.00

Burgers’ equation

t ¼ 3.25

t=1.7

0.30

t=2.5 t=3.25

0.20 0.10

0.20

0.40

0.60

0.80

0.00 0.00

1.00

0.20

0.40

0.60

X

X

(a) GQBG

(b) GCBC

0.0020

0.80

1.00

Figure 1. n ¼ 0:005; N ¼ 200; Dt ¼ 0:01

0.0030

uniform mesh graded mesh

0.0012

uniform mesh graded mesh

0.0020 ERROR

ERROR

0.0016

0.0008

0.0010 0.0004 0.0000 0.00

0.20

0.40

0.60

X (a) GQBG

0.80

1.00

0.0000 0.00

0.20

0.40

0.60

X (b) GCBC

0.80

1.00

Figure 2. Errors ðjNumerical 2 AnalyticaljÞ t ¼ 1:7 with n ¼ 0:005; N ¼ 200

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0.0030

0.0016

uniform mesh graded mesh

uniform mesh graded mesh

0.0020 ERROR

730

ERROR

0.0012

0.0008

0.0010 0.0004

Figure 3. ErrorsðjNumerical2 AnalyticaljÞ t ¼ 2:5 with n ¼ 0:005; N ¼ 200

0.0000 0.00

0.20

0.40

0.60

0.80

0.0000 0.00

1.00

0.40

0.80

1.00

0.20

0.40

0.80

1.00

0.0080 uniform mesh graded mesh

0.0006

ERROR

ERROR

0.0008

Figure 4. Errors ðjNumerical 2 AnalyticaljÞ t ¼ 3:25 with n ¼ 0:005; N ¼ 200

0.0060

0.0004

0.0040

0.0002

0.0020

0.0000 0.00

0.20

0.40

0.60

0.80

0.0000 0.00

1.00

X (a) GQBG

0.50

t=0 0.40 t=1.7

t=1.7

t=2.5 t=3.25

0.30 0.20

U(x,t)

U(x,t)

0.60 X (b) GCBC

0.50

t=0

0.40

t=2.5

0.30

t=3.25 0.20 0.10

0.10 0.00 0.00

0.60 X (b) GCBC

0.0100

0.0010

Figure 5. n ¼ 0:0005; N ¼ 200; Dt ¼ 0:01

0.20

X (a) GQBG

0.20

0.40

0.60

X (a) GQBC

0.80

1.00

0.00 0.00

0.20

0.40

0.60 X (b) GCBC

0.80

1.00

t ¼ 1.7 1

s GQBG QBCM (Dag et al., 2005) CBCM (Dag et al., 2005)

0.9822 3.52912

22.0620 13.8155 27.5770 t ¼ 1.75 5.880 t ¼ 1.7 1 22.4378 13.8155 27.5770 t ¼ 1.75 5.880

Ali et al. (1992)

s GCBC QBCM (Dag et al., 2005) CBCM (Dag et al., 2005) Ali et al. (1992)

t ¼ 2.5

0.9853 5.22052

1 18.2474 16.7712 25.1517 t ¼ 2.5 2.705 t ¼ 2.5 1 16.0589 16.7712 25.1517 t ¼ 2.5 2.705

0.0250

ERROR

ERROR

0.9869 5.52013

1 17.1378 13.8155 21.0489 t ¼ 3.25 2.291 t ¼ 3.25 1 14.8614 13.8155 21.0489 t ¼ 3.25 2.291

0.9563 2.54251

731 0.9869 5.79884

Table II. At different times, L1 £ 103 errors for n ¼ 0:0005 and Dt ¼ 0:01

0.0200 uniform mesh graded mesh

0.0100

0.0150

0.0050

0.0000 0.00

0.0000 0.00

0.20

0.40

0.60 X (a) GQBG

0.80

1.00

uniform mesh graded mesh

0.0100

0.0050

0.0200

0.20

0.40

0.60 X (b) GCBC

0.80

1.00

Figure 6. Errors ðjNumerical 2 AnalyticaljÞ t ¼ 1:7 with n ¼ 0:0005; N ¼ 200

1.00

Figure 7. Errors ðjNumerical 2 AnalyticaljÞ t ¼ 2:5 with n ¼ 0:0005; N ¼ 200

0.0200

0.0160

0.0160 uniform mesh graded mesh

0.0120

ERROR

ERROR

0.9668 3.01278

0.0250

0.0200 0.0150

Burgers’ equation

t ¼ 3.25

0.0080

0.0120 0.0080

0.0040

0.0040

0.0000 0.00

0.0000 0.00

0.20

0.40

0.60 X (a) GQBG

0.80

1.00

uniform mesh graded mesh

0.20

0.40

0.60 X (b) GCBC

0.80

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0.0160

0.0200

0.0120 uniform mesh graded mesh

0.0120

ERROR

732

ERROR

0.0160

0.0080

0.0080

0.0040

0.0040

Figure 8. Errors ðjNumerical 2 AnalyticaljÞ t ¼ 3:25 with n ¼ 0:0005; N ¼ 200

uniform mesh graded mesh

0.0000 0.00

0.20

0.40

0.60 X (a) GQBG

U ðx; tÞ ¼

0.80

1.00

0.0000 0.00

a þ m þ ðm 2 aÞexp h ; 1 þ exp h

0.20

0.40

0.60 X (b) GCBC

0.80

1.00

ð28Þ

0 # x # 1; t $ 0

where h ¼ aðx 2 mt 2 gÞ=n and a; m and g are constants. We choose these parameters as a ¼ 0:4; m ¼ 0:6 and g ¼ 0:125: The solution that represents a travelling wave, moves to the right with speed h: The initial condition is determined from the equation (28) by taking t0 ¼ 0: The boundary conditions are: U ð0; tÞ ¼ 1 and U ð1; tÞ ¼ 0:2;

t $ 0:

We use the viscosity number as n ¼ 0:01 with two space-time combinations. The results are recorded in Table III. The graphs of the solutions are shown in Figure 9 for the uniform mesh and graded mesh together. Maximum errors concentrated just near left -hand side of the centre of the domain as seen from the error distribution in Figures 10-11. Because of this we have decreased the size of the finite interval of the mesh towards the left-hand boundary. Investigation of the best selection of s which minimizes the error is showed to be searched over the interval ½1; 1:4
. Selection of s is done with increment of 0:001. Comparisons between the present solutions of the Burgers’ equation and some previous methods are also presented in Table III. The efficiency of the numerical method is improved partly in such a way that mesh of finite elements is graded wherever the error is high, the elements are small, and where the error is low, the elements are relatively large. It is seen from the results and

s

Table III. At t ¼ 0.5, L1 £ 103 errors for n ¼ 0.01

GQBG GCBC SGA(Christie et al., 1981) PAG(Christie et al., 1981) CD(Christie et al., 1981) CS(Ali et al., 1992)

N ¼ 18 and Dt ¼ 0.001 s¼1 s ¼ 1.167 s ¼ 1.220 14.1003 13.4553

2.79005 9.21057

N ¼ 36 and Dt ¼ 0.025 s¼1 s ¼ 1.185 s ¼ 1.002 5.00291 6.57396

3.82615 5.55096

96 82 151 5

uniform mesh graded mesh

1.20

0.80 t=0

t=0.5

t=1

t=1.3

U(x,t)

U(x,t)

0.80

t=0.5

t=1

0.60 X (b) CBCM

0.80

t=0

t=1.3

733

0.40

0.40

0.00 0.00

Burgers’ equation

uniform mesh graded mesh

1.20

0.20

0.40

0.60

0.80

0.00 0.00

1.00

0.20

X (a) QBGM 0.006

0.40

1.00

Figure 9. n ¼ 0:01; N ¼ 36; Dt ¼ 0:025

0.008

0.006

uniform mesh graded mesh ERROR

ERROR

0.004

uniform mesh graded mesh

0.004

0.002 0.002

0.000 0.00

0.000 0.20

0.40

0.60

0.80

1.00

0.00

0.20

0.0160

0.80

1.00

Figure 10. Errors ðjNumerical 2 AnalyticaljÞ t ¼ 0:5 with n ¼ 0:01; N ¼ 36

0.0160

0.0120

0.0120

uniform mesh graded mesh ERROR

ERROR

0.60

X (b) CBCM

X (a) QBGM

0.0080

0.0040

0.0000 0.00

0.40

uniform mesh graded mesh

0.0080

0.0040

0.20

0.40

0.60

0.80

1.00

0.0000 0.00

0.20

0.40

0.60

X

X

(a) QBGM

(b) CBCM

0.80

1.00

Figure 11. Errors ðjNumerical 2 AnalyticaljÞ t ¼ 0:5 with n ¼ 0:01; N ¼ 18

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graphs that geometrically GQBG yields solutions of higher accuracy than cubic B-spline collocation method. We have also observed wherever the error is high, solution varies most rapidly. Graded meshing is advisable in setting up the finite element schemes to have numerical solutions of the partial differential equations if the error is higher at about end boundaries. If the high error appears in the middle of the problem domain, accuracy of the method with the graded mesh does not increase much. References Ali, A.H.A., Gardner, G.A. and Gardner, L.R.T. (1992), “A collocation solution for Burgers’ equation using cubic B-spline finite elements”, Comput. Methods Appl. Mech. Eng., Vol. 100, pp. 325-37. Ali, A.H.A., Gardner, L.R.T. and Gardner, G.A. (1990), “A Galerkin approach to the solution of Burgers’ equation”, UCNW Maths Pre-print, 90.04. Bateman, H. (1915), “Some recent researches on the motion of fluids”, Monthly Weather Rec., Vol. 43, pp. 163-70. Burger, J.M. (1948), “A mathematical model illustrating the theory of turbulence”, Adv. in App. Mech., Vol. 1, pp. 171-99. Caldwell, J. (1987), “Application of cubic splines to the nonlinear Burgers’ equation”, in Hinton, E. et al. (Eds), Numerical Methods for Nonlinear Problems,Vol. 3, Pineridge Press, Swansea, pp. 253-61. Christie, I., Griffiths, D.F., Mitchell, A.R. and Sanz-Serna, J.M. (1981), “Product approximation for nonlinear problems in the finite element method”, IMA, J. Num. Anal., Vol. 1, pp. 253-66. Cole, J.D. (1951), “On a quasi-linear parabolic equation in aerodynamics”, Quarterly of Applied Math., Vol. 9, pp. 225-36. Dag, I. (1994), “Studies of B-spline finite elements”, PhD thesis, University College of North Wales, Bangor. Dag, I., Irk, D. and Sahin, A. (2005), “B-spline collocation methods for numerical solutions of the Burgers’ equation”, Math. Probl. Eng., Vol. 5, pp. 521-38. Davies, A.M. (1977), “A numerical investigation of errors arising in applying the Galerkin method of the solution of nonlinear partial differential equations”, Comput. Methods Appl. Mech. Eng., Vol. 11, pp. 341-50. Davies, A.M. (1978), “Application of the Galerkin method to the solution of Burgers’ equation”, Comput. Methods Appl. Mech. Eng., Vol. 14, pp. 305-21. Gardner, L.R.T., Gardner, G.A. and Ali, A.H.A. (1991), “A method of lines solutions for Burgers’ equation”, Proceeding of the Asian Pasific Conference on Computational Mechanic, Hong Kong, 11-13 December. Gardner, L.R.T., Gardner, G.A. and Dag, I. (1993), “Hermite infinite elemens and graded quadratic B-spline finite elements”, Internat. J. Numer. Methods Engrg., Vol. 36, pp. 3317-32. Hopf, E. (1950), “The partial differential equation U t þ UU x ¼ mU xx ”, Comm. Pure App. Math., Vol. 3, pp. 201-30. Jain, P.C. and Holla, D.N. (1976), “Numerical solutions of coupled Burgers’ equations”, Int. J. Non-linear Mech, Vol. 13, pp. 213-22. Jain, P.C. and Lohar, B.L. (1979), “Cubic spline technique for coupled non-linear parabolic equations”, Comp. Maths. with Appls., Vol. 5, pp. 179-85.

Jain, P.C., Shankar, R. and Singh, T.V. (1995), “Numerical technique for solving convective-reaction-diffusion equation”, Math. Comput. Modelling., Vol. 22, pp. 113-25. Kutluay, S., Esen, A. and Dag, I. (2004), “The numerical solutions of the Burgers’ equation by least squares quadratic B-spline element method”, J. Comput. Appl. Math., Vol. 167, pp. 21-33. Lohar, B.L. and Jain, P.C. (1981), “Variable mesh cubic spline technique for N-wave solution of Burgers’ equation”, J. Comput, Physc., Vol. 39, pp. 433-42. Miller, E.L. (1966), “Predictor-correcter studies of Burgers’ model of turbulent flow”, MS thesis, University of Delaware, Newark, DE. Rubin, S.G. and Graves, R.A. (1975), “Cubic spline approximation for problems in fluid mechanics”, Nasa TR R-436, Nasa, Washington, DC. Rubin, S.G. and Khosla, P.K. (1976), “Higher-order numerical solutions using cubic splines”, AIAA Journal, Vol. 14, pp. 851-8. Corresponding author Ali S¸ahin can be contacted at: [email protected]

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Hierarchical system of natural grammars and the process of innovations exchange in polylingual fields Svetlana Novikava and Kanstantsin Miatliuk Hierarchical Multilevel Systems Laboratory, Institute of Mathematics and Cybernetics, Minsk, Belarus Abstract Purpose – To define natural grammars with ways of mind activity in cybernetics (design and learning, innovating) technologies by mathematical symbol (image, scheme) of hierarchical systems. Design/methodology/approach – Suggested hierarchical scheme of the whole field of natural grammars connects mathematical images of individual grammars as certain stages of the process in hazy zones when new strata arise. Arrangement of the images and their order in their general scheme correspond to marked lines of grammars in mind activity, and thereby to ways of text organizing by their means. Findings – The paper proves that hierarchical mathematics allows definition of all the strata of its natural history (physical, chemical, biological, demographical, and knowledge). Their definitions are connected in general scheme of knowledge authorized by mathematics (which includes cybernetics means – innovating technologies). Natural languages in the light of suggested scheme are hierarchical systems which have all strata of knowledge and their own means of mind activity in these strata – natural grammars. Originality/value – The scheme developed meets all the requirements of practical cybernetics, it brings new light to theory and practice of connecting nations, allows to simplify innovating technologies and their exchange in polylingual fields. Keywords Cybernetics, Innovation, Semantics, Grammar Paper type Research paper

Kybernetes Vol. 36 No. 5/6, 2007 pp. 736-748 q Emerald Group Publishing Limited 0368-492X DOI 10.1108/03684920710749802

1. The task Mind activity (thinking process) in innovating technologies finds its reflection in symbol systems – mathematics, graphical images processing and others. Among them are natural grammars, grammars of natural languages. They allow us to organize the changes of vague texts like to thinking process with hazy thoughts (active images of systems). In this process, the new questions are asked that go beyond old horizons of thoughts, then they are turned into certain answers or orders, and the orders may lead to many questions again. Together with turning questions into answers and back, the symbols of units (nouns), acts (verbs), signs (adjectives, attributes) and other members of text may be turned one into another – similar to the facts of practice and unlike many theories where they cannot be converted. However, the turning of hazy zones of mind into good arranged systems and back do not have an exact definition in natural grammars. (Since, the innovating technologies in one national mind are hidden for other minds, and an exchange by their individual merits and advantages in the field of one grammar is very limited).

Moreover, the means of natural grammars are too weak to define innovating activity, natural grammars, their links, and the whole field of national languages. Mathematical imaging of hierarchical systems (Novikava et al., 1998) originated in the works of Mesarovic et al. (1970) and Mesarovic and Takahara (1975) allows it to be done. In agreement with this task the paper contains a mathematical scheme of hierarchical systems cohered with cybernetic technologies (innovating processes) and images of natural grammars connected in their hierarchical field. 2. Mathematical symbol of hierarchical systems Mathematical symbol Al of hierarchical systems has now two main images – £ a l and þ l a (Figure 1). £ a l and þ a l define one statute of hierarchical systems with law and mechanism of level increasing. l

£

a l : Al

9 A 8 g >l

r!b >

; :v r s> l

Pl

9 P 8 g >l

r!b >

; :v r s>

Sl

9 S 8 g >l

r!b > < b l= g S ! ; r > ; :v r s>

l

Ll

9 A 8 g >l

r!b >

; :v r s> l

Gl

9 G 8 g >l

r!b >

; :v r s>

Bl

9 B 8 g >l

r!b > < b l= g B ! ; r > ; :v r s>

l

l

Vl

9 V 8 g >l

r!b >

; :v r s>

Ab

9 A 8 g >b

r!? > < ? b= g A ! r > ; :v r s>

l

b

Al in multiplying act ð£ r l : vl0 ! s l ; vl0 $ Al Þ is included into its contents (s lt – field of A l arising in earlier times lt ), and then into its own strata {l; r; g; v; s; b; a}l $ s lt $ {vtl }: Thanks to that singular system Al is turned into many systems – plural number s lt of things {vtl } of level l, its ordinary units {Ll ; Pl ; Gl ; Sl ; Bl } $ vtl $ s l : They have old abilities of Al and new ones. Being the heirs of Al, systems {vtl } are organized by its initial order g lo , and they have their own directions and mechanisms {L; P; G; V; S; B} $ {ttl } of level increasing, and their own vague zones {l b l ;r b l ;g b l ;v b l ;s b l ;b b l } – areas of their own will, hazy horizons where initial might of their origin is increased. Systems {vtl } at first are odd units with chaotic activities {? rtl }, vague links {v vtl } $ {g ?tl }, chimerical statute g sl $g ?sl (sign ? as well as 1 means haze, vagueness, chaos). In this way, the original order g lo of initial unit vlo is turned into haze {g ?tl } $g ?sl , and level of this haze is higher than one of old order – numbers t l of units {vtl } are more than 0, these numbers belong to zone £ l which includes lo (level of origin vlo ), that is any t l includes lo. Systems {vtl } continue acts {þ rlt t } (natural history of vlo , its time of arising) in their contents {slt t }. Hence, times lt are continued in each of

Natural grammars

737

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Figure 1. Mathematical images £ a l and þ a l of hierarchical systems

them, and these multiplied times {lt} look as things {vtl } in time l. Act £ r l £ $£ rl0 of original authority vlo multiplying is turned into many acts {£ rtl } – activities of units {vtl } directed to their environment s l (fields of new level arising). Owing to many acts {£ rtl } the general uniting process þ r l!b ðþ r l!b : l s ! vl10 ! vb0 $ Ab Þ begins in s l. Act þ r l defines new dimension, it is directed to statutes g sl (of the field s l), v g l10 (of leading unit vl10 of time l), g b0 (of original system vb0 , original authority of time b). Sign 10l is number of final authority of level l and 10l is turned into 0b; 10l may be any number, it remains hazy until vb0 begins its multiplying £ r b (if this law will be acting in time b). In this way, þ r l (uniting act) turns chaos v ?tl into new order g b0 at time b – into system Ab with its own haze 1b. It is worth to mark that process r l $ {£ r l ;þ r l } turns initial singular unit into (multiplying) act, this act – into plural number (set, chaos of many odd systems), then – into act of uniting, statute, authority (system of higher level which will arrange its contents by its attributes); and time is turned by r l into many times and things. That is all Al strata are strongly connected in the level increasing process, and they ~ turn into each other. Graphical scheme of process r l are imaged by Figure 2. Acts þr l , £ l þ l r , r of hierarchical arithmetic in Figure 2 remind swaying scales: with chaos – to order – to vagueness of more high level – to new links and new haze ðl~ $ lt ! l ! b ! 1Þ. ~ ~ ~ þ l~ r Þ units {vtl } (including vl1 ,vl2 ) have all marks of hierarchical systems – ~ l~ l~ ~ contents {st }ðl ! lÞ, aims {bt }, and other; {vtl } are multiplied by their own acts ~ ~ £ l~ { rt } in their field sl ; they suggest {v g tl } for exchange; in this exchange their general ~ ~ uniting act þ r l is defined; þ r l must construct statute g l0 of origin vl0 of level l (in s l l l~ l~ the unit v0 looks as v10 – leading unit of levels lt (none of ordinary units {vt } may be ~ ~ equal to vl10 ); vl0 in the still þ r l of Figure 2 are vague (it belongs to hazy zone ~ þ l r $ {vl0 ;£ r l ; . . .}Þ; since that all lower strata are organized by statute g l0 – by its ~ ~ signals {g l =vtl }; these signals attract distinguished systems {vtl } to mainstream g l0 l ~ of time l and send the others wide of g 0 ; it is hidden authority, sway of statute g l0 in

Natural grammars

739

Figure 2. Mathematical mechanism of hierarchical systems changing ðl~ $ lt Þ ~

~

field s l of levels lt (final stage of design technology in times lt); £ r l ) final sway vl10 of times lt and original authority vl0 of time l are acting, and their multiplying act £ r l begins; its origin vl0 is known and its aim s l is hazy, it belongs to £ b l $ {s l ;£ r l ; . . .};£ r l $?£ r l : ~ ~ ~ ~ . leading unit vl10 is connected with {vtl } and links {vl10 ; vtl } acquire abilities of ~ ~ ~ leading unit vl10 and own directions {vtl } of their improving; system vl10 is not ~ included in {vtl }, it only holds them in its order; it is tutor authority (teaching technology); and

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.

signals vl0 of new strata l are able to penetrate all lower strata {lt } and to sway them within all their systems, in this number within the smallest of them (it is included in all lower strata as their earlier time); it is total authority (learned ~ technology); learned units {vtl } may be turned into ordinary systems {vtl } of þ l! b ) act is imaged in Figure 2 by the still where it is hazy higher level l; r (belong to þ b l $ {þ r l ; g b0 ; . . .}Þ; units {vtl } are known; their uniting act þ l r $r ?l is vague; {vtl } have odd contacts {v g tl } in their field s l; here their sway is a united set of many odd images {v g tl } with marks of their own level and lower levels (old strata, history, archives); it is chimerical authority (initial stage of design technology þ r l at level l; þ r l must design new times b). ~

The stills {þ r l ;£ r l ;þ r l } of level increasing process r l connect hierarchical mathematics Al with new tasks of cybernetics, i.e. design ðþ r l Þ and learning ð£ r l Þ. It is for the first time when these tasks (innovating technologies) are defined as process able (together with certain knowledge constructing) to ascend new haze (ask new questions) whose level is higher than one of old order. Initial task of cybernetics (control) acquires in schemes of Figure 2 many new states: control (sway) systems change their states with chimerical authority (in deem haze) to hidden sway, tutor and total ones. All these states have their own aims and strategies of their activities. The strategies correspond to Al strata which prove to be sway systems in certain stages of level increasing process. Similar facts (stages of level increasing process) are in Al history lt which includes physical, chemical, biological, demographical, and knowledge levels authorized by mathematics. In the light of Al they have exact connected definitions (Figure 3), where their times prove to be strata of the whole hierarchical system. Simple scheme of numbers history in mathematics allows to see Al might as authority (sway) of symbol systems. This history connects following stages: . natural numbers (origin of arithmetic and all mathematical figures) are offered within 1 – in order to define positive fractions less than 1 (members of 1, its contents); then the acts with positive real numbers and their links with natural ones are defined; . all positive real numbers are included into 0 to define negative real ones (less than 0), then the acts with real numbers and their links with natural (and integer) are defined and field of real numbers arises; . all real numbers prove to be within negative real numbers to define imaginary ones (whose squares are negative numbers); and . hypercomplex numbers arise thanks to imaginary unit multiplying, new acts and links defining by statute of general number system. Named stages increase levels of number systems. Their every original state is multiplied in its own content (in lower strata), and the higher the level the deeper this penetration. Process of level increasing changes the history, creates new times and dimensions which include all old ones and these new times are earlier than all known levels, they prove to be within the smallest known units. The multiplying process turns every initial (good ordered) system into hazy field, and new haze belongs to a higher level than old order. Then this chaos is turned into organized system of new level by uniting act.

Natural grammars

Mathematics & cybernetics

knowledge level mind strata

language, art, culture

engineering strata

men nonactive

demographic in engineering systems level

n a t u r a l

s free nature t r a t a

men, biological, chemical and physical levels

other knowledge systems

* financial system, monetary mechanisms, trade, conveyance

engineering design & science & learning

engineering for men, training, entertainment, service, medicine

demographic design & science & learning

engineering in nature bioengineering, agriculture, construction equipment, chemical industry, raw material extraction, power engineering

741

*

nature design & science & learning

image (statute) of knowledge systems

other knowledge Zone of knowledge systems systems connecting (Polilingual field of innovations exchange)

Notes: * - strata of State sway (legislative, executive, and justice systems). Hierarchical statute of knowledge system is scheme of (active) data base which contains and connects all known directions of knowledge - or images of known and arising systems of all strata - physical, chemical, biological, demographical, and knowledge (including engineering and mind activity). Strata images include their natural history (all strata below them), own one, and history of their renovating. Renovating history is marked by ranges of their own systems. Active systems are attracted by higher levels to mainstream (included in sway activity), the others are sending wide of sway ranges. Now the mainstream is zone of knowledge systems connecting. It is polylingual field. Individual languages cannot be sway systems in this field since they belong to one level. Their authority must be the system of new level, it is mathematics & cybernetics whose means are general for all strata and for all knowledge systems. These means can sway mind activity - to answer questions and to ask new questions from the level higher than old knowledge. The data base allows to order texts of names, questions and answers

Natural numbers are multiplied within 1 as system with good defined acts (þ) and ( £ ); it leads to positive real numbers where (þ) and ( £ ) must have signs of a higher level. At first they are vague, then process of positive real numbers uniting allows to define (þ) and ( £ ) again, to create the laws (statute) of these numbers, their theory (sway), and the like.

Figure 3. Practical cybernetics (innovating technologies) in polylingual field

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Sway systems of all levels suggest their signals in order to arrange lower levels (for instance (/), then (.) in positive real numbers (1/10, 0.1)). Functions, graphical images and other mathematical directions are described by Al more simple than numbers and number codes. Numbers in codes are the most significant in practice and the nearest to hierarchical systems. In them 11 þ · · · þ 110 ! 1001 þ · · · þ 10010 ! 101 ; 1=0:1 ! 10: Since, that they were beyond (one-level) mathematical theories and have their exact definition only in Al (as well as changeable graphic images). Natural grammars do not have all signs required in exact images of hierarchical systems. However, they allow the organisation of text changing in agreement with process of knowledge level increasing – when questions (hazy zones of mind) are turned into answers or orders (certain areas) and back, and members of texts (units, acts and other) are converted one into another as text is changes. Al and all its strata have their names in natural languages, and these names are similar to grammatical members of text. Any name may have many states, since it must be changed in process of text changing, and the sets of strata names are connected by their contents. Al strata are: L, l – level (hierarchical number, time and space sign, range, strata . . .); P, r – act (process, technology, changing, . . .); G, g – statute (connection, law, characteristic, measure, . . .); V, v – singular system (thing, state, unit, detail, . . .); S, s – many systems (plural number, field, construction, contents, . . .); B, b – hierarchical haze (vagueness, chaos, question, aim, task, . . .), new (arising) strata; A, a – authority (symbol system, sway, . . .); Al original system of level l, Ab – new authority of level l, origin of higher level b. Al as a whole system has its own name – aed. Ahd is ancient Hellenic word, and it denotes the author of symbol images of hierarchical systems – in old times and in arising ones (it is the profession of Homerus). Now in many languages its heirs look as [0 wedz], [0 vedi], [0 wit], [a0 jat], [0 odin] and the like, and all these meanings are connected with knowledge. Here it means – authority, hierarchical mathematics, knowledge measure, symbol of hierarchical multilevel systems. Being the measure of knowledge, aed is similar to 10n or e t in its ability to be a member of mathematical acts as the measuring unit; unlike 10n and e t, it images not only units or processes but also laws and mechanisms of their changing. Al strata have also sets of signs beyond grammars: level may be signed by numbers in their (graphical) codes, r – by arrows ( ! , " ), or by (þ £ /, . . .), g – by united arrows ( $ ), v – by figures 1 or 10, s – by {. . .}, A – by 0 (as marks of origin), b – by (. . .) and the like. Al strata are changing marks, and their whole field may be changed too – new marks can arise in Al contents, and old ones can wane. 3. Cybernetics tasks in hierarchical mathematics Cybernetics tasks (design and learning, innovating) are defined in Al as acts þ r l (design) and £ r l (learning) (Figures 1 and 2). The mights of r l $ {£ r l ;þ r l } (r l – general innovating process, l – hierarchical number which include history lt and new times b (hazy zones of l)) are beyond the aims of known design and learning systems. These odd systems must (by their own strategies) turn a vagueness of mind into good ordered knowledge – in answer to the questions. Act r l must do it, and r l must raise new haze (ask new questions) whose level is higher than one of old order. These joint

tasks look too new and hard. But in fact r l is more simple and natural than its earlier state with odd strategies. Now design and learning technologies prove to be connected, and they activate each other. The turn {þ r lt ;£ r l ;þ r l ;£ r b ; . . .} changes hierarchical scheme in the following way: chaos of lt ! order of l0 ! haze of l ! new order and vagueness of b ! 1. It is similar to swaying scales (whose symbol is sign 1) and may be accounted as hierarchical mechanics which links and orders the process of higher and lower levels. Mechanics of hierarchical systems works with their geometry and allows to define the new dimensions arising; the stratification of their contents (selection of attracting and sending zones within these dimensions); their spin, twist, charge, and ascendancy able to sway them; the ability of graphical images to be renovated by any of their detail (after this detail connecting with the other ones, or owing to the whole image multiplying in its contents), and many other facts which have direct inclusion in £ a l andþ a l . Scheme þ a l changing may be also accounted as hierarchical arithmetic – arithmetic were all members (including acts and laws) have marks of level, hazy zones (new times), history (archives strata, active memory, old times turned into things in contents), and all other signs of Al. This arithmetic is inalienable with hierarchical schemes – as well as its earlier practical state with number codes and notes of acts. It is easy to see that images in Figures 1 and 2 are similar to habitual notes of arithmetical acts in schools. But the new schemes are more rich. Among all Al signs they have zones of numbers contacts. At first these zones are vague; then links of acting numbers and new numbers arise in them; chaos wanes in these areas, and new haze ascends where higher strata will grow. All known arithmetical processors are strongly connected with paper notes of acts in number codes, and it allows to carry out all known mathematical tasks. Besides, notes of acts (þ , £ ) in habitual codes contain laws of polynomial and matrix algebra. Now it is proved exactly since number codes (and changeable graphic images) have mathematical definition by Al means. Till Al they were practical methods without exact statute – hierarchical gist of these methods is beyond onelevel theories. Al image þ a l is graphical scheme of aed-processor – technical means of cybernetics, cohered with its main tasks. It meets the requirements in technical documentation. They were in the list of its aims together with the following ones: . ability to define the known symbol systems (among them mathematics and cybernetics directions – both theories and practical methods which cannot be described by existent theories) and to link their definitions in one symbol system of higher level; . coherence with earlier history of hierarchical systems and with practical cybernetics (innovating technologies) in known strata constructed by this history. Practical cybernetics works with the field of its arising development – with its archives, history of Al. History a lt of Al is defined by aed means in Figure 3. Now its times are strata (physical, chemical, biological, demographical, and knowledge) authorised by mathematics. Figure 3 is a fragment of the whole hierarchical system. It describes one knowledge system and zone of its interactions with the other units of its stratum. This zone is the mainstream where new authority arises. Suggested description is the general statute of knowledge systems. They may be organized as nations with their own States (State sway, i.e. legislative, executive, and justice

Natural grammars

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systems, belongs to knowledge level) or without them – when sway is national language and culture. Knowledge level has engineering strata which include industry and means of its ordering – conveyance, trade, financial systems and other. The main means of engineering strata improving are design and science and learning strata. They have direct contacts with all lower levels (physical, chemical, biological, demographical, and engineering) and send them all mights of theoretical cybernetics r l – in agreement with Al laws. Concrete strata acquire these mights and define applied directions of innovating technologies. Figure 3 is now the only graphical scheme which connects all practical stages of innovating technologies including life cycles of new systems (applied design, making, test, conveyance, sale, work, service, utilization, renovation, staff training, financial and juridical maintenance, applied scientific investigations of systems (united by design strategies and multiplied by other stages of life cycle – making, conveyance, sale)). In fact, Figure 3 is navigator in innovating technologies. It sets level of creating (or learning) a system, its history, contents (lower levels details and their links), its environments (systems of its own stratum), its holding systems (higher strata), its activity and aims in all known and arising systems. Strata images in Figure 3 contain their natural history (time of their arising, i.e. all strata below them, which are included in their contents) and history of their renovating by higher strata – which lie above them. Renovating history is signed in strata images by ranges of their own systems. When new level arises, it stratifies lower ones – attracts their active systems to mainstream (in Figure 3 – to the right) and sends the others to zones wide of its sway. For instance, demographical level contains strata of its natural history (physical, chemical, and biological) and ranges of systems active in engineering and financial layers, in art, science, design, and other directions of creative work. These ranges belong to renovating times (to sway layers). Knowledge systems in Figure 3 are linked by their active zones which contact with mainstream and at the same time lie within these systems as their internal connections. It is one of the merits of hierarchical schemes which allow to image graphically the facts irresistible for known geometry (where areas may be connected only by their boundaries). Another merit is easiness of knowledge organisation in these schemes. In known library codes the new directions of science prove to be far away from the ones close to them by sense. For instance, biophysics cannot have number which connects physics and biology, while in Figure 3 this number will always be found. It is convenient in data bases. Moreover, Figure 3 is just the scheme of data base which contains and connects all known directions of knowledge – or images of all known and creating systems with history of these systems, their contents, activity, environment, holding systems, aims, and means of innovating technologies with these images. 4. Hierarchical system of natural grammars Natural (national) languages belong to knowledge level nðn $ l 2 1Þ. In agreement with statute þ a n of knowledge level (Figure 3) they are hierarchical systems {vtn } ~ which have their history lt ! n ! l contents {stn~} (lower levels systems {vtl } and þ their links {g tn~}), environment sn (other systems of their level), activities { r n~;£ r n~} in known (lt) and new (n,l) strata, authorities (their own sway systems (grammars) {atn } and general authority al0 $ vl0 – higher strata), and aims {btn } in all strata.

