Mathematical research summaries- volume 2. 9781536120226, 1536120227

Table of contents :
Contents
Preface
Chapter 1
Continuous-GRASP Revisited#
Research Summary
Chapter 2
The Noising Methods#
Research Summary
Chapter 3
Matheuristics: Embedding MILP Solvers into Heuristic Algorithms for Combinatorial Optimization Problems#
Research Summary
Chapter 4
An Empirical Investigation of Different Solution Strategies for Meta-Heuristic Optimization: Solution Representation, Diversity and Space Reduction#
Research Summary
Chapter 5
Non-deterministic Decoding with Mapping Rearrangement to Enhance Precision in Binary Encodings#
Research Summary
Chapter 6
Towards a More Efficient Multi-Objective Particle Swarm Optimizer Free of Parameters#
Research Summary
Chapter 7
A Multi-Objective Genetic Algorithm to Search for Pareto Solutions of Series-Parallel System Component Allocation Problems#
Research Summary
Chapter 8
A Survey of Genetic Algorithms for Shop Scheduling Problems#
Research Summary
Chapter 9
A Scheduling Approach for the Design of Flexible Manufacturing Systems#
Research Summary
Chapter 10
Electric Distribution Network Operation Planning Using Chu and Beasley Genetic Algorithm and Particle Swarm Optimization#
Research Summary
Chapter 11
A Distributed Approach for Designing Efficient Search Algorithms: An Application to Solve the Location-Routing Problem#
Research Summary
Chapter 12
The Multi-Depot Vehicle Routing Problem: An Integer Programming-Based Heuristic and Computational Results#
Research Summary
Chapter 13
Optimization for Feature Selection in DNA Microarrays#
Research Summary
Chapter 14
Ant Colony System: Application for the Single and Multi-objective Multidimensional Knapsack Problems#
Research Summary
Chapter 15
Synergistic Combination of Evolutionary Algorithms and Fuzzy Systems: Application to Control Design#
Research Summary
Chapter 16
Analysis of Structures by Total Potential Optimization Using Meta-Heuristic Algorithms (TPO/MA)#
Research Summary
Chapter 17
A Review of Computational Intelligence Algorithms in Insurance Applications#
Research Summary
Chapter 18
Rough Sets in Insurance Sector#
Research Summary
Chapter 19
Prediction of Claims and Selection of Risk Factors in Automobile Insurance Using Support Vector Machines, Genetic Algorithms and Classification Trees#
Research Summary
Chapter 20
Tail Value at Risk. An Analysis with the Normal-Power Approximation#
Research Summary
Chapter 21
Financial Applications of Modal Interval Analysis#
Research Summary
Chapter 22
A Method for Analysis of Transmission Lines Terminated by Nonlinear Loads#
Research Summary
Chapter 23
Markus-Sell’s Theorem for Asymptotically Almost Periodic Systems#
Research Summary
Chapter 24
A Survey of the Method of Lyapunov Functions of Two Variables in the Study of Stability and Persistence of Dynamical Systems#
Research Summary
Chapter 25
Krylov and Schur Subspaces in Construction of Prediction Error Filter: Computational Complexity and Performance Comparison#
Research Summary
Chapter 26
High-Fidelity Modeling and Vibration-Based System Identification and Damage Inspection of Flexible Structures#
Research Summary
Chapter 27
Complexity and Chaos Theory in Social Sciences: Scientific Philosophy or Quantitative Science?#
Research Summary
Chapter 28
Local Stability Analysis of an Age-Structured Hepatitis B Transmission Model#
Research Summary
Chapter 29
Parametric Resonance and Homoclinic Chaos in a Bullard-Type Dynamo#
Research Summary
Chapter 30
Birhythmicity, Synchronization and Chaos in an Enzyme-Substrate Reaction with a Ferroelectric Behavior#
Research Summary
Chapter 31
Dynamics of Low and High Pathogenic Avian Influenza in Wild Bird Population#
Research Summary
Chapter 32
Analysis of a Predator-Prey Model with Sigmoidal Response Function and SIS Disease#
Research Summary
Chapter 33
Modelling the Effects of Multi-Intervention Campaigns for the Malaria Epidemic in Malawi#
Research Summary
Chapter 34
Modelling the Dynamics of HIV-TB Co-Infection in a Variable Size Population#
Research Summary
Chapter 35
Case Detection on Tuberculosis Dynamics with Isolation in a Sanatorium#
Research Summary
Chapter 36
Advances in Discrete Dynamics#
Research Summary
Chapter 37
Simulated Annealing: In Mathematical Global Optimization Computation, Hybrid with Local or Global Search, and Practical Applications in Crystallography and Molecular Modelling of Prion Amyloid Fibrils#
Research Summary
Chapter 38
Handling Equality and Inequality Linear Constraints in Simulated Annealing#
Research Summary
Chapter 39
Aircraft Design with Simulated Annealing for SAE Aerodesign Competition#
Research Summary
Chapter 40
Simulated Annealing Applied to the Resolution of Phylogenetic Reconstruction with Maximum Parsimony#
Research Summary
Chapter 41
Improved Parallel Simulated Annealing Applied to Spacecraft Trajectory Optimization#
Research Summary
Chapter 42
Simulated Annealing Applications in Thermodynamic Calculations#
Research Summary
Chapter 43
SA Optimization of Two-Chamber Mufflers Equipped with Multiple Parallel Perforated Tubes within a Constrained Space#
Research Summary
Chapter 44
A Simulated Annealing Algorithm to Solve the Log-Truck Scheduling Problem#
Research Summary
Chapter 45
Potential Applications of Simulated Annealing to Multi-Species Fish Habitat Conservation in the Gulf of Maine#
Research Summary
Chapter 46
Second-Order Perturbations in Encke’s Method for Spacecraft Flybys#
Research Summary
Chapter 47
Common-Rail Diesel Injectors Bond Graph Modelling Through the AMESim Platform#
Research Summary
Chapter 48
Mathematical Modelling of Filtration and Catalytic Oxidation of Diesel Particulates in Filter Porous Media#
Research Summary
Chapter 49
Water Demand Simplifications Used To Build Mathematical Models For Hydraulic Simulations#
Research Summary
Chapter 50
Dynamic Prediction of Failures: A Comparison of Methodologies for a Wind Turbine#
Research Summary
Chapter 51
Advances in Mathematical Modeling of Supercritical Extraction Processes#
Research Summary
Chapter 52
Pipe Database Analysis Transduction to Assess the Spatial Vulnerability to Biofilm Development in Drinking Water Distribution Systems#
Research Summary
Chapter 53
On Kernel Spectral Clustering for Identifying Areas of Biofilm Development in Water Distribution Systems#
Research Summary
Chapter 54
Unsupervised Methodology for Sectorization of Trunk Depending Water Supply Networks#
Research Summary
Chapter 55
Quantifying the Behavior of the Actors in the Spread of Android Malware Infection#
Research Summary
Chapter 56
A Stochastic Agent-Based Approach to Interregional Migration in Quantitative Sociodynamics#
Research Summary
Chapter 57
A Bayesian Mathematical Model to Analyse Religious Behavior in Spain#
Research Summary
Chapter 58
Model of Problems Cleaning in Education#
Research Summary
Chapter 59
Does VAT Growth Impact Compulsive Shopping in Spain?#
Research Summary
Chapter 60
Is Fitness Activity an Emergent Business? Economic Influences and Consequences of Male Fitness Practice#
Research Summary
Chapter 61
Popular Support to Terrorist Organizations: A Short-Term Prediction Based on a Dynamic Model Applied to a Real Case#
Research Summary
Chapter 62
Mathematical Modelling of the Consumption of High-Invasive Plastic Surgery: Economic Influences and Consequences#
Research Summary
Chapter 63
An Optimal Scheme for Solving the Nonlinear Global Positioning System Problem#
Research Summary
Chapter 64
How to Make a Comparison Matrix in AHP without All the Facts#
Research Summary
Chapter 65
On Optimal Gaussian Preliminary Orbit Determination by Using a Generalized Class of Iterative Methods#
Research Summary
Chapter 66
Solving Engineering Models which Use Matrix Hyperbolic Sine and Cosine Functions#
Research Summary
Chapter 67
RSV Modeling Using Genetic Algorithms in a Distributed Computing Environment Based on Cloud File Sharing#
Research Summary
Chapter 68
Multi-Agent and Clustering in Data Analysis of GPR Images#
Research Summary
Chapter 69
Semi-Automatic Segmentation of IVUS Images for the Diagnosis of Cardiac Allograft Vasculopathy#
Research Summary
Chapter 70
Analysis and Detection of V-Formations and Circular Formations in a Set of Moving Entities#
Research Summary
Chapter 71
Analysis of Noise for the Sparse Givens Method in CT Medical Image Reconstruction#
Research Summary
Chapter 72
Agent-Based Model to Determine the Evolution of the Seroprotection Against Meningococal C over the Next Years#
Research Summary
Chapter 73
Applying Clustering Based on Rules for Finding Patterns of Functional Dependency in Schizophrenia#
Research Summary
Chapter 74
Modeling Mathematical Flowgraph Models in Recurrent Events: An Application to Bladder Carcinoma#
Research Summary
Chapter 75
Numerical Solution of American Option Pricing Models Using Front-Fixing Method#
Research Summary
Chapter 76
Estimation of the Cost of Academic Underachievement in High School in Spain Over the Next Few Years#
Research Summary
Chapter 77
A Finite Difference Scheme for Options Pricing Modeled by Lévy Processes#
Research Summary
Chapter 78
Portfolio Composition to Replicate Stock Market Indexes. Application to the Spanish Index IBEX-35#
Research Summary
Chapter 79
Current Research Topics in Galois Geometry#
Research Summary
Chapter 80
Planning and Scheduling an Emergency Room Workforce Using Linear Programming*
Research Summary
Chapter 81
Neurodynamic Solvers, Robotic Applications and Solution Nonuniqueness of Linear Programming#
Research Summary
Chapter 82
Mathematical Equivalence of Simple Recourse and Chance Constraints in Linear Stochastic Programming#
Research Summary
Chapter 83
A Decomposable Linear Programming Model for Energy Supply Chains#
Research Summary
Chapter 84
High Order Boundary Value Problems: Existence, Localization and Multiplicity Results#
Research Summary
Chapter 85
Mapping Data Processing Neural Networks onto Distributed Computer Systems with Regular Structures#
Research Summary
Chapter 86
Mapping Parallel Program Graphs onto Graphs of Distributed Computer Systems by Neural Network Algorithms#
Research Summary
Chapter 87
Large-Scale and Fine-Grain Parallelism in Plasma Simulation#
Research Summary
Chapter 88
Numerical Modelling of Astrophysical Flow on Hybrid Architecture Supercomputers#
Research Summary
Chapter 89
Efficient Computational Approaches for Parallel Stochastic Simulation on Supercomputers#
Research Summary
Chapter 90
Lattice Gas Cellular Automata for a Flow Simulation and Their Parallel Implementation#
Research Summary
Chapter 91
Parallel Simulation of Asynchronous Cellular Automata#
Research Summary
Chapter 92
XPU: A C++ Metaprogramming Approach to Ease Parallelism Expression: Parallelization Methodology, Internal Design and Practical Application#
Research Summary
Chapter 93
An Approach to the Construction of Robust Systems of Interacting Processes#
Research Summary
Chapter 94
Early Learning in Parallel Programming#
Research Summary
Chapter 95
Sub-Independence: A Useful Concept#
Research Summary
Chapter 96
Minimization of Quadratic Forms and Generalized Inverses#
Research Summary
Chapter 97
The Study of the Invariants of Homogeneous Matrix Polynomials Using the Extended Hermite Equivalence ,?-??.#
Research Summary
Chapter 98
Cramer’s Rule For Generalized Inverse Solutions#
Research Summary
Chapter 99
Feedback Actions on Linear Systems Over Von Neumann Regular Rings#
Research Summary
Chapter 100
How To Characterize Properties of General Hermitian Quadratic Matrix-Valued Functions By Rank and Inertia#
Research Summary
Chapter 101
Introduction to the Theory of Triangular Matrices (Tables)#
Research Summary
Chapter 102
Recent Developments in Iterative Algorithms for Solving Linear Matrix Equations#
Research Summary
Chapter 103
Simultaneous Triangularization of a Pair of Matrices Over A Principal Ideal Domain With Quadratic Minimal Polynomials#
Research Summary
Chapter 104
Relation of Row-Column Determinants with Quasi-determinants of Matrices Over A Quaternion Algebra#
Research Summary
Chapter 105
First Order Chemical Kinetics Matrices and Stability of O.D.E. Systems#
Research Summary
Chapter 106
Stochastic Modelling and Simulations of Structured Investment Plans#
Research Summary
Chapter 107
Limitation of the Least Square Method in the Evaluation of Dimension of Fractal Brownian Motions#
Research Summary
Chapter 108
Parameter Estimation for Weighted Fractional Ornstein-Uhlenbeck Processes with Discrete Observations#
Research Summary
Chapter 109
Comparing Traditional Proofs of the Modulus of Continuity and the Law of the Iterated Logarithm to a New Method Which Yields Rates of Convergence#
Research Summary
Chapter 110
Transporting a Macroscopic Object by Brownian Motion - An Object as a Pollen Particle, Robots As Liquid Molecules -#
Research Summary
Chapter 111
Maximum Principle for Stochastic Discrete-Time Ito Equations#
Research Summary
Chapter 112
On The Controllability for Neutral Stochastic Functional Differential Equations Driven by a Fractional Brownian Motion in a Hilbert Space#
Research Summary
Chapter 113
Controllability of Impulsive Neutral Stochastic Functional Integro-Differential Equations Driven by Fractional Brownian Motion#
Research Summary
Chapter 114
Specific Features of Brownian Diffusion of Nanoparticles in Micro-Nanodroplets#
Research Summary
Chapter 115
Brownian Motion and the Formation of Dark Matter Haloes#
Research Summary
Chapter 116
Literature as a Diffusion Process#
Research Summary
Chapter 117
Almost Periodic Solution of Some Stochastic Difference Equations#
Research Summary
Chapter 118
Impulsive Stochastic Differential Equations Driven by G-Brownian Motion#
Research Summary
Chapter 119
Fractional Stochastic Differential Equations#
Research Summary
Chapter 120
Abstract Second-Order Damped Stochastic Evolution Equations in a Hilbert Space Driven by Fractional Brownian Motion#
Research Summary
Chapter 121
Abstract Convex Functionals Defined on ,ℝ-?. and Their Subdifferentiability#
Research Summary
Chapter 122
Convex-Along-Rays Functionals Defined on ,ℝ-?. and Their Subdifferentiability#
Research Summary
Chapter 123
Increasing Positively Homogeneous Functional Defined on ,ℝ-?. and Their Subdifferentiability#
Research Summary
Chapter 124
The Cutting Angle Method and a Local Search on Optimal Control Problems#
Research Summary
Chapter 125
The Cutting Angle Method for Solving of Variational Problems#
Research Summary
Chapter 126
The Cutting Angle Method on Optimal Control Problems#
Research Summary
Chapter 127
Preserver Problems over Finite Fields#
Research Summary
Chapter 128
Classical Coherent State Transforms over Finite Fields#
Research Summary
Chapter 129
The Structure of Finite mΘ Field Intrinsic Anatomy#
Research Summary
Chapter 130
mΘ Cyclic Codes on a mΘ Field#
Research Summary
Chapter 131
On Two Problems of Carlitz and Their Generalizations#
Research Summary
Chapter 132
Compactons in Carbon Nanotube Arrays#
Research Summary
Chapter 133
Elastic and Plastic Type Behaviours in the Fractal Theory of Motion at Nanoscale#
Research Summary
Chapter 134
Malignant Invasion Model with a Small Amount of Diffusion in the Framework of a Fractal Theory: Implications of Drug Release from the Polymeric Matrix Process#
Research Summary
Chapter 135
Non-Linearities in Drug Release Processes from Polymeric Microparticles: Implications in the Fractal Morpho-Functional Structure of Biological Systems#
Research Summary
Chapter 136
Chaos and Self-Structuring Behaviors in the Dynamics of Biological Structures: Implications of Drug Release from the Polymeric Matrix Process#
Research Summary
Chapter 137
Behaviors of Travelling Waves and Shapiro Steps Types in a Tumour-Growth Model#
Research Summary
Chapter 138
The Astonishing Evolutionary Dynamics of a Class of Nonlinear Discrete 2D Pattern Formation and Growth Models#
Research Summary
Chapter 139
Directed Partial Orders on Quaternions - A Brief Summary#
Research Summary
Chapter 140
Spin 1 Particle with Anomalous Magnetic Moment in the External Uniform Electric Field#
Research Summary
Chapter 141
Techniques of Projective Operators Used to Construct Solutions for a Spin 1 Particle with Anomalous Magnetic Moment in the External Uniform Magnetic Field#
Research Summary
Chapter 142
A Quaternion Approach in the Estimation of the Attitude of an Industrial Robot#
Research Summary
Chapter 143
2D Hermite-Gaussian and Gauss-Laguerre Circular Harmonic Eigenfunction of the Quaternion and Reduced Biquaternion Fourier Transform#
Research Summary
Chapter 144
The Quaternions with an Application of Quadrotors Team Formation#
Research Summary
Chapter 145
Determinantal Representations of the Drazin and W-Weighted Drazin Inverses over the Quaternion Skew Field with Applications#
Research Summary
Chapter 146
A Process Algebra Approach to Quantum Electrodynamics: Physics From the Top Up#
Research Summary
Chapter 147
Realizing Success for Complex Converging Systems#
Research Summary
Chapter 148
Development of the Generalized Nonlinear Schrödinger Equation of Rotating Cosmogonical Body Formation#
Research Summary
Chapter 149
The Application of Neural Network Modeling in Organizing a Hierarchical Teaching System Based on Mentorship#
Research Summary
Chapter 150
Modelling Organisation Networks Collaborating on Health and Environment within ASEAN#
Research Summary
Chapter 151
The Evolution Equation of Lie-Type for Finite Deformations and Its Time-Discrete Integration#
Research Summary
Chapter 152
New Applications of Symmetry Analysis to Nonlinear Evolution Equations#
Research Summary
Chapter 153
A Method for Exponentially Stabilizing a Class of 1-D PDEs#
Research Summary
Chapter 154
The Principal Component Analysis of Omics Data#
Research Summary
Chapter 155
A Factor Analysis of an Outcome Measurement Survey for Science, Technology and Society: A Course of General Education Based on PCA#
Research Summary
Chapter 156
The Application of Principal Component Analysis (PCA) to Performance Enhancement of Hyperspectral Radiative Transfer Computations#
Research Summary
Chapter 157
Random Approximations in Stochastic Programming: A Survey#
Research Summary
Chapter 158
Approximation and Estimation of the Approximation Error in Stochastic Programing Programs#
Research Summary
Chapter 159
Probabilistic Linear Programming Problem with Cauchy Distributed Random Variables#
Research Summary
Chapter 160
Stochastic Modeling of Imperfect Markets#
Research Summary
Chapter 161
Optimizing Derivatives through Stochastic Programming#
Research Summary
Chapter 162
A Guide for the Use of the Stochastic Programming References Reported in the Contributions of this Book#
Research Summary
Chapter 163
Synchronization of Chaotic Dynamic Systems via Nonlinear Observers#
Research Summary
Chapter 164
On Multi-Domain Spectral Relaxation Method for Chaotic Systems of Ordinary Differential Equations#
Research Summary
Chapter 165
Encrypted Real-World Image Communication Design Using Synchronized Discrete-Time Hyper Chaotic Maps#
Research Summary
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MATHEMATICAL RESEARCH SUMMARIES