History lt ! n ! l of languages has three stages: natural lt ! n (time of arising), own n ! l (time of authority) and renovating l ! b (new time, it begins). Natural history of languages (times lt of knowledge level arising) in statute þ a n (Figure 3) is turned into strata of languages contents: demographical nd $ n 2 1, biological nb $ n 2 2, chemical nch $ n 2 3, and physical nph $ n 2 4. Own history n $ {£ n,þ n} is the time when knowledge level was the actual sway of hierarchical systems – £ n is time of multiplying and þ n is time of uniting. These times are turned into engineering strata £ a n and strata of mind activityþ a n . {£ atn } are sway systems directed to lower levels lt which are renovated by {£ atn }. {þ atn } are way of languages to new times. £ a n and þ a n are connected by r n. In time þ n the knowledge systems {vtn } (multiplied in £ n) interact in their field s n. Their links {a g tn } $ g sn are in all known strata. However, the most significant is exchange of knowledge – links {a g sn } of engineering {£ atn } and mind {þ atn } strata. This exchange is realised in polylingual fields s n where systems {vtn } send their knowledge (innovations, ways of thinking and other) and attract alien ones. Process þ r n!l of all strata connecting unites s n and leads to new time l ðþ r n!l : s n ! vl0 ; to new authority vl0 $ al0 $ {þ a l ;£ a l }Þ. Renovating history l ! b begins when al0 (in its multiplying £ r l ) starts to send all its mights to lower strata {lt,n}. Authority al0 $ vl0 of knowledge level is mathematics (which must define all strata {a,g,r,v,s,b,a} of hierarchical systems (including their history lt ! l and mechanism r l!b of new time arising – cybernetics technologies, mind activity). Till now mathematics was the chimerical system b a l $ {10 atn }; {10 atn } – odd theories and practical methods suggested by leading units {10 vtn } of level n; sign 10n is number of final authority vn10 of level (; when this number is in hazy zone b, it means that unit 10 vtn intends to vn10 . Chimerical authority has many untied signs of lower strata. However, it changes all known strata and other knowledge levels. Natural languages which suggest mathematical methods and theories {10 atn } are attracted to mainstream g sn of the whole hierarchical system – to new time l. Symbol systems 10 atn and new ways of thinking 10 rtn (mind activity when the chaos b nof knowledge (questions area) is turned into answers or orders v g n , g sn , and new haze b l ascends beyond old horizons b nof thoughts) are included in sway ranges b a l of arising authority al0 . Owing to that the ancient languages – as authors of mathematical means – are the most active systems of new times. Old languages, being turned into general symbol systems, connect polylingual field s l and are included in other languages (by multiplying act 10£ r n ) as their sway strata. While chimerical authority b a l does not define general scheme al0 and laws g l0 of mind activity r l in whole hierarchical system, the individual languages {vtn } continue working by their own means. In order to exchange their knowledge, the units {vtn } describe their works by one language 10 vtn – leading on the certain time t. It is long practice (with small number of leading languages). Since, all languages {vtn } (and leading ones) are ordinary systems of time n, none of them can be acting sway {vn10 } (in their field s n) able to increase their level with n to l and to b. All languages contain more or less rich knowledge about all strata described in Figure 3. And their knowledge is imaged by texts – changeable symbols of systems. These symbols may be short (one lexical unit – word) or long (when they define all hierarchical signs (Al strata) of systems and stages of their changing). They may be

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hazy or certain, and may be changed with questions to answers or orders and back. There are texts within languages whose level is equal to one of the whole language – since these texts are images-statutes of their languages. These images are natural grammars – sway systems {a0t } of national languages {vtn }. In fact, natural grammars belong to mathematics and cybernetics – as practical methods with the highest significance in mind activity – together with graphical images processing, number codes (first mathematical symbols of hierarchical systems), and notes of laws as functions. Owing to mathematical gist of grammars they are the links (direct contacts) of national languages with general authority of knowledge. And this authority has ascendancy to change level of hierarchical systems. The increase of the level of grammars means the increase of the level of their languages. Mathematical means {þ a l , £ a l } allow it to be done. Suggested above mathematical investigation of languages contents (knowledge strata in Figure 3 – connected images of all known and arising systems), their history, field of exchange, attraction to authority, and other signs of their hierarchical nature was carried out with the named aim. Linguistics distinguishes three main states of natural grammars – root grammars, analytic and synthetic ones, and four states of texts (sentences) – interrogative (questions), narrative, exclamatory, and imperative (answers and orders). Any state of grammars has its own means to order lexical units in texts and to change the texts with questions to answers or orders and back. Root grammars g atn $ g tn : (The instances – Chinese, Vietnamese,. . .). Root grammars (hidden authority) are oriented on syntax g tn – sway of statute. Grammars {g atn } have lexical units {vnt =2 } for making concrete knowledge (members of contents of knowledge statute in Figure 3) and syntax {g tn } – laws of order of lexical units in texts {vnt =1 }. This order defines the state of text – hazy {b vnt =1 } (questions) or certain: {s vnt =1 } (answers) and {v vnt =1 } (orders), and only it assigns the marks of hierarchical strata (thing (v), act (r), characteristic (g), time (l, t) and other). Since, all grammars contain root grammars, the instances of their work may be made in English: two lexical units “symbol” and “system” change their strata signs when their order in text is changed – “symbol system” or “system symbol.” In the first case, “system” is thing and “symbol” is characteristic, then their signs are turned into one another. Sway of root grammars is hidden in text, it is the way (dao) of thinking process. Level of any text in these grammars is always lower than one of grammars. Analytic grammars 10 atn $ vn10t (English, French, German, Hindi, . . .). Analytic grammars (tutor authority) have key texts vn10;t – distinguished lexical n=1 n=1 n=1 units {v10t } (in English {v10t } $ {a, the, to, do, is, have, . . .}) and laws g 10t of their changing and ordering in agreement with mind activity. Hierarchical strata signs are n=1 marked by units {v10t } (in English – “a” for hazy thing, “the” – for certain one, “to” for acts, “was” for earlier times, “will” for arising times, and the like). In mind activity n=1 (when acts are turned into units, and units – into other strata) members {vt10 } of key n=1 text are changed. Texts {vt } in analytic grammars are organized by key text and are tied with concrete systems (with knowledge statute in Figure 3) by lexical symbols (names) of these systems – physical, chemical and other. Sway system (key text) has dual gist in 10 atn languages. It is both – ordinary text (with habitual letters in contents) and image of higher authority. This system is the

only capable to connect symbols of chemical or demographical systems (lower levels) with higher strata (laws of thought changing). It takes into account the concrete state of knowledge (its address in Figure 3) but it holds all texts and changes them in agreement mainly with its will. The tutor authority is the actual leading unit. Synthetic grammars l0 atn $ l0 vtn (Belarusan, Finish, Japanese, certain ancient languages – Khemian, Hellenic, . . .) Synthetic grammars (total authority in time n – chimerical one in time l) turn key texts into system of sway signals {l0 vnt 21 } – the shortest lexical units with laws {l0 g tn } of their activities. The signals {l0 vtn } are included in symbols of concrete systems, possibly – in their means. This including causes the waves of letter changes (phonetic changes) in systems symbols which have hazy zones in their contents, and thanks to that they are able to include sway signals and to be changed by them. It allows to turn long text into one lexical unit – into symbol of this text. This symbol contains and connects both concrete knowledge (name, hierarchical number (address) of concrete system in knowledge statute in Figure 3) and thinking process. In this way the level of text increases (from stn to l0 vtn ) owing to the inclusion of sway signals in its contents by sway system multiplying. Growth of level leads to texts abridging as it must be in the process of symbols arising. Synthetic grammars contain all means of root and analytic grammars, but they prefer their own state which, in practice, is free from syntax. It means that total authority in them may be turned in chimerical one (on a higher level). In that case any unit of text can regard itself as higher sway, and it may lead to its chaotic activity. Since, English was synthetic (and keeps certain lines of this state) it allows to bring instance: characteristic “chimerical” includes three sway signals: “er” “ic” and “al.” They all signify the membership – they are signs of adjective (characteristic, range of sway, the distance from mainstream). Two of them (“er” and “ic”) are included in the means of lexical unit, and their including causes the waves of letters (and phonetic) changes. Its origin is Khemi (Chemy) – name of ancient Egypt. “Chimera” is sphinx – system which has odd features of men and animals (systems of higher and lower strata together); sound changes are [0 kemi] – [kai0 mi@r@] – [kai0 merik@l]. It is easy to see the following. . In order to describe the main states of grammars and texts the marks of hierarchical systems were attracted – since own means of grammars do not allow it to be done. (As well as own means of number codes, graphical images and other mathematical directions do not allow to define their own statutes and natural grammars.) . Suggested description of natural grammars corresponds exactly both to mathematical images of cybernetics process in Figure 2 (the stills in Figure 2 were selected in the whole images of level increasing process r l just to define natural grammars) and to knowledge statute in Figure 3 (Figure 2 is included in Figure 3 with name “mathematics & cybernetics” above all strata). . Individual characteristics of natural grammars are strongly connected with ones of national minds. Mathematical investigations of natural grammars give a chance to understand general lines of diverse nations and to improve the process of their connecting – including innovations exchange in polylingual fields.

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Al schemes are much more rich than natural grammars. All strata {a,g,r,v,s,b,a} of Al may have all other ones as their signs in their contents. For instance, a thing or laws may have sign of time (earlier, current and arising) while in natural grammars this sign is connected habitually with acts. The definition of innovating technologies in Al contains all known ways of thinking in natural grammars and connects them. Hence, mathematics can suggest exact images of cybernetics (innovating technologies) to any language without a danger to limit its abilities. Moreover, when mathematical schemes of these technologies will be included in natural languages it can increase the mights of languages and their abilities for all other minds understanding. Beside that, the including Al means in knowledge systems brings connected definitions of theories and practical methods of mathematics and cybernetics to these systems.

5. Conclusion Hierarchical mathematics Al allows the definition of the all strata of its natural history – physical, chemical, biological, demographical, and knowledge (with engineering directions and mind activity in symbol systems). Their definitions are connected in general scheme of knowledge authorized by mathematics (which includes cybernetics means – innovating technologies). These means correspond to mind activity when hazy zones (questions) are turned into certain areas (answers or orders) and then – into new vagueness with wider horizons of thought. A hierarchical scheme of knowledge strata (active data base) with a cybernetic processor of its changing (in agreement with innovating (design and learning) technologies) is suggested in the paper as a means able to improve the known practice of innovations exchange in polylingual fields. Natural languages in the light of the suggested scheme are hierarchical systems which have all strata of knowledge (physical, chemical and other) and their own means of mind activity (and text) organizing in these strata – natural grammars. Natural grammars are defined by hierarchical mathematics as sway systems of their languages, and these sway systems are linked as stages of mind activity in innovating process. Owing to that the connecting of natural languages in innovations exchange may be simplified. References Mesarovic, M.D. and Takahara, Y. (1975), General Systems Theory: Mathematical Foundations, Academic Press, New York, NY. Mesarovic, M.D., Macko, D. and Takahara, Y. (1970), Theory of Hierarchical Multilevel Systems, Academic Press, New York, NY. Novikava, S., et al., (1998), “Hierarchical mathematics: theory of sway”, Preprints of 8th IFAC/IFIP Symposium on Large Scale Systems, Patras, Greece, Vol. 2, pp. 480-6. Corresponding author Kanstantsin Miatliuk can be contacted at: [email protected]

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Covering properties in intuitionistic fuzzy topological spaces Francisco Gallego Lupia´n˜ez

Intuitionistic fuzzy topological spaces 749

Department of Mathematics, University Complutense, Madrid, Spain Abstract Purpose – D.C¸oker constructed the fundamental theory of intuitionistic fuzzy topological spaces. The purpose of this paper is to introduce a new concept of compactness and a definition of paracompactness for intuitionistic fuzzy topological spaces, and obtain several preservation properties. Design/methodology/approach – Two new covering properties in intuitionistic fuzzy topological spaces are defined and studied. Findings – Relations on these new properties and covering properties on fuzzy topology in the Chang’s sense are obtained. Research/limitations/implications – Clearly, this paper is devoted to intuitionistic fuzzy topological spaces. Practical implications – The main applications are in the mathematical field. Originality/value – The paper shows original results on fuzzy topology. Keywords Cybernetics, Mathematics, Topology, Fuzzy logic Paper type Research paper

Introduction The introduction of “intuitionistic fuzzy sets” is due to Atanassov (1983), and this theory has been developed in many papers (Atanassov, 1986, 1988, 1999). In particular, C¸oker and co-workers have constructed the basic concepts of the intuitionistic fuzzy topological spaces, specially fuzzy compactness and fuzzy connectedness, and have obtained many results on it (C¸oker, 1996, 1997; C¸oker and Demirci, 1995; C¸oker and Es¸ 1995; Es¸ and C¸oker, 1996, 1997). Finally, Lee and Lee (2000) showed that the category of fuzzy topological spaces in the sense of Chang is a bireflective full subcategory of that of intuitionistic fuzzy topological spaces, and Wang and He (2000) showed that every intuitionistic fuzzy set may be regarded as an L-fuzzy set for some appropriate lattice L. In this paper, we define a new concept of compactness for intuitionistic fuzzy topological spaces and the paracompactness for these spaces. Fundamental concepts The fundamental concept of cover is due to C¸oker: Definition 1. (C¸oker, 1997) Let (X, t) be an IFTS. If a family G ¼ {kx; mGj ; gGj ljj [ J } of IFOSs in X satisfies the condition: The author thanks Professor D. C¸oker (now sadly deceased) and to Professor S.J. Lee for making available their papers to him.

Kybernetes Vol. 36 No. 5/6, 2007 pp. 749-753 q Emerald Group Publishing Limited 0368-492X DOI 10.1108/03684920710749811

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> j[J 0 < V > qA þ cr $ f 21 ðguj Þ > > j[J 0 : and this implies that: 8 > >
> : j[J 0

and: f ðAÞ 2 r # kx; mGj ; gGj l ¼ 0, for all j [ J in the complement of a finite subset of J.

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Definition 7. If (X, t) is an IFTS and A is an IFS of X, we will say that A is paracompact if for each fuzzy open cover U ¼ {kx; mGj ; mGj kjj [ J } of A and for each r [ (0, 1], there exists a refinement of u which is locally finite in A and a fuzzy open cover of A 2 r. We will say that X is paracompact if 1, is a paracompact IFS. Remark. An strong intuitionistic compact IFTS is a paracompact IFTS. Note. There is no problem with these concept and the result of Wang and He, because here we used 1-neighbourhoods (Lupian˜ez, 2006). Proposition 4. If (X, t) is a paracompact IFTS, then c1 is a *-paracompact fuzzy set of (X, t1). Proof. The definition of *-paracompact fuzzy set is in (Abd El-Monsef et al., 1992). Let U* ¼ {mGj }j [ J be a family of open fuzzy sets such that: _ c1 # mGj : j[J

Then U* ¼ {kx; mGj ; 1 2 mGj lj j [ J } is a fuzzy open cover of 1, ¼ kx; c1 ; 1 2 c1 l and, by the hypothesis, for each r [ (0, 1] there exists a refinement V* ¼ {kx; y s ; hs ljs [ S} of U* which is locally finite in 1, and a fuzzy open cover of 1, 2 r. Thus, V ¼ {vs js [ S} is an open refinement of U, which covers c1 2 r ¼ c1 2 r and is *-locally finite in c1. Indeed, suppose that there is some fuzzy point e ¼ zl such that zl # c1 and, for every fuzzy open set m which is quasi-coincident with e, we have m ^ vs – 0 for infinitely many s [ S. Now consider the IFP z(a b), where a ¼ 1 2 l, b ¼ l. Hence, there exists an 1-neighbourhood kx; m * ; g * l [ t of z(a b) with akm* ðzÞ; blg* ðzÞ and kx; m * ; g * l > kx; y s ; hs l ¼ 0, for all s [ S in the complement of a finite subset of S. Since, m * ðzÞ þ l . 1 2 l þ l ¼ 1; m* is a fuzzy open set in t 1 which is quasi-coincident with e and m* ^ ys – 0 for infinitely many s [ S. In this case A kx; m * ; g * l > kx; y s ; hs l – 0 ~for infinitely many s [ S, which is a contradiction. Proposition 5. Let (X, t0) be a fuzzy topological space in the sense of Lowen and t ¼ {kx; mA ; 1 2 mA ljA [ t0 } the associate IFT on X. If c1 is a *-paracompact fuzzy set of (X, t0) then (X, t) is a paracompact IFTS. Proof. Let U ¼ {kx; mj ; 1 2 mj lj j [ J } be a fuzzy open cover of 1, , then: _ c1 # mj ; j[J

and by the hypothesis, for each r [ (0, 1] there exists an open fuzzy refinement {vs js [ S} of {mj jj [ J } which is *-locally finite in c1 and: _ c1 2 r # v s : s[S

Thus, V ¼ {kx; vs ; 1 2 vs ljs [ S} is a family of IFOSs in X, which refines U, covers c~1 2 r ¼ 1~ 2 r; and is locally finite in 1, , indeed. If there is some IFP p ¼ z(a b) such that for every 1-neighbourhood kx; m; 1 2 ml [ t of p, we have kx; m; 1 2 ml > kx; vs ; 1 2 vs l – 0, for infinitely many s [ S, then a þ b # 1, a , m(z) and b . 1 2 m(z). Then there exists a fuzzy point zb # c1, and we have that for every fuzzy open set m * such that m * is quasi-coincident with zb, i.e. m *(z) þ b . 1, thus m *(z) . 1 2 b $ a and 1 2 m *(z) , b kx; m * ; 1 2 m * l [ t and

it is an 1-neighbourhood of p. Thus, kx; m * ; 1 2 m * l > kx; vs ; 1 2 vs l – 0 ~ for infinitely many s [ S and this implies that m * ^ vs – 0, for infinitely many s [ S which is contradictory. A References Abd El-Monsef, M.E., Zeyada, F.M., El-Deeb, S.N. and Hanafy, I.M. (1992), “Good extensions of paracompactness”, Math. Japon., Vol. 37, pp. 195-200. Atanassov, K.T. (1983), “Intuitionistic fuzzy sets”, paper presented at VII ITKR’s Session, Sofia (June 1983). Atanassov, K.T. (1986), “Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, Vol. 20, pp. 87-96. Atanassov, K.T. (1988), “Review and new results on intuitionistic fuzzy sets”, preprint IM-MFAIS-1-88, Sofia. Atanassov, K.T. (1999), Intuitionistic Fuzzy Sets, Theory and Applications, Springer-Verlag, New York, NY. C¸oker, D. (1996), “An introduction to fuzzy subspaces in intuitionistic fuzzy topological spaces”, J. Fuzzy Math., Vol. 4, pp. 749-64. C¸oker, D. (1997), “An introduction to intuitionistic fuzzy topological spaces”, Fuzzy Sets and Systems, Vol. 88, pp. 81-9. C¸oker, D. and Demirci, M. (1995), “On intuitionistic fuzzy points”, Notes IFS, Vol. 1 No. 2, pp. 79-84. C¸oker, D. and Es¸, A.H. (1995), “On fuzzy compactness in intuitionistic fuzzy topological spaces”, J. Fuzzy Math., Vol. 3, pp. 899-909. Es¸, A.H. and C¸oker, D. (1996), “More on fuzzy compactness in intuitionistic fuzzy topological spaces”, Notes IFS, Vol. 2 No. 1, pp. 4-10. Es¸, A.H. and C¸oker, D. (1997), “On several types of degree of fuzzy compactness”, Fuzzy Sets and Systems., Vol. 87, pp. 349-59. Lee, S.J. and Lee, E.P. (2000), “The category of intuitionistic fuzzy topological spaces”, Bull. Korean Math. Soc., Vol. 37, pp. 63-76. Lowen, R. (1976), “Fuzzy topological spaces and fuzzy compactness”, J. Math. Anal. Appl., Vol. 56, pp. 621-33. Lupian˜ez, F.G. (2006), “On intuitionistic fuzzy topological spaces”, Kybernetes, Vol. 35, pp. 743-7. Wang, G-J. and He, Y.Y. (2000), “Intuitionistic fuzzy sets and L-fuzzy sets”, Fuzzy Sets and Systems, Vol. 110, pp. 271-4. Corresponding author Francisco Gallego Lupia´n˜ez can be contacted at: [email protected]

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Intuitionistic fuzzy topological spaces 753

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A new look at the Heisenberg’s uncertainty principle A cybernetics and general dynamical systems approach Dwijesh K. Dutta Majumder Computer Communication Science Divisions, Indian Statistical Institute, Kolkata, India and Institute of Cybernetic Systems and Information Technology, Kolkata, India, and

Swapan K. Dutta Institute of Cybernetic Systems and Information Technology, Kolkata, India Abstract Purpose – To develop a mathematical and algorithmic approach of avoiding the limitations of deterministically computing the values of energy, time, position and momentum imposed by Heisenberg’s uncertainity principle (HUP) which is of profound significance from the point of view of some emerging science and technology like quantum computing, nano scale technology and chaotic dynamical systems. Design/methodology/approach – A parametric method of establishing deterministic solutions for energy and momentum on the basis of quantized energy limits (instead of HUP) if developed in the non-infinite non-zero quantized energy limits where hidden deterministic solutions can be obtained for micro/nano structures. Findings – The philosophical foundations of quantum mechanics as developed by Max Planck, Neils Bohrz, Werner Heisenburg, Dirac and Edwein Schrodinger is based on a duality concept of complimentarity notions. In most general logical sense for any physical reality qualitative dualism have to have a quantitative dualism may be hidden or virtual. The upper and lower limits of the dynamical quantum mechanical observables are determined based on the dimensional considerations for the physical constants H, C, G and H0. The conceptual basis and mathematical framework of the paper in based Norbert Wiener’s work on theory of cybernetics and D. Dutta Majumdars’ unified cybernetic and general dynamical systems theory. Research limitations/implications – The testability of the theory needs to be established. Originality/value – Without challenging HUP this is a contribution of tremendous practical implications. Keywords Cybernetics, Uncertainity management, Nanotechnology, Systems theory Paper type Research paper

1. Introduction Heisenberg’s uncertainity principle (HUP), a fundamental concept of quantum physics, indicates to ability of an experimenter or that control system (automation) to measure Kybernetes Vol. 36 No. 5/6, 2007 pp. 754-767 q Emerald Group Publishing Limited 0368-492X DOI 10.1108/03684920710749820

The authors wish to acknowledge with thanks the help and cooperation received from their colleagues at Indian Statistical Institute (ISI) and Institute of Cybernetics Systems and Information Technology (ICSIT), Kolkata – 700 108. Particularly Tapan Adhikary, Madhurima De, Amitava Chanda, S Dutta Majumder and Amrita Ghosh of ICSIT in preparing the manuscript.

an elementary particle’s position to the highest degree of accuracy, leading to an increasing uncertainity in being able to measure the particle’s momentum to an equally high degree of accuracy. This implies that the uncertainity in the value of the energy is significant in extremely small time elements. HUP is mathematically expressed in any of the following forms: DE · Dt $

h ; 4p

Dx · Dp $

h 4p

ð1Þ

The uncertainties in energy, time, position and momentum are DE, Dt, Dx and Dp and h is Planck’s constant (where (h/4p) ¼ 0.527 £ 102 34 Joule-second). This energy uncertainity in extremely small amount of time is of profound significance from the point of view of several emerging science and technology, such as chaotic dynamical systems (Barone et al., 1993; Raymer, 1994; Hall and Regina Ho, 2002), nano science and technology (Raymer, 1994; Drexier, 1992; Koller and Athas, 1992; Technical Proceedings, 2003), and quantum composing (Collins, 2006) among others. It is stated that in classically chaotic systems, irreducible uncertainties required by the Heisenberg’s principle are amplified exponentially some time to macroscopic level in very short times (Barone et al., 1993). In this situation the behavior of the system is unpredictable in the sense that it is not practical to include all perturbations, which have a significant effect on the behavior of the system. This apart from other things brings the uncertainity principle into the realm of classical mechanics. We may also remember that HUP involved the perturbation to a particles’ state by a measurement of one variable, which affects one’s ability to predict the outcome of a subsequent measurement of the conjugate variable, which is not just some form of measurement error but concerns physical variables intrinsic to a particle’s state. For example, at a precise time, t, the energy of an electron is not determinable to a precision greater that (h/4p) because the energy of the electron physically varies by this amount within a Planck like time parameter. This means electrons’ energy fluctuates in this narrow range – which might suggest a violation of the conservation of energy. To avoid these and several other limitations of indeterminacy relations, we use the frame work by Dutta Majumder (Dutta Majumdar, 1979; Dutta Majumdar and Majumdar, 2004a, b; Dutta Majumder and Bhattacharya, 2000) in which observer, observed, and act of observing are combined in a unified general dynamical systems framework consisting of machines, human being and relevant environment, with the legitimate assumption that these observations and interactions are cybernetic process which is an extension of the formalism enunciated by Norbert Weiner in his celebrated work in 1944 (Heisenberg, 1930). In this framework we develop a computationally realizable deterministic solution to quantum measurement problems in the non-infinite non-zero quantized energy as in Dutta (1995). 1.1 Perspective A problem of fundamental importance in nature, man, society and machines in developing a general dynamical theory of physical systems and also that of cybernetic systems are the unifying concept of state space and system causality (Dutta Majumdar, 1979; Dutta Majumdar and Majumdar, 2004a). In an n-dimensional state space there are n independent attributes and may be denoted by Xn. The time evolution law is a continuous function f: Xn £ T(Xn, where T is the space of time. A dynamical system is

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formally denoted by (Xn, f ) or just by f, when there is no confusion about the state space Xn. To determine any physical dynamical system (Xn, f ) it is essential to be able to measure each input state and each output state. In other words, we must be able to measure each point in the state space Xn. The time evolution law is a continuous function Dutta Majumdar and Majumdar (2004a): f : Xn £ T ! Xn

ð2aÞ

Here T is the space of time. A dynamical system is formally denoted by (Xn, f ) or just by f, when there is no confusion about the state space Xn. The concept of state has long played an important role in physical sciences. It was H. Poincare who attempted to give a more precise formulation to the concept of state, and subsequent works by Birkoff (1977), Kalman (1962) Markov (1931) as elaborated in Dutta Majumdar and Majumdar (2004a). To determine the system in any (Xn, f ) it is essential to be able to measure each input state and each output state. In other words, we must be able to measure each point in the state space Xn. By HUP Heisenberg (1930) (Werner Heisenberg 1930, 1949) for any dynamical system, we have as in equation (1). DxDt $

h 2p

ð2bÞ

Here Dx is the error in measuring x [ X1 (assuming the state space to be one-dimensional for simplicity), Dt is the error in measuring t, and h is Planck’s constant. The uncertainity principle, the doctrine that inspired Albert Einstein’s remark that he could not believe that God played dice with universe, was announced in 1927 (Heisenberg, 1930; Roy and Dutta Majumdar, 1996 and Roy et al., 1996). According to equation (2b) if we want to make Dx ! 0, we get Dt ! a. If we want to locate the position of point in X1 by a computer or automation it will take infinite time. So from the point of view of real-life situation of computability, algorithm city and complexity analysis (Dutta Majumdar and Majumdar, 2004a; Heisenberg, 1930; Roy and Dutta Majumdar, 1996) and also from the point of nano-science and classical physics it seemed to be the limiting case of visualization of a fundamentally unvisualisable microphysics, or micro-nanophysics. The more accurate realization attempt is made the more Planck’s constant vanishes relative to the parameters of the system. One of the authors (Dutta Majumdar, 1979) in his Norbert Wiener Award Paper formulated that: The method of special theoretical systems and empirical testing breaks down at two points. One is at the point of Heisenberg’s principle of indeterminacy, where the information that the investigator, endeavourer to extract from the system has the same order of magnitude as the system itself. Though the principle was first noted in physical systems, it is equally important in biological and social systems at different levels of observations.