MATHEMATICAL RESEARCH SUMMARIES VOLUME 2

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MATHEMATICAL RESEARCH SUMMARIES Additional books in this series can be found on Nova’s website under the Series tab.

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MATHEMATICAL RESEARCH SUMMARIES

MATHEMATICAL RESEARCH SUMMARIES VOLUME 2

MATTHEW A. ROWE EDITOR

Copyright © 2017 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. We have partnered with Copyright Clearance Center to make it easy for you to obtain permissions to reuse content from this publication. Simply navigate to this publication’s page on Nova’s website and locate the “Get Permission” button below the title description. This button is linked directly to the title’s permission page on copyright.com. Alternatively, you can visit copyright.com and search by title, ISBN, or ISSN. For further questions about using the service on copyright.com, please contact: Copyright Clearance Center Phone: +1-(978) 750-8400 Fax: +1-(978) 750-4470 E-mail: [email protected]. NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Additional color graphics may be available in the e-book version of this book.

Library of Congress Cataloging-in-Publication Data ISBN: H%RRN

Published by Nova Science Publishers, Inc. † New York

CONTENTS Preface

xix

Chapter 1

Continuous-GRASP Revisited Benjamin Martin, Xavier Gandibleux and Laurent Granvilliers

1

Chapter 2

The Noising Methods Irène Charon and Olivier Hudry

3

Chapter 3

Matheuristics: Embedding MILP Solvers into Heuristic Algorithms for Combinatorial Optimization Problems Federico Della Croce, Andrea Grosso and Fabio Salassa

Chapter 4

Chapter 5

Chapter 6

Chapter 7

An Empirical Investigation of Different Solution Strategies for Meta-Heuristic Optimization: Solution Representation, Diversity and Space Reduction Mario Vanhoucke and Broos Maenhout Non-deterministic Decoding with Mapping Rearrangement to Enhance Precision in Binary Encodings Orhan Dengiz, Alice E. Smith and Gerry Dozier

5

7

9

Towards a More Efficient Multi-Objective Particle Swarm Optimizer Free of Parameters Nadia Smairi, Patrick Siarry and Khaled Ghedira

11

A Multi-Objective Genetic Algorithm to Search for Pareto Solutions of Series-Parallel System Component Allocation Problems Yasushi Kambayashi, Yasuhiro Tsujimura, Hidemi Yamachi and Hisashi Yamamoto

13

Chapter 8

A Survey of Genetic Algorithms for Shop Scheduling Problems Frank Werner

Chapter 9

A Scheduling Approach for the Design of Flexible Manufacturing Systems L. Deroussi and M. Gourgand

15

17

vi Chapter 10

Chapter 11

Chapter 12

Contents Electric Distribution Network Operation Planning Using Chu and Beasley Genetic Algorithm and Particle Swarm Optimization Ricardo A. de Araújo, Santiago P. Torres, Madson C. de Almeida and Carlos A. Castro A Distributed Approach for Designing Efficient Search Algorithms: An Application to Solve the Location-Routing Problem Jose Eduardo Pecora Jr., Angel Ruiz and Patrick Soriano The Multi-Depot Vehicle Routing Problem: An Integer Programming-Based Heuristic and Computational Results Damon Gulczynski, Bruce Golden, Martin Savelsbergh and Edward Wasil

19

21

23

Chapter 13

Optimization for Feature Selection in DNA Microarrays Vincent Gardeux, René Natowicz, Maria Fernanda Barbosa Wanderley and Rachid Chelouah

Chapter 14

Ant Colony System: Application for the Single and Multi-objective Multidimensional Knapsack Problems Prakash Shelokar

27

Synergistic Combination of Evolutionary Algorithms and Fuzzy Systems: Application to Control Design Nazmul H. Siddique

29

Analysis of Structures by Total Potential Optimization Using MetaHeuristic Algorithms (TPO/MA) Y. C. Toklu and N. E. Toklu

31

Chapter 15

Chapter 16

Chapter 17

A Review of Computational Intelligence Algorithms in Insurance Applications S. Salcedo-Sanz, L. Cuadra, A. Portilla-Figueras, S. Jiménez-Fernández and E. Alexandre

25

33

Chapter 18

Rough Sets in Insurance Sector M.J. Segovia-Vargas and Z. Díaz-Martínez

Chapter 19

Prediction of Claims and Selection of Risk Factors in Automobile Insurance Using Support Vector Machines, Genetic Algorithms and Classification Trees A. Heras-Martínez, C. Bousoño-Calzón and P. Tolmos Rodríguez-Piñero

37

Tail Value at Risk. An Analysis with the Normal-Power Approximation A. Castañer, M.M. Claramunt and M. Mármol

39

Chapter 20

Chapter 21

Financial Applications of Modal Interval Analysis R. Adillon and L. Jorba

35

41

Chapter 22

Chapter 23

Chapter 24

Chapter 25

Chapter 26

Chapter 27

Chapter 28

Chapter 29

Chapter 30

Chapter 31

Chapter 32

Chapter 33

Contents

vii

A Method for Analysis of Transmission Lines Terminated by Nonlinear Loads Vasil G. Angelov

43

Markus-Sell’s Theorem for Asymptotically Almost Periodic Systems David Cheban and Cristiana Mammana

45

A Survey of the Method of Lyapunov Functions of Two Variables in the Study of Stability and Persistence of Dynamical Systems Jorge Lewowicz, Jorge Groisman and Juan Tolosa

47

Krylov and Schur Subspaces in Construction of Prediction Error Filter: Computational Complexity and Performance Comparison Hong Son Hoang and Rémy Baraille

49

High-Fidelity Modeling and Vibration-Based System Identification and Damage Inspection of Flexible Structures P. Frank Pai

51

Complexity and Chaos Theory in Social Sciences: Scientific Philosophy or Quantitative Science? Rosalia Condorelli

53

Local Stability Analysis of an Age-Structured Hepatitis B Transmission Model Ousmane M. Tessa, Bisso Saley, Herieth Rwezaura and Jean M. Tchuenche

55

Parametric Resonance and Homoclinic Chaos in a Bullard-Type Dynamo O. Foupouapouognigni, M. Siewe Siewe and C. Tchawoua

57

Birhythmicity, Synchronization and Chaos in an Enzyme-Substrate Reaction with a Ferroelectric Behavior H. G. Enjieu Kadji and P. Woafo

59

Dynamics of Low and High Pathogenic Avian Influenza in Wild Bird Population Necibe Tuncer, Juan Torres and Maia Martcheva

61

Analysis of a Predator-Prey Model with Sigmoidal Response Function and SIS Disease J. J. Tewa, P. Tchinda Mouofo, V. Kamla and S. Bowong

63

Modelling the Effects of Multi-Intervention Campaigns for the Malaria Epidemic in Malawi P. M. Mwamtobe, J. M. Tchuenche, M. Maliyoni and S. D. Hove-Musekwa

65

viii Chapter 34

Chapter 35

Contents Modelling the Dynamics of HIV-TB Co-Infection in a Variable Size Population Agraj Tripathi, Ram Naresh, and Dileep Sharma

67

Case Detection on Tuberculosis Dynamics with Isolation in a Sanatorium Nyimvua Shaban

69

Chapter 36

Advances in Discrete Dynamics Jose S. Cánovas

Chapter 37

Simulated Annealing: In Mathematical Global Optimization Computation, Hybrid with Local or Global Search, and Practical Applications in Crystallography and Molecular Modelling of Prion Amyloid Fibrils Jiapu Zhang

Chapter 38

Chapter 39

Chapter 40

Chapter 41

Handling Equality and Inequality Linear Constraints in Simulated Annealing Danilo R. Velis Aircraft Design with Simulated Annealing for SAE Aerodesign Competition Diego Movio Borburema, Marcos de Sales Guerra Tsuzuki, Antonio Luis de Campos Mariani, Andre Kubagawa Sato and Thiago de Castro Martins

71

73

75

77

Simulated Annealing Applied to the Resolution of Phylogenetic Reconstruction with Maximum Parsimony Jean-Michel Richer, Karla E. Vazquez-Ortiz and David Lesaint

79

Improved Parallel Simulated Annealing Applied to Spacecraft Trajectory Optimization Ya-Zhong Luo and Guo-Jin Tang

81

Chapter 42

Simulated Annealing Applications in Thermodynamic Calculations Ahmed O. Elnabawy, Seif-Eddeen K. Fateen and Adrian Bonilla-Petriciolet

Chapter 43

SA Optimization of Two-Chamber Mufflers Equipped with Multiple Parallel Perforated Tubes within a Constrained Space Min-Chie Chiu

85

A Simulated Annealing Algorithm to Solve the Log-Truck Scheduling Problem Mauricio Acuna and John Sessions

87

Potential Applications of Simulated Annealing to Multi-Species Fish Habitat Conservation in the Gulf of Maine Rosamonde R. Cook and Peter J. Auster

89

Chapter 44

Chapter 45

83

Contents Chapter 46

Chapter 47

Chapter 48

Chapter 49

Chapter 50

Chapter 51

Chapter 52

Chapter 53

Chapter 54

Chapter 55

Chapter 56

ix

Second-Order Perturbations in Encke’s Method for Spacecraft Flybys L. Acedo

91

Common-Rail Diesel Injectors Bond Graph Modelling Through the AMESim Platform F. J. Salvador, M. Carreres, J. V. Romero and M. D. Roselló

93

Mathematical Modelling of Filtration and Catalytic Oxidation of Diesel Particulates in Filter Porous Media N. V. Vernikovskaya, T. L. Pavlova, N. A. Chumakova and A. S. Noskov Water Demand Simplifications Used To Build Mathematical Models For Hydraulic Simulations J. Izquierdo, E. Campbell, I. Montalvo, R. Pérez-García and D. Ayala-Cabrera

95

97

Dynamic Prediction of Failures: A Comparison of Methodologies for a Wind Turbine S. Carlos, A. Sanchez, I. Marton and S. Martorell

99

Advances in Mathematical Modeling of Supercritical Extraction Processes Florian Meyer, Marko Stamenic, Irena Zizovic and Rudolf Eggers

101

Pipe Database Analysis Transduction to Assess the Spatial Vulnerability to Biofilm Development in Drinking Water Distribution Systems E. Ramos-Martínez, J. A. Gutíerrez-Pérez, M. Herrera, J. Izquierdo and R. Pérez-García

103

On Kernel Spectral Clustering for Identifying Areas of Biofilm Development in Water Distribution Systems M. Herrera, E. Ramos-Martínez, J. A. Gutíerrez-Pérez, J. Izquierdo and R. Pérez-García

105

Unsupervised Methodology for Sectorization of Trunk Depending Water Supply Networks E. Campbell, R. Pérez-García, J. Izquierdo and D. Ayala-Cabrera

107

Quantifying the Behavior of the Actors in the Spread of Android Malware Infection J. Alegre, J. C. Cortés, F. J. Santonja and R. J. Villanueva

109

A Stochastic Agent-Based Approach to Interregional Migration in Quantitative Sociodynamics Minoru Tabata, Nobuoki Eshima, Keiko Kanenoo and Ichiro Takagi

111

x Chapter 57

Contents A Bayesian Mathematical Model to Analyse Religious Behavior in Spain R. Cervelló-Royo, A. Sánchez-Sánchez, F. Guerrero, F. J. Santonja and R. J. Villanueva

113

Chapter 58

Model of Problems Cleaning in Education Jan M. Myszewski, Malgorzata Gromek and Joanna Oczkowicz

115

Chapter 59

Does VAT Growth Impact Compulsive Shopping in Spain? E. de la Poza, I. García, L. Jódar and P. Merello

117

Chapter 60

Is Fitness Activity an Emergent Business? Economic Influences and Consequences of Male Fitness Practice M. S. S. Alkasadi, E. De la Poza and L. Jódar

Chapter 61

Chapter 62

Chapter 63

Popular Support to Terrorist Organizations: A Short-Term Prediction Based on a Dynamic Model Applied to a Real Case Matthias Ehrhardt, Miguel Peco, Ana C. Tarazona, Rafael J. Villanueva and Javier Villanueva-Oller

119

121

Mathematical Modelling of the Consumption of High-Invasive Plastic Surgery: Economic Influences and Consequences M. S. S. Alkasadi, E. De la Poza and L. Jódar

123

An Optimal Scheme for Solving the Nonlinear Global Positioning System Problem Manuel Abad, Alicia Cordero and Juan R. Torregrosa

125

Chapter 64

How to Make a Comparison Matrix in AHP without All the Facts J. Benítez, L. Carrión, J. Izquierdo and R. Pérez-García

Chapter 65

On Optimal Gaussian Preliminary Orbit Determination by Using a Generalized Class of Iterative Methods Alicia Cordero, Juan R. Torregrosa and María P. Vassileva

129

Solving Engineering Models which Use Matrix Hyperbolic Sine and Cosine Functions Emilio Defez, Jorge Sastre, Javier J. Ibáñez and Jesús Peinado

131

Chapter 66

Chapter 67

RSV Modeling Using Genetic Algorithms in a Distributed Computing Environment Based on Cloud File Sharing J. Gabriel García Caro, Javier Villanueva-Oller and J. Ignacio Hidalgo

Chapter 68

Multi-Agent and Clustering in Data Analysis of GPR Images D. Ayala-Cabrera, E. P. Carreño-Alvarado, S. J. Ocaña-Levario, J. Izquierdo and R. Pérez-García

Chapter 69

Semi-Automatic Segmentation of IVUS Images for the Diagnosis of Cardiac Allograft Vasculopathy Damián Ginestar, José L. Hueso, Jaime Riera and Ignacio Sánchez Lázaro

127

133

135

137

Contents Chapter 70

Chapter 71

Chapter 72

Chapter 73

Chapter 74

Chapter 75

Chapter 76

Chapter 77

Chapter 78

Analysis and Detection of V-Formations and Circular Formations in a Set of Moving Entities Francisco Javier Moreno Arboleda, Jaime Alberto Guzmán Luna and Sebastián Alonso Gómez Arias Analysis of Noise for the Sparse Givens Method in CT Medical Image Reconstruction A. Iborra, M. J. Rodríguez-Álvarez, A. Soriano, F. Sánchez, M. D. Roselló, P. Bellido, P. Conde, E. Crespo, A. J. González, L. Hernández, F. Martos, L. Moliner, J. P. Rigla, M. Seimetz, L. F. Vidal and J. M. Benlloch Agent-Based Model to Determine the Evolution of the Seroprotection Against Meningococal C over the Next Years L. Pérez-Breva, R. J. Villanueva, J. Villanueva-Oller, L. Acedo, F. J. Santonja, J. A. Moraño, R. Abad, J. A. Vázquez and J. Díez-Domingo

xi

139

141

143

Applying Clustering Based on Rules for Finding Patterns of Functional Dependency in Schizophrenia Karina Gibert and Luis Salvador Carulla

145

Modeling Mathematical Flowgraph Models in Recurrent Events: An Application to Bladder Carcinoma B. García-Mora, C. Santamaría, G. Rubio and J. Camacho

147

Numerical Solution of American Option Pricing Models Using Front-Fixing Method V. Egorova, R. Company and L. Jódar

149

Estimation of the Cost of Academic Underachievement in High School in Spain Over the Next Few Years J. Camacho, R. Cervelló-Royo, J. M. Colmenar and A. Sánchez-Sánchez

151

A Finite Difference Scheme for Options Pricing Modeled by Lévy Processes R. Company, M. Fakharany and L. Jódar

153

Portfolio Composition to Replicate Stock Market Indexes. Application to the Spanish Index IBEX-35 J. C. Cortés, A. Debón and C. Moreno

155

Chapter 79

Current Research Topics in Galois Geometry Leo Storme and Jan De Beule

Chapter 80

Planning and Scheduling an Emergency Room Workforce Using Linear Programming Ciro Alberto Amaya, Nubia Velasco and Silebis Aguirre

157

159

xii Chapter 81

Chapter 82

Chapter 83

Chapter 84

Chapter 85

Chapter 86

Contents Neurodynamic Solvers, Robotic Applications and Solution Nonuniqueness of Linear Programming Yunong Zhang, Ying Wang, Dechao Chen, Chen Peng and Qing Xie

161

Mathematical Equivalence of Simple Recourse and Chance Constraints in Linear Stochastic Programming Masatoshi Sakawa, Hitoshi Yano and Ichiro Nishizaki

163

A Decomposable Linear Programming Model for Energy Supply Chains Tsan Sheng Ng, Buse Aras, Charlle Lee Sy and Wu Biao

165

High Order Boundary Value Problems: Existence, Localization and Multiplicity Results João Fialho and Feliz Minhós

167

Mapping Data Processing Neural Networks onto Distributed Computer Systems with Regular Structures Mikhail S. Tarkov

169

Mapping Parallel Program Graphs onto Graphs of Distributed Computer Systems by Neural Network Algorithms Mikhail S. Tarkov

171

Chapter 87

Large-Scale and Fine-Grain Parallelism in Plasma Simulation A. Snytnikov

Chapter 88

Numerical Modelling of Astrophysical Flow on Hybrid Architecture Supercomputers I. Kulikov, I. Chernykh, A. Snytnikov, V. Protasov, A. Tutukov and B. Glinsky

Chapter 89

Chapter 90

175

Efficient Computational Approaches for Parallel Stochastic Simulation on Supercomputers Mikhail A. Marchenko

177

Lattice Gas Cellular Automata for a Flow Simulation and Their Parallel Implementation Yury G. Medvedev

179

Chapter 91

Parallel Simulation of Asynchronous Cellular Automata Konstantin Kalgin

Chapter 92

XPU: A C++ Metaprogramming Approach to Ease Parallelism Expression: Parallelization Methodology, Internal Design and Practical Application Nader Khammassi and Jean-Christophe Le Lann

Chapter 93

173

An Approach to the Construction of Robust Systems of Interacting Processes Igor N. Skopin

181

183

185

Contents

xiii

Chapter 94

Early Learning in Parallel Programming Igor N. Skopin

187

Chapter 95

Sub-Independence: A Useful Concept G. G. Hamedani and Mehdi Maadooliat

189

Chapter 96

Minimization of Quadratic Forms and Generalized Inverses Predrag S. Stanimirović, Dimitrios Pappas and Vasilios N. Katsikis

191

Chapter 97

The Study of the Invariants of Homogeneous Matrix Polynomials Using the Extended Hermite Equivalence εrh Grigoris I. Kalogeropoulos, Athanasios D. Karageorgos and Athanasios A. Pantelous

193

Chapter 98

Cramer’s Rule For Generalized Inverse Solutions Ivan I. Kyrchei

Chapter 99

Feedback Actions on Linear Systems Over Von Neumann Regular Rings Andrés Sáez-Schwedt

197

How To Characterize Properties of General Hermitian Quadratic Matrix-Valued Functions By Rank and Inertia Yongge Tian

199

Chapter 100

195

Chapter 101

Introduction to the Theory of Triangular Matrices (Tables) Roman Zatorsky

Chapter 102

Recent Developments in Iterative Algorithms for Solving Linear Matrix Equations Masoud Hajarian

203

Simultaneous Triangularization of a Pair of Matrices Over A Principal Ideal Domain With Quadratic Minimal Polynomials Volodymyr M. Prokip

205

Relation of Row-Column Determinants with Quasi-determinants of Matrices Over A Quaternion Algebra Aleks Kleyn and Ivan I. Kyrchei

207

First Order Chemical Kinetics Matrices and Stability of O.D.E. Systems Victor Martinez-Luaces

209

Stochastic Modelling and Simulations of Structured Investment Plans Ling Feng, Yile Li, Xuerong Mao and Zhigang Huang

211

Limitation of the Least Square Method in the Evaluation of Dimension of Fractal Brownian Motions Siming Liu and Bingqiang Qiao

213

Chapter 103

Chapter 104

Chapter 105

Chapter 106

Chapter 107

201

xiv Chapter 108

Chapter 109

Chapter 110

Contents Parameter Estimation for Weighted Fractional Ornstein-Uhlenbeck Processes with Discrete Observations Xiuwei Yin, Guangjun Shen and Longjuan Deng Comparing Traditional Proofs of the Modulus of Continuity and the Law of the Iterated Logarithm to a New Method Which Yields Rates of Convergence Lisa Marano Transporting a Macroscopic Object by Brownian Motion - An Object as a Pollen Particle, Robots As Liquid Molecules Teturo Itami

Chapter 111

Maximum Principle for Stochastic Discrete-Time Ito Equations N. I. Mahmudov

Chapter 112

On The Controllability for Neutral Stochastic Functional Differential Equations Driven by a Fractional Brownian Motion in a Hilbert Space El Hassan Lakhel

Chapter 113

Chapter 114

215

217

219 221

223

Controllability of Impulsive Neutral Stochastic Functional IntegroDifferential Equations Driven by Fractional Brownian Motion El Hassan Lakhel and Mark A. McKibben

225

Specific Features of Brownian Diffusion of Nanoparticles in Micro-Nanodroplets Sergey P. Fisenko and Yuliya A. Khodyko

227

Chapter 115

Brownian Motion and the Formation of Dark Matter Haloes N. Hiotelis

229

Chapter 116

Literature as a Diffusion Process Agamirza E. Bashirov and Gunash Bashirova

231

Chapter 117

Almost Periodic Solution of Some Stochastic Difference Equations Mamadou Moustapha Mbaye

233

Chapter 118

Impulsive Stochastic Differential Equations Driven by G-Brownian Motion Lanying Hu and Yong Ren

235

Chapter 119

Fractional Stochastic Differential Equations P. Balasubramaniam and P. Tamilalagan

Chapter 120

Abstract Second-Order Damped Stochastic Evolution Equations in a Hilbert Space Driven by Fractional Brownian Motion Mark A. McKibben and Micah Webster

239

Abstract Convex Functionals Defined on Rn and Their Subdifferentiability Seyedalireza Seyedi, Iraj Sadegh Amiri and Sara Chaghervand

241

Chapter 121

237

Contents Chapter 122

Chapter 123

Chapter 124

xv

Convex-Along-Rays Functionals Defined on Rn and Their Subdifferentiability Seyedalireza Seyedi, Iraj Sadegh Amiri and Sara Chaghervand

243

Increasing Positively Homogeneous Functional Defined on Rn and Their Subdifferentiability Seyedalireza Seyedi, Iraj Sadegh Amiri and Sara Chaghervand

245

The Cutting Angle Method and a Local Search on Optimal Control Problems Seyedalireza Seyedi, Iraj Sadegh Amiri, Sara Chaghervand, Rohanin Ahmad and Mohd Ismail abd Aziz

247

Chapter 125

The Cutting Angle Method for Solving of Variational Problems Seyedalireza Seyedi, Iraj Sadegh Amiri, Sara Chaghervand, Rohanin Ahmad and Mohd Ismail abd Aziz