This was also the cause that lead Zadeh’ (1973) principle of incompatibility uncertainty management in man-machine-nature systems in different scales of the evolving information systems (Dutta Majumdar and Majumdar, 2004a; Heisenberg, 1930; Roy and Dutta Majumdar, 1996; Roy et al., 1996; Zadeh, 1973; Pal and Dutta Majumdar, 1986). The existential truth in decision making and uncertainty minimization/elimination problem in real-life design problems in computational mathematics, information technology

components and system design, and non-numerical information processing like pattern recognition, speech/image analysis, computer vision, intelligent systems and their hardware/software implementation and in emerging micro/nano technology development is of profound implications (Dutta Majumdar et al., 2006; Pal and Bezodek, 1994; Dutta Majumder and Das, 1980; Pal and Mitra, 2001). It may be noted that all previous investigation on complexity analysis and uncertainty management for decision-making purposes in science/society and engineering (Dutta Majumdar and Majumdar, 2004a; Heisenberg, 1930; Dutta Majumdar, 1993; Pal and Dutta Majumdar, 1986) using diverse types of soft computing approaches including Fuzzy, ANN Neuro-Fuzzy, etc. (Zadeh, 1973; Pal and Dutta Majumdar, 1986; Pal and Bezodek, 1994; Dutta Majumder and Das, 1980; Pal and Mitra, 2001) or otherwise in the unitary discipline of cybernetics and general systems theory was a conceptual reality under the limitations of HUP (Dutta Majumdar, 1979). In this paper, we present a somewhat different non-conventional method of establishing a virtual or hidden, but computationally realizable deterministic solutions to quantum measurement problems in the non Infinite non zero quantized energy limits (Dutta, 1995), to avoid limitations of HUP in real life design problems in nano or nano-micro regions. In this method the Planckian wavelength is used as the lower cutoff, while the upper cutoff is calculated using Yukawa – de Broglie graviton hypothesis and some cosmological assumptions concerned with the big bang theory and Einstein’s field equation and a general equation for quantized energy (Eg) of the graviton (Roychowdhury, 1979; Dutta, 1995). Neither the new approach nor its generalization by Dutta Majumdar (1979) in his Unified theory of cybernetics and general dynamical systems is in contradiction of HUP (Heisenberg, 1930), rather, it provides a deeper understanding, interpretation and a wider implication of the issues involved in formulating a computationally realizable deterministic solutions in the quantum mechanical framework. 2. The algorithm for the non-infinite non-zero quantized energy limits of upper and lower cutoffs Max Planck in 1899 Dirac (1932) calculated his quantities lp (Planck length), tp (Planck time), Ep (Planck energy) based on the dimensional considerations of the physical constants h (Plancks’ quantum constant), c (the velocity of light in vacuum) and G (Newton’s gravitational constant). Similarly, in the present case the deterministic parameters (E; p~; x~ and t) are obscure from direct observation. It is shown here that they are (nevertheless) mathematically determinable as functions of uncertainity, E ¼ f(DE) and p ¼ f(Dp). In the measurement process, an observer gets {E ^ (DE)} and {p ^ (Dp)} as the observed values of the energy (E) and momentum ( p) of a particle. A dynamical variable in uncertainity relations after imposing the non-zero and ~ l~ and t become as in Figures 1 and 2. non-infinite quantization limits of E; P; Here h is Planck’s quantum of action; c is velocity of light; G is Newtons gravitational constant, and H0 is Hubble’s cosmological constant. All the above mentioned constants and the terms given in Figures 1 and 2, serve as the absolute limits of the micro and macro dimensional scale for an observer, in a physically perceptible universe. It needs to be mentioned that the values of E p ; tp ; pmax and lmax were calculated by Max Planck from pure dimensional

Heisenberg’s uncertainty principle 757

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758

Figure 1. Energy – time

Figure 2. Momentum – wave length

consideration of the universal constants, h, c and G (Planck, 1899; Dirac, 1932). The other values of E min ; tmax ; pmin and lmax are variables of the macro time scale ð2H 21 0 Þ and length scale ð2H 21 0 cÞ of our finite universe. H0 being the Hubble’s parameter, a time interval greater than H 21 0 ; is not dimensionally conceivable, and so a light signal cannot travel a distance greater than cH 21 0 ; which is Hubble length and is considered as the radius of the observable is considered as the diameter of the universe, and so is the universe. So 2cH 21 0 maximum wavelength ðlmax Þ that correspond to the minimum non-zero quantized energy (Emin). so: 3 lmax ¼ 2CH 21 0 7 7 tmax ¼ 2h21 ð3aÞ 7 0 5 H0 E min ¼ h 2 The expressions (3) are valid for a particular instant of time t0 when H ¼ H (t0). H0 is considered as constant for all practical quantum measurements.

2.1 The energy – time uncertainty relations The energy – time uncertainity relations, ½DEDT $ ðh=2Þ in the extreme limiting cases by relating with the Bohr’s complimentary principle (Heisenberg, 1986a, b; Born, 1986) on the basis of dimensional equivalence can be presented as follows:

Heisenberg’s uncertainty principle

ðDTÞmin ¼ tp so: ðDEÞmax

Ep ¼ 4p




h {E p ¼ tp

{ðDEÞmax ðDTÞmin ¼

759



h 4p

ð3bÞ


 h { [É ¼ tp Dividing both sides of equations (3b) byðDTÞ2min ; we get: ðDEÞmax h h 1 ¼ ¼ pffiffiffiffiffiffi  pffiffiffiffiffiffi  2 ðDTÞmin 4pðDTÞmin 4pðDTÞmin 4pðDTÞ min or: pffiffiffiffiffiffi ðDEÞmax h ðE p = 4pÞ ¼ pffiffiffiffiffiffi ¼ pffiffiffiffiffiffi ðDTÞmin ð 4ptp Þ 4ptp

ð4Þ

Similarly, by substituting: ðDEÞmin ¼ E min ¼


 hH 0 2

We get: pffiffiffiffiffiffi pffiffiffiffiffiffi 4pE min 4pðhH 0 =2Þ ðDEÞmin pffiffiffiffiffiffi ¼ pffiffiffiffiffiffi ¼ ðDTÞmax ðtmax = 4pÞ ð2H 21 0 = 4pÞ

ð5Þ

From equation (1), we can write: Ep 1=2 pffiffiffiffiffiffi ¼ {E 1=2 p ðDEÞ max } 4p

ð6Þ

Also, from equation (5), we can write: pffiffiffiffiffiffi 4pE min ¼



pffiffiffiffiffiffi 1 4pE min ðDEÞ 2

 ð7Þ

The required maximum and minimum pffiffiffiffiffiffi cut poff ffiffiffiffiffiffi limits, which were determined dimensionally, are modified as ðE p = 4pÞ and ð 4pE min Þ, respectively, by taking the uncertainity relations into account.

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The geometric mean of Ep and Emin is written as: [¼ ½E p E min
1=2

ð8Þ

From equations (4), (5) and (6) a generalized equation for E as a function of ðDEÞ is: pffiffiffiffiffiffi 1=2 1=2 E ¼ {E p þ 4pE min }ðDEÞ1=2 2 [0 ð9aÞ The satisfies all possible values of quantized Energy E ranging from p pffiffiffiffiffiffi ffiffiffiffiffiffi equation (9a) 4pE min to E p = 4p for values of ðDEÞ ranging from ðDEÞmin ¼ ðE p =4pÞ: Subsisting the values of the constants in equations (9a) the energy equation becomes: "

#1=2 
 #1=2 1=2 "
5 1=2
5 1=2 he hH hc hH 0 ðDEÞ þ 4p 2p ðDEÞ E ¼ 2p 2 G G 2

ð9bÞ

This is deterministic equation of E in terms of DE and some universal constants. It may be noted that from the computational point of view the equation (9a) and (9b) are deterministic equation of E in terms of DE and some universal constants, and is a quadratic equation with two roots, one positive and other negative in conformity with behaviour of quantum relativistic particles. 2.2 Position – momentum uncertainty relations The momentum p of a particle has three components px, py and pz in the directions of the three co-ordinate axes, and say the position of the particle in space is (x, y and z). qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Then p ¼ p2x þ p2y þ p2z and the uncertainity relations for components of p are: h h ðDpx ÞðDxÞ ¼ ðDpy ÞðDyÞ $ 2 2

and

ðDpz ÞðDzÞ $

h 2

ð10Þ

Applying similar methods, equations of the form: px ¼ f ðDpx Þ; py ¼ f ðDpy Þ and

pz ¼ f ðDpz Þ

are given below: 
 
  
 Ep 4pE min [0 px ¼ ðDpx Þ1=2 þ ððDpx Þ1=2 Þ 2 c c c 
 
  
 Ep 4pE min [0 py ¼ ðDpy Þ1=2 þ ððDpy Þ1=2 Þ 2 c c c and


pz ¼

ð11Þ

ð12aÞ


  
  Ep 4pE min [0 ðDpz Þ1=2 þ ððDpz Þ1=2 Þ 2 c c c

Here, we can be using the energy equations 9(a-f) and not equations 12 (a-d) to avoid the complexities. We can also deduce an equation for p in terms of Dx ; Dy and Dz as given below:

 p ¼ K1









1=2 ð12bÞ

Heisenberg’s uncertainty principle

h ðE p þ 4pp1 þ 4pp0 Þ K1 ¼ 2C

ð12cÞ

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1=2 E0 h ½ðE p Þ1=2 þ ð4pp1 Þ1=2
K2 ¼ 2 2C C

ð12dÞ

1 1 1 þ þ Dx Dy Dz

2 K2

1 1 1 þ þ 1=2 1=2 ðDxÞ ðDyÞ ðDzÞ1=2

Where: 

And:

Equation (12b) is the deterministic equation for the momentum of a particle in terms of the respective uncertainties of the co-ordinate. 2.3 Momentum using Dirac’s relativistic equation The momentum can be calculated from Dirac’s quantum relativistic equation: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E ¼ p 2 c 2 þ m20 c 4

ð13Þ

Knowing E and m0 of a particle, the momentum p can be calculated. Equations 9(a-f) and (13) are both quadratic equation and E has two roots, which are equal in magnitude, but opposite in sign that correspond to Dirac’s positive and negative energy states. We shall now calculate ðDEÞ, from observational data, and then evaluate E, by substituting the same in equations 9(a-f). 3. Computation of energy E Computation of energy E under different constraints will lead to interesting results: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð14Þ ðDEÞSD ¼ E
2 ðE
2 Þ 3.1 Single observer multiple observation When an observer can make any number of observation (say n) for the energy E of a particle, and the values thus found are say E1, E2, E3, . . . ,En. The standard deviation (SD) of the said values of E is given by equation (14), where: ! 1 2 2 E þ E þ · · · þ E 2 2 2 n ðE
Þ ¼ ð14aÞ n and: ðE
2 Þ ¼




E1 þ E2 þ · · · þ En n

2 ð14bÞ

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This statistical method required multiple observations to be made on the state to be measured. 3.2 Single observer single observation The observer has only one opportunity to measure E: the observer finds the observed value of the energy of a particle as {E þ ðDEÞ}, then equation (9a) and (9b) can be written as: pffiffiffiffiffiffi 1=2 1=2 ð9cÞ {E þ ðDEÞ} ¼ {E p þ 4pE p }ðDEÞ1=2 2 [0 ðDEÞ Similar, when the observed value of the energy of a particle is found to be {E þ ðDEÞ}equation (9c) can be written as: pffiffiffiffiffiffi 1=2 ð9dÞ {E þ ðDEÞ} ¼ {E p þ 4pE 1=2 }ðDEÞ1=2 2 [0 ðDEÞ when the recoil photon (signal used to observe a particle) after interaction with the observable, looses energy (DE) is positive: and when the same gains energy in the process of interaction with observable, (DE) is negative equation (9a) and (9b) represents the two possible cases, respectively. As, the left hand sides of equation (9a) and (9b) are known to an observer, the equation can be solved for finding (DE); which when substituted in equation (9d) gives the value of E. 3.3 A simplified algorithm for determination of total quantized energy E It is shown that equation (9a) can be written as more general and simpler form in terms of “ [ 0” is an universal constant as shown before and “n” represents integral whole numbers, n ¼ 1,2,3, . . . ,N. Substituting ðDEÞ ¼ {nðDEÞmin } in equation (7), one gets: pffiffiffiffiffiffiffiffiffi ð9eÞ E ¼ {ðnÞ1=2 [0 þ 4ppðnÞ1=2 [0 }2 [0 or:

pffiffiffiffiffiffiffiffiffi E ¼ {ðnÞ1=2 [0 þ 4ppðnÞ1=2 [ 21} [0

m¼

ð9fÞ

[0 E min ¼ Ep [0

Putting n ¼ 1,2,3, . . . ,.N, etc. we can get them set of precise quantizedpenergy states, ffiffiffiffiffiffi Effi2 ; . . . ; E n Þ where N is the largest number, and E 1 ¼ 4p; E min and as, S u ¼ ðEp1 ;ffiffiffiffiffi E N ¼ ðE p = 4pÞ: 4. The deduction of graviton wavelength (lG) and energy (EG) It is assumed that the presently observable evolutionary universe is the effect of a massive explosion, the big bang which occurred initially at t ¼ 0, but all the considerations regarding the calculations are done by take tp as the epoch time. Dutta (1995) in his paper presented the formula for calculating the matter density, the total matter content and initial volume of the universe, which was used to calculate the quantized energy of the said Graviton (EG) (Milne, 1935):

ðE G Þ ¼ 4ðph 2 H 20 C 2 mÞ1=3

ð15Þ

Here the item 4ðph 2 H 20 C 2 mÞ1=3 is a dimensional constant, and “m” is the mass of the body. However, it may be mentioned here that, so far, all experimental efforts to detect gravitons have failed, and future experimenter, may design the detectors for detecting the gravitons radiated from a source of known mass according to the required sensitivity demanded by equation (15). 5. The discussion on the perspective for the need for a new look Historically, the underlying ideas and the laws governing the classical mechanics has been developed in an elegant fashion from the time of Sir Isaac Newton and were applied in an ever widening range of dynamical systems until necessity for departure were clearly shown by experimental results. A very attractive new scheme, called quantum mechanics, was set up, which was more suitable for description of atomic scale phenomena including electro dynamics and optics, in some respects more elegant than, the classical scheme, not clashing with features of classical theory. Those could be incorporated in the new scheme. A galaxy of scientists like Max Planck, Neils Bohr, Erwin Schrodinger Max Born, Werner Heisenberg, Albert Einstein, Wolfgang Pauli and Paul A. M. Dirac among other (Heisenberg, 1986a, b; Born, 1986; Dirac, 1986) contributed in the process. One major limitation pointed out by Werner Heisenberg and supported by Albert Einstein was the HUP about which we have discussed at length and attempted to present a deterministic alternative for energy and momentum in the non-infinite non-zero quantized energy limits, that opens up technological possibility of by-passing uncertainity relations. 5.1 The limitations because of HUP In the simplest language the HUP can be stated as, it is not possible to determine, measure, or know – simultaneously the position and momentum of a particle in the same level of accuracy: the more precise the measurement of a position, for example the less precise the knowledge of its momentum and vice-versa. That is a process of measuring its position alters its momentum unpredictably. Secondly, as we venture further and further into the subatomic world our vision becomes less and less clear – because there are limits beyond which we cannot measure accurately – (Dutta Majumdar, 1979; Dutta Majumdar and Majumdar, 2004a; Heisenberg, 1930; Roy and Dutta Majumdar, 1996; Roy et al., 1996). The contrast between quantum theory and causal laws of classical physics, is evident Dirac in his article “The need for a quantum theory” (Dirac, 1932) made following two important statements (Dirac, 1986): (1) . . . science is concerned only with observable things and that we can observe an object only by letting it interact with some outside influence. (2) . . . there is a limit to the fineness of our power of observation and the smallness of accompanying disturbance – a limit which is inherent in the nature of things and can never be surpassed by improved technique or increased skill on the part of the observer.

From the discussion above it was imperative that we must revise our ideas of causality. There was an unavoidable indeterminacy in the calculation of straight forward observational results. In order to obviate the difficulty – a new set of accurate law’s of

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nature were required and was provided by the principle of superposition of states (Born, 1986). It is important to remember that the superposition that occurs in quantum mechanics is of an essentially different nature from any occurring in classical theory – as the quantum superposition principle demands indeterminacy in the results of observations in order to be capable of a sensible physical interpretation.

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5.2 Indeterminacy, observations and cybernetics It is well known that the development of cybernetics as a modern discipline emerged following from Wieners’ (1948) publications on the subject – when scientists and engineers faced with a set of problems concerned with control, communication and computation in dynamical systems – both in mechanization of intelligent activity in machines and living issues about “observed systems” Dutta Majumder in a series of papers (1975, 1979, 1999, 2000, 2004) enunciated his combined formalism of “Observer systems” “Observed systems” and the “act of observing” in the environment into one unitary discipline of general dynamical systems from the point of perspective, motivation, requirements, characteristics attributes and behaviour, and developed a unified general theory of systems and cybernetics in terms of causality, signal predictability and the notions of state in dynamical systems comprising of machines and human beings with successful implementations. From this theory we venture to conclude that all observations and interactions in machines and living tissues can be considered as cybernetic process. Dirac’s statement as quoted above published in 1958 – can be considered as a deterministic conclusion about indeterminacy, and observability should be taken as approximate with the emerging newer and newer mathematical tools, techniques and their advance realizations. Our contribution in this paper is a decisive proposal in that direction. 5.3 Indeterminacy limits and nano technology It was in December 29, 1959 Feynman (1960) in his celebrated talk at the Annual Meeting of the American Physical Society entitled “There is plenty of room at the bottom” presented a technological vision of the miniaturization of materials, manipulating and controlling things in a small scale called “Nanotechnology”. Feyneman visualized a technology using a toolbox of nature to build nanoobject – atom by atom by atom or molecule by molecule – with structural features in the range of about 102 9 to 102 7 m. Nature seems to have bypassed or disregarded indeterminacy relations and has made many objects and processes that function on a micro to nano scale (Dirac, 1986) in a deterministic fashion. The understanding of these functions can guide us in initiating and producing new nanomaterials. Present day technology is fantastic – but it pales when compared to what will be possible when we learn to build things at the ultimate level of control one atom at a time. We should also understand that, new behavior at the nanoscale may not necessarily be predictable from that observed at the molecular scale of to-day. 6. Conclusion The philosophical foundation of quantum mechanics is based on the well known duality concept of complimentary notions namely – particles and continues, localized

and non-localized characteristics of quantum behaviour expressed through the well known equations of energy and momentum as E ¼ ðR=2pÞv and p ¼ hl 21 , respectively. These equations mainly manifest the qualitative aspect of quantum mechanics as the quantitative aspect is governed by the Heisenberg’s uncertainty relations. Logically in most general sense for any physical reality quality and quantity are interdependent and so qualitative dualism should have a hidden or virtual quantitative dualism is an outcome of this hypothesis that has manifested as the reality of quantitive dualism cum qualitative dualism as presented below: . The generalized equations of energy and momentum as given by equations (7) and (10) are deterministic and algorithmically computable though expressed as functions of uncertainity terms. . The four universal physical constants, H, C, G, and H0 are utilized to impose the cutoffs on a dimensional basis. . Similar cutoffs are also imposed on the uncertainity relations on the basis of dimensional, equivalence, thereby avoiding the observer-observed – observation interdependence phenomena to derive the cutoff energies Thus, the exclusion on the causes of determinacy renders the computation a deterministic status. . Conventional determination of the uncertainity parameter DE requires the standard deviation to be calculated from a number of observations calculated in terms of (DE). . The uncertainity of measurement of E is true even for a single measurement. If we take, a single measurement of the energy of a particle it gives a value E ¼ E ^ DE which is known. Using equations 9(a-f) we can measure E. References Barone, S.R., Kunhardt, E.E., Bentson, J. and Syljuasen, A. (1993), “Newtonian chaos þ Heisenberg uncertainity ¼ macroscopic indeterminacy”, American Journal of Physics, Vol. 61 No. 5. Born, M. (1986), “The statistical interpretation of quantum mechanics”, in Weaver, J.H. (Ed.), The World of Physics, Simon and Schuster, New York, NY, pp. 368-80. Collins, P.G. (2006), “Graham computing with quantum knots”, Scientific American, April. Dirac, P.A.M. (1932), Principles of Quantum Mechanics, Oxford University Press, Oxford, p. 3. Dirac, P.A.M. (1986), “The principle of superposition”, in Weaver, J.H. (Ed.), The World of Physics, Simon and Schuster, New York, NY, pp. 411-26. Drexier, K.E. (1992), Nano Systems: Molecular Machinery, Manufacturing and Computation, Wiley, New York, NY. Dutta, S.K. (1995), “The non infinite, non zero quantized limites and their physical significance”, Physics Essays, Vol. 8 No. 4. Dutta Majumdar, D. (1979), “Cybernetics and general systems theory: a unitary science”, Norbert Wiener Award Winning Paper, 1978, UK Kybernetes,Vol. 8, pp. 7-15. Dutta Majumdar, D. (1993), “Fuzzy mathematics and uncertainty management for decision making science and society”, Journal of Computer Science and Informatics, Computer Society of India, Vol. 23 No. 3, pp. 1-31.

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Dutta Majumder, D. and Bhattacharya, M. (2000), “Cybernetic approach to medical technology: application to caner screening and other diagnostics”, Kybernetes, Vol. 29, pp. 896-927. Dutta Majumder, D. and Das, J. (1980), “Digital computers’ memory technology”, Limitations of Existing Memory Technologies and Prospects for Biochemical Memories, 2nd ed., Wiley Eastern Limited, New Delhi, Chapter 10, pp. 516-28. Dutta Majumdar, D. and Majumdar, K.K. (2004a), “Complexity analysis, uncertainity management and fuzzy dynamical systems: a cybernetic approach”, Kybernetes: The International Journal of Systems & Cybernetics, Vol. 33 No. 7, pp. 1143-84, (Norbert Wiener Award Paper 2005 – Literati Club, Emerald). Dutta Majumder, D. and Majumder, K.K. (2004b), “Fuzzy differential inclusions in atmospheric and medical cybernetics”, IEEE Trans Systems Morn and Cybernetics, Part B: Cybernetics, Vol. 34 No. 2, pp. 877-87. Dutta Majumdar, D., Chatterjee, R. and Goswami, A. (2006), “Challenges of nanoscience and nanotechnology – in material science and medical science including drug design”, ICSIT Technical Report, April 2006, Institute of Cybernetics Systems and Information Technology, Kolkata. Feynman, R.P. (1960), “Plenty of room at the bottom”, Engineering and Science, February. Hall, M.J.W. and Regina Ho, M. (2002), “Schroedinger equation from an exact uncertainity principle”, Journal of Physics A, Vol. 35. Heisenberg, W. (1930), The Physical Principles of the Quantum Theory, University of Chicago Press, Chicago, IL, Dover Publications, 1947. Heisenberg, W. (1986a), “The development of quantum mechanics”, in Weaver, J.H. (Ed.), The World of Physics, Simon and Schuster, New York, NY, pp. 353-65. Heisenberg, W. (1986b), “The Copenhagen interpretation of quantum theory”, in Weaver, J.H. (Ed.), The World of Physics, Simon and Schuster, New York, NY, pp. 397-409. Koller, J.G. and Athas, W.C. (1992), Adiabatic Switching, Low Energy Computing, and the Physics of Storing and Erasing Information, Physics of Computation Workshop, Dalls, Texas. Milne, A.E. (1935), Relativity, Graviton and World Structure, Oxford University Press, Oxford. Pal, N.R. and Bezodek, J.C. (1994), “Measuring fuzzy uncertainity”, IEEE Trans. on Fuzzy Systems, Vol. 2 No. 2, pp. 107-18. Pal, S.K. and Dutta Majumdar, D. (1986), Fuzzy Mathematical Approach to Pattern Recognition, Wiley, New York, NY. Pal, S.K. and Mitra, S. (2001), Nero-Fuzzy Pattern Recognition Methods in Soft Computing, Willey Series on Intelligent Systems, Wiley, New York, NY. Planck, M. (1899) Ober irreversible Strahlungs Vorgange (funfte Mitteilund) Sitzungsberichite der Preupssis chen Akademic der Wissenchaften, p. 440. Raymer, M.G. (1994), “Uncertainity principle for joint measurement of non computing variables”, American Journal of Physics, Vol. 62 No. 11. Roy, S. and Dutta Majumdar, D. (1996), “Indeterminacy relations unsharp observables and wholeness of individual quantum process”, The National Academy of Science India Letters, Vol. 19 Nos 5/6. Roy, S., Kundu, M.K. and Granlund, G.H. (1996), “Uncertainity relations and time – frequency distributions for unsharp observables”, Informatics and Computer Science, North Holland, Information Sciences, Vol. 89, pp. 193-209. Roychowdhury, A.K. (1979), Theoretical Cosmology, Oxford University Press, Oxford, pp. 36, 189.

Technical Proceedings (2003), Nano technology Conference, Vol. 2, San Francisco, CA. Zadeh, L.A. (1973), “Outline of a new approach to the analysis of complex systems and decision processes”, IEEE Trans. SMC, Vol. SMC-3, pp. 28-44. Further reading Carrol, S.M., Press, W.H. and Turner, E.L. (1992), “Annu Rev”, Astron Astrophys, Vol. 30, pp. 502-3. Dutta Majumder, D. (1993a), “Mind – body duality problem and artificial consciousness for computing machines: a cybernetic approach”, in Ghoshal, A. and Murthy, P.N. (Eds), Recent Advances in Cybernetics and Systems, Tata McGraw-Hill, New Delhi, pp. 337-45. Dutta Majumder, D. (1993b), “Mind-body duality: its impact on pattern recognition and computer vision research”, Third APRDT, ISI, P.C. Mahalanobis Birth Centenary Volume, December, pp. 3-17. Dutta Majumder, D. Kr, Banerjee, R., Ulrichs, C., Mewis, I., Adhikary, S., Samanta, A., Mukhopadhyay, S.K. and Goswami, A. (2006), “Nano – fabricated materials in cancer treatment and agri-biotech applications: buckyballs in quantum holy grails”, IETE Journal of Research on Technology, Vol. 52 No. 5, pp. 339-56. Fasching, R., Tao, E., Bai, S-J., Hammerick, K., Smith, R.L., Gereco, R.S. and Prinz, F.B. (2005), “Next generation sensors for measuring ionic flax in live cells”, Nano Scale Technology in Biological Systems, CRC Press, London, pp. 55-72. Treder, H.J., Merwe, A.V., Borzeszkowski, H.M.V. and Yourgrau, W. (1980), Fundamental Principles of General Relativity Theories, Plenum, New York, NY, pp. 57,59. Wiener, N. (1948), Cybernetics or Control and Communication in the Animal and the Machine, Wiley, New York, NY. Corresponding author Dwijesh K. Dutta Majumder can be contacted at: [email protected]; [email protected]

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Homomorphisms of fuzzy recognizers S.R. Chaudhari

768

Department of Mathematics, Shivaji University, Kolhapur, India Abstract Purpose – The purpose of this research paper is to develop an algorithm/methodology for the reduction of a fuzzy recognizer through an algebraic concept such as homomorphism. Design/methodology/approach – The approach of this research is to introduce the concepts, compatible with the purpose of this paper, and then to find a necessary and sufficient condition for the reduction of a fuzzy recognizer. Findings – A fuzzy S-recognizer M with non-empty fuzzy initial state and the behavior A is reduced if and only if it is isomorphic to M A. Research limitations/implications – The research proposes an algebraic method for the reduction of a fuzzy recognizer. The problem of finding dispensable fuzzy productions of a regular fuzzy grammar may be tackled by the use this algebraic method, as fuzzy recognizers and fuzzy regular grammars are equivalent. Originality/value – The concepts and the methodology are original. The work is useful to the researchers in the field of fuzzy automata, fuzzy grammars and pattern recognition. Keywords Cybernetics, Fuzzy logic, Grammar Paper type Research paper

Kybernetes Vol. 36 No. 5/6, 2007 pp. 768-775 q Emerald Group Publishing Limited 0368-492X DOI 10.1108/03684920710749839

1. Introduction Wee and Fu (1969) introduced fuzzy recognizers (fuzzy automata) as a model of learning system. Santos introduced and studied various types of fuzzy automata (maximin, minimax, max-product, etc.) and used them to characterize various fuzzy grammars and fuzzy languages (Ray et al., 1991; Santos and Wee, 1968; Santos, 1968a, b, 1972a, b, 1975a). Since, then fuzzy automata have been studied from several angles. Some of the major topics are pattern recognition and pattern classification (Mordeson and Malik, 2002; Pal and Majumdar, 1986; Ray et al., 1991), fault tolerant decision (Dal Cin, 1975a, b; Gupta et al., 1977; Kandel and Lee, 1980; Mordeson and Malik, 2002; Peeva and Kyosev, 2004), formal languages and computing (Gerla, 1992; Honda and Nasu, 1975; Lan and Zhiwen, 1995; Mordeson and Malik, 2002; Peeva, 1988; Shen, 1996; Santos, 1972c, 1975a, b), etc. Malik and Mordeson (1999) introduced fuzzy recognizers with fuzzy initial states, fuzzy final states and non-fuzzy inputs. In this paper, we introduced the concept of homomorphism of fuzzy recognizers of these types. Malik and Mordeson show that the fuzzy recognizer M A exists for every recognizable subset A # S* , which recognizes A. We have proved that if M is any fuzzy S-recognizer, which recognizes A and the fuzzy set of initial states of M is non-empty, then M A, is the homomorphic image of M. We also prove that if M is complete accessible fuzzy S-recognizer with behavior A and the fuzzy set of initial states of M is non-empty, then M is isomorphic to M A. For the terminology regarding (crisp) algebraic automata theory used in this paper, we refer to Eilenburg (1974) and Holcombe (1982) and their fuzzy analogue studied by

various authors (Dubois and Prade, 1980; Mordeson and Malik, 2002; Peeva and Kyosev, 2004). 2. Preliminaries Throughout this paper, a triplet m ¼ ðQ; S; mÞ denotes a fuzzy finite state machine, where Q and S are non-empty finite sets and m is a fuzzy subset of Q £ S £ Q. S is called the alphabet, S* is a set of words including empty word ^, with alphabet S. It is obvious that S* is a monoid *under usual juxtaposition of words. If a [ S* and A [ S* , then a 21 A ¼ {b [ S jab [ A}. The fuzzy set m : Q £ S £ Q ! ½0; 1
induces the function m * : Q £ S* £ Q ! ½0; 1
defined by:

m * ð p; s; qÞ ¼ mð p; s; qÞ; m * ð p; s1 s2 . . .sk ; qÞ ¼ _{mð p; s1 ; t 1 Þ ^ mðt1 ; s2 ; t2 Þ ^ . . . ^ mðt k21 ; sk ; qÞjt i [ Q} and: (

m * ð p; ^; qÞ ¼

1;

if p ¼ q

0;

if p – q

; p; q [ Q and si ; s [ S:

Clearly m * ð p; xy; qÞ ¼ _{mð p; x; tÞ ^ mðt; y; qÞjt [ Q}; ; x; y [ S* : With “abuse of notations,” when there is no room for confusion we will use m for m * . Definition 2.1. A fuzzy S-recognizer of a fuzzy finite state machine m is a triplet M ¼ ðm; I ; TÞ, where I and T are fuzzy subsets of Q. I is called fuzzy set of initial states; T is called fuzzy set of final states (Kumbhojkar and Chaudhari, 2000a, b,2002a,b; Malik and Mordeson, 1999; Mordeson and Malik, 2002). Let X: Q ! [0,1], Y: Q ! [0,1]. Then X*Y : S* ! ½0; 1
is defined by X *Y ðxÞ ¼ and X 21 +Y ¼ {x [ S* jX *Y ðxÞ . 0}. _ðXð pÞ ^ Y ðqÞ ^ mð p; x; qÞjp; q [ Q} * If A # S , then X *A : Q ! ½0; 1
is defined by X *AðqÞ ¼ _{Xð pÞ ^ mð p; x; qÞjp [ Q; x [ A}: Definition 2.2. Let M ¼ (m,I,T) be a fuzzy S-recognizer. Then the word x [ S* is said to be recognized by M or M recognizes x, if I *TðxÞ . 0 (Kumbhojkar and Chaudhari, 2000b, 2002b; Malik and Mordeson, 1999; Mordeson and Malik, 2002). The set of all words that are recognized by M will be denoted by jMj and will be called the behavior of M. Definition 2.3. A subset A of S* is called S-recognizable, if there exists a fuzzy S-recognizer M which recognizes every word of A, i.e. jMj ¼ A (Kumbhojkar and Chaudhari, 2000b, 2002b; Malik and Mordeson, 1999; Mordeson and Malik, 2002). Definition 2.4 (Kumbhojkar and Chaudhari, 2002b; Malik and Mordeson, 1999; Mordeson and Malik, 2002). Let M ¼ (m,I,T) be a fuzzy S-recognizer of a fuzzy finite state machine m ¼ ðQ; S; mÞ and R ¼ {q [ QjI *S*ðqÞ . 0} (Kumbhojkar and Chaudhari, 2002b; Malik and Mordeson, 1999; Mordeson and Malik, 2002). If Q ¼ R, then M is called accessible.

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Theorem 2.5. Let M ¼ (m,I,T) be a fuzzy S-recognizer of a fuzzy finite state machine m ¼ ðQ; S; mÞ such that jMj ¼ A (Kumbhojkar and Chaudhari, 2002b). If a ¼ S* , then a 21 A ¼ ðI *aÞ21 +T. Definition 2.6. Let A # S* be a S-recognizable set and QA {a 21 Aja [ S* } (Kumbhojkar and Chaudhari, 2002b). Define m A : QA £ S £ QA ! ½0; 1
by:

770 m A ða 21 A; s; b 21 AÞ ¼

8 < 1;

if ðasÞ21 A ¼ b 21 A

: 0;

otherwise

I A : QA ! ½0; 1
by: ( A

I ða

21

AÞ ¼

1;

if a 21 A ¼ A

0;

otherwise

and: T A : QA ! ½0; 1
by: ( A

T ða

21

AÞ ¼

1;

if a [ A

0;

otherwise

Then m A ¼ ðQA ; S; m A Þ is a fuzzy finite state machine and M A ¼ ðm A ; I A ; T A Þ is a fuzzy S-recognizer. Definition 2.7. A fuzzy S-recognizer M ¼ (m,I,T) of a fuzzy finite state machine m ¼ ðQ; S; mÞ is called complete, if for each p £ s [ Q £ S there exists q [ Q, such that mð p; s; qÞ . 0 (Kumbhojkar and Chaudhari, 2002b; Malik and Mordeson, 1999). Theorem 2.8. The fuzzy S-recognizer M A is complete and accessible such that jM Aj ¼ A (Kumbhojkar and Chaudhari, 2002b; Mordeson and Malik, 2002).

3. Homomorphism of fuzzy recognizers Homomorphism of fuzzy recognizers is introduced in this section. Theorem 3.1. Let M ¼ (m,I,T) be a fuzzy S-recognizer of a fuzzy finite state machine m ¼ ðQ; S; mÞ such that jMj ¼ A. Then A ¼ I 21 +T. If q [ Q and I( p) ^ m( p,a,q) . 0, for some p [ Q and a [ S * then a 21 A ¼ 121 {q} +T, where 1{q} denotes the fuzzy representation of {q}. Proof. Recall that I 21 +T ¼ {x [ S* jI *TðxÞ . 0} ¼ jM j ¼ A. Let I ð pÞ ^ mð p; a; qÞ . 0, for some p [ Q and a [ S* .

Homomorphisms of fuzzy recognizers

Then: * 121 {q} +T ¼ {x [ S j1{q} *TðxÞ . 0} ¼ {x [ S* j _ {1{q} ðrÞ ^ TðtÞ ^ mðr; x; tÞjr; t [ Q} . 0} ¼ {x [ S* j’ t 0 [ Q such that Tðt0 Þ ^ mðq; x; t0 Þ . 0} ¼ {x [ S* j’ t0 [ Q such that I ð pÞ ^ mð p; a; qÞ ^ Tðt 0 Þ ^ mðq; x; t 0 Þ . 0
¼ {x [ S* j’ t 0 ; p [ Q such that I ð pÞ ^ Tðt0 Þ ^ mð p; ax; t0 Þ . 0} ¼ {x [ S* jI *TðaxÞ . 0 ¼ {x [ S* jax [ I 21 +T} ¼ a 21 A In the rest of this paper we will write q 21 +T for 121 A {q} +T. Definition 3.2. Let M ¼ (m,I,T) be a fuzzy S-recognizer of m ¼ ðQ; S; mÞ and M 0 ¼ ðm0 ; I 0 ; T 0 Þ be fuzzy S0 -recognizer of m0 ¼ ðQ0 ; S; m0 Þ. Let f : Q ! Q0 and g ¼ S ! S0 be a mappings. Then the pair ( f,g) is called homomorphism form M to M 0 , symbolically ð f ; gÞ : M ! M 0 , if: . mð p; s; qÞ # m0 ð f ð pÞ; gðsÞ; f ðqÞÞ . I ð pÞ # I 0 ð f ð pÞÞ . Tð pÞ # T 0 ð f ð pÞÞ; ; p; q [ Q; s [ S. If both f and g are objective, then the homomorphism ð f ; gÞ : M ! M 0 is called an isomorphism. In this case, we will write M ø M 0 . Definition 3.3. A homomorphism ð f ; gÞ : M ! M 0 from M to M 0 is called strong, if: . mð p; s; qÞ ¼ m0 ð f ð pÞ; gðsÞ; f ðqÞÞ . I ð pÞ ¼ I 0 ð f ð pÞÞ . Tð pÞ ¼ T 0 ð f ð pÞÞ; ; p; q [ Q; s [ S. Note that if M and M 0 are fuzzy S and S0 -recognizers, respectively, and ð f ; gÞ : M ! M 0 is a strong isomorphism, then A is S-recognizable if and only if g(A) is S0 -recognizable. Theorem 3.4. Let ð f ; gÞ : M ! M 0 be a homomorphism form M to M 0 . Then mð p; x; qÞ # m0 ð f ð pÞ; gðxÞ; f ðqÞÞ; ; p; q [ Q; x [ S* Proof. Proof of this theorem is by induction on the length of x ¼ S* . If M ¼ (m,I,T) is a fuzzy S-recognizer of a fuzzy finite state machine m ¼ ðQ; S; mÞ, A then the identity mapping 1Q of Q is a strong homomorphism from M to itself. Theorem 3.5. If ð f ; gÞ : M ! M 0 and ðh; i Þ : M 0 ! M 00 are homomorphisms from M to M00 and M 0 to M 00 , respectively. Then ðh+f ; i+gÞ : M ! M 00 is a homomorphism from M to M00 . Proof. Let p,q [ Q and s [ S. Then mð p; x; qÞ # m0 ð f ð pÞ; gðxÞ; f ðqÞÞ # 00 m ðh+f ð pÞ; i+gðxÞ; h+f ðqÞÞ: I ð pÞ # I 0 ð f ð pÞÞ # I 00 ðh+f ð pÞÞ

and

Tð pÞ # T 0 ð f ð pÞÞ # T 00 ðh+f ð pÞÞ: A

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Definition 3.6. Let M ¼ (m,I,T) be a fuzzy S-recognizer of a fuzzy finite state machine m ¼ ðQ; S; mÞ and P # Q. Define m0 : P £ S £ P ! ½0; 1
by: ( mð p; s; qÞ; if p; q [ P 0 m ð p; s; q; Þ ¼ 0; otherwise

772

I 0 : P ! ½0; 1
by: ( I 0 ð pÞ ¼

I ð pÞ; 0;

if p [ P

otherwise

and: T 0 : P ! ½0; 1
by: ( 0

T ð pÞ ¼

Tð pÞ; 0;

if p [ P

otherwise

Then mjP ¼ ðP; S; m0 Þ is a fuzzy finite state machine and M jP ¼ ðmjP ; I 0 ; T 0 Þis a fuzzy S-recognizer called restriction of M to P. The inclusion mapping f : M jP ! M is a strong homomorphism. Theorem 3.7. Let M ¼ (m,I,T) be a complete accessible fuzzy S-recognizer of a fuzzy finite state machine m ¼ ðQ; S; mÞ such that jMj ¼ A. Then there exists a homomorphism from M to M A. Further, if I – f then M A is homomorphic image of M. Proof. Define f : Q ! QA by f ðqÞ ¼ q 21 +T; ;q [ Q. Since, M is accessible, ’a [ S* and r [ Q such that I(r) ^ m(r,a,q) . 0. By Theorem 3.1, a 21 A ¼ q 21 +T. Let p [ Q. Then ’a [ S* and r [ Q such that a 21 A ¼ p 21 +T, where I ðrÞ ^ mðr; a; pÞ . 0: If I( p) ¼ 0 then trivially I ð pÞ # I 0 ð f ð pÞÞ: Let I( p) . 0: p 21 +T ¼ {x [ S* j’t0 [ Q such that Tðt 0 Þ ^ mð p; x; t 0 Þ . 0} ¼ {x [ S* j’t 0 [ Q such that I ð pÞ ^ Tðt 0 Þ ^ mð p; x; t 0 Þ . 0} ¼ {x [ S* j’t0 ; p [ Q such that I ð pÞ ^ Tðt 0 Þ ^ mðr; x; t 0 Þ . 0} ¼ {x [ S* jI *TðxÞ . 0} ¼ {x [ S* jx [ I 21 +T} ¼ jM j ¼ A: Thus, a 21 A ¼ p 21 +T ¼ A: Therefore; I 0 ð f ð pÞÞ ¼ I 0 ð p 21 +TÞ ¼ I 0 ða 1 AÞ ¼ 1 $ I ð pÞ: Let p [ Q. Then ’a [ S* and r [ Q such that a 21 A ¼ p 21 +T; where I ðrÞ ^ mðr; a; pÞ . 0: If T( p) ¼ 0 then trivially Tð pÞ # T 0 ð f ð pÞÞ:

Let T( p) . 0. Then I ðrÞ ^ Tð pÞ ^ mðr; a; pÞ . 0: i.e. a [ jM j ¼ A: Therefore, T 0 ð f ð pÞÞ ¼ T 0 ð p 21 +TÞ ¼ T 0 ða 21 AÞ ¼ 1 $ Tð pÞ: Let p,q [ Q and s [ S. Then ’a; b [ S* and r,t [ Q such that 21 a A ¼ p 21 +T; b 21 A ¼ q 21 +T, where I ðrÞ ^ mðr; a; pÞ . 0 and I ðtÞ ^ mðt; b; qÞ . 0: If m( p,s,q) ¼ 0, then trivially mð p; s; qÞ # m0 ð f ð pÞ; gðsÞ; f ðqÞÞ: Let m( p,s,q) . 0: q 21 +T ¼ {x [ S* j’t 0 ; [ Q such that Tðt 0 Þ ^ mðq; x; t0 Þ . 0} ¼ {x [ S* j’t 0 ; [ Q such that mð p; s; qÞ ^ Tðt 0 Þ ^ mð p; x; t 0 Þ . 0} ¼ {x [ S* j’t 0 ; [ Q such that Tðt 0 Þ ^ mð p; sx; t 0 Þ . 0} ¼ {x [ S* j’t 0 ;[ Q such that I ðrÞ^ mðr; a;pÞ^Tðt 0 Þ^ mð p; sx;t 0 Þ . 0} ¼ {x [ S* j’t 0 ;[ Q such that I ðrÞ^Tðt0 Þ^ mðr; asx;t 0 Þ . 0} ¼ {x [ S* jas x [ I 21 +T} ¼ {x [ S* jðasÞx [ I 21 +T} ¼ {x [ S* jðasÞx [ A} ¼ {x [ S* jx [ ðasÞ21 A} ¼ ðasÞ21 A: i.e. b 21 A ¼ q 21 +T ¼ ðasÞ21 A. Therefore, m A ða 21 A; s; b 21 AÞ ¼ 1 $ mð p; s; qÞ. Hence, f: M ! M A is a homomorphism. Let a 2 1 A [ QA. Since, I – f, there exist p [ Q such that I ( p) . 0. Then ’ q [ Q such that m( p, a, q) . 0, since M is complete. Therefore, I ð pÞ ^ mð p; a; qÞ . 0. Hence, a 21 A ¼ q 21 +T. Thus; f ðqÞ ¼ a 21 A: A Hence, M A is a homomorphic image of M. The reduction of (finite) L-fuzzy machines of Mealy type was introduced and studied by Peeva (1988, 2004). The concept of reduced fuzzy recognizers is introduced here and its algebraic study, through the concept isomorphism, is given. Definition 3.8. Let M ¼ (m, I, T) be a complete accessible fuzzy S-recognizer of a 21 fuzzy finite state machine m ¼ (Q, S m). Then M is called reduced, if q21 1 +T ¼ q2 +T implies that q1 ¼ q2. Theorem 3.9. Let M ¼ (m, I, T) be a complete accessible fuzzy S-recognizer of a fuzzy finite state machine m ¼ (Q, S m) such that jMj ¼ A. Then M is reduced if and only if f is injective, where f: M ! M A is a homomorphism. Corollary 3.10. Let M ¼ (m, I, T) be a complete accessible fuzzy S-recognizer of a fuzzy finite state machine m ¼ (Q, S m) such that jMj ¼ A and I – f. Then M is reduced if and only if M ø M A.

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4. Summary A reduced fuzzy S-recognizer M with behavior A and non-empty fuzzy set of initial states is isomorphic to M A. The problem of identification of dispensable fuzzy production of regular fuzzy grammar with initial fuzzy state is highly tedious one. The concept of fuzzy recognizer and regular fuzzy grammar with initial fuzzy state are equivalent in the sense that they generate the same language. The notion of reduced fuzzy recognizer will play crucial role in handling the above vary problem, which precisely the aim of future work. References Dal Cin, M. (1975a), “Fuzzy state automaton: their stability and fault tolerance”, Int. J. of Computer and Information Sciences, Vol. 4 No. 1, pp. 63-80. Dal Cin, M. (1975b), “Modification tolerance of fuzzy automata”, Int. J. of Computer and Information Sciences, Vol. 4 No. 1, pp. 81-93. Dubois, D. and Prade, H. (1980), Fuzzy Sets and Systems: Theory and Applications, Academic Press Inc., Burlington, MA. Eilenburg, S. (1974), Automata, Languages and Machines,Vol. A, Academic press, London. Gerla, G. (1992), “Fuzzy grammars and recursively enumerable fuzzy languages”, Information Sciences, Vol. 60, pp. 137-43. Gupta, M.M., Saridas, G.N. and Gaines, B.R. (1977), Fuzzy Automaton and Decision Processes, North Holland, New York, NY. Holcombe, W.M.L. (1982), Algebraic Automata Theory, Cambridge University Press, Cambridge. Honda, N. and Nasu, M. (1975), “Recognition of fuzzy languages”, in Zadeh, L.A. et al. (Eds), Fuzzy Sets and their Applications to Cognitive and Decision Processes, Academic Press Inc, Burlington, MA, pp. 279-99. Kandel, A. and Lee, S.C. (1980), Fuzzy Switching and Automata: Theory and its Applications, Crane Russak, New York, NY. Kumbhojkar, H.V. and Chaudhari, S.R. (2000a), “Fuzzy recognizers-I”, in Pal, N.R., De, A.K. and Das, J. (Eds), Advances in Pattern Recognition and Digital Techniques, Narosa Publishing House, New Delhi, pp. 261-4. Kumbhojkar, H.V. and Chaudhari, S.R. (2000b), “Fuzzy recognizers-II”, in Meenakshi, A.R., Paularaja, P. and Dheena, P. (Eds), Recent Trends in Algebra and its Applications, Annamalai University, Annamalainagar, pp. 72-90. Kumbhojkar, H.V. and Chaudhari, S.R. (2002a), “On coverings of products of fuzzy finite state machines”, Int. J. of Fuzzy Sets and Systems, Vol. 125, pp. 215-22. Kumbhojkar, H.V. and Chaudhari, S.R. (2002b), “Fuzzy recognizers and recognizable sets”, Int. J. of Fuzzy Sets and Systems, Vol. 131, pp. 381-92. Lan, S. and Zhiwen, M. (1995), “Closure of finite-state automaton languages”, Int. J. of Fuzzy Sets and Systems, Vol. 75 No. 3, pp. 393-7. Malik, D.S. and Mordeson, J.N. (1999), “On fuzzy recognizers”, Kybernetics, Vol. 28 No. 1, pp. 47-60. Mordeson, J.N. and Malik, D.S. (2002), Fuzzy Automata and Languages: Theory and Applications, Chapman and Hall/CRC, London. Pal, S.K. and Majumdar, D.K.D. (1986), Fuzzy Mathematical Approach to Pattern Recognition, Wiley, New York, NY.

Peeva, K. (1988), “Behavior, reduction and minimization of finite L-automata”, Int. J. of Fuzzy Sets and Systems, Vol. 28 No. 2, pp. 171-81. Peeva, K. (2004), “Finite L-fuzzy machines”, Int. J. of Fuzzy Sets and Systems, Vol. 141, pp. 415-37. Peeva, K. and Kyosev, Y. (2004), Fuzzy Relational Calculus: Theory, Applications and Software, World Scientific, Hackensack, NJ. Ray, A.K., Chatterjee, B. and Majumdar, A.K. (1991), “A formal power series approach to the construction of minimal fuzzy automata”, Information Sciences, Vol. 55, pp. 189-207. Santos, E.S. (1968a), “Maximin automata”, Information and Control, Vol. 13, pp. 363-77. Santos, E.S. (1968b), “Maximin, minimax and composite sequential machines,”, J. Math. and Anal. Appl., Vol. 24, pp. 246-59. Santos, E.S. (1972a), “Probabilistic grammar and automata”, Information and Control, Vol. 21, pp. 27-47. Santos, E.S. (1972b), “Max-product machines”, J. Math. and Anal. Appl., Vol. 37, pp. 677-86. Santos, E.S. (1972c), “On reduction of max-min machines”, J. Math. and Anal. Appl., Vol. 40, pp. 60-78. Santos, E.S. (1975a), “Realization of fuzzy languages by probabilistic, max-product and maximin automata”, Information Science, Vol. 8, pp. 39-53. Santos, E.S. (1975b), “Max-product grammars and languages”, Information Science, Vol. 9, pp. 1-23. Santos, E.S. and Wee, W.G. (1968), “General formulation of sequential machines”, Information and Control, Vol. 12, pp. 5-10. Shen, J. (1996), “Fuzzy languages on free moniod”, Information Sciences, Vol. 88, pp. 149-68. Wee, W.G. and Fu, K.S. (1969), “A formulation of fuzzy automata and its application as a model of learning systems”, IEEE Trans Syst. Sci. Cyber, Vol. 5, pp. 215-23. Corresponding author S.R. Chaudhari can be contacted at: [email protected]

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Systems view, emergence and complexity J. Korn Visiting Academic, Middlesex University, London, UK

776 Abstract

Purpose – To describe a view of parts of the world as assemblies with emergent properties constructed from related properties or objects, and the modelling of production of emergent properties arising by chance or design. Design/methodology/approach – One and two place sentences of a homogeneous language are combined in a static state to show a variety of possibilities of new structures. Combinations of such sentences in a dynamic state derived from narratives that show how static states are produced. Findings – Using Cartesian products and network theory the kind and number of new structures can be calculated. Semantic diagrams exhibit the propagation of dynamic states leading to the use of predicate logic statements as carriers of properties of objects with uncertainties. Research limitations/implications – The approach is based on linguistic analysis being able to encapsulate linguistic complexities, expressions of feelings, emotions, etc. in homogeneous language. Interpretation of semantics is restricted to human mind. Research may lead to a science and design of complex systems. Practical implications – The method embedded in the approach can be developed into a design aid for managers subject to its passing the test of debate and development of software. Originality/value – The research has led to a more rigorous approach to the analysis and design of scenarios including those with human activities. Keywords Cybernetics, Language, Logic, Uncertainty management Paper type Research paper

Background We introduce a classification of parts of the world and their activities.

Concrete (1) Inanimate natural (rock, water, air, earth. . .), . artificial (artefacts, chair, gear box, motors, knife. . .), . natural activity (hurricane, volcano, earthquake. . .), (2) Animate individual activity at existence level (tree, zebra, man. . .), (3) Technical activity (control and computer systems, energy conversion. . .), (4) Animate activity at social level (cells in organs, forest, herd, human social (family, family..) and production organisations (factory. . .)), Kybernetes Vol. 36 No. 5/6, 2007 pp. 776-790 q Emerald Group Publishing Limited 0368-492X DOI 10.1108/03684920710749848

Helpful comments by Professor K. D. Bailey, University of California and Dr A. Radvanyi, Computer and Automation Research Institute of the Hungarian Academy of Sciences, are gratefully acknowledged.

Symbolic Carried by medium (usually a combination of geometric and material properties like a piece of paper) in which means with meaning for handling thoughts are embedded by a sender to be deciphered by a receiver (Korn, 2001). Means with meaning: . images (icons, indexes, pictures, sculptures, diagrams, signs and objects to which means with meaning can be attributed: devil, works of art, gestures (with a fist. . .)); . natural language (letters, words, sentences); . music (symbols to express tunes, rhythm); and . mathematics (symbols like letters, numbers and relations). Correspondingly, humanity has produced the basic disciplines of: . arts; . literature; . music; and . conventional science (CS), plus the cross disciplines of engineering, medicine, law, economics, etc. CS in its pursuit of reliable knowledge, views a part of the world in terms of quantifiable properties abstracted from objects and events. Thus, it is applicable only to selected quantitative aspects of scenarios in any part of the classification. CS strives for pervasive generalities which may reflect the fundamentals of a subject and can be related to experience through the concept of “property” defined as that the magnitude of which is independent of the path used to reach it (Rogers and Mayhew, 1963). Properties can be used to formulate judgments about the truth, or otherwise, of a pronouncement with varying degrees of precision by exposing it to the test of experience. Using properties CS constructs models for reasoning to deduce precise predictive statements about the possible occurrence of a future event subject to conditions contained in the inferential mechanism. In order to do this CS employs mathematics as the symbolism that can deal with quantifiable properties and can be manipulated. CS creates intellectual order by arranging objects according to their properties into classes, mechanics or electricity, for example. It restricts its interest to parts of the world which recur with “unfailing” regularity. However, it is uncomfortable with irreversibility incurred in imperfections like friction, interdisciplinary problems like energy conversion, dynamics of many objects like networks and purposive activity in machines and living, human activities (Korn, 1987, 1995). It passes these topics to engineering. CS cannot cope with activities with “restricted” regularity exhibited by human components due to will, caprices, mood changes and so on. It has no interest in design (Korn, 1996). There is another view of parts of the world, the view of “systems”: collections of related properties or qualified objects themselves regarded as conjunctions of properties. Each collection or complexity is organized by qualified relations or interactions (static or dynamic system) into a “whole”. A particular whole itself will have a property which is meaningful to the whole but not to any of its constituents and is called emergent (Checkland, 1982). We may say that wholes are created to produce emergent properties. An intention of this paper is to enquire into how emergent properties appear.

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There is an immense variety and diversity of things which can be viewed as “systems” or complexities throughout the inanimate, animate, symbolic, technical and human activity fields. The question is how and why such variety and diversity have come about. The doctrine of emergence appears to be an answer to “how” and Darwin’s theory of evolution is that to “why”. The doctrine is of particular interest in the animate or living field (Bailey, 2003). The doctrine asserts that certain feature/property of an entity or a thing called a “whole” is novel not merely in the sense of being unexpected but in the theoretical sense of being unexplainable or unpredictable from the knowledge of features of the parts of which a whole is perceived to consist (Nagel, 1961). The property which satisfies this criterion is called emergent. Water regarded as a whole is the classical example with emergent properties like being transparent, liquid and so on. It is said that from the properties of its constituents, hydrogen and oxygen, it is impossible to predict the emergent properties. An objection to the doctrine of emergence is that the unpredictability condition is subject to prevailing knowledge concerning properties of wholes and parts. From the material and geometric properties of its components and their spatial relations we can predict a possible property of a chair as “supporting a person in sitting position under the buttocks and thighs”. We can also predict the “volume of a number of bricks stacked together and standing upright to form a wall” from the volume of each brick and their spatial relations. None of these emergent properties is unique. However, with the present state of knowledge we cannot predict the properties of water. In any case we shall see that the constituents of water as a whole are water molecules which consist of hydrogen and oxygen. A hierarchy has emerged. We intend to introduce an interpretation of the doctrine of emergence which is free from the unpredictability condition. This leads to an explicit expression for the emergent property of a whole as a description of combination of parts and their relations which together define the conceptual boundary of the whole, view of complexity. We can divide any part of a whole and any part of that and so on, leading to a hierarchy. An emergent property may usually be summed up by a name or a label and may be regarded as outcome which may occur by chance or design (Korn, 2006, b). A central aim of systems theory is to model complexity and hierarchy and to show how to design interacting objects for producing outcomes. In order to attempt such an enterprise we need to extract general principles from the classification of parts of the world and to introduce a symbolism that can cope with objects with predominantly qualitative properties. Mathematics in so far as the “real” world is concerned, deals with quantifiable properties and their relations, the object to which the properties refer, is lost. Natural language, the only other alternative symbolism, in so far as the “real” world is concerned, deals with qualified objects and their relations. Accordingly, the application of mathematics in a comprehensive systems theory is restricted. Natural language formalized into a homogeneous language can serve as the basis of a symbolism. Systems view of parts of the world A number of statements about parts of the world are suggested. Statement 1. Any part of the world is perceived in its entirety or as a “whole” When such whole is judged to be complete it is capable of creating an impression on living especially human objects. Complete entities are also capable of producing

relations and interactions as physical power or influence (Korn, 1995, 2001). Relations are: space (left, above. . .), time (before. . .), order (first. . .), kinship (father. . .), relational (and, or. . .), stative verbs (to be, to stay. . .) and passive voice of dynamic verbs (to be pushed). For example, a “royal palace” or “courage of the soldier” can create an impression on an observer, “the book is next to the pencil” expresses a relation. In the sentences “The boxer hits his opponent on the chin” and “the motor drives the cleaner” objects interact in a power – like way as shown by dynamic verbs (Korn, 2002). “The announcer says to the passengers that ‘the next train will be late’” is an influence interaction between “announcer” and “passengers” as indicated by the dynamic verb “say” which carries information signaled by the connective “that”. Perception of parts of the world as wholes has survival value: in face of danger the impression “snake (dangerous)” requires instant action “jump”. We distinguish the following entities as wholes: . Tangible objects which can be qualified by concrete properties (geometric, material, numerical, energetic and informatic) (Korn, 1995, 2001) as adjectives as well as by abstract properties (complex, mental, of condition and particular) and labeled by common noun phrases. No concrete property can exist on its own, everything consists of concrete properties, therefore, nothing can exist on its own. For example, we cannot have “length” which is not attached to some material object, similarly we cannot have a property “red” without geometry of what is “red”. . Intangible objects which can be qualified by adjectives expressing extensity, intensity, behavior or by abstract properties and labeled by abstract or collective noun phrases (Burton, 1984). . Activities are labeled by dynamic verbs qualified by adverbial phrases. All verbs are abstract in the sense that they can be broken down into series of verbs closer to experience. For example, “to move house (change place of residence)” involves number of activities. We can only perceive tangible objects. Intangible objects or abstract properties are used to describe static or dynamic experiences involving states or activities of tangible objects. Any intangible object, therefore, must be anchored to a tangible one, tangible objects are classified by means of properties and located in the spectrum in their meaning by adjectival phrases. For example, we can describe the “sadness of man (anchor noun)” or conclude that “man is sad” (mental property) by saying “man wears black suit” “eyes have tears” “face is distorted by lines”, etc. We can say that “soldier is combat ready” or “combat readiness of soldier” when “body is toughened by exercise” “mind is trained by instructors” “soldier knows how to handle rifle”, etc. Abstract properties or intangible nouns and abstract verbs have evolved to avoid repetition of listing concrete nouns and their relations or interactions, i.e. to increase effectiveness of natural language as a means of communication. Ideas, however, can be carried by and created using abstract language. Statement The term properties (effect or

2. Any part of the world can be seen as related properties or objects “entirety” implies “to consist of something”: related parts, objects or which are aggregated so as to POTENTIALLY produce an impression use), a new relation or interaction, each is regarded as OUTCOME.

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The potentiality may be labeled by an emergent property through abstract adjectival phrases or clauses (view of complexity). An entirety, a tangible object, can be divided into related parts or components which can be further divided and so on until an agreed limit is reached. Atoms, molecules or concrete properties can act as “limit”. Conversely, entities can be aggregated either by chance (evolution) or in accordance with purpose (design) until a new property is seen to have emerged (view of hierarchy) (Korn, 2006a). When a tangible or intangible object is seen as a collection of related properties or objects, we have a static view of a part of the world. When a number of objects are seen as interacting entities we have a dynamic view or activity. Impressions as outcomes are created by activities. Statement 3. The systems (or systemic) view (views of complexity and hierarchy) is pervasive, indivisible and empirical We experience an immense variety and diversity of particular instances of parts of the world as indicated by the classification above which transcends divisions imposed by views like technical systems, information systems, cybernetic systems, management systems, etc. There is an enormous variation of details but the underlying systems view is general. Statement 4. The symbolism of building blocks forming a homogeneous language is used to model instances of complexity, hierarchy and activities Natural language as a primary model for expressing views, beliefs or opinions through sentences of the subject – predicate form has evolved an aid for human beings to navigate in their environment. For the successful accomplishment of this natural language must be isomorphic to parts of the world, just like any other model. We have asserted that any part of the world is seen as related objects, natural language as part of the classification above satisfies this requirement. For example, a word like “mile” is a set of related “letters” which, when the spatial relations change, becomes “lime” with outcome or meaning of the whole completely different. A sentence of the subject-predicate form reflects the idea of related objects: there is a noun phrase, the subject, a tangible or intangible object, the centre of attention, the initiating object, about which something is alleged which is expressed as a relation, a verb, plus the “object” of relation in the grammatical sense (Burton, 1984; Korn et al., 1991; Korn, 2003). A sentence acquires meaning, its outcome or emergent property, through referring to a part of the world seen as “objects in relations”. The minimal linguistic element that retains this feature is the “one or two place” declarative sentence. This kind of sentences called building blocks or ordered pairs are used for constructing a description of an instance of the immense variety and diversity of parts of the world. Just like bricks are used for constructing the large variety of buildings. This notion is used extensively in CS and is called reductionism (Korn, 2006b). When a story or narrative in natural language describing complexity, hierarchy or activity, a scenario, is expressed as a collection of one and two place sentences the result is homogeneous language. Sentences in natural language are transformed with acceptable fidelity into a combination of ordered pairs by linguistic analysis (Korn, 2004). Homogeneous language leads to the construction of predictive, reasoning schemes called static and dynamic linguistic modeling.

Static linguistic modeling The intention is to describe how a variety of possibilities of aggregates with or without identifiable emergent properties can occur. The identification of an emergent property sets the upper limit to aggregation. Concrete properties act as the lower limit. The possibilities can then be exposed to scrutiny for acceptance or rejection by agents with interest outside the conceptual boundary of an aggregate or whole called environmental agents. One and two place sentences are used for exhibiting the variation of aggregates. They are regarded as “propositional functions” used for creating “ordered pairs” (Lipschutz, 1964) of objects or properties designated as “nouns phrases”. In general, a series of two place sentences can be written as: ni ðadjix Þreli ðadviy Þnj ðadjjz Þ

ð1Þ

where adj – adjectival qualifiers of nouns “n” adv – adjectival or adverbial qualifiers of relations “rel”. These are contingent properties which locate a sentence element at a point in its spectrum of meaning and selected so as to be relevant to the nouns and relations. Without such properties a sentence is context free, its truth value can never be ascertained (Magee, 1985). In a one place sentence the subscript j ¼ 0. For each “I” designating a noun, we can have a number of adjectival qualifiers: for i ¼ 1

x ¼ 1; 2; . . .Xð1Þ

i¼2

x ¼ 1; 2; . . .Xð2Þ

and so on

where “X” is a positive integer. Subscript “j” can be similarly expanded. Each noun as the subject of the sentence has a relation attached to it, therefore, the “rel” carries subscript “i” as well with a number of qualifiers, y ¼ 1, 2,. . .Y. We assume that we have a set of qualified, unrelated objects designated by noun phrases “A” randomly distributed in a group: A ¼ {ðni ðadjix ÞÞðreli ðadviy ÞÞ}

ð2Þ

each member of the set is called “a”. To each object “n” we attach a qualified relation which designates the static relationship that the object is judged to be capable of entering into. Another set “B” with members “b” is formed: B ¼ {ðni ðadjix ÞÞ}

ð3Þ

The two sets enter into a product set A £ B, or Cartesian product, consisting of ordered pairs (a, b). This notion can be written as: A £ B ¼ {ða; bÞj a1A; b1B}

ð4Þ

Each unrelated object in equation (2), “i ¼ a” enters into relationship with itself and with others designated by the subscript “k ¼ b” in the same group to form ordered pairs arranged according to equation (4): A £ B ¼ {ðnik ðadjix ÞÞðreli ðadviy ÞÞ}

ð5Þ

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for i ¼ 1

k ¼ 1; 2; 3. . .K

i¼2

k ¼ 1; 2; 3. . .K

i¼3

k ¼ 1; 2; 3. . .K

and so on

here “i” and “k” are the vertical and horizontal expansion subscripts with “i ¼ k” leading to a square array representing equation (5) with the number of ordered pairs: Number of ordered pair ¼ n 2

ð6Þ

For example, we let: i ¼ k ¼ 4 and x ¼ y ¼ 0, i.e. we consider context-free sentences then equation (5) becomes: n11

n12

n13

n14

n21

n22

n23

n24

n31

n32

n33

n34

n41

n42

n43

n44

ð7Þ

Each term in equations (5) and (7) is an ordered pair. For example, the sentence or the story “Top of the table is supported by legs which stand on the carpet” is expressed following equation (2) as: i ¼ 1 ¼ “top is supported” i ¼ 2 ¼ “legs stand on” and i ¼ 3 ¼ “carpet is”. Using equation (5) we have: 0

ðtop is supported by legsÞ ðtop is supported by carpÞ

n11

n12

n13

ðlegs stand on topÞ

0

ðlegs stand on carpÞ

n21

n22

n23

ðcarp is topÞ

ðcarp is legsÞ

ðcarp is carpÞ

n31

n32

n33

ð8Þ

In equation (8) one selected term in each row is part of the sentence. In the first row “top is supported by legs” in the second row “legs stand on carpet” and in the third row “carpet is carpet”. The three relations together may be described as: “table supporting arrangement” the emergent property of the whole bounded by the conjunction of the three ordered pairs. However, the array offers a choice of aggregation. For example, we have in the first row “top is supported by the carpet” in the second row “legs stand on top” and in the third row “carpet is carpet”. This aggregate also makes sense, we can name it “upside down table” as its emergent property. We can conclude that the arrays in equations (5), (7) and (8) offer possibilities for choice of wholes and show how a variety of structures emerge from a collection of separate objects for existence, possible use or potential accomplishment of change in the context of design.