249

Chapter 126

The Cutting Angle Method on Optimal Control Problems Seyedalireza Seyedi, Iraj Sadegh Amiri, Sara Chaghervand, Rohanin Ahmad and Mohd Ismail abd Aziz

251

Chapter 127

Preserver Problems over Finite Fields Marko Orel

253

Chapter 128

Classical Coherent State Transforms over Finite Fields Arash Ghaani Farashahi

255

Chapter 129

The Structure of Finite mΘ Field Intrinsic Anatomy Ayissi Etémé

257

Chapter 130

mΘ Cyclic Codes on a mΘ Field Fidèle Ayissi Etémé and Jean Armand Tsimi

259

Chapter 131

On Two Problems of Carlitz and Their Generalizations Ioulia N. Baoulina

261

Chapter 132

Compactons in Carbon Nanotube Arrays Raïssa S. Noule and Victor K. Kuetche

263

Chapter 133

Elastic and Plastic Type Behaviours in the Fractal Theory of Motion at Nanoscale Maricel Agop, Alina Gavriluţ, Gabriel Gavriluţ, Irina Butuc and Dan Dezideriu Iacob

Chapter 134

Malignant Invasion Model with a Small Amount of Diffusion in the Framework of a Fractal Theory: Implications of Drug Release from the Polymeric Matrix Process Decebal Vasincu, Daniel Timofte, Lăcrămioara Ochiuz, Maricel Agop and Alina Gavriluţ

265

267

xvi Chapter 135

Chapter 136

Chapter 137

Chapter 138

Contents Non-Linearities in Drug Release Processes from Polymeric Microparticles: Implications in the Fractal Morpho-Functional Structure of Biological Systems Lăcrămioara Ochiuz, Daniel Timofte, Decebal Vasincu, Alina Gavriluţ, Gabriel Gavriluţ and Maricel Agop

269

Chaos and Self-Structuring Behaviors in the Dynamics of Biological Structures: Implications of Drug Release from the Polymeric Matrix Process Daniel Timofte, Lăcrămioara Ochiuz, Decebal Vasincu, Gabriel Crumpei, Alina Gavriluţ and Maricel Agop

271

Behaviors of Travelling Waves and Shapiro Steps Types in a Tumour-Growth Model Cipriana Ştefănescu, Daniel Timofte, Decebal Vasincu, Dan Tesloianu, Maricel Agop and Alina Gavriluţ The Astonishing Evolutionary Dynamics of a Class of Nonlinear Discrete 2D Pattern Formation and Growth Models Leonid Yaroslavsky

Chapter 139

Directed Partial Orders on Quaternions - A Brief Summary Jingjing Ma

Chapter 140

Spin 1 Particle with Anomalous Magnetic Moment in the External Uniform Electric Field E. M. Ovsiyuk, Ya. A. Voynova, V. V. Kisel, V. Balan and V. M. Red’kov

Chapter 141

Chapter 142

Chapter 143

Chapter 144

Techniques of Projective Operators Used to Construct Solutions for a Spin 1 Particle with Anomalous Magnetic Moment in the External Uniform Magnetic Field V. V. Kisel, Ya. A. Voynova, E. M. Ovsiyuk, V. Balan and V. M. Red'kov A Quaternion Approach in the Estimation of the Attitude of an Industrial Robot Bernardino Benito Salmerón-Quiroz, Gerardo Villegas-Medina, José Fermi Guerrero-Castellanos, Elena O. Milhacea and Rodolfo Villalobos-Martinez 2D Hermite-Gaussian and Gauss-Laguerre Circular Harmonic Eigenfunction of the Quaternion and Reduced Biquaternion Fourier Transform Soo-Chang Pei and Yu-Zhe Hsiao The Quaternions with an Application of Quadrotors Team Formation Wesam Jasim and Dongbing Gu

273

275 277

279

281

283

285

287

Contents Chapter 145

Chapter 146

xvii

Determinantal Representations of the Drazin and W-Weighted Drazin Inverses over the Quaternion Skew Field with Applications Ivan Kyrchei

289

A Process Algebra Approach to Quantum Electrodynamics: Physics From the Top Up William Sulis

291

Chapter 147

Realizing Success for Complex Converging Systems Geerten Van de Kaa

Chapter 148

Development of the Generalized Nonlinear Schrödinger Equation of Rotating Cosmogonical Body Formation Alexander M. Krot

295

The Application of Neural Network Modeling in Organizing a Hierarchical Teaching System Based on Mentorship A. Dashkina and D. Tarkhov

297

Modelling Organisation Networks Collaborating on Health and Environment within ASEAN P. Mazzega and C. Lajaunie

299

The Evolution Equation of Lie-Type for Finite Deformations and Its Time-Discrete Integration Zdeněk Fiala

301

New Applications of Symmetry Analysis to Nonlinear Evolution Equations Renat Zhdanov and Qing Huang

303

Chapter 149

Chapter 150

Chapter 151

Chapter 152

293

Chapter 153

A Method for Exponentially Stabilizing a Class of 1-D PDEs Abdelhadi Elharf and Ahmed Sani

305

Chapter 154

The Principal Component Analysis of Omics Data Hiroyuki Yamamoto

307

Chapter 155

A Factor Analysis of an Outcome Measurement Survey for Science, Technology and Society: A Course of General Education Based on PCA Tzu-Yi Pai, Yi-Ti Tung, Ming-Ray Lin, Su-Hwa Lin, Lung-Yi Chan and Chia-Fu Lin

Chapter 156

Chapter 157

The Application of Principal Component Analysis (PCA) to Performance Enhancement of Hyperspectral Radiative Transfer Computations Robert Spurr, Vijay Natraj, Pushkar Kopparla and Matt Christi Random Approximations in Stochastic Programming: A Survey Silvia Vogel

309

311 313

xviii Chapter 158

Chapter 159

Contents Approximation and Estimation of the Approximation Error in Stochastic Programing Programs Carlos N. Bouza–Herrera, Sira M. Allende Alonso and Rajesh Singh Probabilistic Linear Programming Problem with Cauchy Distributed Random Variables Manas Kumar Pal

315

317

Chapter 160

Stochastic Modeling of Imperfect Markets Tobias Baltensperger and Ruud Egging

319

Chapter 161

Optimizing Derivatives through Stochastic Programming Carlos N. Bouza-Herrera and Sira M. Allende Alonso

321

Chapter 162

A Guide for the Use of the Stochastic Programming References Reported in the Contributions of this Book Carlos N. Bouza-Herrera and José M. Sautto-Vallejo

Chapter 163

Chapter 164

Chapter 165

Synchronization of Chaotic Dynamic Systems via Nonlinear Observers Ricardo Aguilar-López, Ricardo Femat, Santo Banerjee and Juan Luis Mata-Machuca

323

325

On Multi-Domain Spectral Relaxation Method for Chaotic Systems of Ordinary Differential Equations Sandile S. Motsa, Vusi M. Magagula and Precious Sibanda

327

Encrypted Real-World Image Communication Design Using Synchronized Discrete-Time Hyper Chaotic Maps Sonia Hammami

329

PREFACE This new book compiles research summaries of top professionals in the field of mathematics from a number of different focuses in this important field.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 1

CONTINUOUS-GRASP REVISITED# Benjamin Martin, Xavier Gandibleux and Laurent Granvilliers * Université de Nantes-LINA UMR CNRS 6241 UFR Sciences-Cedex, France

RESEARCH SUMMARY C-GRASP is a metaheuristic introduced in 2006 by Hirsch et al. for continuous global optimization. It is a multi-start neighborhood-based metaheuristic derived from the greedy randomized adaptive search procedure proposed by Féo and Resende in 1989. The main difference with most other metaheuristics designed for continuous optimization is the use of a construction procedure. This chapter presents novel mechanisms and components to reinforce the efficiency of the original C-GRASP. The proposals concern (1) the construction procedure, (2) the improvement procedure, and (3) additional new mechanisms. Among the noticeable changes, the improvement procedure is now based on direct searches. The revisions perfect the metaheuristic in reducing its computational effort and facilitating the parameters management. Numerical experiments are performed using benchmark problem functions commonly used in unconstrained continuous global optimization. The collected results are compared with the best results known in the literature for competitive metaheuristics. The good performances of the proposed version confirm the advantage of coupling C-GRASP with direct searches and validate the extensions introduced.

#

This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 2

THE NOISING METHODS# Irène Charon and Olivier Hudry Telecom ParisTech, Paris Cedex, France

RESEARCH SUMMARY This chapter provides a review of the principles and of applications of the noising methods. We detail the features and the variants of the noising methods and we summarize the tunings of their parameters when these methods are applied to different combinatorial optimization problems. We also study the links between the noising methods and other metaheuristics (namely, the simulated annealing method, the threshold accepting algorithm or the descents with mutations).

#

This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013.  Corresponding author. E-mail: [email protected]. The material of this chapter is adapted from Charon, I., and Hudry, O., “The noising methods: a generalization of some metaheuristics”, European Journal of Operational Research 135 (1), 2001, 86-101.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 3

MATHEURISTICS: EMBEDDING MILP SOLVERS INTO HEURISTIC ALGORITHMS FOR COMBINATORIAL OPTIMIZATION PROBLEMS# Federico Della Croce1*, Andrea Grosso2† and Fabio Salassa1‡ 1

2

D. A. I. Politecnico di Torino, Italy D. I. Universitàdegli Studi di Torino,Italy

RESEARCH SUMMARY Combinatorial Optimization Problems (COPs) have always been studied because of their relevant practical importance. Solution techniques for solving COPs have traditionally been split into exact (mostly based on the optimal solution of the integer programming formulation of the real problem) and heuristic algorithms. Recently the hybridization of these two approaches has become very popular. So called Matheuristics, which rely on the idea of exploiting the better of the two, have raised much attention. In this chapter, the authors discuss a general matheuristic framework embedding general MILP solvers into heuristic approaches to solve COPs. Different applications are presented related to different kind of problems. For all applications, the use of MILP solvers within the heuristic framework is described.

#

This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013. * e-mail address: [email protected] † e-mail address: [email protected] ‡ e-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 4

AN EMPIRICAL INVESTIGATION OF DIFFERENT SOLUTION STRATEGIES FOR META-HEURISTIC OPTIMIZATION: SOLUTION REPRESENTATION, DIVERSITY AND SPACE REDUCTION #

Mario Vanhoucke* and Broos Maenhout Ghent University, Gent, Belgium Vlerick Leuven Gent Management School, Gent, Belgium University College of London, London (UK)

RESEARCH SUMMARY In this chapter the authors study the characteristics of population based meta-heuristics that distinguish the procedures from a standard meta-heuristic and that positively contribute to the quality of the solutions obtained. More precisely, the authors investigate and discuss the importance of a well-considered solution representation, the beneficial effect of diversity in the solution population and the possible improving effect of solution space reduction techniques on the overall quality of the solution. Empirical results are obtained by a computational experiment of different meta-heuristics on resource-constrained project scheduling and personnel scheduling problems.

#

This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 5

NON-DETERMINISTIC DECODING WITH MAPPING REARRANGEMENT TO ENHANCE PRECISION IN BINARY ENCODINGS #

Orhan Dengiz1, Alice E. Smith2, and Gerry Dozier3 1

DnD Technological Solutions, Ankara, Turkey Department of Industrial and Systems Engineering, Auburn University, Auburn, Alabama, US 3 Department of Computer Science, North Carolina A&T University, Greensboro, North Carolina, US 2

RESEARCH SUMMARY This chapter presents a non-deterministic decoding algorithm for binary encodings used with iterative metaheuristics that use discrete type of encodings such as genetic algorithms or evolutionary strategies. The proposed algorithm enables binary encodings to represent a continuum in the search space instead of a set of discrete points as is the case when conventional deterministic decoding is used. Non-deterministic decoding is done by adding a controlled Gaussian (Normally distributed) perturbation to the conventional decoding function. Thereby, the encodings are mapped to a continuous region on the search space, following a Gaussian probability density. As the search evolves, information gathered from superior members is continuously used to rearrange the decoding function such that the global optimum can be precisely located with a specified resolution. This is referred to as the mapping rearrangement property. In contrast to previous approaches to solve the binary encoding precision problem, the proposed method does not prune the search space. Results show that the proposed method performs better than previously developed approaches that

#

This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013.  Corresponding author. E-mail: [email protected].

10

Orhan Dengiz, Alice E. Smith and Gerry Dozier

address the precision limitation of binary encodings. The new method is not sensitive to its single parameter, and provides better results at improved CPU times.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 6

TOWARDS A MORE EFFICIENT MULTI-OBJECTIVE PARTICLE SWARM OPTIMIZER FREE OF PARAMETERS #

Nadia Smairi1, Patrick Siarry2 and Khaled Ghedira1, 1

2

SOIE Laboratory, University of Tunis, Tunis, Tunisia LISSI Laboratory, University of Paris-Est Val de Marne, Créteil, France

RESEARCH SUMMARY Tuning the parameters of any evolutionary algorithm is a very difficult task. In this chapter, we present a new adaptive multi-objective technique which consists of an adaptation of an adaptive particle swarm optimization approach (Tribes) to the multi-objective case. This multi-objective particle swarm optimizer (MOPSO) is characterized for using different schemes of hybridization. The main idea behind this hybridization is to combine the high convergence rate of Tribes with local search (LS) techniques such as tabu search (TS) and simulated annealing (SA). In fact, we propose three different places where we are going to apply the local search: applying LS on the non-dominated particles, applying LS only on the best particle among each tribe, and applying LS on each particle of the swarm. Besides, we study the impact of the place where we apply local search on the performance of the obtained algorithms. The proposed approaches are validated using standard test functions and performance measures reported in the specialized literature.

#

This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013.  E-mail: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 7

A MULTI-OBJECTIVE GENETIC ALGORITHM TO SEARCH FOR PARETO SOLUTIONS OF SERIES-PARALLEL SYSTEM COMPONENT ALLOCATION PROBLEMS #

Yasushi Kambayashi1,, Yasuhiro Tsujimura1, Hidemi Yamachi1 and Hisashi Yamamoto2 1

Department of Computer and Information Engineering, Nippon Institute of Technology, Miyashiro-machi, Saitama, Japan 2 Faculty of System Design, Tokyo Metropolitan University, Hino, Tokyo, Japan

RESEARCH SUMMARY This chapter discusses the optimal system component allocation problems for seriesparallel systems with interchangeable elements. A series-parallel system consists of subsystems that are connected in series and each subsystem consists of components in parallel. In many applications it is important to obtain the optimal solutions for the component allocation problem of series-parallel systems. Since this problem is one of the NPcomplete problems, it is difficult to obtain exact solutions for large scale problems. On the other hand, obtaining quasi-optimal solutions is good enough for most practical problems. We have formulated this kind of problem as multi-objective optimization problems minimizing the system cost and maximizing the system reliability, and have developed various algorithms for their solution. Some of these algorithms can provide exact solutions, and some of them provide fairly useful quasi optimal solutions. Many of the algorithms employ heuristic methods for efficiency. In this chapter, we demonstrate that a Multi-Objective Genetic Algorithm (MOGA) is an extremely promising method of problem solving. When solving #

This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013.  Corresponding Author. E-mail: [email protected].

14

Yasushi Kambayashi, Yasuhiro Tsujimura, Hidemi Yamachi et al.

multi-objective optimization problems, it is important to search as many Pareto solutions as possible. Even though MOGA is recognized as a powerful tool for the solution of multiobjective optimization problems, we need to construct an appropriate mechanism to search many Pareto solutions evenly along the Pareto frontier. In order to achieve this goal, we developed the double-structured representation in our MOGA to provide the capability for effective genetic search. In order to search a maximal number of Pareto solutions as evenly as possible along the Pareto frontier, in addition to the novel representation, we introduce Pareto-based selection. In order to confirm that our MOGA produces the correct solutions, we have constructed an algorithm to obtain the exact solutions utilizing depth-first search to eliminate useless searches and employing branch-and-bound method to obtain the Pareto solutions. Then we have conducted numerical experiments over a standard problem and compared the results obtained from both MOGA and the depth-first search based algorithm. MOGA produces almost the same results as the exact solutions in much less computation time. As a practical application, we have applied our MOGA to the N-version program design problem. The results demonstrate that our MOGA is not only theoretically feasible but also practically useful for solving multi-objective optimization problems that minimize the system costs and maximize the system reliabilities.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 8

A SURVEY OF GENETIC ALGORITHMS FOR SHOP SCHEDULING PROBLEMS #

Frank Werner* Otto-von-Guericke-Universität, Fakultät für Mathematik, Magdeburg, Germany

RESEARCH SUMMARY Genetic algorithms are a very popular heuristic which have been successfully applied to many optimization problems within the last 30 years. In this chapter, the authors give a survey on some genetic algorithms for shop scheduling problems. In a shop scheduling problem, a set of jobs has to be processed on a set of machines such that a specific optimization criterion is satisfied. According to the restrictions on the technological routes of the jobs, the authors distinguish a flow shop (each job is characterized by the same technological route), a job shop (each job has a specific route) and an open shop (no technological route is imposed on the jobs). the authors also consider some extensions of shop scheduling problems such as hybrid or flexible shops (at each processing stage, the authors may have a set of parallel machines) or the inclusion of additional processing constraints such as controllable processing times, release times, setup times or the no-wait condition. After giving an introduction into basic genetic algorithms discussing briefly solution representations, the generation of the initial population, selection principles, the application of genetic operators such as crossover and mutation, and termination criteria, the authors discuss several genetic algorithms for the particular problem types emphasizing their common features and differences. Here the authors mainly focus on single-criterion problems (minimization of the makespan or of a particular sum criterion such as total completion time or total tardiness) but mention briefly also some work on multi-criteria problems. The authors discuss some computational results and compare them with those obtained by other heuristics.

#

This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] or [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 9

A SCHEDULING APPROACH FOR THE DESIGN OF FLEXIBLE MANUFACTURING SYSTEMS #

L. Deroussi1,2, and M. Gourgand1,3 1

LIMOS CNRS UMR 6138, Université Blaise Pascal, Clermont-Ferrand, France 2 IUT d’Allier, Montluçon, France 3 ISIMA, Campus des Cézeaux, Aubière, France

RESEARCH SUMMARY The aim of this chapter is to show that it could be of great interest to consider the operational level (scheduling problems) for solving higher-level decision problems (design problems). To illustrate this point, a case study is considered in the context of flexible manufacturing systems (FMS). The goal is to rethink the design of an FMS by evaluating its performance according to a lower-level measure, and more precisely here by solving an offline scheduling problem. The experimental results we have obtained show that, in many cases, a simple reorganization of the production cells can improve the overall productivity of the FMS. The design problem we have considered in this chapter is called the machine assignment problem. At the operational level, we consider the simultaneous scheduling of material handling system and production tools. The function to be minimized is the time required for the production of a given set of jobs (makespan). We propose a hybridized solution approach that combines different optimization strategies: Integer Linear Programming (ILP), Ant colony System (ACS), Iterated Local Search (ILS) and Discrete Event Simulation (DES). ILP is used for elaborating an initial machine assignment (an optimal one for the high-level model). Ants generate new solutions. These solutions are evaluated by solving the resulting scheduling problem, for which an

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This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013.  Corresponding author, E-mail: [email protected], Tel: (33) 4.70.02.20.97.

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efficient hybrid approach (combining ILS and DES) has been developed in previous work. The results obtained show clearly the effectiveness of the proposed approach.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 10

ELECTRIC DISTRIBUTION NETWORK OPERATION PLANNING USING CHU AND BEASLEY GENETIC ALGORITHM AND PARTICLE SWARM OPTIMIZATION #

Ricardo A. de Araújo*, Santiago P. Torres†, Madson C. de Almeida and Carlos A. Castro Power Systems Department School of Electrical and Computer Engineering University of Campinas, São Paulo, Brazil

RESEARCH SUMMARY The operation planning problem consists of finding the best network control variable settings to improve its performance, while meeting its physical and operational constraints, given the daily load change. The presence of continuous (such as distributed generation) and discrete control variables (such as substation transformer taps, voltage regulators and switchable capacitor banks), along with the nonlinearity of the objective function and constraints, results in a very complex optimization problem. Those difficulties make room for opportunities for the development of new solution approaches and their application through efficient optimization tools. In this chapter, voltage regulator tap positions and capacitors banks have been used as discrete control variables to provide the distribution system operator with alternative measures to minimize real power losses. The presence of distributed generation as continuous variables has also been taken into account. Additionally, four metaheuristic optimization tools have been proposed and compared, namely the Chu-Beasley

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This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] † E-mail address: [email protected]

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Ricardo A. de Araújo, Santiago P. Torres, Madson C. de Almeida et al.

Genetic Algorithm and three Particle Swarm Optimization variants. Results are presented using data from both test and realistic electric distribution networks.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 11

A DISTRIBUTED APPROACH FOR DESIGNING EFFICIENT SEARCH ALGORITHMS: AN APPLICATION TO SOLVE THE LOCATION-ROUTING PROBLEM #

Jose Eduardo Pecora Jr.1*, Angel Ruiz2,4† and Patrick Soriano3,4‡ 1

Departamento de Administração Geral e Aplicada, Universidade Federal do Paraná, Brazil 2 Faculté des sciences de l'administration, Université Laval, Québec (Québec), Canada 3 Service de l'enseignement des méthodes quantitatives de gestion, HEC Montréal, Montréal (Québec), Canada 4 Centre interuniversitaire de recherche sur les réseaux d'entreprise, la logistique et le transport (CIRRELT)

RESEARCH SUMMARY Despite recent advances in both heuristic and implicit enumeration methods, exploring the whole solution space for large scaled problems remains, in most of practical cases, intractable. Indeed, enumeration and heuristic methods share their ability to thoroughly explore limited regions of the solution space. However, for different reasons they both fail to do it efficiently when the size of the solution space increases as in the case of most of real-life problems. Therefore, most of the research efforts in the last ten years have been concentrated in increasing the robustness of solution methods. In particular, the idea of hybridizing two or several methods has been brought in to address what the authors call the intensification/ diversification dilemma. The distributed approach here presented proposes a framework for the design of efficient search algorithms where the main idea is to separate the problem to solve into at least two #

This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013. * [email protected] † [email protected] ‡ [email protected]

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Jose Eduardo Pecora Jr., Angel Ruiz and Patrick Soriano

subproblems which will be linked in a hierarchical manner. Specific solving methods will be designed for each of these subproblems. Collaboration mechanisms allow the exchange of information between the two solving methods, which are tackled by a subgradient method. Therefore, most of the work done in hybrid algorithms is generally concerned by how to adapt two or more specific solution methods. However, little has been done towards the developing of a generic hybrid algorithmic structure independent of the search methods used. This chapter suggests a distributed framework for designing efficient search algorithms based on the idea of decomposition. The authors say that the approach is distributed because first, rather than following a monolithic perspective, it will elaborate methods based on a distributed decision making approach where complex decision problems will be split up into their components or subsystems by exploiting hierarchical or temporal dependencies. In fact, such a hierarchical decomposition lead us to define at least two subproblems named the higher level problem and lower level problem, respectively. By this separation, the algorithmic approach is able to iteratively perform two different phases of search: a macro search where only the (highest hierarchical level) variables are considered, and a micro search where the lower level problem is explored provided a restriction on the structural variables – also known as restricted spaces or RS. This search approach implies two potentially interesting advantages. Firstly, it emphasizes the information exchange between the macro and micro views, leading to a natural intensification/diversification scheme. Secondly, since it relies on the synergy between the two search phases rather than on the efficiency of each of the phases alone, it does not require, a priori, specific or dedicated methods to perform them. Therefore, models already available in the literature (exact methods, heuristics, metaheuristics) could be used in a straightforward manner within the algorithmic framework. The reminder of this chapter is structured as follows: in Section 2 the key concepts of the approach, such as structural variables and Restricted Spaces (RS), are introduced and formalized. Section 3 is dedicated to the description of the framework, its phases and components. Section 4 illustrates the method by applying it to the well-known Location Routing Problem (LRP). Computational results assessing the efficient of the method are provided in Section 5. Finally, Section 6 concludes the chapter.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 12

THE MULTI-DEPOT VEHICLE ROUTING PROBLEM: AN INTEGER PROGRAMMING-BASED HEURISTIC AND COMPUTATIONAL RESULTS #

Damon Gulczynski1*, Bruce Golden2†, Martin Savelsbergh3‡ and Edward Wasil4§ 1

RouteSmart Technologies, Inc., Columbia, MD, US Robert H. Smith School of Business, University of Maryland, US 3 School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, Australia 4 Kogod School of Business, American University, Washington DC, US 2

RESEARCH SUMMARY The multi-depot vehicle routing problem (MDVRP) is a variant of the standard vehicle routing problem in which there are multiple depots at which vehicles can start and end their routes. The authors develop an integer programming-based heuristic for the MDVRP. In the authors’ heuristic, the authors use integer programming to improve solutions to the MDVRP by relocating strings of consecutive customers on routes. The authors apply their heuristic to 23 benchmark instances and produce high-quality results.

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This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected] § E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 13

OPTIMIZATION FOR FEATURE SELECTION IN DNA MICROARRAYS #

Vincent Gardeux1, René Natowicz2, Maria Fernanda Barbosa Wanderley3 and Rachid Chelouah1 1

L@RIS, EISTI, Avenue du Parc, Cergy, France ESIEE-Paris, University of Paris-Est, Noisy-le-Grand, France 3 Federal University of Minas Gerais, Belo Horizonte, Brazil

2

RESEARCH SUMMARY We present two methods for feature selection in high throughput transcriptomic data, in which the subsets of selected variables (the genes) are optima of a multi-objective function. In the clinical trials, the number of embedded patient cases is never higher than in the hundreds, while the number of gene expressions measured for each patient is higher than tens of thousands. These trials aim to better understand the biology of the phenotypes at the genomic level, and to better predict the phenotypes in order to give each patient the best treatment. Our first method states that the gene subsets are the optima of a bi-objective function. This function is a tradeoff between the size of the gene subset and the discrimination of the phenotypes, expressed as the inter-class distance. Because the gene selection stage is independent of the prediction model, it is a filter method of feature selection. The second method aims to select gene subsets that will optimize the performance of a specific prediction model. It is a wrapper approach of the feature selection problem. The optimal gene subsets are computed by a line search optimization heuristic which maximizes the performances of a linear discriminant analysis. Using public datasets in oncology we compared our results to those of the main previous methods. Our optimization approach of the gene subset selection almost always returned subsets that were significantly smaller than those of the previous methods, the performance of #

This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013.  E-mail address: [email protected]

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our predictors almost always being higher, and being more robust. In the two methods we searched the space of gene subsets for optima of an explicit multi-objective function. Metaheuristic methods are well suited to address these optimization problems, specifically in high dimensional spaces.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 14

ANT COLONY SYSTEM: APPLICATION FOR THE SINGLE AND MULTI-OBJECTIVE MULTIDIMENSIONAL KNAPSACK PROBLEMS #

Prakash Shelokar* European Centre for Soft Computing, Mieres, Spain

RESEARCH SUMMARY The multidimensional 0-1 knapsack problem (MKP) is one of the most well-known integer programming problems and has received wide attention from the operational research community during the last five decades. This chapter presents an ant colony system (ACS) based heuristic for the MKP problem. The ACS method is the most successful algorithm from the rapidly growing field of ant colony optimization (ACO) for hard discrete optimization problems.

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This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 15

SYNERGISTIC COMBINATION OF EVOLUTIONARY ALGORITHMS AND FUZZY SYSTEMS: APPLICATION TO CONTROL DESIGN #

Nazmul H. Siddique School of Computing and Intelligent Systems, University of Ulster, NI, UK

RESEARCH SUMMARY The design of fuzzy systems mainly relies on human experts and heuristics. Even if it can be constructed using expert knowledge, the system needs further adjustment or tuning of the rule-base, membership functions and several other parameters. Mostly these adjustments are done by empirical methods, which are very often time consuming but do not guarantee any optimal performance. An automated procedure is sought which can ensure an optimal performance of the system according to some optimality criterion. Therefore, the design parameters of the fuzzy system can be formulated as an optimisation problem. An evolutionary algorithm based optimisation approach with dynamic crossover and mutation is applied to a PD-PI-type fuzzy controller for tuning the membership functions. In this context, different synergies of fuzzy systems and evolutionary algorithms are also discussed.