A novel emergent property is produced by a new structure. Varying the qualifiers of nouns and verbs enables an existing structure to adapt or fail to adapt to objects external to it called environmental objects. We construct a pattern of relations which gives rise to an emergent property by selecting one relation from each row of an array like equations (7) or (8). The converse would mean that the same object would be related to more than one other object, an indeterminacy. In other words, we allow a single instance in the domain with multiple range which creates a function (Lipschutz, 1964). Accordingly: Y Emergent property ¼ ðnik Þ ¼

i¼I Y

ððniðwith

any one of k¼1;2;3...Þ ðadjix ÞÞðverbi ðadviy ÞÞÞ

Systems view, emergence and complexity 783

ð9Þ

i¼1

Q in which for each “i” we select a specific “k”. is the operator which defines the conceptual boundary of a whole and indicates that an emergent property describes a whole which is greater than the “sum of its parts”. In other words, a whole is not an algebraic sum but an aggregate of parts with relationships. Application of equation (9) to (8) results: Table supporting arrangement ¼

i¼3 Y

ðn12 þ n23 þ n33 Þ

ð10Þ

i¼1

where the “ þ ” sign signifies simultaneous occurrence. Representation of arrays by graphs The array of ordered pairs in equations (5) and (7) is a collection of objects and relationships which can be represented as a graph (Ore, 1962, Korn, 1995). The “nouns” in an array as equation (5) are depicted as “nodes” which are connected by lines designating the ordered pairs. Using equation (7) as a demonstration we construct Figure 1 which stands for equation (3), i.e. the objects are unrelated. Each object can enter into relationships with the others in (n 2 1) ways and with itself making the total number of relations equal to “n”. Thus, Figure 1 is modified to in Figures 2 with 4 relations at each node.

n1

n2

n3

n4

Figure 1. Graph of unrelated objects

n14, n41 n33

n13, n31 n1

n2 n12, n21

n11

n3 n23, n32

n22

n44 n4

n34, n43 n24, n42

Figure 2. Graph of related objects

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Selection of one term in each row of an array means in graph terms that only one line is allowed to leave a node but a node can have any number of lines entering. “Leaving” and “entering” are defined by the order of subscripts. The graph shows the choice thus offered by combining objects in a group in a variety of ways to create emergent properties if the choice “makes sense” semantically. Selection of one term also obviates the possibility of the same two or more objects having the same relationships with different objects at the same time. Equation (8) demonstrates this restriction: “carp is legs” “carp is tops”. “Carp” cannot be both at the same time, it must be either. The selection of a particular choice is given by the tree of a graph (Ore, 1962, Korn, 1995). Tree is defined as a graph which connects all nodes without forming a loop (self loops are exempted). A tree of the graph in Figure 2 is shown in Figure 3. When constructing a tree we insert a line or branch which connects two nodes. Each additional branch inserted subsequently connects one additional node. Thus: Number of tree branches ¼ n 2 1

ð11Þ

According to equation (11) the number of relationships equals the number of tree branches. Since, the number of rows is “n” one self-relationship can be included. If the number of relations is less than “n 2 1” we have one or more nodes, i.e. objects without relationships disconnected from the rest of the aggregate. If the number of relationships is more than the number of tree branches the surplus relations may contravene the “function” requirement. The number of trees for an undirected graph which can be constructed on “n” nodes is given by (Ore, 1962): Number of trees ¼ n ðn22Þ :

ð12Þ

The tree which represents an emergent property in equation (8) is shown in Figure 4. The number of trees from equation (12) equals 3.

n14

Figure 3. Graph of a tree

n1

n12

n2

n23

n3

n4

legs n2

top n1 supported by n12

Figure 4. Graph of “table supporting arrangement”

stand on n23 is n33

carp n3

The increase of possibilities as shown by the increasing number of trees as the number of objects in a group grows, is demonstrated by the table: n ¼ 1; 2; 3; 4; 5. . .

Systems view, emergence and complexity

Number of trees from equation ð12Þ ¼ 0; 1; 3; 16; 125. . .

785 When directed graph representation of arrays, equation (5), is considered the growth of the number of trees is much greater. Introduction to dynamic linguistic modeling Emergent properties or outcomes can occur by chance or by design. In either case, they are caused by or emerge as a result of being assembled by activities or dynamic systems acting in accordance with an algorithm, with or without purpose, as an organization in a scenario described by a story. The story is expressed in terms of homogeneous language which is turned into a semantic diagram leading to series of predicate logic statements with uncertainties (Durkin, 1994) due to the nature of components especially human. This process is outlined here. Dynamic linguistic modeling consists of stages: (1) Identification of linguistic complexities to be converted by linguistic analysis into homogeneous language while preserving the meaning of the original story to an acceptable degree. (2) Construction of semantic diagram which is a pictorial representation of one and two place sentences showing the topology of scenario. (3) Derivation of series of pairs of predicate logic expressions from the diagram which carry expressions for graded qualifiers carrying uncertainties associated with components. Uncertainties arise due to mood changes, caprices, ambitions, likes and dislikes, etc. of human beings and are superimposed on the functional activities which such beings are expected to perform. (4) Computation of possibility of outcomes of a scenario explicitly available as a result of progression of states in time expressed as acquired properties. Linguistic analysis has made explicit the dynamic verbs which attract one or two nouns with their qualifiers. These are the building blocks of which a complete scenario is constructed as a semantic diagram. Dynamic verbs denote processes, events and actions which cannot occur by themselves, they are caused. This implies a relation between contingent properties, interaction and change: (1) The interaction (in) represented by a dynamic verb is related to the relevant, contingent properties of an object initiating interaction. An interaction is assumed to be caused by a driving (dp) property supplemented by properties which facilitate/hinder (ip) interaction, (2) The change of property of an affected object or change of state leading to an acquired property (ap) driven by the interaction, is causally related to the interaction (in) itself supplemented by facilitating/hindering (ep) properties of the affected object,

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(3) A property once acquired (ap) can function as a driving property (dp), can support an interaction as an “ip” property or the change of property of another object as “ep” property, in the course of propagation of change of state as a scenario unfolds. In addition we introduce the notion of calculating property (cp) to qualify causation which is used to perform comparison, decision or calculations as required in a scenario with purposive activities. Uncertainties associated with properties or qualifiers can be introduced into linguistic modeling by graded adjectives, measure of grades and personality profiles to which certainty factor can be assigned (Durkin, 1994; Korn, 2003). The causal relations between a driving property and an interaction and an interaction and an acquired property lead to expressing a one- or two-place sentence as a pair of logical conditionals. For instance, the sentence or story of a scenario “As part of his duty with care about the job (dp) and with good eye sight (ip), the postman sorts (in) according to code (adverbial phrase) properly addressed (ep) letters” can be formulated into: IF (it is part of his duty and with care about the job) AND (he has good eye sight) THEN the postman sorts letters (according to code). IF the postman sorts letters (according to code) AND the letters are (properly addressed) THEN the letters become sorted (ap – acquired property) (OUTCOME).

The result of the “postman’s” action in the example above is a change of physical property of the “letters” referred to as outcome. Exercising his skilled power, the “postman” converted letters from unsorted into sorted, he has created order out of chaos.

Examples of building blocks We use the scenario just described for a two place sentence. Homogeneous language of context-free sentences (from the story) Postman sorts letters. (Skilled power carrier) Semantic diagram Shown in Figure 5 where the object labels are enclosed in contours connected by solid, directed lines of interaction pointing from initiating towards the affected object. The dotted directed line indicates change in time, not explicitly stated here. Undirected lines carry qualifiers.

dp(1,1) – duty/care ip(1,1) –eyesight

Figure 5. Semantic diagram of a two-place sentence, a basic constituent

1

postman

ep(2,2) - addressed

letters sorts (accord..) in (1,2)

2

3

letters

ap(3,3) sorted ??? (OUTCOME)

Systems view, emergence and complexity

Adjectival qualifiers with grading (from the story) dpð1;1Þ2part of his duty ðstrong; med; weakÞ; care ðhigh; lowÞ; ðdp2driving propertyÞ ipð1;1Þ2eyesight ðexcellent; poorÞ; epð2;2Þ2addressed ðperfect; mistakeÞ;

787 Logic sequences/topology of scenario (from the semantic diagram) 1=1:dpð1;1Þ^ipð1;1Þ!inð1;2Þ 1=2:inð1;2Þ^epð2;2Þ!apð3;3Þ Interactions with adverbial qualifiers inð1;2Þ2sorts: sorts ðaccording to codeÞ ðskilled power carrierÞ Logic sequences with graded adjectives/data for certainty factors 1=1: dpðpman;1;1; ðdutyðstrong;90=:8; med;70=:6:weak; 40=:4ÞÞ; ðcareðhigh; 80=:8; low;60=:5ÞÞÞð:Þ^ipðpman;1;1;ðeyeðexcel;90=:7; poor;30=:2ÞÞÞð:Þ! ðcf of ruleÞ inðsorts;pman;1;letters;2;ðhowðacctocodeÞÞÞðcf of input functionÞ 1=2: inðsorts;pman;1;letters;2;ðhowðacctocodeÞÞÞðcf of input functionÞ^ epðletters;2;2;ðpropadðperfect;90=:2;mistake;40=:8ÞÞÞð:Þ! ðcf of rule: 1 or21Þ apðletters;3;3;ðlettersðsorted;...ÞÞÞ which enables us to compute that the OUTCOME occurs, i.e. the “letters get sorted” with certainty ranging from 0.05 (unknown) to 0.7 (nearly certain). A one-place building block is given by the story “Depressed, strong willed man with financial problems, tried to kill himself two weeks ago by jumping off a cliff” is diagrammed in Figure 6. A further example In general, a story is replaced by a collection of interconnected one and two place sentences or homogeneous language which can be read just like the story itself. These are joined as a semantic diagram representing the story from which the inferential

dp(1,1) – with financial.... ip(1,1) – depressed ep(1,1) - strong willed

1

man

man in(1,1) – tried (....)

ap(2,2) – at bottom of cliff ??? (OUTCOME) 2

Figure 6. Semantic diagram of one-place sentence, a basic constituent

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mechanism of predicate logic statements is constructed. This is demonstrated by the following story of a scenario and the subsequent semantic diagram in Figure 7. The story: “An assortment of labeled sandwiches (sw) all mixed up are delivered to a food shop. Staff in the shop are under pressure so the skilled assistant whose job is to sort out the sw for customers’ attention, works fast”. The shop keeper wants sw to be available for easy access and selection by customers. This is the emergent property of sw as stipulated by the shop keeper. “Access” means that sw are to be placed on shelves. “Selection” means that sw are to be arranged and priced according to their content (cheese, ham or tuna). From equation (3) we have four nouns or objects: sw, sh (shelves), co (content) and pr (price) to which we assign stative verbs as in equation (2). “sw are placed on (pl), sh are ready to receive (rec), co is used to arrange (use), pr are attached to (att)” from which we construct the array as in equation (5).

cp(1,1) cp(1,6) cp(1,7) dp(1,1) – has job ip(1,1) – skilled, under pressure 1

cp(2,3) ep(2,2) – delivered, mixed, labelled

asistant

sw

2

places (quickly, on shelves..) in(1,2) time 2. ap(6,6) aware... (on shelves)

time 1. checked by in(3,1)

ap(3,5) on shelves

assistant

sw

6

3

arranges (quickly, as ch/h/t..) in(6,3)

time 4. ap(7,7) aware... (arranged) 7 assistant

time 3. checked by in(4,6)

ap(4,5) arranged... sw

4

attaches (quickly, prices...) in(7,4) time 6. ap(8,8) aware.. assistant

time 5.

checked by in(5,7) 8 OUTCOME !!

ap(5,5) priced 5

time 7.

Figure 7. Semantic diagram of scenario

customers aware... ap(10,10)

10 OUTCOME !!

customers 9

sw

noted by in(5,9) ep(9,9) interested

0

sw pl sh

sw pl co

sw pl pr

n11

n12

n13

n14

sh rec sw n21

sh rec sh n22

sh rec co n23

sh rec pr n24

co use sw n31

co use sh n32

0 n33

co use pr n34

pr att sw

pr att sh

pr att co

0

n41

n42

n43

n44

We can generate from the array the emergent properties which make sense: (1) sw are placed on sh, sh are ready to receive sh, co is used to arrange sw, pr are attached to sw; (2) sw are placed on sh, sh are ready to receive sh, co is used to arrange sw, pr are attached to sh; (3) sw are placed on sh, sh are ready to receive sh, co is used to arrange sw, pr are attached to co. Using equation (9) for the first case only: Emergent property 1 ¼

i¼4 Y

ðn12 þ n22 þ n31 þ n41 Þ

i¼1

Any one of the emergent properties can be put into practice by the shopkeeper who is environmental agent who makes the selection and instructs the “assistant” who will act accordingly as depicted in the semantic diagram in Figure 7. Further, to Figure 7 “customers” will become aware of “sw” when the conditions as acquired properties (ap) for an emergent property are all present: ap(3, 5) ¼ “sw are on shelves” ap(4,5) ¼ “sw are arranged” and ap(5, 5) ¼ “sw are priced”. Conclusions A view of parts of the world as a continuum of bounded tangible objects has been developed. States and activities of these are designated by intangible objects, all labeled as noun phrases. Activities themselves are designated by verbs. Qualified nouns and verbs are organized into sentences which as a story describe scenarios. We have shown how to construct objects and their activities from elementary building blocks to create the “systemic view” of related objects leading to a unified treatment of diverse parts of the classification in “BACKGROUND”. Tangible and intangible objects create impressions on human beings which may lead to response to these impressions such as their physical use (pair of shoes) or change of mental state (alteration of life style). The method outlined here may be used in the: (1) analysis of objects to find out whether they have the impression prompted by their emergent properties and expected of them; (2) analysis of interacting objects to see the total impression, if any including chaos, they have produced;

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(3) design of objects with specifically stated impression together with that of the interacting dynamic systems necessary for their production; and (4) study of evolution of objects from simple to complex through the vast number of choices which an array like equation (5) generates and the possibilities of aggregation by assigning sources and sinks using network theory. CS is driven by curiosity, systems science, the subject of this paper, is driven by investigation and creation of outcomes of aggregates produced by chance or in accordance with purpose. Chemistry although regarded as part of CS has been concerned with atoms and molecules related through the chemical bond. References Bailey, K. (2003), “Emergence in LST”, Proceedings of 47th Annual Conference of ISSS, Iraklion, Crete, July 7-11. Burton, S.H. (1984), Mastering English Grammar, Macmillan, London. Checkland, P. (1982), Systems Thinking, Systems Practice, Wiley, Chichester. Durkin, J. (1994), Expert Systems, Macmillan, New York, NY. Korn, J. (1987), “Modelling of devices as generalised system components”, Journal of the Franklin Inst., Vol. 324 No. 3, pp. 479-489. Korn, J. (1995), “Theory of spontaneous processes”, Structural Eng Review, Vol. 7 No. 1, pp. 23-33. Korn, J. (1996), “Domain-independent design theory”, Journal of Engineering Design, Vol. 7 No. 3, pp. 293-311. Korn, J. (2001), “Design and delivery of information”, European Journal of Information Systems, Vol. 10 No. 1, pp. 41-54. Korn, J. (2002), “‘Physics approach’ to general systems theory”, Kybernetes, Vol. 31 Nos 9/10, pp. 1442-51. Korn, J. (2003), “Concept and a theory of systems”, Systemist, Vol. 25 No. 1, pp. 31-62. Korn, J. (2004), “Elicitation of systems and products from scenarios”, Systemist, Vol. 26 No. 1, pp. 7-39. Korn, J. (2006a), “Systemic view of parts of the world”, paper presented at ISSS 50th Annual Meeting, Sonoma State University, CA, July 3-14. Korn, J. (2006b), “Reductionism in systems science”, paper presented at UKSS Conference, Oxford, September 11-13, pp. 138-50. Korn, J., Huss, F. and Cumbers, J. (1991), “Analysis and design of socio-economic systems”, in Jackson, M.C. et al. (Eds), Systems Thinking in Europe, Plenum Pub., NY. Lipschutz, S. (1964), Set Theory, McGraw-Hill Book Co., New York, NY. Magee, B. (1985), Popper, Fontana Press, London. Nagel, E. (1961), The Structure of Science, Routledge & Kegan Paul, London. Ore, O. (1962), Theory of Graphs, American Mathematical Society, New York, NY. Rogers, G.F.S. and Mayhew, Y. (1963), Engineering Thermodynamics, Longman, London. Corresponding author J. Korn can be contacted at: [email protected]

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Time-splitting procedures for the solution of the two-dimensional transport equation Mehdi Dehghan

Time-splitting procedures

791

Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran Abstract Purpose – The diffusion-advection phenomena occur in many physical situations such as, the transport of heat in fluids, flow through porous media, the spread of contaminants in fluids and as well as in many other branches of science and engineering. So it is essential to approximate the solution of these kinds of partial differential equations numerically in order to investigate the prediction of the mathematical models, as the exact solutions are usually unavailable. Design/methodology/approach – The difficulties arising in numerical solutions of the transport equation are well known. Hence, the study of transport equation continues to be an active field of research. A number of mathematicians have developed the method of time-splitting to divide complicated time-dependent partial differential equations into sets of simpler equations which could then be solved separately by numerical means over fractions of a time-step. For example, they split large multi-dimensional equations into a number of simpler one-dimensional equations each solved separately over a fraction of the time-step in the so-called locally one-dimensional (LOD) method. In the same way, the time-splitting process can be used to subdivide an equation incorporating several physical processes into a number of simpler equations involving individual physical processes. Thus, instead of applying the one-dimensional advection-diffusion equation over one time-step, it may be split into the pure advection equation and the pure diffusion equation each to be applied over half a time-step. Known accurate computational procedures of solving the simpler diffusion and advection equations may then be used to solve the advection-diffusion problem. Findings – In this paper, several different computational LOD procedures were developed and discussed for solving the two-dimensional transport equation. These schemes are based on the time-splitting finite difference approximations. Practical implications – The new approach is simple and effective. The results of a numerical experiment are given, and the accuracy are discussed and compared. Originality/value – A comparison of calculations with the results of the conventional finite difference techniques demonstrates the good accuracy of the proposed approach. Keywords Cybernetics, Difference equations, Stability (control theory), Numerical analysis Paper type Research paper

1. Introduction It is essential to approximate the solution of advection-diffusion partial differential equations numerically in order to investigate the prediction of the mathematical models, as the exact solutions are usually unavailable. This paper will be concerned with the applications of time-splitting procedure for solving the two-dimensional advection-diffusion equation.

Kybernetes Vol. 36 No. 5/6, 2007 pp. 791-805 q Emerald Group Publishing Limited 0368-492X DOI 10.1108/03684920710749857

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The time-splitting method can be applied to one equation incorporating several different physical processes by splitting it into a number of equations each involving only one physical process. The type of time-splitting method which appears most frequently in the literature is called the “Locally One-Dimensional” method, so named because the solution of one complicated multi-dimensional partial differential equation is replaced by a sequence of solutions of simpler one-dimensional partial differential equations in progressing from one time level to the next. In some cases the latter may only involve a single physical process, such as diffusion or advection. The transport equation is split so that the transport process in each of the two dimensions take place separately in two fractional time steps in a LOD procedure. Then the advection and diffusion components of each one-dimensional transport process can be separated into two smaller fractional time steps. This approach will not be employed in this research. The transport equation is the basis of many mathematical models of physical, chemical and biological phenomena, and their use has also spread into economics, financial forecasting and other fields. The present paper deals with the two-dimensional transport equation:

›u ›u ›u ›2 u ›2 u þ bx þ b y ¼ ax 2 þ a y 2 ; ›t ›x ›y ›x ›y

0 , t # T;

ð1Þ

in the domain 0 # x # 1, 0 # y # 1, with initial condition: uðx; y; 0Þ ¼ f ðx; yÞ;

0 # x; y # 1;

0 , t # T;

ð2Þ

uð0; y; tÞ ¼ g 0 ð y; tÞ;

0 , t # T;

0 , y , 1;

ð3Þ

uð1; y; tÞ ¼ g 1 ð y; tÞ;

0 , t # T;

0 , y , 1;

ð4Þ

uðx; 0; tÞ ¼ h0 ðx; tÞ;

0 , t # T;

0 , x , 1;

ð5Þ

and boundary conditions:

ð6Þ uðx; 1; tÞ ¼ h1 ðx; tÞ; 0 , t # T; 0 , x , 1; where f, g0, g1, h0, h1, are known functions, while the function u is unknown. Note that u(x,y,t) is a transported (advected and diffused) scalar variable, bx . 0 and by . 0, being constant speeds of advection and ax . 0 and ay . 0 being constant diffusivities in the x-and y-direction, respectively. The transport equation occurs in many other physical situations. These include the transport of heat in fluids, flow through porous media, and the spread of contaminants in fluids, water transport in soils (Parlarge, 1990), absorption in beds (Lapidus and Amundston, 1952), tidal flow, etc. (Chatwin and Allen, 1985; Chaudhry et al., 1983; Dehghan, 2005; Fattah and Hoopes, 1985; Gane and Stephenson, 1979; Guvanasen and Volker, 1983; Hindmarsh et al., 1984; Holly and Usseglio-Polatera, 1984; Isenberg and Gutfinger, 1972; Kumar, 1988; Lapidus and Amundston, 1952; Lax and Wendroff, 1964; Salmon et al., 1980; Zlatev et al.; 1984). The two-dimensional form of the transport equation has been used to describe heat transfer in a draining film (Isenberg and Gutfinger, 1972), dispersion of dissolved material in porous media and in flowing ground water, the dispersion of pollutants in

rivers and streams (Chatwin and Allen, 1985) the spread of contaminants in estuaries and coastal seas, spread solute in a liquid flowing through a tube, long range transport of pollutants in the atmosphere, and forced cooling by fluids of solid material such as winding in turbo-generators, thermal pollution in river systems (Chaudhry et al., 1983), flow in porous media (Kumar, 1988) and dispersion of dissolved salts in ground water (Guvanasen and Volker, 1983). Unfortunately, little progress has been made toward analytical solution to the two-dimensional transport equation with ax, ay and bx, by constant when initial and boundary conditions are complicated. Consequently, much efforts should be put into developing stable and accurate numerical solution of equation (1). Various numerical techniques such as finite difference and finite element methods have been used in the past to solve the one-dimensional version of equation (1) approximately. When convection dominates diffusion, the general finite difference or finite element methods often result in numerical oscillation. Several finite difference techniques are discussed in Dehghan, 2005. The modified equivalent approach (Warming and Hyett, 1974) is employed in Dehghan (2004) to compare the existing schemes and also to develop new higher order procedures. In Patrico (1990), three implicit finite difference schemes are considered for the solution of the one-dimensional constant coefficient transport equation. Two of them are first and second-order accurate in time. These methods are seen to be L – stable and L0 – stable, depending on the relation between the convection and diffusion parameters and the step size. The third formula is shown to be third-order accurate in time and is also L – stable. However, some oscillations may appear in the solution. To avoid these oscillations some restrictions are suggested. No numerical results are presented in the work of Patrico (1990). Using semi-discretization, the partial differential equation and its boundary and initial conditions are approximated with a first-order initial value system of ordinary differential equations. A multi-step method is chosen for solving the resulting system of ordinary differential equations. Twizell (1985) developed some L – stable and L0 – stable techniques which were first and second-order accurate with respect to the time variable. Unfortunately, the numerical solution can present oscillations if the order is two. Kohler and Voss (1999) employed the method of lines for solving several time-dependent partial differential equations including the one-dimensional constant coefficient advection-diffusion equation. However, the numerical solution of the resulting ordinary differential system can present difficulties depending on the method used. In particular, oscillations may appear in the solution when standard methods are applied to the ordinary differential equations system arising from the semi-discretization of the diffusion-convection equation. Second-order methods are examined in Kohler and Voss (1999) for such system. The resulting predictor-corrector schemes are L – stable, economical and oscillation free. In Ruxun et al. (1999), based on the idea of the modified partial differential equation of finite difference schemes (Warming and Hyett, 1974), a new designing approach is proposed to develop finite difference schemes for solving some partial differential equations including the one-dimensional convection-diffusion equation. According to the consistency, monotonicity or positivity, the remainder-effect analysis of finite difference equations (Ruxun, 1995), the coefficients of finite difference equations can be determined. Thus, the approach is much more constructional and directional. Moreover, it is a designing way for the high resolutional and high-order accuracy finite

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difference schemes. The results of some numerical experiments are given in Ruxun et al. (1999). It is worth noting that these authors only discuss the one-dimensional model. Author of Chaudhry et al. (1983) developed a high order upwind scheme. The upwind scheme is an efficient technique but is only first order accurate. In Zlatev et al. (1984), an alternative direction iterative method combining with one-dimensional second order upwind scheme is given for two-dimensional problem. It also can be used as a high speed algorithm on parallel computers. Some numerical examples are given in Rui (2003). Several finite difference techniques have been developed to solve convection-diffusion problems approximately. The majority of them are either first-order or second-order accurate with respect to the space variable. They also have poor quality for convection dominated flows if the mesh is not sufficiently refined. High order schemes are generally produce banded linear systems with large band-width. Thus, they need a large number of arithmetic operations, especially for three-dimensional problems. To obtain satisfactory higher order numerical schemes with reasonable computational cost, there have been attempts to develop higher order compact techniques, which utilize only the grid nodes directly adjacent to the central node. A nine-point higher order compact implicit method for unsteady two-dimensional convection-diffusion equation with constant coefficient is proposed in Noye (1989). This scheme is third-order accurate with respect to the space variable. Some compact finite difference procedures of order four in space are derived in Rigal (1994). Karaa and Zhang (2004) developed a high order alternating direction implicit scheme for solving the unsteady convection-diffusion equation. It permits multiple use of the one-dimensional tridiagonal algorithm with a considerable saving in computing time, and produces a very efficient solver. The unconditional stability of the method is given using a discrete Fourier analysis. Results of numerical computations are presented to test its high accuracy and to compare it with some well known schemes. Some second-order three-level finite difference methods which are easy to use, are introduced in Varah (1980) for solving the one-dimensional convection-diffusion equation. The stability analysis for such schemes is given and the restrictions are discussed. A systematic approach is given in Kwok and Tam (1993) for deriving von Neumann stability conditions for three-level finite difference procedures for approximating the multi-dimensional convection-diffusion equation. Some three-level second-order methods which are easy to use are developed. The treatise includes von Neumann stability analysis for pure initial-value problems and matrix stability analysis for Dirichlet boundary-value problems. Four leap-frog schemes considered, only one of them is conditionally stable. The other leap-frog methods are practically useless since they are all unconditionally unstable. Stability analysis for finite difference schemes for solving the three-dimensional convection-diffusion equation, in particular for three-level schemes, is often quite tedious. The simple strategy of deducing the stability conditions for the convective-diffusion equation by satisfying simultaneously stability requirements for both the heat and wave equations has been proven to be incorrect in many cases. A comprehensive study of stability analysis of difference approximations for pure initial-value problems of one-dimensional convection-diffusion equations has been performed by Chan, 1984. Fourier stability analysis of leap-frog finite difference schemes for pure initial-value problems of multi-dimensional constant-coefficient convective-diffusion equations is attempted by Schumann (1975) and Cushman-Roisin (1984). In dealing with the numerical solution of

fluid flow problems by finite difference methods. Cushman-Roisin (1984) discusses criteria for predicting critical time steps for the stability of multi-level schemes. Combined leapfrog and Dufort-Frankel, leapfrog and time-lagged Euler, and upwind differences and Euler schemes are examined in Kwok and Tam (1993). The work of Cushman-Roisin (1984) is devoted to the development of a new scheme for the discussion of the stability of finite difference methods. The general technique is described for the case in which the amplification factor is given by a complex quadratic equation. The methodology is shown to be very powerful for the study of combined schemes. It is successfully applied to the analysis of the stability of the leap frog Dufort-Frankel method. In Kwok and Tam (1993) a systematic procedure is developed for analyzing von Neumann stability for leap-frog-type finite-difference schemes for pure initial-value problems of the mixed initial-boundary-value problem of the three-dimensional advection-diffusion equation. Discrepancies on time-step restrictions between von Neumann stability analysis and matrix stability analysis are observed in Kwok and Tam (1993). A number of mathematicians developed the method of time-splitting to divide complicated time-dependent partial differential equations into sets of simpler equations which could then be solved separately by numerical means over fractions of a time-step. For example, they split large multi-dimensional equations into a number of simpler one-dimensional equations each solved separately over a fraction of the time-step in the so-called locally one-dimensional (LOD) method. In the same way, the time-splitting process can be used to subdivide an equation incorporating several physical processes into a number of simpler equations involving individual physical processes. Thus, instead of applying the one-dimensional advection-diffusion equation over one time-step, it may be split into the pure advection equation and the pure diffusion equation each to be applied over half a time-step. Known accurate computational procedures of solving the simpler diffusion and advection equations may then be used to solve the advection-diffusion problem. It is worth pointing out that a special type of time-splitting technique, called the “Alternating Direction Implicit Scheme” introduced by Peaceman and Rachford (Lapidus and Pinder, 1982). Alternating direction implicit procedures require only the inversion of a tri-diagonal system of equations at each fractional step. The complete partial differential equation for the original problem is used at each fractional step, but the differencing is done in such a way that there are only three unknown values in a single spatial direction in the finite difference equation used for each step. In this way, the inversion of a large sparse matrix at each time step is replaced by a number of applications of the very efficient Thomas algorithm. The approach in this paper is not of this type. Note that Gourlay and Mitchell (Lapidus and Pinder, 1982) have shown the equivalence of the alternating direction implicit method and the LOD scheme for a wide class of partial differential equations. In the present research several numerical finite difference schemes (Dehghan, 2006) will be developed and compared for solving the two-dimensional transport equation. An outline of this work is as follows: Section 2 describes some applications of the time-splitting technique to the numerical solution of the two-dimensional advection-diffusion equation. Firstly, LOD procedures are examined and some second and fourth-order methods are developed. Various finite difference methods for the solution of equations (1)-(6) are described in

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Sections 2 and 3. The accuracy and efficiency of the developed methods are also presented in this section. Numerical experiments have been performed to test the effectiveness of the algorithms presented, results of which are discussed in Section 4. Section 5 is devoted to a brief conclusion. Finally, some references are introduced at the end.