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This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013.  E-mail: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 16

ANALYSIS OF STRUCTURES BY TOTAL POTENTIAL OPTIMIZATION USING META-HEURISTIC ALGORITHMS (TPO/MA) #

Y. C. Toklu1 and N. E. Toklu2 1

Department of Civil Engineering, Faculty of Engineering, Bayburt University, Bayburt, Turkey 2 Istituto Dalle Molle di Studi sull'Intelligenza Artificiale (IDSIA), Manno, Switzerland

RESEARCH SUMMARY Use of meta-heuristic algorithms in analysis of structures is much more recent than their use in design of structures. Effectively, while design optimization makes use of genetic algorithms, simulated annealing, swarm optimization, etc. since about half a century with an increasing interest, these techniques are being used in structural analysis since a decade only. Total Potential Optimization using Meta-heuristic Algorithms (TPO/MA), though being an emerging method at the moment, has proved to be very efficient in solving nonlinear problems, involving both material and geometric nonlinearities. The capabilities of the method in treating under-constrained problems and problems with non-unique solutions are much more advanced than the classical methods including the well-known Finite Element Method.

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This chapter was previously published in Heuristics: Theory and Applications, edited by Patrick Siarry, New York: Nova Publishers Inc., 2013.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 17

A REVIEW OF COMPUTATIONAL INTELLIGENCE ALGORITHMS IN INSURANCE APPLICATIONS #

S. Salcedo-Sanz*, L. Cuadra†, A. Portilla-Figueras‡, S. Jiménez-Fernández§ and E. Alexandre¶ Department of Signal Theory and Communications Universidad de Alcalá, Madrid, Spain

RESEARCH SUMMARY Insurance sector, one of the cornerstones the financial system is based on, is currently facing major changes because of the urgent necessity of being adapted to the new context of global economic crisis. Within this frame, the financial system of any modern country needs to develop novel procedures aiming to make it more competitive and efficient, along with the compliance with commitment agreed with the policyholders. Part of this important responsibility relies on the inclusion of more effective and accurate computing techniques able to provide better solutions for crucial problems in different key components of the system, including, of course, the insurance sector. In this respect, this chapter presents a review of those Soft-Computing applied in the field of insurance companies and related problems, which have been very active and successful over the past 10 years. The aims of this chapter are thus: 1) to illustrate in a comprehensive way those features of Soft-Computing algorithms that make them suitable to tackle insurance problems; 2) to provide a good and updated review of their main applications in insurance-related problems; and 3) to show to what extent Soft-Computing algorithms work accurately in a real application. Just in this regard, #

This chapter was previously published in Statistical and Soft Computing Approaches in Insurance Problems, edited by Sancho Salcedo-Sanz, Mercè Claramunt-Bielsa, Jose Luis Vilar-Zanón and Antonio Heras, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected] § E-mail address: [email protected] ¶ E-mail address: [email protected]

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this chapter ends up with details about the application of several of these techniques in predicting vehicle accidents using drivers and vehicles’ data, which is useful for vehicle insurance companies.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 18

ROUGH SETS IN INSURANCE SECTOR

#

M.J. Segovia-Vargas* and Z. Díaz-Martínez† Department of Financial Economics and Accounting I, Universidad Complutense de Madrid, Spain

RESEARCH SUMMARY Rough Set theory belongs to the domain of Artificial Intelligence (AI) and has demonstrated a very high performance in financial issues, especially in classifying problems. Yet, there is little AI research devoted to the insurance industry, although it plays a growing and crucial role in modern economies. The present chapter shows three relevant rough sets researches in insurance sector concluding that this method is an effective tool for supporting managerial decision making in general, and for insurance sector in particular.

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This chapter was previously published in Statistical and Soft Computing Approaches in Insurance Problems, edited by Sancho Salcedo-Sanz, Mercè Claramunt-Bielsa, Jose Luis Vilar-Zanón and Antonio Heras, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] † E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 19

PREDICTION OF CLAIMS AND SELECTION OF RISK FACTORS IN AUTOMOBILE INSURANCE USING SUPPORT VECTOR MACHINES, GENETIC ALGORITHMS AND CLASSIFICATION TREES #

A. Heras-Martínez*, C. Bousoño-Calzón† and P. Tolmos Rodríguez-Piñero‡ Department of Financial Economy and Accounting I, Universidad Complutense, Madrid, Spain Department of Signal Theory and Communications, Universidad Carlos III, Madrid, Spain Department of Financial Economy and Accounting II, Universidad Rey Juan Carlos, Madrid, Spain

RESEARCH SUMMARY In this chapter we study the problem of the classification of the policies of an insurance company according to the prediction of their claims for the next year. The usual approach is based on the application of multivariate statistical techniques to the set of risk factors that characterize the policies. Our approach is based on the Learning Machines methodology. We use for this purpose sets of risk factors obtained from two data bases of an important Spanish insurance company. The algorithm we suggest is based on the application of a standard Support Vector Machine (SVM), hybridized with Genetic and Random Forest algorithms. The SVM is used to classify the policies as failed (reporting claims) or not failed, according #

This chapter was previously published in Statistical and Soft Computing Approaches in Insurance Problems, edited by Sancho Salcedo-Sanz, Mercè Claramunt-Bielsa, Jose Luis Vilar-Zanón and Antonio Heras, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected]

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A. Heras-Martínez, C. Bousoño-Calzón and P. Tolmos Rodríguez-Piñero

to their risk factors, whereas GA and RF are used to perform a pre-selection in the risk factors space of the SVM. We will show that one of these risk factors, the Bonus-Malus level, has a crucial importance. The obtained results are very encouraging and show that learning techniques in general, and SVM in particular, can be useful tools for solving classification problems in insurance.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 20

TAIL VALUE AT RISK. AN ANALYSIS WITH THE NORMAL-POWER APPROXIMATION

#

A. Castañer*, M.M. Claramunt† and M. Mármol‡ Department of Economic, Financial and Actuarial Mathematics Universitat de Barcelona, Spain

RESEARCH SUMMARY The problem of risk measurement is one of the most important problems in the risk management. In this chapter we discuss risk measures based on loss distributions in the context of insurance and finance. We concentrate on the most known risk measures: the Value at Risk and the Tail Value at Risk. The aim of this chapter is to analyze the applicability of the Normal-Power approximation for the calculus of TVaR. We obtain a new analytical expression of the TVaR using the NP approximation and we analyze its precision. The chapter ends up with an application to underwriting and credit risk.

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This chapter was previously published in Statistical and Soft Computing Approaches in Insurance Problems, edited by Sancho Salcedo-Sanz, Mercè Claramunt-Bielsa, Jose Luis Vilar-Zanón and Antonio Heras, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 21

FINANCIAL APPLICATIONS OF MODAL INTERVAL ANALYSIS #

R. Adillon* and L. Jorba† Department of Economic, Financial and Actuarial Mathematics Universitat de Barcelona, Spain

RESEARCH SUMMARY In this chapter, we present a new mathematical tool that allows us to develop a new approach for calculations in insurance problems. This new tool is based on modal intervals, since it can be assumed that most of the data in real world applications can be represented by intervals. Classic intervals are simply sets of numbers between two given bounds. After processing the interval data, we also obtain results in terms of intervals, and the interpretation of this fact is sometimes ignored. The proposed modal intervals are designed as pairs consisting of a classic interval and a quantifier. The use of modal intervals provides a new instrument that allows for a correct semantical interpretation of the obtained results by using the existential and universal quantifiers. In this chapter, we detail the basic concepts and results of this theory, and we also make an illustration based on some examples from economics and insurance.

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This chapter was previously published in Statistical and Soft Computing Approaches in Insurance Problems, edited by Sancho Salcedo-Sanz, Mercè Claramunt-Bielsa, Jose Luis Vilar-Zanón and Antonio Heras, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] † E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 22

A METHOD FOR ANALYSIS OF TRANSMISSION LINES TERMINATED BY NONLINEAR LOADS #

Vasil G. Angelov, PhD Department of Mathematics, Faculty of Mine Electromechanics, University of Mining and Geology, Sofia, Bulgaria

RESEARCH SUMMARY It is known that transmission lines model various guiding structures such as power lines, wires, cables, printed circuit board traces, buses for carrying digital data in electronic circuits, and microwave circuits and so on. The transmission line theory has received renewed attention because of important applications in the area of high-speed VLSI interconnect, while it has retained its significance in the area of power transmission. The behavior of the transmission lines is described by transmission line equations. From a mathematical point of view they represent a hyperbolic system of first order partial differential equations. The transmission lines are terminated by various configurations of linear or nonlinear loads. The Kirchoff’s laws regulate the behavior of these lumped circuits and define boundary conditions. Adding appropriate initial conditions, we can formulate a mixed problem for the transmission line system with unknown functions of the voltage and current of the line. The main purpose of the present book is to propose a method for solving the mixed problem for transmission line systems reducing it to a neutral equation (or system) on the boundary. Arising nonlinearities in the neutral systems are caused by nonlinear characteristics of the RGCL-loads. In view of the applications we consider mainly periodic and oscillatory problems for lossless transmission lines. We point out, however, that here we propose an extended procedure for reducing the mixed problem for lossless and lossy transmission lines. We introduce also an extension of Heaviside condition and this way we can consider the case of time-varying specific parameters-per-unit length resistance, conductance, inductance and capacitance. We find a solution of the obtained neutral equations by discovering operators #

This chapter was previously published as a book: A Method for Analysis of Transmission Lines Terminated by Nonlinear Loads, by Vasil G. Angelov, New York: Nova Publishers Inc., 2014.

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whose fixed points in suitable function spaces are periodic or oscillatory solutions of the formulating problems. Using fixed point theorems for contractive mappings in uniform and metric spaces (proved by the author in the previous papers) we prove existence-uniqueness results for periodic and oscillatory problems. We obtain also successive approximations of the solution with respect to a suitable family of pseudo-metrics and give an estimate of the rate of convergence. Although the question of finding the initial approximation is not trivial. We show that one can begin with a simple harmonic initial approximation. The rate of convergence depends on the parameters of the transmission lines and characteristics of the nonlinear RCL-loads. Our conditions are applicable even in some cases to non-uniform transmission lines. Numerical examples demonstrate the applicability of the main results to design of circuits. It is easy to verify a system of inequalities between basic parameters without examining the proofs of the theorems.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 23

MARKUS-SELL’S THEOREM FOR ASYMPTOTICALLY ALMOST PERIODIC SYSTEMS #

David Cheban1,* and Cristiana Mammana2,† 1

State University of Moldova, Department of Mathematics and Informatics Chişinău, Moldova 2 Dept. of Economic and Financial Institutions University of Macerata, Macerata, Italy

RESEARCH SUMMARY This chapter is dedicated to the study of asymptotic stability of asymptotically almost periodic systems. We formulate and prove the analog of Markus-Sell’s theorem for asymptotically almost periodic systems (both finite and infinite dimensional cases). We study this problem in the framework of general non-autonomous dynamical systems. The obtained general results we apply to different classes of non-autonomous evolution equations: Ordinary Differential Equations, Difference Equations, Functional Differential Equations and Semi-Linear Parabolic Equations.

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This chapter was previously published in Dynamical Systems: Theory, Applications and Future Directions, edited by Jean Michel Tchuenche, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] † E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 24

A SURVEY OF THE METHOD OF LYAPUNOV FUNCTIONS OF TWO VARIABLES IN THE STUDY OF STABILITY AND PERSISTENCE OF DYNAMICAL SYSTEMS #

Jorge Lewowicz1,*, Jorge Groisman1,† and Juan Tolosa2,‡ 1

IMERL, Facultad de Ingeniería, Universidad de la República Montevideo, Uruguay 2 Department of Natural Sciences and Mathematics Richard Stockton College of New Jersey, Galloway, USA

RESEARCH SUMMARY In this chapter, we describe Lewowicz’s method of Lyapunov functions of two variables, for the study of structural stability of dynamical systems, and related concepts, such as topological stability and persistence. We include a wide scope of applications of this method, among others, to perturbations of hyperbolic maps on the plane, Anosov diffeomorphisms, expansive homeomorphisms on surfaces and on the plane, geodesic flows on compact manifolds, and billiards.

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This chapter was previously published in Dynamical Systems: Theory, Applications and Future Directions, edited by Jean Michel Tchuenche, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 25

KRYLOV AND SCHUR SUBSPACES IN CONSTRUCTION OF PREDICTION ERROR FILTER: COMPUTATIONAL COMPLEXITY AND PERFORMANCE COMPARISON #

Hong Son Hoang and Rémy Baraille SHOM/HOM, Toulouse, France

RESEARCH SUMMARY The authors discuss the questions of complexity and performance of two subspace methods for filtering problem with very high dimensional system state, the Krylov subspace method and the dominant Schur subspace method. It will be shown that compared to the Schur subspace method, the Krylov subspace is computationally much less demanding and allows to construct the filter with nearly the same performance as that based on the Schur subspace. The advantages and disadvantages of these two subspaces in connection with the performance of the prediction error filter as well as its computational complexity will be studied in detail. These two subspace methods are also viewed from the point of view of the Ritz vector approach. As will be seen, for the very high dimensional systems, the Krylov subspace method will contribute to improvement of the filter performance by making possible utilization of the larger set of prediction error samples. Numerical results from the experiments with a simple dynamical model of moderate dimension as well as with data assimilation problems with very high dimensional Miami Isopycnic Coordinate Ocean Model (MICOM) will be also presented to show how work the algorithms in practice. Comparison of the performance of the prediction error filter (and its adaptive version) based on different sets of prediction error samples simulated by the two subspace algorithms are also exhibited.

#

This chapter was previously published in Dynamical Systems: Theory, Applications and Future Directions, edited by Jean Michel Tchuenche, New York: Nova Publishers Inc., 2013.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 26

HIGH-FIDELITY MODELING AND VIBRATION-BASED SYSTEM IDENTIFICATION AND DAMAGE INSPECTION OF FLEXIBLE STRUCTURES #

P. Frank Pai Mechanical and Aerospace Engineering Dept., University of Missouri, Columbia, Missouri, US

RESEARCH SUMMARY Structural systems are often built with unwanted/wanted nonlinearities, damage introduces additional nonlinearities, and aging aggravates nonlinearities. Hence, high-fidelity nonlinear modeling is needed in development of techniques for system identification and damage inspection of structures. This chapter presents a geometrically exact modeling technique that can fully account for geometric nonlinearities of beams by using Jaumann strains, exact coordinate transformations, and orthogonal virtual rotations. The derivations are presented in detail, and fully nonlinear governing equations and boundary conditions are presented. For damage inspection and system identification of thin-walled structures, this chapter presents a dynamics-based methodology that combines a boundary-effect evaluation method (BEEM) for space-wavenumber analysis of measured operational deflection shapes (ODSs) and a conjugate-pair decomposition (CPD) method for time-frequency analysis of time traces of measured points. BEEM can locate and estimate structural damage by processing ODSs measured by a full-field measurement system (e.g., a scanning laser vibrometer or a camera-based motion measurement system). BEEM is a nondestructive spatial-domain method based on sliding-window processing of ODSs and it works without using any structural model or historical data for comparison. Similar to the short-time Fourier transform and wavelet transform, CPD uses adaptive windowed regular harmonics and function orthogonality to perform time-frequency analysis of time traces by extracting timelocalized regular/distorted harmonics. Moreover, solutions from perturbation analysis of #

This chapter was previously published in Dynamical Systems: Theory, Applications and Future Directions, edited by Jean Michel Tchuenche, New York: Nova Publishers Inc., 2013.

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P. Frank Pai

nonlinear dynamical systems provide excellent guidance and formulas for quantitative estimation of nonlinearity and system parameters. Both BEEM and CPD are local spectral analysis based on adaptive curve fitting. The first estimation of the wavenumber for BEEM and the frequency for CPD can be obtained using an enhanced five-point Teager-Kaiser algorithm based on finite difference. Numerical examples are used to demonstrate how to use high-fidelity structural models to help the development of techniques for system identification and damage inspection. Numerical simulations and experimental results show that the combination of BEEM and CPD for space-wavenumber and time-frequency analyses provides an accurate and efficient tool for damage inspection and system identification of thin-walled structures. Moreover, current status and remaining challenges in modeling and vibration-based system identification and damage inspection of flexible structures are also addressed.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 27

COMPLEXITY AND CHAOS THEORY IN SOCIAL SCIENCES: SCIENTIFIC PHILOSOPHY OR QUANTITATIVE SCIENCE? #

Rosalia Condorelli Department of Political and Social Sciences, Catania University, Catania, Italy “Scientific genius is the capacity to be surprised.” Henry Poincarè

RESEARCH SUMMARY This chapter deals with the possibility of applying Complexity and Chaos Theory to Social Sciences. There are many theorists in the field of the Physical Sciences who share Ruelle’s thesis that it is more controversial to use nonlinear dynamical system analysis in the field of the Social Sciences. This is not a theoretical difficulty. No doubt even in non-physical systems we observe complex time evolutions and chaotic processes dynamics. No doubt even in social systems we observe dynamics so unstable and discontinuous that self-organizational processes no longer work ending up in chaos. According to Ruelle, the real problem arises when one shifts from the level of “scientific philosophy” to the domain of “quantitative science”. Even though the time evolution of social systems may be as discontinuous and chaotic as physical ones, they cannot be analyzed in the same manner. The reasons for this have been duly presented, discussed and reviewed. Ruelle’s main objection, the intrinsic impossibility of the Social Sciences to achieve basic equations or models of deterministic evolution “really convincing”, cannot be accepted in its general absoluteness. Proof of this is the fact that in the soft Sciences we often find the successful application of the logistic map. Outside the physical sciences, this well-known non-linear model is the rule and not the exception (May, 1976). Contrary to Ruelle’s assertion, the application of complexity and

#

This chapter was previously published in Dynamical Systems: Theory, Applications and Future Directions, edited by Jean Michel Tchuenche, New York: Nova Publishers Inc., 2013.

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Rosalia Condorelli

chaos theory in the Social Sciences is a real possibility. As a result, this chapter discusses the implications of Complexity and Chaos Theory for social science research.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 28

LOCAL STABILITY ANALYSIS OF AN AGESTRUCTURED HEPATITIS B TRANSMISSION MODEL

#

Ousmane M. Tessa1,*, Bisso Saley1, Herieth Rwezaura2 and Jean M. Tchuenche2 1

Department of Mathematics and Computer Science, Abdou Moumouni University, Niamey, Niger 2 Department of Mathematics, University of Dar es Salaam, Dar es Salaam, Tanzania

RESEARCH SUMMARY This chapter deals with the analysis of the local stability of a modified age-structured deterministic model for the transmission dynamics of Hepatitis B virus first proposed by Zhao et al.†. The model exhibits two equilibria, namely: the disease-free equilibrium which is locally asymptotically stable if a certain disease threshold parameter R0 which depends solely on the parameters associated with the model is less than unity; a public health implication of this result is that Hepatitis B could be eliminated in the population - an endemic equilibrium which exists for R0 > 1 and is locally asymptotically stable under certain condition and consequently, the disease may persist.

#

This chapter was previously published in Dynamical Systems: Theory, Applications and Future Directions, edited by Jean Michel Tchuenche, New York: Nova Publishers Inc., 2013. * E-mail addresses: [email protected], [email protected] (Corresponding Author) † Xua and Y. Xua and Y. Lub. A Mathematical model of hepatitis B virus transmission and its application for vaccination strategy in China. Int. J. Epidemiol. 2000 Vol. 29, 744-752.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 29

PARAMETRIC RESONANCE AND HOMOCLINIC CHAOS IN A BULLARD-TYPE DYNAMO #

O. Foupouapouognigni*, M. Siewe Siewe† and C. Tchawoua‡ Université de Yaoundé I, Faculté des sciences, Département de Physique, Laboratoire de Mécanique, Yaoundé, Cameroun

RESEARCH SUMMARY The authors show that magnetic flux created by radial current in a Bullard disk dynamo modeled by bistable oscillator under parametric excitation can be used to investigate generic properties such as instability or bifurcation of more realistic mean field dynamos. Using the theory of dynamical systems, a differential equation is constructed to study the nonlinear vibration of the magnetic flux. Based on the harmonic balance method, the first approximate solution and corresponding solution of the primary parametric resonance are obtained, followed by the stability analysis of the steady state. Magnetic fluxes created by radial current driven by parametric excitation with constant frequency can display stationary, saddle-node bifurcations, and hysteresis. The Melnikov method is used to detect the parametric threshold of instability of the dynamo, i.e., the value from which chaotic reversals of the generated current are observed. Finally this system is integrated numerically via the fourth-order RungeKutta to show fractal dimension spectra and basin boundaries associated with fast dynamo magnetic field. These results have implication for the expected behavior of stellar dynamos.

#

This chapter was previously published in Dynamical Systems: Theory, Applications and Future Directions, edited by Jean Michel Tchuenche, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 30

BIRHYTHMICITY, SYNCHRONIZATION AND CHAOS IN AN ENZYME-SUBSTRATE REACTION WITH A FERROELECTRIC BEHAVIOR #

H. G. Enjieu Kadji1,2 and P. Woafo2 1

Monell Chemical Senses Center, Philadelphia, Pennsylvania, US Laboratory of Modelling and Simulation in Engineering and Biomimetics and Prototypes, University of Yaoundé I, Yaoundé, Cameroon

2

RESEARCH SUMMARY This chapter addresses the issues of birhythmicity, synchronization and chaos in an enzyme-substrate reaction with ferroelectric behavior modeled by a multi-limit cycles van der Pol oscillator, a self-sustained system that possesses mechanisms to damp oscillations that grow too large and a source of energy to pump those that become too small. Theoretical analyses based on the method of perturbation are utilized to determine the amplitudes and frequencies of limit cycles for autonomous oscillatory states. The unidirectional and bidirectional synchronization processes in the model are addressed and their stability boundaries are determined using the Floquet theory and Whittaker’s method. Routes leading to chaos and strange attractors are investigated via the bifurcation diagrams and maximum Lyapunov exponent. Chaos synchronization is also investigated for unidirectional and bidirectional coupling schemes. The fourth order Runge-Kutta algorithm coded in Pascal is used to perform the numerical simulations.

#

This chapter was previously published in Dynamical Systems: Theory, Applications and Future Directions, edited by Jean Michel Tchuenche, New York: Nova Publishers Inc., 2013.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 31

DYNAMICS OF LOW AND HIGH PATHOGENIC AVIAN INFLUENZA IN WILD BIRD POPULATION #

Necibe Tuncer 1,*, Juan Torres2,† and Maia Martcheva2,‡ 1

Department of Mathematics, University of Tulsa, Oklahoma, USA Department of Mathematics, University of Florida, Gainesville, Florida, US

2

RESEARCH SUMMARY This chapter introduces an avian influenza model which includes the dynamics of low pathogenic avian influenza (LPAI) and high pathogenic avian influenza (HPAI). The model structures the LPAI-recovered individuals by time-since-recovery and involves the cross𝐿 𝐻 immunity that LPAI infection generates toward the HPAI. Reproduction numbers (𝑅0𝑤 , 𝑅0 𝑤 ) and invasion reproduction numbers (𝑅̂ 𝐻𝑤 , 𝑅̂ 𝐿𝑤 ) of LPAI and HPAI are computed. It is shown 𝐿

that the system has a unique disease-free equilibrium that is locally and globally stable if 𝑅0𝑤 𝐻

𝐿

< 1 and 𝑅0 𝑤 < 1. If 𝑅0𝑤 > 1, a unique LPAI dominance equilibrium exists. Similarly, if 𝐻

𝑅0 𝑤 > 1, a unique HPAI dominance equilibrium exists. The equilibria are locally stable if 𝑅̂ 𝐻𝑤 < 1 (𝑅̂ 𝐿𝑤 < 1 correspondingly). A unique coexistence equilibrium is present if both invasion numbers are larger than one. Simulations show that this coexistence equilibrium can lose stability and coexistence in the form of sustained oscillations is possible. Cross-immunity and duration of protection increase the probability of coexistence. Simulations also show that increasing LPAI transmission increases LPAI prevalence and decreases HPAI prevalence. This observation in part may explain why wild birds which have much higher transmission of LPAI compared to domestic birds also have much lower prevalence of HPAI.

#

This chapter was previously published in Dynamical Systems: Theory, Applications and Future Directions, edited by Jean Michel Tchuenche, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 32

ANALYSIS OF A PREDATOR-PREY MODEL WITH SIGMOIDAL RESPONSE FUNCTION AND SIS DISEASE

#

J. J. Tewa1,5*,, P. Tchinda Mouofo2,5, V. Kamla3,5 and S. Bowong4,5 1

Department of Mathematics and Physics, National Advanced School of Engineering (Polytechnic), University of Yaounde I, Yaounde, Cameroon 2 Department of Mathematics, Yaounde, Cameroon University of Yaounde I, Faculty of Science, 3 Department of Mathematics and Computer Science, Cameroon University of Ngaoundere, ENSAI, 4 Department of Mathematics and Computer Science, Cameroon University of Douala, Faculty of Science, 5 GRIMCAPE team project, LIRIMA, Yaounde, Cameroon UMI 209 IRD/UPMC UMMISCO, University of Yaounde I, Cameroon

RESEARCH SUMMARY A predator-prey system with prey harvesting, sigmoidal response function is considered. Three derived models with SIS disease only among the prey population, the predator population and the two populations respectively are obtained. Global qualitative and bifurcation analysis are combined to determine the global dynamics of these models. The bifurcation analysis of the model depending on all parameters indicates that it exhibits bifurcations phenomena, including the saddle-node bifurcation and the transcritical bifurcation. There is no limit cycle for these models. Mathematical analysis of the models regarding stability and influence of disease has been performed. The disease modifies considerably the qualitative analysis of our systems since it can disappear or persist inside population. Numerical simulations are given in order to illustrate analytical results. #

This chapter was previously published in Dynamical Systems: Theory, Applications and Future Directions, edited by Jean Michel Tchuenche, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected], Tel: +(237) 77 71 13 69 (Corresponding author).

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 33

MODELLING THE EFFECTS OF MULTI-INTERVENTION CAMPAIGNS FOR THE MALARIA EPIDEMIC IN MALAWI #

P. M. Mwamtobe1,* , J. M. Tchuenche2,†, M. Maliyoni3 and S. D. Hove-Musekwa4 1

Department of Mathematics and Statistics, University of Malawi, The Malawi Polytechnic, Chichiri, Blantyre, Malawi 2 Mathematics Department, University of Dar es Salaam, Dar es Salaam, Tanzania 3 Mathematics Department, DMI-St. John the Baptist University, Mangochi, Malawi 4 Department of Applied Mathematics, National University of Science and Technology, Ascot, Bulawayo, Zimbabwe

RESEARCH SUMMARY Malaria is a public health problem for about 2.4 billion people despite decades of efforts to control the disease. A mathematical model is developed to assess the potential impact of protection (insecticide-treated mosquito bed-nets and indoor residual spraying) and treatment on the transmission dynamics of malaria in Malawi. The model is analyzed qualitatively to determine, the effective reproduction number which is necessary for country-wide control of malaria is computed. The equilibria of the model are determined. The disease-free equilibrium is locally asymptotically stable whenever Re < 1 and unstable when Re > 1, the existence of a unique endemic equilibrium case. Numerical simulations indicate that the two control strategies (protection and treatment) in lowering the number of exposed and infected people. Our results highlight the population-level impact of some model parameters such as the infection and biting rates. #

This chapter was previously published in Dynamical Systems: Theory, Applications and Future Directions, edited by Jean Michel Tchuenche, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] † E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 34

MODELLING THE DYNAMICS OF HIV-TB CO-INFECTION IN A VARIABLE SIZE POPULATION

#

Agraj Tripathi1*, Ram Naresh2, and Dileep Sharma3 1

Department of Mathematics, Bhabha Institute of Technology, Kanpur, India 2 Department of Mathematics, Harcourt Butler Technological Institute, Kanpur, India 3 Department of Mathematics, DBS(PG) College, Dehradun, India

RESEARCH SUMMARY In this chapter, a nonlinear mathematical model is proposed to study the transmission dynamics of HIV and a curable TB pathogen within a population of varying size. The population, under consideration, is divided into five sub-classes, namely, the susceptibles, the TB infectives, the HIV infectives, the HIV-TB co-infectives and the AIDS patients. The model is analyzed qualitatively using stability theory of nonlinear differential equations. The model exhibits five equilibria, namely, the disease- free, the TB only, the HIV only, the coinfection only, and the nontrivial endemic equilibrium. The basic reproduction number R0 is the key factor of the model. It is observed that if R0 >1 then at least one of the diseases always persists in the population otherwise both the diseases die out. It is shown that the positive endemic equilibrium may be locally stable under certain conditions showing that the disease becomes endemic due to constant migration of the population into the habitat. A numerical study of the model is also carried out to investigate the influence of certain key parameters on the spread of the disease, and to support the analytical results.