796

2. The finite difference schemes 2.1 Notations The solution domain of the problem is covered by a mesh of grid-lines: xi ¼ iDx;

i ¼ 0; 1; 2; . . . ; M 1 ;

ð7Þ

yj ¼ jDy;

j ¼ 0; 1; 2; . . . ; M 2 ;

ð8Þ

tn ¼ nDt;

n ¼ 0; 1; 2; . . . ; N ;

ð9Þ

parallel to the space and time coordinate axes, respectively. Approximations uni; j to u(iDx,jDy,nDt) are calculated at the point of intersection of these lines, namely, (iDx,jDy,nDt) which is referred to as the (i, j,n) grid-point. The constant spatial and temporal grid-spacing are Dx ¼ 1=M 1 , Dy ¼ 1=M 2 , and Dt ¼ T=N , respectively. The notation ui;nðj pÞ will be used to denote the temporary value of u at grid point (iDx, jDy) at the end of the pth fractional time step. 2.2 The time-splitting procedures Rather than discretising the complete two-dimensional advection-diffusion equation to give an approximating finite-difference formula based on a two-dimensional computational stencil, equation (1) can be splitted into the following two one-dimensional equations: 1 ›u ›u ›2 u þ bx ¼ ax 2 ; 2 ›t ›x ›x

ð10Þ

1 ›u ›u ›2 u þ by ¼ ay 2 : 2 ›t ›y ›y

ð11Þ

Each of these equations can be solved over half of the time-step to be used for the complete two-dimensional problem, using the procedures developed for the one-dimensional problems. This is advantageous since accurate and stable one-dimensional techniques are much easier to develop and use than two-dimensional schemes. The time-splitting method has a major advantage in that separate numerical algorithms (not necessarily finite difference methods) can be applied at each fractional step, thus avoiding the difficulties associated with a single complicated algorithm for the complete problem. In fact, sometimes the analytical solution of the initial value problem for some of the fractional steps can be found and such exact solution can be used with numerical solution for the remaining steps to yield the final solution.

In advancing a calculation by one time step it is assumed that equation (10), which governs the transport process in the x-direction, holds in the first half time step and that equation (11), which governs the transport process in the y-direction, holds in the second half time step. Either implicit or explicit one-dimensional finite-difference techniques may be used to solve either of these equations.

Time-splitting procedures

3. Locally one-dimensional techniques This method is based on the use of a LOD time splitting procedure to convert the two-dimensional problem into a set of one-dimensional problems which are solved using the explicit or implicit one-dimensional finite difference formulas (Lapidus and Pinder, 1982). Note that solving equations (10) and (11) in each half time step is equivalent to solving the following equations over a full time-step. Thus, we can write:

797

›u ›u ›2 u þ bx ¼ ax 2 ; ›t ›x ›x

ð12Þ

›u ›u ›2 u þ by ¼ ay 2 : ›t ›y ›y

ð13Þ

Hence, any of the schemes given for solving the one-dimensional advection-diffusion equation can be used to find approximate solutions for equations (12) and (13). 3.1 LOD with the Lax-Wendroff explicit procedure We use the following approximation in the first step of our LOD procedure:   nþð1=2Þ
ui; j 2 uni; j ›u

n ; . Dt ›t


ð14Þ

i; j

   
n n n n n u 2 u u 2 u
i; j i21; j iþ1; j i21; j ›u
þ ð1 2 cÞ ; .c Dx 2Dx ›x
i; j

2

›u n j . ›x 2 i; j



uniþ1; j 2 2uni; j þ uni21; j ðDxÞ2

ð15Þ

 :

ð16Þ

The following approximation will be employed in the second step of our LOD procedure:   nþð1=2Þ
nþð1=2Þ nþ1 u 2 u
i; j i; j ›u
; ð17Þ . Dt ›t
i; j

    nþð1=2Þ nþð1=2Þ nþð1=2Þ nþð1=2Þ
ui; j 2 ui; j21 ui; jþ1 2 ui; j21 ›u

nþð1=2Þ þ ð1 2 cÞ ; .c Dy 2Dy ›y
i; j

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  nþð1=2Þ nþð1=2Þ nþð1=2Þ
nþð1=2Þ ui; jþ1 2 2ui; j þ ui; j21 ›2 u

. : ›y 2
i; j ðDyÞ2

798

ð18Þ

ð19Þ

So if we use the LOD method in which the Lax-Wendroff finite difference scheme is used for both half time steps, then the component finite-difference formulas are: nþð1=2Þ

ui; j

¼

    1 1 2sx þ cx þ c2x uni21; j þ 1 2 2sx 2 c2x uni; j þ 2sx 2 cx þ c2x uniþ1; j : ð20Þ 2 2

unþ1 i; j ¼

   1 nþð1=2Þ nþð1=2Þ 2sy þ cy þ c2y ui; j21 þ 1 2 2sy 2 c2y ui; j 2  1 nþð1=2Þ þ 2sy 2 cy þ c2y ui; jþ1 : 2

ð21Þ

Since, both equations (20) and (21) are explicit, the equivalent one-step (1, 9) finite difference equation for this method may be found by substitution of the former into the nþð1=2Þ nþð1=2Þ nþð1=2Þ latter in order to eliminate the intermediate values ui21; j , ui; j and uiþ1; j . So the resulting one step finite difference formula is: 2   1 1 2sy þ cy þ c2y uni21;j21 þ 2sy þ cy þ c2y 1 2 2sx 2 c2x uni;j21 2 2     1 1 2 þ 2sx 2 cx þ cx 2sy þ cy þ c2y uniþ1;j21 þ 2sx þ cx þ c2x 1 2 c2y 2 2sy uni21;j 4 2      1 2 2 n þ 1 2 cx 2 2sx 1 2 cy 2 2sy ui;j þ 1 2 c2y 2 2sy 2sx 2 cx þ c2x uni;jþ1 2     1 1 þ 2sy 2 cy þ c2y 2sx þ cx þ c2x uni21;jþ1 þ 1 2 c2x 2 2sx 2sy 2 cy þ c2y uniþ1;j 4 2    1 þ 2sx 2 cx þ c 2 2sy 2 cy þ c2y uniþ1;jþ1 ; 2 ð22Þ

unþ1 i;j ¼

The MEPDE of this finite difference technique is (Warming and Hyett, 1974) in the following form:

Time-splitting procedures

 ›4 u ›u ›u ›2 u ›u ›2 u bx ðDxÞ2  þ bx 2 ax 2 þ by 2 ay 2 þ 1 2 6sx 2 c2x ›t ›x ›x ›y ›y 6 ›x 4 þ

 ›4 u b ðDxÞ3   4 by ðDyÞ2  x 2 2 2 4 › u ð23Þ 1 2 6sy 2 c2y 22s þ þ 3c þ 12s 2 12c s 2 3c x x x x x x 6 ›y 4 24 ›x 4

þ

 ›4 u by ðDyÞ3  22sy þ 3c2y þ 12s2y 2 12c2y sy 2 3c4y þ O{ðDxÞ4 ;ðDyÞ4 } ¼ 0: 24 ›y 4

799

This equation indicates that the formula (22) is second-order convergent. Similar to the time-split methods of the one-dimensional advection-diffusion equation and the two-dimensional diffusion equation, error terms in the MEPDE of the corresponding one-step formula are the sum of those in the MEPDEs of the component formulas. In particular, the coefficients of the cross-derivative terms are always zero. The corresponding one-step finite-difference formula has the same stability region, i.e.: 0,s#

12c2 : 2

ð24Þ

This region includes the stability region for the upwind-type method (Strikwerda, 1989). The stability region of this LOD scheme is the same as the Lax-Wendroff finite difference scheme. Note that the Lax-Wendroff procedure has non-negative coefficients when: cð1 2 cÞ 12c #s# : 2 2

ð25Þ

Nonnegative values are always produced when the initial and boundary values are nonnegative if equation (25) is satisfied. 3.2 The LOD (1,5) technique In this procedure, the following approximation will be used for the corresponding derivatives in the first half of the time-splitting step:   nþð1=2Þ
n n u 2 u
i; j i; j ›u
; ð26Þ . Dt ›t
i; j      n   n
n  n n 2 2 u 2 u u 2 u 12sx þ 2cx 2 3cx 2 2 12sx þ 2cx þ 3cx 2 2 iþ2;j i;j i;j i22;j ›u

þ . 2Dx 2Dx ›x
i;j 12 12   2  n n cx þ 6sx 2 4 uiþ1;j 2 ui21;j 2 ; 3 2Dx ð27Þ

   n
n  4 n n 2cx þ 4c2x 2 12s2x 2 12sx c2x þ 8sx uiþ1;j 2 2ui;j þ ui21;j ›2 u

. ›x 2
i;j 6sx ðDxÞ2   4  n n n 2 2 2 u 2 2u þ u c 2 4cx þ 12sx þ 12sx cx 2 2sx iþ2;j i;j i22;j þ x : 2 6sx ðDxÞ

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ð28Þ

This yields the following finite difference equation: nþð1=2Þ

ui;j

   1  12sx sx þ c2x þ 2sx ð6cx 2 1Þ þ cx ðcx 2 1Þðcx þ 1Þðcx þ 2Þ uni22;j 24    1  12sx sx þ c2x 2 2sx ð6cx þ 1Þ þ cx ðcx 2 1Þðcx þ 1Þðcx 2 2Þ uni21;j þ 24   1  2 12s sx þ c2x þ 2sx ð3cx 2 4Þ þ cx ðcx 2 2Þðcx þ 1Þðcx þ 2Þ uni;j 6   1 2 12sx sx þ c2x 2 2sx ð3cx þ 4Þ þ cx ðcx 2 1Þðcx 2 2Þðcx þ 2Þ uniþ1;j 6     1 þ 12sx sx þ c2x 2 10sx þ ðcx 2 1Þðcx 2 2Þðcx þ 1Þðcx þ 2Þ uniþ2;j 4

¼

ð29Þ

Then the following finite difference approximations will be employed in the second half of the time-splitting procedure:   nþð1=2Þ
nþð1=2Þ nþ1 u 2 u i;j i;j ›u

; ð30Þ . Dt ›t
i;j

   nþð1=2Þ nþð1=2Þ
12sy þ2c2y 23cy 22 ui;jþ2 2ui;j ›u

nþð1=2Þ . 12 2Dy ›y
i;j       nþð1=2Þ nþð1=2Þ nþð1=2Þ nþð1=2Þ 12sy þ2c2y þ3cy 22 ui;j 2ui;j22 c2y þ6sy 24 ui;jþ1 2ui;j21 2 ; þ 12 3 2Dy 2Dy ð31Þ    nþð1=2Þ nþð1=2Þ nþð1=2Þ
nþð1=2Þ 4 2 2 2 2c þ4c 212s 212s c þ8s u 22u þu y y
y y y y i;jþ1 i;j i;j21 › u
. 6sy ›y 2
i;j ðDyÞ2 ð32Þ    nþð1=2Þ nþð1=2Þ nþð1=2Þ 4 2 2 2 cy 24cy þ12sy þ12sy cy 22sy ui;jþ2 22ui;j þui;j22 þ : 2 6sy ðDyÞ 2

This yields the following finite difference equation:

   1 nþð1=2Þ 12sy sy þc2y þ2sy ð6cy 21Þþcy ðcy 21Þðcy þ1Þðcy þ2Þ ui;j22 24    1 nþð1=2Þ 12sy sy þc2y 22sy ð6cy þ1Þþcy ðcy 21Þðcy þ1Þðcy 22Þ ui;j21 þ 24    1 nþð1=2Þ 2 12sy sy þc2y þ2sy ð3cy 24Þþcy ðcy 22Þðcy þ1Þðcy þ2Þ ui;j 6    1 nþð1=2Þ 2 12sy sy þc2y 22sy ð3cy þ4Þþcy ðcy 21Þðcy 22Þðcy þ2Þ ui;jþ1 6    1 nþð1=2Þ þ 12sy sy þc2y 210sy Þþðcy 21Þðcy 22Þðcy þ1Þðcy þ2Þ ui;jþ2 : 4

Time-splitting procedures

unþ1 i;j ¼

ð33Þ

Note that in implementing the (1,5) computational finite-difference formula, special nþ1 nþ1 nþ1 boundary treatment is required in order to find unþ1 1;j , uM 21;j and then ui;1 , ui;M 21 . The equivalent one-step finite difference formula of this LOD procedure in the case where cx ¼ cy ¼ c and sx ¼ sy ¼ s, can be easily obtained. This will be referred to as the (1,25) method because the computational molecule involves one grid point at the new time level and twenty five at the old level. Note that the new fourth-order formula cannot be used to compute an approximate value for u at the grid point next to the boundary on each side of the solution domain. Instead, extrapolation techniques or alternative finite-difference formula based on other computational molecules and of the appropriate accuracy must be used to compute them. The modified equivalent partial differential equation of this method is in the following form:

›u ›u ›2 u ›u ›2 u þ bx 2 ax 2 þ by 2 ay 2 ›t ›x ›x ›y ›y  ›5 u bx ðDxÞ4  2 60sx 2 5c2x þ c4x 2 30sx þ 20cx s2x þ 4 2 120 ›x 5 i 4 h by ðDyÞ ›5 u 60s2y 2 5c2y þ c4y 2 30sy þ 20cy s2y þ 4 2 þ OððDxÞ5 ; ðDyÞ5 Þ ¼ 0; 120 ›x 5 ð34Þ which verifies that this technique is fourth-order accurate. The leading error terms of this time-splitting procedure are the sums of the leading error terms in the MEPDEs of the component finite difference formulas (29) and (33). This formula (1,25) will be seen to be fourth-order convergent and has the same stability region as that equation (33). We end the paper by giving some numerical results. 4. Experimental evaluations The object of this section is to compare the results obtained with the new finite difference procedures discussed in this report. To demonstrate the proposed algorithms, a test has been carried out. A special two-dimensional problem for

801

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which the exact solution is known is required so that approximate results obtained using the numerical techniques may be compared with a theoretical solution. Note that equation (1) is solved in the square region x [ [0,1], and y [ [0,1] with given initial and boundary conditions. We consider equations (1)-(6) with:

1 ð0:8t þ 0:5Þ2 ð y 2 0:8t 2 0:5Þ2 exp 2 2 g 0 ð y; tÞ ¼ ; ð4t þ 1Þ 0:01ð4t þ 1Þ 0:01ð4t þ 1Þ

802

0 , y , 1;

ð35Þ

0 , t # T;

and:

1 ð0:5 2 0:8tÞ2 ð y 2 0:8t 2 0:5Þ2 exp 2 2 g 1 ð y; tÞ ¼ ; ð4t þ 1Þ 0:01ð4t þ 1Þ 0:01ð4t þ 1Þ 0 , y , 1;

ð36Þ

0 , t # T;

and: h0 ðx; tÞ ¼



1 ðx 2 0:8t 2 0:5Þ2 ð0:8t þ 0:5Þ2 exp 2 2 ; ð4t þ 1Þ 0:01ð4t þ 1Þ 0:01ð4t þ 1Þ

0 , x , 1;

ð37Þ

0 , t # T;

and:

1 ðx 2 0:8t 2 0:5Þ2 ð0:5 2 0:8tÞ2 exp 2 2 h1 ðx; tÞ ¼ ; ð4t þ 1Þ 0:01ð4t þ 1Þ 0:01ð4t þ 1Þ 0 , x , 1;

ð38Þ

0 , t # T;

and:

ðx 2 0:5Þ2 ð y 2 0:5Þ2 2 f ðx; yÞ ¼ exp 2 ; 0:01 0:01

ð39Þ

with:

ax ¼ ay ¼ 0:01;

bx ¼ by ¼ 0:8;

ð40Þ

for which the exact solution is:

1 ðx 2 0:8t 2 0:5Þ2 ð y 2 0:8t 2 0:5Þ2 exp 2 2 uðx; y; tÞ ¼ ; ð4t þ 1Þ 0:01ð4t þ 1Þ 0:01ð4t þ 1Þ 0 , x; y , 1;

0 , t # T:

ð41Þ

The results obtained for various points computed for c ¼ 0.5 and s ¼ 0.35 are presented in Table I. Note that the values chosen for s and c are in the range of the stability of all finite difference procedures described in this report. Results will show that the LOD (1,5) technique and the (1,25) technique can produce errors of similar magnitude. The results obtained for the LOD procedure using Lax-Wendroff are compared with those of the method of time-splitting using the (1,5) explicit formula, showed that the average error of the former is bigger than the latter. The results also showed that among the schemes discussed in this research, the most efficient method is the LOD (1,5) procedure. Inspection of Table I shows that the size of the average error obtained is closely related to the size of the dominant error term in the modified equivalent equation of the method used. Note that the time needed using the LOD finite difference (1,5) method was about 14 times shorter than using the fully explicit finite difference procedure. Also the time needed using the fully explicit (1,5) finite difference method was about 11 times longer than using the method of time-splitting with Lax-Wendroff.

Time-splitting procedures

803

5. Outlook and conclusions In this paper, numerical methods were applied to the two-dimensional transport equation. The proposed numerical procedures solved our model quite satisfactory. The LOD procedure is simple to implement and economical to use. It is very efficient and it needs less CPU time than the fully explicit finite difference technique. The method of time-splitting with finite difference schemes is very easy to implement for similar three-dimensional problems, but it may be more difficult when dealing with the classical fully implicit finite difference scheme. The numerical results show a significant improvement over the traditional schemes. The LOD approach is more generally applicable than the classic approach and it represents a promising idea to derive further new algorithms which have wider stability range. One direction for future research will be to generalize the LOD procedure for higher-dimensional case. There also remain plenty of questions for future investigations: one can try to improve our approach for developing more accurate finite difference schemes in the LOD procedure. Retention of accuracy by proper treatment on boundaries at intermediate

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

y

LOD Lax-Wendroff Error

LOD (1,5) Error

(1,25) Explicit Error

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

2.5 £ 102 3 2.4 £ 102 3 2.3 £ 102 3 2.6 £ 102 3 2.8 £ 102 3 2.7 £ 102 3 2.9 £ 102 3 2.8 £ 102 3 2.7 £ 102 3

4.4 £ 102 4 4.6 £ 102 4 4.4 £ 102 4 4.7 £ 102 4 4.9 £ 102 4 4.8 £ 102 4 4.8 £ 102 4 4.3 £ 102 4 4.7 £ 102 4

4.2 £ 102 4 4.5 £ 102 4 4.3 £ 102 4 4.5 £ 102 4 4.3 £ 102 4 4.7 £ 102 4 5.0 £ 102 4 4.7 £ 102 4 4.5 £ 102 4

Table I. Results for u with c ¼ 0:5; s ¼ 0:35

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times should be given special consideration. It will also be interesting to generalize the LOD procedure for the case with variable coefficients. Finally, developing new numerical algorithms that perform well on a parallel computer calls for more analysis. References Chan, T.F. (1984), “Stability analysis of finite difference schemes for the convection-diffusion equation”, SIAM J. Numer. Anal., Vol. 20, pp. 272-84. Chatwin, P.C. and Allen, C.M. (1985), “Mathematical models of dispersion in rivers and estuaries”, Ann. Rev. Fluid Mech., Vol. 17, pp. 119-49. Chaudhry, M.H., Cass, D.E. and Edinger, J.E. (1983), “Modelling of unsteady-flow water temperatures”, J. Hydraul. Eng., Vol. 109 No. 5, pp. 657-69. Cushman-Roisin, B. (1984), “Analytical linear stability criteria for the leap frog, Dufort-Frankel method”, J. Comput. Phys., Vol. 53 No. 2, pp. 227-39. Dehghan, M. (2004), “Weighted finite difference techniques for the one-dimensional advection-diffusion equation”, Appl. Math. Comput., Vol. 147 No. 2, pp. 307-19. Dehghan, M. (2005), “Quasi-implicit and two-level explicit finite-difference procedures for solving the one-dimensional advection equation”, Appl. Math. Comput., Vol. 167 No. 1, pp. 46-67. Dehghan, M. (2006), “Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices”, Mathematics and Computers in Simulation, Vol. 71 No. 1, pp. 16-30. Fattah, Q.N. and Hoopes, J.A. (1985), “Dispersion in anisotropic homogeneous porous media”, J. Hydraul, Eng., Vol. 111, pp. 810-27. Gane, C.R. and Stephenson, P.L. (1979), “An explicit numerical method for solving transient combined heat conduction and convection problems”, Int. J. Numer. Methods Eng., Vol. 14, pp. 1141-63. Guvanasen, V. and Volker, R.E. (1983), “Numerical solutions for solute transport in unconfined aquifers”, Int. J. Numer. Methods Fluids, Vol. 3, pp. 103-23. Hindmarsh, A.C., Gresho, P.M. and Griffiths, D.F. (1984), “The stability of explicit Euler time-integration for certain finite difference approximations of the advection-diffusion equation”, Int. J. Numer. Methods Fluids, Vol. 4, pp. 853-97. Holly, F.M. and Usseglio-Polatera, J.M. (1984), “Dispersion simulation in two-dimensional tidal flow”, J. Hydraul. Eng., Vol. 111, pp. 905-26. Isenberg, J. and Gutfinger, C. (1972), “Heat transfer to a draining film”, Int. J. Heat Transfer, Vol. 16, pp. 505-12. Karaa, S. and Zhang, J. (2004), “High order ADI method for solving unsteady convection-diffusion problems”, J. Comput. Phys., Vol. 198, pp. 1-9. Kohler, T. and Voss, D. (1999), “Second-order methods for duffusion-convection equations”, Commun. Numer. Meth. Eng., Vol. 15, pp. 689-99. Kumar, N. (1988), “Unsteady flow against dispersion in finite porous media”, Journal of Hydrology, Vol. 63, pp. 345-58. Kwok, U.K. and Tam, T.T. (1993), “Stability analysis of three-level difference schemes for initial-boundary problems for multidimensional convective-diffusion equations”, Commun. Numer. Meth. Eng., Vol. 9, pp. 595-605. Lapidus, L. and Amundston, N.R. (1952), “Mathematics of absorption in beds”, Journal of Physical Chemistry, Vol. 56 No. 8, pp. 984-8.

Lapidus, L. and Pinder, G.F. (1982), Numerical Solution of Partial Differential Equations in Science and Engineering, Wiley, New York, NY. Lax, P.D. and Wendroff, B. (1964), “Difference schemes with high order of accuracy for solving hyperbolic equations”, Commun. Pure Appl. Math, Vol. 17, pp. 381-98. Noye, B. (1989), Numerical Solution of Partial Differential Equations, Amsterdam, North-Holland. Parlarge, J.Y. (1990), “Water transport in soils”, Ann. Rev. Fluids Mech., Vol. 2, pp. 77-102. Patrico, F. (1990), “Implicit methods for diffusion-convection equations”, Commun. Appl. Numer. Methods, Vol. 6, pp. 27-33. Rigal, A. (1994), “High order difference schemes for unsteady one-dimensional diffusion-convection problems”, J. Comput. Phys., Vol. 114, pp. 59-76. Rui, H. (2003), “An alternative direction iterative method with second-order upwind scheme for convection-diffusion equations”, Intern. J. Comput. Math., Vol. 80 No. 4, pp. 527-33. Ruxun, L. (1995), “The remainder-effect analysis of finite difference schemes and the applications”, Appl. Math. and Mech., Vol. 16, pp. 87-95. Ruxun, L., Meng-Ping, Z., Jin, W. and Xiao-Yuan, L. (1999), “The designing approach of difference schemes by controlling the remainder-effect”, Int. J. Numer. Meth. Fluids, Vol. 31, pp. 523-33. Salmon, J.R., Liggett, J.A. and Gallager, R.H. (1980), “Dispersion analysis in homogeneous lakes”, Int. J. Numer. Methods Eng., Vol. 15, pp. 1627-42. Schumann, U. (1975), “Linear stability of finite difference equations for three-dimensional flow problems”, J. Comput. Phys., Vol. 18 No. 4, pp. 465-70. Strikwerda, J.C. (1989), Finite Difference Schemes and Partial Differential Equations, Chapman and Hall, New York, NY. Twizell, E.H. (1985), “The extraploation of implicit methods for the constant coefficient diffusion-convection equations”, Commun. Appl. Numer. Methods, Vol. 1, pp. 129-35. Varah, J.M. (1980), “Stability restrictions on second order, three level finite difference schemes for parabolic equations”, SIAM J. Numer. Anal., Vol. 17 No. 2, pp. 300-9. Warming, R.F. and Hyett, B.J. (1974), “The modified equation approach to the stability and accuracy analysis of finite-difference methods”, J. Comput. Phys., Vol. 14 No. 2, pp. 159-79. Zlatev, Z., Berkowicz, R. and Prahm, L.P. (1984), “Implementation of a variable stepsize variable formula in the time-integration part of a code for treatment of long-range transport of air pollutants”, J. Comput. Phys., Vol. 55, pp. 278-301. Further reading Jin, W. and Ruxun, L. (2001), “Some generalization of classical MPDE approach”, Journal of China University of Science and Technology, Vol. 31 No. 2, pp. 143-50. Liang, D. and Zhao, W. (1997), “A high order upwind method for the convection-diffusion problem”, Comput. Methods Appl. Mech. Eng., Vol. 17, pp. 105-15. Ruxun, L. (1992), “The study of the remainder-effects of finite difference schemes”, J. Comput. Phys., Vol. 9, pp. 479-88. Corresponding author Mehdi Dehghan can be contacted at: [email protected] To purchase reprints of this article please e-mail: [email protected] Or visit our web site for further details: www.emeraldinsight.com/reprints

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A simulation study of a new family of test statistics for the Behrens-Fisher problem

806

Julio Angel Pardo and Marı´a del Carmen Pardo Department of Statistics and O.R., Complutense University of Madrid, Madrid, Spain Abstract Purpose – To provide a new family of test statistics to solve the Behrens-Fisher problem and to compare it with the classic test statistics through a different simulation studies. Design/methodology/approach – A general procedure for testing composite hypothesis to k samples of different size problems on the basis of the Renyi’s divergence is used to develop a new parametric family of test statistics that contains as a particular case the classical likelihood ratio test. The scope of the paper is to find out if some member of the new family of test statistics it is preferable to the classical ones. Findings – Some members of the new parametric family of test statistics behave remarkably well in comparison to the classic ones, as the different computational studies reveal. Originality/value – This paper offers a new way to solve the Behrens-Fisher problem that it is preferable in some cases to the known procedures. Keywords Cybernetics, Statistics, Simulation Paper type Research paper

1. Introduction In many situations, it is necessary to test the equality of the means of two normal populations. The use of a t-test based on a pooled variance is often illustrated in many elementary textbooks. It is known, however, that this t-test is not applicable when the underlying population variances differ. An early solution to this problem was proposed by Behrens (1929), and this solution was endorsed by Fisher (1939). So it is called the Behrens-Fisher problem. The Behrens-Fisher solution is not acceptable to many statisticians, however, because the actual size of the associated test is often less than the nominated size. The Behrens-Fisher problem can be stated as follows. Let ðX i1 ; . . . ; X ini ; i ¼ 1; 2Þ, represent two independent normal random samples and assume that E½X ij
¼ mi and V ½X ij
¼ s2i for i ¼ 1; 2 and j ¼ 1; . . . ; ni and we wish to test the null hypothesis: H 0 : m1 ¼ m2 against: H 1 : m1 – m2 Kybernetes Vol. 36 No. 5/6, 2007 pp. 806-816 q Emerald Group Publishing Limited 0368-492X DOI 10.1108/03684920710749866

where the variances are not equal ðs21 – s22 Þ and are unknown. One of the most common procedures for testing the equality of means under these assumptions is the Welch’s (1937, 1947) procedure. This work was supported partially by Grant DGI (BMF2003-00892).

The Welch solution to the Behrens-Fisher problem rejects H0 at level a if and only if:


X 1 2 X 2
V ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi     . tn;a=2 S 2ð1Þ =n1 þ S 2ð2Þ =n2

Study of a new family of test statistics 807

where: S 2ði Þ ¼

ni X j¼1

ðX ij 2 X i Þ ðni 2 1Þ

2

and X i ¼

ni X j¼1

X ij ni

with i [ {1; 2}. The value tn;a=2 verifies that Pðjtn j . t n;a=2 Þ ¼ a being tv a Student t-distribution in which degrees of freedom are   2  the data  dependent  n ¼ S 2ð1Þ =n1 þ S 2ð2Þ =n2 = S 4ð1Þ = n31 2 n21 þ S 4ð2Þ = n32 2 n22 . Other test statistics used to solve this problem are the Wald test which is given by:  2 X1 2 X2    ; W¼ ðn1 2 1Þ S 2ð1Þ =n21 þ ðn2 2 1Þ S 2ð2Þ =n22 the likelihood ratio test: LRT ¼

2 X i¼1

and the score test:

ni log

2 S~ i

!

S 2i



2 X1 2 X2 S¼ 2   2  S~ =n1 þ S~ =n2 1

Pn i

2

2 S~ i

where S 2i ¼ j¼1 ðX ij 2 X i Þ2 =ni and is the maximum likelihood estimator (MLE) of s2i under the null hypothesis with i [ {1; 2}. Asymptotically, W, LRT and S all have x 2 distributions with 1 degree of freedom under H0. When H 0 : m1 ¼ m2 ð¼ mÞ holds, then MLEs are the roots of the set of three equations: n1 ðX 1 2 mÞ n2 ðX 2 2 mÞ þ ¼0 s21 s22 n1 1X s21 ¼ ðX 1j 2 mÞ2 ¼ S 21 þ ðX 1 2 mÞ2 n1 j¼1

s22 ¼

n2 1X ðX 2j 2 mÞ2 ¼ S 22 þ ðX 2 2 mÞ2 n2 j¼1

From here, we see that m~, the MLE under H 0 of m, solves the cubic polynomial in m:       2 2 n1 S 22 þ X 2 2 2X 2 m þ m 2 X 1 2 m þ n2 S 21 þ X 1 2 2X 1 m þ m 2 X 2 2 m ¼ 0:

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Bozdogan and Ramirez (1986) proposed an iterative process to obtain the MLE of m and s2i ; i ¼ 1; 2 under null model. Suguira and Gupta (1985) have shown that the cubic equation has either unique solution with large probability, or three solutions with small probability. If there are three real roots to this equation, it is necessary to check which solution maximizes the likelihood. It is well known that for the Behrens-Fisher problem, there is no uniformly most powerful (unbiased) test for all sample sizes. Best and Rayner (1987) studied the performance of the asymptotically optimal test provided by V, W, LRT and S. So it is of interest to extend this study to a new test statistic based on Re´nyi divergence proposed in the next section. On the basis of Monte Carlo size and power comparisons, in the last section, a comparative study is carried out for the classical test statistics defined in this section and some members of the new family of test statistics introduced in Section 2. 2. Test statistic based on Re´nyi’s divergence It is clear the importance that the divergence measures are taken in the last years for solving many statistical problems. In fact when we want to obtain an estimator or to carry out a hypothesis test, we measure the distance between the observed and the theoretical. Now then a divergence is a distance in the wide sense. There are many important families of divergences whose properties have been studied by different authors. In this paper, we consider the Re´nyi’s (1961) divergence to define a new family of statistics for testing equality of means. Recently, this divergence has been used to test equality of variances (Morales et al., 2001) and for testing equality of coefficients of variation (Pardo and Pardo, 2000). In the following, we describe the general procedure used there which can be particularized to solve the Behrens-Fisher problem. Let ðx; bx ; P u Þu[Q be a measurable space, where x , R is the sample space, bx the corresponding s-field and Q , R t ; t $ 1. Assume that measures Pu can be described by densities f u ðxÞ ¼ ðdP u =dmÞðxÞ w.r.t. a dominating s-finite measure m on x. The Re´nyi’s divergence for arbitrary densities f u1 and f u2 belonging to the family {f u ; u [ Q}, is given by: Z 1 Dr ðu1 ; u2 Þ ¼ rðr21Þ log f u1 ðxÞr f u2 ðxÞ12r dm x

if r
{0; 1}, and: lim Dr ðu1 ; u2 Þ ¼ D1 ðu1 ; u2 Þ ¼

Z

r"1

lim Dr ðu1 ; u2 Þ ¼ D0 ðu1 ; u2 Þ ¼

Z

r#0

x

x

f u2 ðxÞlog

f u1 ðxÞlog

f u1 ðxÞ dm f u2 ðxÞ

f u2 ðxÞ dm ¼ D1 ðu2 ; u1 Þ f u1 ðxÞ

The measures of divergences D1 ðu1 ; u2 Þ and D0 ðu1 ; u2 Þ are called Kullback-Leibler divergence and reversed Kullback-Leibler divergence, respectively. Morales et al. (1997) studied the problem of testing composite hypothesis H 0 : u [ Q0 , Q versus H 1 : u [ Q 2 Q0 on the basis of the Re´nyi’s divergence using the statistic:

S rn ¼ 2nDr ðu^n ; u~n Þ where u^n is the MLE of u [ Q and u~n is the MLE restricted to the subset Q0 . Under standard regularity assumptions, they established that S rn is asymptotically x 2 distributed with d0 degrees of freedom, where d0 is the difference of dimensions between Q and Q0 . For large n, when S rn ¼ t, H0 should be rejected at a level a if Pðx2d0 . tÞ # a. The previous testing procedure is applicable to one sample problems and to balanced k sample problems (i.e. with n1 ¼ · · · ¼ nk ). When we have a problem with k samples of different size, S rn must be generalized in some sense. This generalization was presented in Morales et al. (2001). They proposed for testing the hypothesis H 0 ; G0 , G being G ¼ Qk , R k the statistic: Z 2 log g g^n ðzÞr gg~n ðzÞ12r dm n T rn ¼ 2Dr ðg^n ; g~n Þ ¼ rðr 2 1Þ n x

n

j with z ¼ ðx11 ; . . . ; x1n1 ; . . . ; xk1 ; . . . ; xknk Þ, g g ðzÞ ¼ Pkj¼1 Pi¼1 f uj ðxji Þ, g^n ; MLE in G and g~n ; MLE in G0. Under standard regularity assumptions, they established that T rn is asymptotically x 2 distributed with d0 degrees of freedom, where d0 is the difference between the dimension of the parameter space G and the hypothesis space G0. In the particular but important case of exponential model, the statistic T 1n ¼ limr"1 T rn for testing any hypothesis coincides with the likelihood ratio test statistic. The model that we present in this paper belongs to the exponential family so our statistic T 1n coincides with the likelihood ratio test. In our case k ¼ 2 and we are interested in testing:

H 0 : m1 ¼ m2 ¼ m Let X i1 ; . . . ; X ini ; i ¼ 1; 2 be two independent samples from normal distributions N ðmi ; si Þ with density functions f mi ;si ; i ¼ 1; 2. The likelihood function is: gm;S ðzÞ ¼

nj 2 Y Y

f mj ;sj ðxji Þ

j¼1 i¼1

  where m ¼ ðm1 ; m2 Þ and S ¼ diag s21 ; s22 . Then: G ¼ {ðx1 ; x2 ; y1 ; y2 Þjxi [ R; yi [ R and yi . 0;

i ¼ 1; 2}

and: G0 ¼ {ðx1 ; x2 ; y1 ; y2 Þ [ Gjx1 ¼ x2 }: So we introduce the new statistic for testing H0 as: where:

^ ðm~; SÞÞ ~ T rn ¼ 2Dr ððm^; SÞ;

    m^ ¼ X 1 ;...n1 Þ ...;X 1 ;X 2 ;...n2 Þ ...X 2 and S^ ¼ diag S 21 ;...n1 Þ ...;S 21 ;S 22 ;...n2 Þ ...;S 22

are the MLEs and:

Study of a new family of test statistics 809

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810

2

2

2

2

m~ ¼ ðm~1 ;...n1 Þ ...; m~1 ; m~2 ;...n2 Þ ...; m~2 Þ and S~ ¼ diagðS~ 1 ;...n1 Þ ...; S~ 1 ; S~ 2 ;...n2 Þ ...; S~ 2 Þ the restricted MLEs of m and S. This statistic is distributed asymptotically as a x21 (Morales et al., 1997). Using the Re´nyi’s divergence, given in Burbea (1982), between two two-dimensional normal populations we obtain the following expressions for T rn : 0 1 2 2 2 2 X B ðX i 2 m~i Þ 1 ð1 2 rÞS þ r S~ C log  12r i  ir A T rn ¼ ni @ þ 2 2 2 ð1 2 rÞS i þ r S~ i rð1 2 rÞ i¼1 S 2i þ S~ i if r
{0; 1}, and: T 1n ¼ lim T rn ¼ r"1

T 0n

¼

lim T rn r#0

¼

2 X i¼1

ni

2 X

ni log

i¼1

ðX i 2 m~i Þ2 S 2i

2 S~ i

S 2i

2 S~ i

S2 þ 2 2 1 þ log 2i Si S~

!

i

for r ¼ 1 and 0, respectively. Note that T 1n is the likelihood ratio test that it was studied by Best and Rainer (1987). Now it emerges as a particular case of our new family of statistics. This allows to study it jointly as a member of the Re´nyi‘s family. 3. Size and power comparison We have performed a computational study for comparing size as well as power of the statistics V, W, LRT and S with the proposed test. We have obtained Monte Carlo powers using 1,000 simulations for ðn1 ; n2 Þ ¼ ð10; 25Þ and ð20; 20Þ. Firstly, test sizes of approximately a ¼ 0:05, a^n , for a population of size n ¼ ðn1 ;n2 Þ are achieved by ordering 1,000 values of each statistic and taking the critical value as the 950th such value. Five different null hypotheses, H 0;j j ¼ 1; . . . ; 5 were considered which consists on two independent normal populations with means m1 ¼ m2 ¼ 1 and variances s2i;j i ¼ 1; 2, and j ¼ 1; . . . ; 5 with s21;1 ¼ 1; s22;1 ¼ 16; s21;2 ¼ 1; s22;2 ¼ 4; s21;3 ¼ 1; s22;3 ¼ 1; s21;4 ¼ 4; s22;4 ¼ 1; s21;5 ¼ 16; s22;5 ¼ 1 (Tables I and II). A criterion to study the closeness of the simulated exact size a^n to the nominal size a ¼ 0:05 consist on considering the inequality proposed by Dale (1986): jlogitð1 2 a^n Þ 2 logitð1 2 aÞj # d;

ð1Þ

where logitð pÞ ¼ logð p=ð1 2 pÞÞ. The two probabilities a^n and a are considered to be “close” if they satisfy equation (1) with d ¼ 0:35 and “fairly close” if they satisfy equation (1) with d ¼ 0:7. Note that for a ¼ 0:05; d ¼ 0:35 corresponds to a^n [ ½0:0357; 0:0695
, and d ¼ 0:7 corresponds to a^n [ ½0:0254; 0:0959
. Note that all values of the simulated size verify the criterion to be “close.” For this reason, we shall include all of them in our study. In Tables III-X, we present the powers of all the test statistics. To obtain the powers we consider the data generated from two independent random variables X1 and X2

W S V T 21 n T n20:6 T n20:3 T on T 0:3 n T 0:5 n T 0:7 n T 1n T 1:3 n T 1:6 n T 2n

W S V T 21 n T n20:6 T n20:3 T on T 0:3 n T 0:5 n T 0:7 n T 1n T 1:3 n T 1:6 n T 2n

H0,1

H0,2

n1 ¼ 10; n2 ¼ 25 H0,3

0.056 0.056 0.061 0.057 0.057 0.059 0.059 0.057 0.057 0.056 0.057 0.056 0.056 0.056

0.063 0.060 0.052 0.058 0.062 0.058 0.058 0.058 0.059 0.059 0.062 0.063 0.063 0.063

0.045 0.045 0.047 0.044 0.045 0.049 0.050 0.045 0.045 0.046 0.046 0.045 0.045 0.044

0.061 0.065 0.057 0.065 0.065 0.065 0.066 0.066 0.066 0.067 0.064 0.064 0.062 0.061

0.053 0.052 0.055 0.052 0.052 0.052 0.052 0.052 0.052 0.052 0.052 0.052 0.053 0.053

H0,1

H0,2

n1 ¼ 20; n2 ¼ 20 H0,3

H0,4

H0,5

0.054 0.054 0.058 0.054 0.054 0.052 0.053 0.053 0.054 0.054 0.054 0.054 0.054 0.054

0.052 0.052 0.054 0.052 0.052 0.053 0.053 0.053 0.052 0.052 0.052 0.052 0.052 0.051

0.044 0.044 0.040 0.042 0.044 0.044 0.043 0.042 0.044 0.044 0.044 0.044 0.044 0.042

0.050 0.048 0.058 0.048 0.049 0.046 0.048 0.047 0.048 0.048 0.049 0.050 0.050 0.049

0.047 0.047 0.056 0.047 0.047 0.047 0.047 0.047 0.047 0.047 0.047 0.047 0.047 0.047

H0,4

H0,5

with means m1 and m2 and variances s2i;j , i ¼ 1; 2 and j ¼ 1; . . . ; 5 defined above. The alternative hypotheses considered are as follows: H 1 : m1 ¼ 2 – m2 ¼ 1; s21;1 ; s22;1

H 6 : m1 ¼ 4 – m2 ¼ 1; s21;1 ; s22;1

H 2 : m1 ¼ 2 – m2 ¼ 1; s21;2 ; s22;2

H 7 : m1 ¼ 4 – m2 ¼ 1; s21;2 ; s22;2

H 3 : m1 ¼ 2 – m2 ¼ 1; s21;3 ; s22;3

H 8 : m1 ¼ 4 – m2 ¼ 1; s21;3 ; s22;3

H 4 : m1 ¼ 2 – m2 ¼ 1; s21;4 ; s22;4

H 9 : m1 ¼ 4 – m2 ¼ 1; s21;4 ; s22;4

H 5 : m1 ¼ 2 – m2 ¼ 1; s21;5 ; s22;5

H 10 : m1 ¼ 4 – m2 ¼ 1; s21;5 ; s22;5

Study of a new family of test statistics 811

Table I. Simulated exact sizes

Table II. Simulated exact sizes

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Table III. Simulated power for normal populations

Table IV. Simulated power for normal populations

W S V T 21 n T 20:6 n T 20:3 n T 0n T 0:3 n T 0:5 n T 0:7 n T 1n T 1:3 n T 1:6 n T 2n

W S V T 21 n T 20:6 n T 20:3 n T 0n T 0:3 n T 0:5 n T 0:7 n T 1n T 1:3 n T 1:6 n T 2n

H1

H2

H3

H4

0.207 0.205 0.214 0.203 0.204 0.204 0.204 0.205 0.205 0.205 0.206 0.207 0.207 0.206

0.502 0.503 0.507 0.495 0.494 0.496 0.503 0.501 0.503 0.503 0.502 0.501 0.502 0.502

0.764 0.770 0.783 0.769 0.766 0.772 0.772 0.770 0.771 0.771 0.773 0.771 0.767 0.759

0.312 0.311 0.303 0.322 0.325 0.323 0.314 0.311 0.310 0.311 0.313 0.312 0.312 0.313

H1

H2

H3

H4

0.176 0.174 0.181 0.174 0.174 0.174 0.174 0.174 0.174 0.174 0.174 0.175 0.176 0.176

0.523 0.523 0.541 0.528 0.527 0.525 0.524 0.524 0.524 0.524 0.525 0.523 0.523 0.520

0.831 0.831 0.827 0.832 0.832 0.831 0.830 0.830 0.831 0.831 0.830 0.831 0.831 0.830

0.509 0.506 0.538 0.500 0.502 0.504 0.504 0.506 0.506 0.508 0.510 0.511 0.511 0.504

n1 ¼ 10; n2 ¼ 25 H5 H6 H7

H8

H9

H10

hð · Þ

0.078 0.080 0.100 0.081 0.080 0.080 0.080 0.080 0.081 0.082 0.082 0.082 0.077 0.078

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

0.985 0.986 0.986 0.987 0.986 0.986 0.986 0.986 0.986 0.986 0.986 0.986 0.985 0.985

0.520 0.523 0.515 0.532 0.531 0.527 0.523 0.520 0.520 0.520 0.519 0.519 0.519 0.521

0.022 0.020 0.022 0.019 0.020 0.020 0.020 0.020 0.019 0.018 0.018 0.018 0.023 0.024

H8

H9

H10

hð · Þ

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.899 0.901 0.909 0.901 0.901 0.901 0.901 0.901 0.901 0.900 0.899 0.899 0.899 0.898

0.029 0.032 0.042 0.038 0.036 0.034 0.034 0.032 0.032 0.030 0.028 0.027 0.027 0.034

0.933 0.931 0.929 0.928 0.928 0.930 0.930 0.931 0.931 0.931 0.931 0.933 0.933 0.933

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

n1 ¼ 20; n2 ¼ 20 H5 H6 H7 0.167 0.171 0.185 0.174 0.174 0.173 0.173 0.173 0.171 0.170 0.170 0.169 0.167 0.167

0.863 0.861 0.822 0.864 0.861 0.861 0.861 0.861 0.862 0.863 0.863 0.863 0.863 0.862

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

In Tables III and IV, V and VI, VII and VIII and IX and X, X1 and X2 are normal, gamma, LogNormal and double exponential, respectively. From results displayed in Tables III –X we can obtain some conclusions. For normal (Tables III and IV) and double exponential (Tables IX and X) populations, if we fix the variances, the more the means of the populations are different, the higher the power of the tests is. On the other hand, for the alternatives with the same means (H 1 2 H 5 or H 6 2 H 10 ) the power of the tests increases when the values of the variances come closer. Moreover, the behavior of the power is comparable for equal and unequal sample sizes. In relation to gamma populations (Tables V and VI), the above conclusions are true except that the power does not increase for similar variances when we fix the means. In this case, if m1 is similar to m2 , then the highest powers are

W S V T 21 n T n20:6 T n20:3 T 0n T 0:3 n T 0:5 n T 0:7 n T 1n T 1:3 n T 1:6 n T 2n

W S V T 21 n T n20:6 T n20:3 T 0n T 0:3 n T 0:5 n T 0:7 n T 1n T 1:3 n T 1:6 n T 2n

H1

H2

H3

H4

0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999

0.049 0.051 0.044 0.051 0.051 0.051 0.051 0.051 0.051 0.050 0.050 0.050 0.049 0.048

0.181 0.172 0.164 0.168 0.168 0.170 0.174 0.172 0.173 0.177 0.181 0.176 0.179 0.179

0.472 0.481 0.471 0.480 0.479 0.479 0.483 0.479 0.479 0.476 0.478 0.476 0.475 0.472

H1

H2

H3

H4

0.997 0.997 0.998 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997

0.040 0.047 0.033 0.053 0.053 0.052 0.051 0.048 0.045 0.045 0.042 0.042 0.041 0.040

0.266 0.267 0.265 0.269 0.266 0.266 0.266 0.265 0.267 0.266 0.266 0.266 0.266 0.265

0.836 0.836 0.800 0.828 0.832 0.834 0.835 0.836 0.835 0.835 0.836 0.836 0.836 0.836

n1 ¼ 10; n2 ¼ 25 H5 H6 H7

H8

H9

H10

hð · Þ

0.430 0.429 0.435 0.418 0.423 0.425 0.429 0.429 0.429 0.429 0.430 0.431 0.430 0.429

0.998 0.996 0.996 0.995 0.996 0.996 0.996 0.996 0.996 0.996 0.998 0.998 0.998 0.998

0.962 0.966 0.977 0.964 0.959 0.960 0.964 0.965 0.964 0.964 0.960 0.960 0.961 0.961

0.927 0.934 0.938 0.934 0.934 0.934 0.934 0.933 0.933 0.933 0.933 0.933 0.932 0.927

0.015 0.011 0.017 0.017 0.018 0.017 0.013 0.012 0.013 0.013 0.017 0.017 0.016 0.016

n1 ¼ 20; n2 ¼ 20 H5 H6 H7

H8

H9

H10

hð · Þ

0.997 0.998 0.997 0.998 0.998 0.998 0.998 0.998 0.998 0.997 0.997 0.997 0.997 0.997

0.998 0.998 0.998 0.997 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.034 0.026 0.052 0.020 0.022 0.023 0.024 0.026 0.026 0.026 0.028 0.029 0.034 0.038

0.169 0.177 0.181 0.178 0.178 0.178 0.176 0.176 0.176 0.173 0.173 0.172 0.170 0.169

0.722 0.726 0.676 0.728 0.728 0.726 0.726 0.726 0.726 0.724 0.722 0.722 0.722 0.721

0.990 0.992 0.992 0.994 0.993 0.992 0.992 0.992 0.991 0.991 0.991 0.991 0.990 0.989

0.932 0.940 0.966 0.946 0.944 0.943 0.942 0.940 0.940 0.940 0.938 0.937 0.932 0.928

0.334 0.342 0.335 0.353 0.352 0.351 0.349 0.343 0.342 0.340 0.337 0.335 0.334 0.332

obtained when s21 is much lower than s22 . Finally, the worst behavior of these tests is for LogNormal populations (Tables VII and VIII) since the powers are very small for all the alternatives not only for the new statistics, but also the classical ones. Apart from the similar behavior for equal and unequal sample sizes and the improvement of the powers when s21 , s22 , it is difficult to obtain any conclusions for this population. As there is not a test statistic that maximize the power for all sets of alternative hypotheses and all sets of sample sizes, Morales et al. (1997) introduced an alternative concept of optimality based on “relative inefficiency” in a given class of tests. This criterion of comparison has been used in other papers such as Morales et al. (2001).

Study of a new family of test statistics 813

Table V. Simulated power for gamma populations

Table VI. Simulated power for gamma populations

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Table VII. Simulated power for LogNormal populations

Table VIII. Simulated power for LogNormal populations

W S V T 21 n T 20:6 n T 20:3 n T 0n T 0:3 n T 0:5 n T 0:7 n T 1n T 1:3 n T 1:6 n T 2n

W S V T 21 n T 20:6 n T 20:3 n T 0n T 0:3 n T 0:5 n T 0:7 n T 1n T 1:3 n T 1:6 n T 2n

n1 ¼ 10; n2 ¼ 25 H5 H6 H7

H8

H9

H10

hð · Þ

0.073 0.068 0.077 0.047 0.056 0.060 0.064 0.068 0.068 0.069 0.070 0.073 0.073 0.074

0.061 0.048 0.050 0.033 0.036 0.041 0.044 0.047 0.049 0.051 0.058 0.060 0.061 0.065

0.051 0.025 0.026 0.009 0.012 0.015 .019 0.024 0.027 0.030 0.037 0.042 0.048 0.052

0.019 0.049 0.036 0.104 0.082 0.070 0.062 0.050 0.045 0.042 0.033 0.023 0.019 0.019

n1 ¼ 20; n2 ¼ 20 H5 H6 H7

H8

H9

H10

hð · Þ

0.089 0.079 0.090 0.068 0.072 0.073 0.075 0.078 0.080 0.080 0.083 0.086 0.088 0.092

0.084 0.087 0.087 0.095 0.092 0.090 0.089 0.088 0.086 0.086 0.086 0.086 0.085 0.083

0.083 0.081 0.081 0.073 0.073 0.075 0.077 0.080 0.081 0.081 0.081 0.081 0.083 0.083

0.054 0.050 0.055 0.047 0.047 0.049 0.050 0.050 0.050 0.050 0.051 0.052 0.053 0.055

0.011 0.013 0.022 0.024 0.020 0.019 0.017 0.014 0.012 0.012 0.009 0.009 0.010 0.012

H1

H2

H3

H4

0.188 0.192 0.193 0.198 0.195 0.194 0.194 0.193 0.193 0.191 0.189 0.190 0.188 0.188

0.109 0.116 0.117 0.128 0.123 0.119 0.117 0.116 0.116 0.116 0.114 0.113 0.109 0.109

0.056 0.062 0.068 0.053 0.055 0.059 0.061 0.062 0.062 0.064 0.064 0.063 0.058 0.054

0.087 0.064 0.062 0.043 0.053 0.058 0.061 0.062 0.064 0.073 0.079 0.081 0.085 0.089

0.146 0.101 0.114 0.046 0.068 0.080 0.088 0.100 0.105 0.108 0.117 0.127 0.135 0.150

H1

H2

H3

H4

0.262 0.256 0.261 0.252 0.253 0.256 0.256 0.256 0.256 0.257 0.260 0.260 0.262 0.263

0.155 0.154 0.156 0.151 0.152 0.154 0.154 0.154 0.154 0.155 0.155 0.155 0.155 0.154

0.062 0.066 0.065 0.071 0.069 0.069 0.068 0.067 0.066 0.066 0.065 0.062 0.062 0.061

0.032 0.032 0.038 0.031 0.031 0.031 0.032 0.032 0.032 0.033 0.033 0.033 0.033 0.031

0.248 0.245 0.244 0.245 0.245 0.245 0.247 0.246 0.245 0.245 0.245 0.247 0.248 0.248

0.288 0.289 0.268 0.290 0.290 0.289 0.289 0.289 0.289 0.289 0.289 0.289 0.288 0.288

0.148 0.146 0.148 0.142 0.142 0.142 0.142 0.145 0.145 0.146 0.146 0.148 0.148 0.147

0.164 0.169 0.171 0.174 0.172 0.168 0.169 0.169 0.168 0.166 0.165 0.165 0.164 0.163

We consider the set of test statistics:   T ¼ W ; S; V ; T rn ; r ¼ 21; 20:6; 20:3; 0; 0:3; 0:5; 0:7; 1; 1:3; 1:6; 2 : We define the relative inefficiency hðE; H j Þ of E [ T at a given alternative H j as:

hðE; H j Þ ¼ P MAXi ðH j Þ 2 P E ðH j Þ where P MAXi ðH j Þ ¼ maxP E ðH j Þ, i ¼ 1; 2 with P E ðH j Þ the power of a statistic E against E[T

the alternative Hj, i.e. how far is the power of a statistic behind the maximum power achieved in T. The optimum represents the tests E * [ T with the minimax relative inefficiency:

W S V T 21 n T n20:6 T n20:3 T 0n T 0:3 n T 0:5 n T 0:7 n T 1n T 1:3 n T 1:6 n T 2n

W S V T 21 n T n20:6 T n20:3 T 0n T 0:3 n T 0:5 n T 0:7 n T 1n T 1:3 n T 1:6 n T 2n

H1

H2

H3

H4

0.229 0.225 0.235 0.222 0.223 0.224 0.224 0.225 0.225 0.225 0.227 0.228 0.229 0.229

0.496 0.509 0.510 0.513 0.512 0.510 0.510 0.508 0.509 0.508 0.506 0.503 0.501 0.496

0.763 0.773 0.785 0.765 0.764 0.768 0.772 0.771 0.774 0.774 0.773 0.774 0.768 0.755

0.403 0.397 0.386 0.411 0.414 0.411 0.405 0.397 0.396 0.397 0.399 0.400 0.404 0.403

H1

H2

H3

H4

0.220 0.219 0.230 0.215 0.217 0.217 0.219 0.219 0.219 0.219 0.220 0.219 0.220 0.219

0.544 0.544 0.572 0.553 0.550 0.547 0.548 0.546 0.544 0.544 0.543 0.544 0.543 0.544

0.839 0.841 0.840 0.846 0.843 0.843 0.840 0.841 0.841 0.840 0.840 0.839 0.839 0.837

0.493 0.497 0.528 0.490 0.493 0.494 0.495 0.497 0.497 0.497 0.496 0.496 0.493 0.493

n1 ¼ 10; n2 ¼ 25 H5 H6 H7 0.107 0.108 0.130 0.109 0.109 0.109 0.108 0.109 0.109 0.109 0.109 0.109 0.107 0.107

0.918 0.920 0.918 0.922 0.920 0.920 0.920 0.920 0.920 0.919 0.918 0.918 0.918 0.919

0.995 0.995 0.995 0.998 0.996 0.996 0.996 0.995 0.995 0.995 0.995 0.995 0.995 0.995

n1 ¼ 20; n2 ¼ 20 H5 H6 H7 0.188 0.190 0.202 0.190 0.191 0.190 0.189 0.189 0.190 0.188 0.188 0.188 0.188 0.189

0.847 0.851 0.825 0.854 0.853 0.852 0.851 0.851 0.851 0.851 0.851 0.850 0.849 0.847

0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999

H8

H9

H10

hð · Þ

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.952 0.959 0.959 0.961 0.961 0.960 0.959 0.959 0.959 0.958 0.956 0.953 0.953 0.950

0.582 0.585 0.581 0.593 0.589 0.588 0.586 0.584 0.583 0.583 0.582 0.582 0.582 0.583

0.023 0.022 0.028 0.021 0.021 0.021 0.022 0.021 0.021 0.021 0.021 0.021 0.023 0.030

H8

H9

H10

hð · Þ

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999

0.881 0.881 0.896 0.883 0.883 0.882 0.881 0.881 0.881 0.881 0.880 0.881 0.881 0.881

0.035 0.031 0.029 0.038 0.035 0.034 0.033 0.031 0.031 0.031 0.032 0.032 0.035 0.035

max hðE * ; H j Þ ¼ min max hðE; H j Þ: j

E[T

j

In the last column of each table, it can be seen the maximum relative inefficiency of each statistic for the different alternatives. If we choose the three best statistics in the sense of the minimax relative inefficiency for each table T n1:3 appears more times than the rest following by T 1n ¼ LRT. As a result of this numerical analysis, we recommend T n1:3 since it is placed four times the first, one time the second and one

Study of a new family of test statistics 815

Table IX. Simulated power for double exponential populations

Table X. Simulated power for double exponential populations

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time the third. It is clear that T n1:3 emerges as a good alternative to the classical V, W and S-test statistics. The same procedure explained in Section 2 but with the corresponding changes was used by Pardo and Pardo (2000) to test for the equality of coefficients of variation. It was compared with the known test statistics: Bennett, modified Bennett, Miller, Wald and Score. One of the best members of the family of the statistics based on Re´nyi’s divergence is T 1:3 n . So it does not seem that this statistic emerges as the best to solve the Behrens-Fisher problem by chance. References Behrens, W.V. (1929), “Ein beitrag zur fehlerberechnung beiwenigen beobachtungen”, Landwirtsch, Jahrbu¨cher, Vol. 68, pp. 807-37. Best, D.J. and Rayner, J.C.W. (1987), “Welch’s approximate solution for the Behrens-Fisher problem”, Technometrics, Vol. 29 No. 2, pp. 205-10. Bozdogan, H. and Ramirez, D.E. (1986), “An adjusted likelihood-ratio approach to the Behrens-Fisher problem”, Communications in Statistics (Theory and Methods), Vol. 15 No. 8, pp. 2405-33. Burbea, J. (1982), “The convexity with respect to Gaussian distributions of divergences of order a”, Utilitas Mathematica, Vol. 24, pp. 171-92. Dale, J.R. (1986), “Asymptotic normality of goodness-of-fit statistics for sparse product multinomials”, Journal of Royal Statistical Society, Series B, Vol. 41, pp. 48-59. Fisher, R.A. (1939), “The comparison of samples with possibly unequal variances”, Annals of Eugenics, Vol. 9, pp. 174-80. Morales, D., Pardo, L. and Pardo, M.C. (2001), “Likelihood divergence statistics for testing hypotheses about multiple population”, Communications in Statistics (Simulation and Computation), Vol. 30 No. 4, pp. 867-84. Morales, D., Pardo, L. and Vajda, I. (1997), “Some new statistics for testing hypotheses in parametric models”, Journal of Multivariate Analysis, Vol. 62, pp. 137-68. Pardo, M.C. and Pardo, J.A. (2000), “Use of Re´nyi’s divergence to test for the equality of the coefficients of variation”, Journal of Computational and Applied Mathematics, Vol. 116, pp. 93-104. Re´nyi, A. (1961), “On measures of entropy and information”, Proceedings of the Forth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, pp. 547-61. Suguira, N. and Gupta, A.K. (1985), “Maximum likelihood estimates for Behrens-Fisher problem”, Technical Report No. 85-32, Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH. Welch, B.L. (1937), “The significance of the difference between two means when the population variances are unequal”, Biometrika, Vol. 29, pp. 350-62. Welch, B.L. (1947), “The generalization of ‘Student’s’ problem when several different population variances are involved”, Biometrika, Vol. 34, pp. 28-35. Corresponding author Julio Angel Pardo can be contacted at: [email protected] To purchase reprints of this article please e-mail: [email protected] Or visit our web site for further details: www.emeraldinsight.com/reprints

COMMUNICATIONS AND FORUM

Cybernetics tutorial The following e-mail has been received from the Cybernetics Discussion Group on behalf of Stuart Umpleby and will be of particular interest to all readers of Kybernetes:

Communications and Forum

817

Nagib Callaos (President of the IIIS – www.iiis.org/iiis) has videotaped a one-day tutorial that I gave at the 2006 Conference in Orlando, FL. Today I received a shipment. Each plastic package, about the size of a book, contains five disks. There are four 1.5 h lectures and one disk with exercises and PPT slides. You can see some of this material at: www.gwu.edu/, umpleby/cybernetics/. I shall send to each member of the American Society for Cybernetics (ASC) one of these collections and also a DVD of the conversation with George Soros on reflexivity and fallibility, which was held at George Washington University in May 2006. (www.gwu.edu/, rpsol/lectures/2006%20Lecture%20Soros.htm and www.gwu.edu/ , rpsol/lectures/ 2006%20Lecture%20Umpleby%20.htm). I hope you will find this material helpful in explaining cybernetics to colleagues and students. Needless to say, I welcome comments and suggestions. If you are not currently a member of the ASC, you may want to join (www.asc-cybernetics. org) in order to receive these materials. For a short (25 min) slideshow on the history and development of cybernetics see www.gwu. edu/ , asc/slideshow/cybernetics_web/slideshow.html

Stuart Umpleby, Research Program in Social and Organizational Learning 2033 K Street NW, Suite 230, The George Washington University, Washington, DC 20052. Web site: www.gwu.edu/ , umpleby; Tel: 202-994-1642; Fax: 202-994-5284.

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News, conferences and technical reports World Organisation Of Systems and Cybernetics (WOSC) New WOSC address The director general of WOSC has given details of the change of address of the organization. These are given in full in Dr Andrew’s internet commentary published in this issue. He writes that a new page has been set up and for the time being can be accessed at: http://myweb.tiscali.co.uk/alexandrew/wosc.htm He notes that the link with the Cybernetics Society has been updated accordingly and that other possibilities for the WOSC site are under consideration. WOSC Secretariat The WOSC Secretariat is still at: 95 Finch Road, Earley, Reading RG6 7JX, UK Tel/Fax: (þ 44 or 0) 118 9269328 WOSC sponsorships WOSC will be represented at most of the important meetings, conferences and events held in the Systems and Cybernetics Community. Many of these occasions will include WOSC as one of the sponsors. In particular, WOSC will be academic/scientific co-sponsors of: . The 11th World Multi-Conference on Systemics, Cybernetics and Informatics held jointly with The 13th International Conference on Information Systems Analysis and Synthesis at Orlando, Florida, USA (8-11 July 2007) WMSCI 2007 and ISAS 2007 details are included at: www.iiis-cyber.org/wmsci2007 . XVI International Conference on Systems Science to be held at Wroclaw University of Technology, Wroclaw, Poland (4-6 September 2007) Information about the conference are available at: www.iit.pwr.wroc.pl/icss/. The Committee of Automation and Robotics and also the Polish Academy of Sciences are co-sponsors. It has been arranged that selected papers or their extended versions will be published in Systems Science journal (available in English) or in Kybernetes the official publication of WOSC. Contact: Adam Grech, Wroclaw University of Technology, Wybrzez Wyspianskiego 27, 50-370 Wroclaw Poland. Tel: þ 48 71 320 33 28; Fax: þ 48 71 32038 84; e-mail: [email protected] Details of other events that will be supported by WOSC’s federated organisations and institutions are given in the Announcements and Special Announcements sections of this journal.

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WOSC Institute of Systems and Cybernetics Discussion and consultation meetings of the Norbert Wiener Institute of Systems and Cybernetics have been held at a number of venues. These have centred on a number of issues and on future planning of its structure and functions. WOSC federated bodies are encouraged to contact the Institute about these and in particular about the following:

Appointment of leading cyberneticians and systemists as consultants in some of the many interdisciplinary areas of the field. Currently the appointments are either sponsored or honorary. . Membership of the Institute should a graded system of individual and/or corporate membership be instituted? . Research contribution currently research and developments are published in academic journals and other publications. . Kybernetes being the officially chosen publication of WOSC encourages research to be peer-reviewed and included if suitable, in its special and regular issues – should the institute consider other means of publicising these endeavours? WOSC news . Arrangements are being completed for the next WOSC Congress which is to have a venue in Europe. The Director-General Dr Andrew will announce details on his web site as soon as they are finalised. . WOSC’s President, Professor Robert Valle´e has expressed the organisation’s support for Stafford Beer’s Memorial Lectures to be held. The first of the series is currently being arranged in the context of the WMSCI 2007 conference to be held in Orlando USA in July 2007 and co-sponsored by WOSC. . Professor Raul Espejo a Director of WOSC, has accepted an invitation to become a member of the Editorial Advisory Board of Kybernetes WOSC’s official publication. Professor Robert Valle´e will represent WOSC at a number of important events in 2007. Members of the Directorate will also attend and have accepted invitations to join the programme committees and to participate in the events. . Literati Awards for outstanding contributions to Kybernetes in Volume 36 Nos. 1-10, 2006, are being decided. The nominations which have the full support of WOSC, which participated in the selections, have been submitted to the publishers Emerald. The list of awards will be announced in the next issues of the journal. .

Conference notes American Society for Cybernetics (ASC) The following ASC meetings were organised for 2007: (1) Urbana Illinois Meeting of the ASC Constructivism, Design, Cybernetics: Radical Social Order, 2nd Order (29 March-1 April 2007 at Urbana, Illinois, USA). This Working Conference was organised for creating a three-way bridge spanning the thought and practise of: . Radical constructivism – that the reality we describe and perceive arises from our manner of living as perceivers & describers. . Social, archictectural and artistic design – deliberate and improvised actions and structures that define and perturb what we call the social and aesthetic. . Second-order cybernetics – an interdisciplinary weave of intellectual pathways connecting feedback, circular causality, self-organization, self-reference, cybernetics of cybernetics, taking ourselves into account. (2) ASC participation with the ISSS meeting in Tokyo, Japan, (5-7 August). Details of the conference are given at: www.isss.org/conferences/tokyo2007/

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The ASC track at the meeting is described as: 2.12 Cybernetics (organized by the American Society for Cybernetics) TST Chair: Louis H. Kauffman, E-mail: [email protected]

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This track is devoted to cybernetics, particularly to fundamentals of cybernetics and to cybernetic epistemology and second-order cybernetics in the sense of Margaret Mead and Heinz von Foerster. We welcome papers and workshop proposals from non-ASC members as well as ASC members. The workshops will be arranged during the main conference period, and maximum time allowed for a workshop is one-and-half hours. The workshop proposals should be directly sent to Professor Kauffman, The American Society for Cybernetics will also organize tutorials or workshops prior to the conference in the time period Sunday, 5 August 2007: 11:00 a.m. - 4:00 p.m. It will be opened to all ISSS participants. ASC participation in the Heinz-von Foerster Conference Vienna, Austria (November 2007). ASC members have been invited to contact Karl Mueller e-mail: [email protected]

Further details of this Conference will be published in Kybernetes in coming issues. Complex control systems and quality management – CCSQM 2007 This conference was organised by the Ministry of Higher Education and Science of the Russian Federation-Russian Academy of Sciences and a group of technical universities of Central Russia: . Lipetsk State Technical University. . Voronez State Technical University. . Voronez State Architectural University. . Stary Oskol Technological Institute. . Institute of Control Sciences. Held in Stary Oskol (12-14 March) The conference was arranged to cover the following topics: . Systems theory. . System identification. . Information systems. . Technical and business applications. . Logistics and scheduling. . Modelling and simulation. . Software engineering. . Control theory. . Systems and control engineering. . Operation and manufacturing systems. . Quality management. . Industrial control systems.

. . . .

Uncertain systems. Fuzzy systems and models. Decision support systems. Knowledge engineering and intelligent systems.

Details of the proceedings can be obtained from L.A. Kuznetsov, e-mail: lgtu.asu. [email protected]. A review of the conference is to be published in coming issues of Kybernetes. Sociocybernetics, Technology and Social Complexity – 2007 The 7th International Conference was arranged at Murcia, Spain (18-23 June). Information about the proceedings is given at the web site: http://socioeybernetics. unizar.es/ or from Chaime Marcuello Servos -E.U Estudios Sociales, Universidad de Zaragoza, Violante de Hungria 23,50009-Zaragoza, Espan˜a.

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Book reviews Organizations as Complex Systems: An Introduction to Knowledge Cybernetics Maurice Yolles Information Age Publishing Greenwich, Connecticut 2006 xii þ 866 pp. ISBN 978-1-59311-433-6 (hardcover); 978-1-59311-432-9 (pbk) Paper $34.95; hardcover $69.95 Vol. 2 in series on Managing the Complex Keywords Cybernetics, Social behaviour, Knowledge Review DOI 10.1108/03684920710749875 This single-author work is the second volume in its series and it is mentioned in the introduction by the series editors that the previous one was a multi-author collection, and the intention is that subsequent volumes will also be collections. Rather surprisingly, details of the previous volume are not given but can be obtained from the publishers’ website. The earlier volume is entitled: Managing Organizational Complexity: Philosophy, Theory and Application, published in 2005 and edited by Kurt Richardson, one of the series editors, with a long list of contributors including well-known names The ISBN numbers are 1-59311-319-6 (hardcover); 1-59311-318-8 (pbk), with respective prices $105.95 and $62.50. In their brief introduction the series editors hail the new book as a tour-de-force. They say that the treatment impinges on various previous areas, including (they say) third-order cybernetics, viable systems theory and social constructivism. It was initially expected that the disparate theories would be covered but with possible links between them only indicated as topics for future research. It is suggested, however, that the author has arrived at something that could be the beginnings of a unified theory. The book has a total of 16 chapters, divided into five Parts. The titles of these are: “Fundamentals” “Complex organizations” “Knowledge and cybernetics” “The cybernetics of communication” and “Social behavior”. Near the beginning of Chapter 2 in the first part a distinction is drawn between ontological and epistemological approaches, referred to frequently in the later treatment. I found the distinction unconvincing, since ontology, the study of Being or existence, is held to imply the creation of a referencing system with symbolic expression, which would seem to bring it into the realm of epistemology. The distinction is, however, maintained, and in Chapter 6 in the second part the ideas behind Stafford Beer’s viable system model are extended to a social viable system with the comment that the VSM is fundamentally an epistemological approach that benefits from being supplemented by ontological considerations.

In the final chapter, a number of interactions of knowledge and belief with social behaviour are discussed, in ways that are held to constitute a novel theme of Knowledge Cybernetics. In the Introduction to the book it is said that this developed from a mathematical theory of Sociohistory developed by the author and a colleague. There is however, nothing in the nature of mathematics in the present book, unless for some hint of it on pages 765-9. A distinction is made between three levels of what can be loosely termed “information” namely data, information and knowledge, with references also to “wisdom” and there is emphasis on knowledge as migrating,.rather than passing along identifiable channels. The theory also bears on less tangible aspects like attitudes and emotions, for instance associated with ethics and traditions. Its application to analysis of a Liverpool docks dispute is described in considerable detail in the final Chapter. This tour-de-force was initially expected to take a year to write but in fact required three, and cannot have left much time for leisure even then. Although it seems mean in the face of such an achievement, I have to admit to failing to get fully to grips with the treatment and also to having uneasy feelings about it. An early reason for unease is in the introduction by the series editors, where “third-order cybernetics, viable systems theory and social constructivism” are referred to as though these were established and well-defined subject areas, instead of rather loose headings for ongoing (though no doubt valuable) discussion. There is an undue readiness to represent these topic headings as though they were, to use a current buzzword, “set in stone”. (Actually, third order cybernetics does seem to be a reasonably well-defined topic, as the study of systems where the operation of observation inevitably alters what is observed. This must be common in social systems and is reminiscent of a much-used illustration of Heisenberg’s uncertainty principle by reference to observation of a particle under a microscope.) The treatment in the book, as a whole, has a didactic flavour that seems inappropriate to the subject matter and is in contrast to the relatively diffident approach in a review by Herting and Stein (2007). The latter contains the surprising statement that in Germany it has been decided that the notion of “Systemtheorie” should be used only in a sociological sense, a restriction that would presumably not have pleased Stafford Beer, whose viable system model was launched in a paper (Beer, 1962) that invoked parallels with neurology. As mentioned, I have to admit to not having really got to grips with the content of this book. I feel sure there is a coherent thread running through it, but familiarity with earlier material is needed in order to discern it. The author mentions that his treatment builds on the earlier one of Sorokin (1962) published in no less than four volumes. I also feel, though, that my difficulty is not entirely attributable to ignorance, since the author’s Introduction that is meant to set the scene contains a great deal of ponderous matter and covers no less than 26 pages without subdivision by section headings. The list of references occupies 33 pages and must be a pretty comprehensive review of the relevant literature. There is also a very complete subject index, which however could have been made more convenient to use by indicating, for instance by bold print, which page or pages are most relevant to a topic. The coverage of the work is indicated by a note on the back cover, as follows: This book develops a cybernetic theory of the organization as a complex and autonomous and self-organizing, self-producing and self-creating social community, and in so doing it will set

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the scene to discuss a variety of aspects of organization and social processes and forms that arise from a systemic view. It begins by creating a philosophical foundation, it develops a viable systems approach that proceeds to cover a whole range of topics in a coherent and integrated way that are today seen to be important to social communities. Fundamentally developing as a knowledge management text, topics covered include community mission, purposes, interests, structure, politics, ethics, control, communications, management and conflict processes. It will also deliver an appreciation of the nature and use of information, knowledge and intelligence to assist the management of social communities.

Alex M. Andrew References Beer, S. (1962), “Toward the cybernetic factory”, in von Foerster, H. and Zopf, G. (Eds), Principles of Self-Organization, Pergamon, Oxford, pp. 25-89. Herting, S. and Stein, L. (2007), “The evolution of Luhmann’s systems theory with focus on the constructivist influence”, International Journal of General Systems, Vol. 36 No. 1, pp. 1-17. Sorokin, P.A. (1962), Social and Cultural Dynamics, in 4 volumes, Bedminster Press, New York, NY, (quoted from the work under review, previously published during 1937-1942 by Amer. Book Co., New York, NY).

Risk Management for IT Projects – How to Deal with Over 150 Issues and Risks Bennet Lientz and Lee Larssen Butterworth-Heinemann 2006 ISBN 978-0-12-370534-1 £29.99 Keywords Cybernetics, IT, Risk management, Project management Review DOI 10.1108/03684920710749884 Anyone who is involved with an IT project is well aware of the risk issues that occur. Risk managers bear a responsibility to manage the risks that arise and are employed because, hopefully, they know how to handle them. Unfortunately, many researchers and developers in systems, cybernetics and management may not be trained to resolve such risk situations and learn to take the responsibility through their experience. The authors of this book, however, give both professionally trained and the untrained project leader the benefit of their wide experience in dealing with the many unforeseen risk issues that arise during a project’s cycle. They do this by providing case histories with a clear and detailed analysis of each stage of the project in hand. The importance of risk prevention is emphasised and risk detection is discussed in some depth. The subject is dealt with in a very clear and simple style, which involves the detection of a risk at the early stages, to the formulation of plans to deal with it. Benner Lientz and Lee Larsen have used their extensive experience in risk management to classify risk into recognisable types based on their source. The ways of dealing with the various types discussed with specific reference to the case studies they have introduced. All of these concepts and the resulting methodology recommended

are clearly explained with extensive use of illustrations that pinpoint the relevant tools used and the actions taken. As a result the topic of risk management was given excellent coverage. What proved to be attractive about the text was the author’s decision to treat all the issues from the viewpoint of the risk manager and to identify the risks that occur at the various phases of the project. Advice is then offered to enable the risk to be dealt with efficiently and in a manner which is directly based on their own rich experience. The book therefore provides excellent advice to the manager and the indeed to any of the project group who need to deal with the issues that, as we all know, are almost certain to arise in an IT project. One IT professional publication has already chosen the book as its “IT book of the month” other publications will no doubt agree with their choice. Cyberneticians, systemists and those involved with management will also benefit. The book’s authors subtitle “How to Deal with Over 150 Issues and Risks” is more than justified and readers can expect to find this an easily read text that is both reliable and worthwhile. D.M. Hutton Norbert Wiener Institute and University of Wales, UK

Thinking about Android Epistemology Kenneth M. Ford, Clark Glymore and Patrick J. Hayes (Editors) AAAI Press 2006 384 pp. ISBN 0-262-5617-0 Keywords Cybernetics, Systems, Philosophy, Epistemology Review DOI 10.1108/03684920710749893 This edited text we are told, is an updated version of Android Espistemology which was published in 1995. It presents an introduction by philosophers and computer scientists to alternative systems of cognition. The editors have been guided by the need to examine “minds” other than “human minds”. They take the opinion that we should consider these “other sorts of minds” and also develop physical systems so that they too can be structured to “produce both knowledge and competence”. Philosophy has always been very much concerned with humans and their minds. The advent of advanced technology has provided us with the opportunity to consider systems, their functions and their properties. The introduction of sophisticated computing systems enables us to study their capacity to learn, to analyse, to theorize to such an extent that they actively show their competence. The contributors to this book include many well-known writers in the field. They endeavour to introduce these systems as “systems of cognition” which demand our study and attention. Android epistemology is looked at from not only a very necessary theoretical standpoint, but also from the practical viewpoint.

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Since, 1995 when the first version was published, we have seen the advances in fields such as artificial intelligence which have despite their rather slow emergence, enabled us to study such systems. This is a book that sets its readers thinking along new lines and should interest the “traditional philosopher” as well as readers whose main interests lie in alternative systems, which can supplement the human mind’s activity. Whilst both the capacities and the limitations of the human mind has through the ages fascinated epistemologists and philosophers, the editors of this book believe that now is the time for us to earnestly consider alternative systems as well. They have given readers in this book an introduction to current thinking which is well worth their consideration. Further information about the book can be obtained at: www.aaai.org D.M. Hutton Norbert Wiener Institute and University of Wales, UK

Maths for the Mystified Michael J. de Smith Matador 2006 203 pp. ISBN 1-905237-81-2 Price: £14.99 (Paperback) Keywords Cybernetics, Mathematics, Systems Review DOI 10.1108/03684920710749901 De-mystifying mathematics is an enormous challenge to any author. Michael de Smith does however tackle it to some purpose. From the outset it appears: to be a text aimed at students from the sciences and social sciences. It is not clear whether these students have taken any previous courses in mathematics or if they have, to what standard they have reached. We would expect readers of this book to have at least studied the basics so that they are better equipped to understand the author’s gallant attempts at making matters much clearer. Is it a “refresher course”? – Is it a study that aims to fill the gaps in the reader’s understanding of mathematics? Or does it hope to inspire those who believe they have already failed to grasp what mathematics is all about? The result is a book that attempts to do all these things. It provides introductions to numerous topics and provides a background to many mathematical initiatives and developments. All of these sections have been written in an interesting and well-presented, way. It is true, of course, that a book of this size facing the enormity of the subject can only hope to stimulate the reader to further study. Choosing the right topics and giving the necessary applications that will fascinate, as well as inform has to be the prime concern. The book does provide much that is of value to students who follow courses in computing and cybernetics as well as systems. Often such students are not mathematically inclined or qualified to pursue these courses but still persist in believing that they can make progress without being conversant with the basics of

mathematics. The same is, unfortunately, true of some researchers in these fields who still avoid anything mathematical. This book could well interest them because it includes the most important basics. After all, mathematics is an international language and proficiency in it is essential. What the author provides is of great interest and should spur the book’s readers to want to study the subject to an even greater depth. W.R. Howard Computer Science International, Dinslaken, Germany

Acting with Technology: Activity Theory and Interaction Design Victor Kaptelinin and Bonnie A. Nardi MIT Press 2006 344 pp. ISBN 0-252-11298-1 Keywords Cybernetics, Technology, Systems Review DOI 10.1108/03684920710749910 This is an unusual book which tells us what we have always appreciated, that everyday activity shapes the human mind. This means that our interactions each day with other humans and with artifacts may be structured into a viable theory based on activity. It goes further and suggests that there is a case for using activity theory to help us understand our relationship with technology. To do this, Kaptelinun and Nardi need to introduce and describe what the theory is. This is completed at the beginning of the text where a full background to the development of the theory is presented. Only then is consideration given to its application to what we know as technology. With the most important tenets of the theory of activity discussed the authors then describe the links between interaction design and the theory. References are presented to back up their thesis. Many of the present-day issues in the development of activity theory are given and future progress discussed. This book provides an excellent analysis of activity theory and will be of much interest and value to readers involved with cybernetic and systemic applications in many diverse’ fields of endeavour. Anyone researching the area of interaction design will also find that the notions and descriptions provided are particularly helpful in their project development. W.R. Howard Computer Science International, Dinslaken, Germany

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Book reports Object-Oriented Metrics in Practice: Using Software Metrics to Characterize, Evaluate, and Improve the Design of Object-Oriented Systems Michele Lanza and Radu Marinescu Springer Heidelberg, Germany 2006 I-XIV, 206 pp., 80 illustrations (33 in colour) ISBN 3-540-24429-8 US $59.95 (Hardcover) Keywords Cybernetics, Metrics, Software The subtitle of this book clearly sets out the aims of the authors who want to take out the mystery, they say, from design metrics used to assess object-oriented software systems. Design metrics has been applied to these systems for some time in an effort to assess the size, quality and complexity of the system. The authors show in some detail, how to identify collaboration and classification disharmony patterns in code and how to visualise their results. The CodeCrawler visualization tool is used and they indicate that this is now freely available. This process allows the practitioner to decide about possible remedies and the authors discuss how this can be achieved. The publisher Springer quote Richard C. Gronback of the Borland Software Corporation who believes that this: . . . well written book is an important piece of work that takes the seemingly forgotten art of object-oriented metrics to the next level in terms of relevance and usefulness.

Model-Driven Design Using Business Patterns Pavel Hruby Springer Heidelberg, Germany 2006 i-xvi 368 pp., 285 illustrations ISBN 3-540-30154-2 US $59.95 (Hardcover) Keywords Business, Cybernetics, Management, Systems

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Management scientists have a special interest in business applications and practical implementations of research and developments in the field. This book illustrates how it is possible to apply the pattern ideas in business applications. To do this Pavel Hruby presents more than 20 structural and behavioral business patterns. These patterns use the resources, events and agents (REA) pattern as a common base. The author believes that:

If you are a developer working on business frameworks, you can use the patterns presented to derive the right abstractions (e.g. business objects) and to design and ensure that the meta-rules (e.g. process patterns) are followed by the actual applications.

It also points out that if you are an application developer you can use these patterns to design your business application to ensure that it does not violate the domain rules, and to adapt the application to changing requirements. This can be done without the need to change the overall architecture. Readers will find that the detail of the 20 or so structural and behavioral patterns that use the REA pattern as a common backbone in their application to business are particularly useful and form an excellent reference source

Advanced Dynamic-system Simulation: Model-replication Techniques and Monte Carlo Simulations Granino A. Korn Wiley 2007 (January) ISBN 978-0-470-08199-4 US $89.95 (Cloth cover) Keywords Cybernetics, Simulation, Software, Systems Granino Korn’s book describes new computer programs for the interactive modeling and simulation of dynamic systems such as: . aerospace vehicles; . control systems; and . biological systems. It is introduced by a brief review of simulation programming and demonstrates computer software for extremely fast and quite large simulation studies on relatively cheap personal computers and on workstations. What the book does is to introduce fundamental and basic techniques and software and the author has included explicit programs to illustrate his theme. These programs can be run with the software which is included with the book on a CD. The publishers claim that this CD contains an industrial-strength software package rather than a toy demonstration program. There is no doubt that many CDs included with books are not suitable for extensive use and many systems are better downloaded from a reliable site. To use this book properly there has to be “hands-on experimentation” and the robustness of the software package is soon tested. Further, information about the book may be obtained from: www.wiley.com It should be noted that members of some professional organisations may receive a discounted price when ordering the book. C.J.H. Mann Book Reviews and Reports Editor

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Announcements July 2007 ISCC 2007 – 12th International Symposium on Computers and Communications (IEEE Sponsored), Aveiro, Portugal, 1-4 July Contact: Web site: www.av.it.pt/iscc07 ICME 2007 – International Conference on Multimedia and Expo (IEEE), Beijing, China, 2-5 July Contact: Web site: http://research.microsoft.com/conferences/icme07/ The 11th World Multi-Conference on Systemics, Cybernetics and Informatics – WMCI 2007, Orlando, Florida, USA, 8-11 July Contact: IIIS-WMSCI 2007, PMB-115, 3956 Town Centre Blvd., Orlando, Florida 32837 USA, Web site: www.iiis.cyber.org/wmsci2007 CIVR ’07 – International Conference on Image and Video Retrieval – 2007, Amsterdam, The Netherlands, 9-11 July Contact: Nicu Sebe, Tel.: þ 31 20 5257552; e-mail: [email protected] ICIS/COMSAR 2007 – International Conference on Computer and Information Science (IEEE sponsored), Melbourne, Australia, 11-13 July Contact: Web site: http://acis.cps.cmich.edu:8080/ICIS2007 NCA 2007 – 6th IEEE International Symposium on Network Computing and Applications, Cambridge, Massachusetts, USA, 12-14 July Contact: Web site: www.ieee-nca.org RSS 2007 – Royal Statistical Society (UK) – International Conference, York, UK, 16-20 July Contact: Web site: www.rss.org.uk/rss2007 ICALT 2007 – 7th International Conference on Advanced Learning Technologies, Niigata, Japan, 18-20 July Contact: Web site: www.ask.iti.gr/icalt/2007 HCI International 2007 – 12th International Conference on Human-Computer Interaction, Beijing, China, 22-27 July Contact: Web site: www.hcii27.org

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COMMPSAC 2007 – 31st Annual International Conference on Computer Software and Applications, Beijing, China, 24-27 July Contact: Web site: http//:conferences.computer.org/compsac/2007

GECCO 2007 – Genetic and Evolutionary Computation Conference, London, UK, (Dates to be set) July Contact: Hod Lipson, Tel.: þ 607 255 1686; e-mail: [email protected] ECOOP 2007 – 21st European Conference on Object-Oriented Programming, Berlin, Germany, 30 July-3 August Contact: Web site: www.idt.mdh.se/esec-fse-2007/ August 2007 ECOOP ’07 – 21st European Conference on Object-Oriented Programming, Berlin, Germany, 30 July-3 August Contact: Web site: http://ecoop07.swt.cs.tu-berlin.de/index.html EDT ’07 – Emerging Display Technologies 2007, USA, (venue to be announced), 4-5 August Contact: Greg Welch, Tel.: þ 919 962 1819; e-mail: [email protected] PODC ’07 – ACM Symposium on Principles of Distributed Computing 2007, Portland, Regan, USA, 12-15 August Contact: Matk Tuttle, Tel.: þ 781 883 9409; e-mail: [email protected] KDD ’07 – The 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 2007, San Jose, California, USA, 12-15 August Contact: Rakesh Agrawal, Tel.: þ 408 927 1734; e-mail: [email protected] IRI-2007 – International Conference on Information Reuse and Integration (IEEE Systems, Man and Cybemetics Soc.), Las Vegas, USA, 13-15 August Contact: Web site: www.sis.pitt.edu/-iri07/ ICGSE 2007 – International Conference on Global Software Engineering, Munich, Germany, 27-30 August Contact: Web site: www.inf.pucrs.br/icgse FCT 2007 – 16th International Symposium on Fundamentals of Computation Theory, Budapest, Hungary, 27-30 August Contact: Web site: www.conferences.hu/fct2007 September 2007 XVI International Conference on Systems Science, Wroclaw, Poland, 4-6 September Contact: Adam Grzech, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw 27, Poland, Tel.: þ 48 71 320 33 28; e-mail: AdamGrzech@pwr. wroc.p1; Web site: www.iit.pwr.wroc.pl/icss/ ESEC/FSE ’07 – Joint 11th European Software Engineering Conference (ESEC) and 15the ACM SIGSOFT Symposium on the Foundations of Software Engineering (FSE), Cavar (Dubrovnik), Croatia, 3-7 September Contact: Ivica Crnkovic, Tel.: þ 46 70 533 7557; e-mail: [email protected]

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SEFM 2007 – 5th International Conference on Software Engineering and Formal Methods, London, UK, 10-11 September Contact: Web site: www.iist.unu.edu/SEFM07 Numerical Linear Algebra and Optimisation, Birmingham, UK, 13-15 September Contact: Lucy Nye, Institute of Mathematics and Its Applications, Catherine Richards House 16, Nelson Street, Southend-on-Sea, Essex SSI IEF UK, Tel.: þ 01702 356104; e-mail: [email protected] PACT 2007 – 16th International Conference on Parallel Architectures and Compilation Techniques, Brasov, Romania, 15-19 September Contact: Web site: http://parasol.tamu.edu/pact07 ESEM 2007 – International Symposium on Empirical Software Engineering and Measurement, Madrid, Spain, 20-21 September Contact: Web site: www.esemconferences.org MM ’07 – The 15th International Conference on Multimedia 2007 (ACM), Augsburg, Bavaria, Germany, 23-28 September Contact: Rainer Lienhart, Tel.: þ 49 821 598 5703; e-mail: rainer.lienhart@informatik. uni-augsburg.de MSST 2007 – 24th Conference on Mass Storage Systems, and Technologies (IEEE), San Diego, USA, 24-27 September Contact: Web site: http://storageconference.org/2007 October 2007 SIGTE ’07 – The 20th ACW Special Interest Group for Information Technology Education Conference 2007 (Formerly CITC), Mobile, Alabama, USA, 1-4 October Contact: Bob Sweeney, Tel.: þ 251 460 6390; e-mail: [email protected] UIST ’07 – The 20th Annual ACM Symposium on User Interface Software and Technology 2007, Boston, Massachusetts, USA, 7-10 October Contact: Chia Shen, Tel.: þ 617 621 7528; e-mail: [email protected] ATS 2007 – 16th Asian Test Symposium, Beijing, China, 9-11 October Contact: Web site: http://ats07.ict.ac.cn FIE 2007 – Frontiers in Education Conference, Milwaukee, Wis., USA, 10-13 October Contact: Web site: www.fie-conference.org/fie07 International Conference on Requirements Engineering 2007, Delhi, India, 15-19 October Contact: Pankaj Jalote, e-mail: [email protected]

Special announcements Conference reminder Sponsored by Ercim ECOOP ’07 – 21st European Conference on Object-Oriented Programming Berlin 30 July-3 August 2007

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The ECOOP 2007 conference will feature high quality papers presenting research results or experience in all areas relevant to object technology, including work that takes inspiration from or builds connections to areas not commonly considered object-oriented. Many different research methods can be applied, e.g. both experimentally-based work and mathematical results. ECOOP 2007 will also host a number of workshops addressing different areas of object-oriented technology. Workshops serve as a forum for exchanging late breaking ideas and theories in an evolutionary stage. They typically focus on either in depth analysis or broad-ranging approaches to areas related to object-oriented technology. The conference also is offering a number of opportunities for tutorials and demonstrations of research and production systems. For more information: http://ecoop07.swt.cs.tu-berlin.de/index.html

Kybernetes Vol. 36 No. 5/6, 2007 p. 833–838 q Emerald Group Publishing Limited 0368-492X

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The 2007 IEEE International Conference on Information Reuse and Integration With rapidly increasing volumes of information in digital forms, we are constantly charged with the challenges of efficiency in information usage and knowledge extraction. Information reuse and integration (IRI) seeks to maximize the availability of information and creation of knowledge, and to reuse these information and knowledge in addressing new issues. IRI plays a pivotal role to capture, maintain, integrate, validate, extrapolate, and apply both information and knowledge to augment decision-making capacity in application domains. The IEEE IRI conference serves as a forum for researchers and practitioners from academia, industry, and government to present, discuss, and exchange ideas that address real-world problems with real-world solutions. The IEEE IRI will feature contributed as well as invited papers. Theoretical and applied papers are both included in this call. The conference program will include special sessions, open forum workshops and keynote speeches. Several funding agency program directors – including NSF, ONR, et al. – will present an open panel discussion entitled Funding Opportunities in Information Reuse and Systems Engineering. The conference includes, but is not limited to, the areas listed below: . large scale data and system integration; . component-based design and reuse; . unifying data models (UML, XML, etc.) and ontologies; . database integration . structured/semi-structured data; . middleware and web services; . reuse in software engineering; . data mining and knowledge discovery; . sensory and information fusion; . reuse in modeling and simulation; . case-based reasoning; . natural language understanding; . knowledge management and e-government; . command and control systems (C4ISR); . human-machine information systems;

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biomedical and healthcare systems; homeland security and critical infrastructure protection; manufacturing systems and business process engineering; information security and privacy; automation, integration and reuse across applications; survivable systems and infrastructures AI and decision support systems; heuristic optimization and search; knowledge acquisition and management; fuzzy and neural systems; soft/evolutionary computing; space and robotic systems; multimedia systems; service-oriented architecture; autonomous agents in web-based systems; information integration in grid, mobile and ubiquitous computing environment; systems of systems; semantic web and emerging applications; and information reuse, integration and sharing in collaborative environments.

General Chairs Stuart Rubin, SPA WAR Systems Center, USA, E-mail: [email protected] Shu-Ching Chen, Florida International University, USA, E-mail: chens@ cs.flu.edu Program Chairs Weide Chang, California State University, USA, E-mail: [email protected] James B. D. Joshi University of Pittsburgh, USA, E-mail: [email protected] For further conference information see: www.sls.pitt.edu/ , iri07/

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Call for participation FCT2007-16th International Symposium on Fundamentals of Computation Theory Budapest, Hungary 27-30 August 2007 The Symposium on Fundamentals of Computation Theory was established in 1977 for researchers interested in all aspects of theoretical computer science, in particular in algorithms, complexity, formal and logical methods. It is a biennial series of conferences previously held in Poznan (1977), Wendisch-Rietz (1979), Szeged (1981), Borgholm (1983), Cottbus (1985), Kazan (1987), Szeged (1989), Gosen-Berlin (1991), Szeged (1993), Dresden (1995), Krakow (1997), Iasi (1999), Riga (2001), Malmo (2003) and Lubeck (2005). Topics of interest include (but not limited to): . automata and formal languages; . design and analysis of algorithms; . computational and structural complexity; . semantics; . logic, algebra and categories in computer science; . circuits and networks; . learning theory; . specification and verification; . parallel and distributed systems; . concurrency theory; . cryptography and cryptographic protocols; . approximation and randomized algorithms; . computational geometry; . quantum computation and information; and . bio-inspired computation. The proceedings will be published in the Lecture Notes in Computer Science series of Springer-Verlag and it will be distributed at the conference. We anticipate that a special issue of Theoretical Computer Science will be devoted to selected papers published at the conference. For more information: www.conicrences.hu/fct2007/

XVI International Conference on Systems Science Wroclaw, Poland, 4-6 September 2007 Organised by: . Institute of Information Science and Engineering, Wroclaw University of Technology Scientific co-sponsors: . World Organisation of Systems and Cybernetics (WOSC). . Committee of Automation and Robotics, Polish Academy of Sciences. Partly sponsored by: . Ministry of Science and Higher Education. Starting from 1980, this event is organised on a rotational basis among three institutions: Wroclaw University of Technology (Poland), Coventry University (UK), and University of Nevada, Las Vegas (USA). Conference topics: . general systems and control theory; . systems identification, modelling and simulation; . systems optimisation; . large scale control systems; . manufacturing systems; . distributed computer systems and computer networks; . knowledge-based and intelligent systems; . decision support systems and expert systems; and . applications of systems analysis to technical, management, communication, transport and biomedical systems Conference information. The first Call for Papers has already been made and a submission date set. Details are, however available at: www.iit.pwr.wroc.pl/icss/ and e-mail submissions made at [email protected]

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Call for participation: PACT 2007 – 16th International Conference on Parallel Architectures and Compilation Techniques Brasov, Romania 15-19 September 2007 The purpose of PACT is to bring together researchers from architecture, compilers, applications and languages to present and discuss innovative research of common interest. PACT features cutting-edge research on a broad range of topics, that include, but are not limited to: . parallel architectures and computational models; . compilers and tools for parallel computer systems; . multicore, multithreaded, superscalar, and VLIW architectures; . compiler/hardware support for hiding memory latencies; . support for correctness in hardware and software (esp. with concurrency); . reconfigurable computing; . dynamic translation and optimisation; . I/O issues in parallel computing and their relation to applications; . parallel programming languages, algorithms and applications; . middleware and run-time system support for parallel computing; and . high performance application specific systems. For more information: www.pactconf.org/pact07