#

This chapter was previously published in Dynamical Systems: Theory, Applications and Future Directions, edited by Jean Michel Tchuenche, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] (Corresponding author)

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 35

CASE DETECTION ON TUBERCULOSIS DYNAMICS WITH ISOLATION IN A SANATORIUM #

Nyimvua Shaban* Department of Mathematics, University of Dar es Salaam, Dar es Salaam, Tanzania

RESEARCH SUMMARY This chapter presents a deterministic-model for assessing the impact of early detection on the dynamics of tuberculosis (TB) epidemic. Qualitative analysis of the model reveals conditions under which the model can exhibit backward bifurcation where a stable diseasefree equilibrium co-exists with a stable endemic equilibrium when the effective reproduction number is less than unity. Furthermore, an explicit expression for the effective reproduction number was derived, above which the disease will persist and below which TB could be eliminated in community. Graphical representations are provided to support the analytical results. The higher the detection rate the better the control of the disease.

#

This chapter was previously published in Dynamical Systems: Theory, Applications and Future Directions, edited by Jean Michel Tchuenche, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 36

ADVANCES IN DISCRETE DYNAMICS

#

Jose S. Cánovas Universidad Politecnica de Cartagena, Spain

RESEARCH SUMMARY Discrete dynamical systems, the main topic of this book, have had a fast development due to the development of computer science. Programming an iteration with the form xn+1 = f(xn), where f is a real function is made easy with modern computers. So, with the modern computer, it is relatively easy and fast to obtain simulations related with the dynamics of their models. Finding analytical proofs for computer simulations of models are natural and exciting problems for mathematicians and, like in a feedback process, new powerful analytical results motivate the use of discrete models. This new book examines the theory of dynamical systems. In Chapter 1 the authors are mainly interested in the study of the periodic points of a discrete dynamical system and its application to the knowledge of the asymptotical behavior of such system. The authors will also analyze the topic of global periodicity of autonomous difference equations. The purpose of Chapter 2 is to make a brief survey about some new results concerning various shadowing properties and their relationships with different kinds of chaos. Dynamical systems is the study of long-term behavior of evolving systems. An orbit represents the evolution of a particular state of a dynamical system. The cluster set of an orbit is an ω-limit set or attractor. The structure of such sets has been and it still is widely investigated, as a way to view “complexity” of iterative patterns of a map is to analyze the types of ω-limit sets it possesses. Themes that repeatedly appear in the study of dynamical systems are: properties of individual ω-limit sets, periodic orbits, minimal sets, typical behavior of ω-limit sets, forms of chaos and their associated ω-limit sets. Chapter 3 discusses some features of them for discrete-time dynamical systems. #

This chapter was previously published as a book: Advances in Discrete Dynamics, by Jose S. Canovas, New York: Nova Publishers Inc., 2013.

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Topological entropy was introduced in 1965 by Adler, Konheim and McAndrew, inspired by the notion of metric entropy (or measure theoretic entropy), which had been deeply studied in ergodic theory. Now, topological entropy is one of the main tools to characterize whether a discrete dynamical system is chaotic or not. The aim of Chapter 4 is to summarize the most relevant results for topological entropy in the setting of one dimensional dynamics, that is, continuous selfmaps on the interval and the real line. Some open questions can be found along the paper. Chapter 5 is the study of topics for minimality and transitivity within some discrete and continuous dynamical systems are examined. In the continuous systems there are surface flows: where the authors show the classification of transitive surfaces obtained and introduce the classification of minimal orientable surfaces by J.C. Benière. For non-orientable surfaces the minimality has been recently classified and they state the classification given by Peralta Soler. The discrete dynamical systems described are concerned with interval exchange transformations (i.e.t.’s). Gutierrez et al. posed the question of finding minimal i.e.t.’s with an arbitrary finite number of discontinuity points and with flips. We present the answer to a problem which is contained in Soler. Surface flows and i.e.t.’s have a strong relation, in particular the main result on i.e.t.’s has allowed to prove the classification of non-orientable minimal surfaces. We also present some other related questions on transitivity and minimality and the suspension method that allows to build a surface flow from an i.e.t. In Chapter 6 the authors aim at presenting applications of notions from Information Theory to the study of the statistical properties of dynamical systems. In particular the authors review the notion of Algorithmic Information Content, or Kolmogorov Complexity, and recall the definition of complexity of an orbit of a dynamical system. The main result is that for ergodic dynamical systems, the complexity of an orbit is almost everywhere constant and coincides with the Kolmogorov-Sinai entropy of the system. The authors remark that the interest in these results has at least two motivations: applications of this approach to time series of e.g. physical or biomedical origin; investigations on statistical properties of dynamical systems which present “critical” behaviours with respect to other classical indicators or for which it may be difficult to compute them. In Chapter 7 the authors introduce a two dimensional economic model by Tönu Puu in 1991. The authors analyze the model with some recent mathematical techniques and show that the firms may produce in a chaotic way by giving a rigorous mathematical proof. However, the less efficient firm (in terms of higher production costs) take profit of this chaotic or destabilized scenario. Some techniques to stabilize the equilibrium point without the agreement of one of the firms are pointed out. Finally, the authors introduce several modifications of the above mentioned model and start with the analysis of the analogous oligopoly model. The aim of Chapter 8 is to analyze current status of the question about how to conduct causality inference from realizations of stochastic dynamical processes and to put forward a new test for non-causality based on symbolic dynamics.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 37

SIMULATED ANNEALING: IN MATHEMATICAL GLOBAL OPTIMIZATION COMPUTATION, HYBRID WITH LOCAL OR GLOBAL SEARCH, AND PRACTICAL APPLICATIONS IN CRYSTALLOGRAPHY AND MOLECULAR MODELLING OF PRION AMYLOID FIBRILS #

Jiapu Zhang* School of Science, Informatics Technology, Engineering and Centre of Informatics and Applied Optimisation, The University of Ballarat, MT Helen Campus, Victoria, Australia

RESEARCH SUMMARY Simulated annealing (SA) was inspired from annealing in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects, both are attributes of the material that depend on its thermodynamic free energy. In this Chapter, firstly we will study SA in details on its initial feasible solution choosing, initial temperature selecting, neighbourhood solution searching, efficient way of calculating for the difference of objective function values of two neighbourhood solutions, acceptance function (Metropolis function), temperature cooling, and the criteria of inner and outer loops’ stopping, etc. Then, hybrid pure SA with local (or global) search optimization methods allows us to be able to design several effective and efficient global search optimization methods. In order to keep the original sense of SA, we clarify our understandings of SA in crystallography and molecular modelling field through the studies of prion amyloid fibrils. #

This chapter was previously published in Simulated Annealing: Strategies, Potential Uses and Advantages, edited by Marcos de Sales Guerra Tsuzuki and Thiago de Castro Martins, New York: Nova Publishers Inc., 2014. * Tel: 61-423487360; 61-353276335, Email: [email protected], [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 38

HANDLING EQUALITY AND INEQUALITY LINEAR CONSTRAINTS IN SIMULATED ANNEALING #

Danilo R. Velis* Universidad Nacional de La Plata, Facultad de Ciencias Astronómicas y Geofísicas, Argentina; and CONICET, Argentina

RESEARCH SUMMARY Simulated annealing (SA) has become an algorithm of choice when dealing with nonlinear global optimization problems, specially when the objective function is ill-behaved or multimodal, and when derivative in- formation is not available or difficult to evaluate. In general, most SA algorithms are devised for unconstrained optimization, though the use of lower and upper bounds to delimit the feasible region is a common practice. When additional constraints such as equality or inequality constraints are to be taken into account, the development of appropriate strategies to force the solution to satisfy those constraints is critical. In this sense, and for the sake of efficiency, the exploration of the model space to evaluate new and unknown areas within the feasibly region is a key issue that requires further investigation. This work presents a simple strategy for handling arbitrary linear constraints in SA or other ``random search'' optimization technique. Both equality and inequality linear constraints are taken into account. In the case of inequality constraints, the optimization problem is reformulated as an unconstrained optimization one with dynamically adapted bounding constraints, which are easily implemented in SA algorithms. In the case of equality constraints, the optimization problem is also transformed into an unconstrained optimization problem with bounding constraints, but, instead, the original unknowns are expressed in terms of a new set of variables through the singular value decomposition (SVD) of the constraint matrix. The key of the proposed technique lies in the fact that, once an initial point within the feasible region is provided, new points are generated by adding random perturbations that lie #

This chapter was previously published in Simulated Annealing: Strategies, Potential Uses and Advantages, edited by Marcos de Sales Guerra Tsuzuki and Thiago de Castro Martins, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

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Danilo R. Velis

in the null space at each annealing iteration. Hence, feasibility is maintained at every stage of the SA search process, avoiding unnecessary evaluations of the objective function due to constraints violations. Further, the proposed technique is general and easy to use, requiring neither modifications nor any parameter tuning to work in different problems, making it an interesting alternative to other constraint- handling techniques available in the literature. The strategy is illustrated using SA to minimize testing functions that contain both bounding and equality or inequality linear constraints, including the classical loaded die problem.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 39

AIRCRAFT DESIGN WITH SIMULATED ANNEALING FOR SAE AERODESIGN COMPETITION #

Diego Movio Borburema, Marcos de Sales Guerra Tsuzuki, Antonio Luis de Campos Mariani, Andre Kubagawa Sato and Thiago de Castro Martins* Computational Geometry Laboratory, Escola Politécnica da Universidade de São Paulo, São Paulo, SP, Brazil

RESEARCH SUMMARY The SAE Aero-Design competition aims to reward the aircraft with the best design and with the best performance. The performance is measured as the ratio between the lifted weight and the aircraft weight. This competition has grown in the last few years, as well the teams' competitiveness; they are getting very close to reaching the perfect aircraft configuration. This research aims at determining an efficient methodology to get a competitive aircraft design and performance. Simulated annealing is applied as an optimization algorithm to determine such aircraft design. It is shown that the aircraft design can be represented by a parametric model. Before evaluating the aircraft design performance, it is necessary to check if the aircraft design obeys the competition constraints. If the constraints are not obeyed the aircraft design is invalid. Several parametric schemes can be used to represent the aircraft design. However, a key point is defining one parameter scheme in which few parametric models are invalid. Thus way, the domain search by the simulated annealing is more effective. An effective parametric scheme is proposed here and a simulated annealing with crystallization heuristic is used to determine an optimal aircraft design. Several results are shown and compared with other parametric schemes as well with Genetic Algorithm. #

This chapter was previously published in Simulated Annealing: Strategies, Potential Uses and Advantages, edited by Marcos de Sales Guerra Tsuzuki and Thiago de Castro Martins, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected], [email protected], [email protected], [email protected], [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 40

SIMULATED ANNEALING APPLIED TO THE RESOLUTION OF PHYLOGENETIC RECONSTRUCTION WITH MAXIMUM PARSIMONY

#

Jean-Michel Richer, Karla E. Vazquez-Ortiz and David Lesaint* LERIA, Université d'Angers, France

RESEARCH SUMMARY In Bioinformatics, the Maximum Parsimony (MP) problem aims at reconstructing a phylogenetic tree from DNA sequences while minimizing the total number of genetic transformations. Different metaheuristics have been applied to solve this problem like tabu search, genetic and memetic algorithms. In this paper we propose a carefully devised simulated annealing implementation called SAMPARS (Simulated Annealing for Maximum PARSimony). Different possibilities for the key components (initial temperature, cooling schedule, improved neighborhood function), and input parameter values of SAMPARS were carefully analyzed and tuned. Its performance is investigated through extensive experimentation over well known benchmark instances showing that our algorithm is able to improve some previous best-known solutions.

#

This chapter was previously published in Simulated Annealing: Strategies, Potential Uses and Advantages, edited by Marcos de Sales Guerra Tsuzuki and Thiago de Castro Martins, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected], [email protected], [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 41

IMPROVED PARALLEL SIMULATED ANNEALING APPLIED TO SPACECRAFT TRAJECTORY OPTIMIZATION #

Ya-Zhong Luo* and Guo-Jin Tang† College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, China

RESEARCH SUMMARY Combining the advantages of simulated annealing (SA) with that of the simplex method, a new kind of parallel simulated annealing using the simplex method (PSASM) is proposed. PSASM is first compared with other popular stochastic optimization algorithms through the solution of several mathematical example problems in which it obtains the best-known solutions for two benchmark nonlinear constrained optimization problems, and with the lowest computational cost. PSASM is then applied to two representative types of spacecraft trajectory optimization problems. The first is a low-thrust Earth-to-Mars orbit transfer problem. The optimization results show that PSASM is superior to sequential SA, genetic algorithms, and the classical optimization algorithms. The second problem is the impulsive rendezvous trajectory optimization. A new optimization approach combining primer vector theory with PSASM for a fuel-optimal non-linear impulsive rendezvous is proposed. PSASM is demonstrated to be able to guarantee solutions that satisfy Lawden’s necessary optimality conditions. These two applications show that PSASM is a successful global optimizer for spacecraft trajectory optimization design.

#

This chapter was previously published in Simulated Annealing: Strategies, Potential Uses and Advantages, edited by Marcos de Sales Guerra Tsuzuki and Thiago de Castro Martins, New York: Nova Publishers Inc., 2014. * Professor, [email protected] † Professor, [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 42

SIMULATED ANNEALING APPLICATIONS IN THERMODYNAMIC CALCULATIONS #

Ahmed O. Elnabawy1, Seif-Eddeen K. Fateen1 and Adrian Bonilla-Petriciolet2 1

2

Cairo University, Department of Chemical Engineering, Cairo, Egypt Instituto Tecnológico de Aguascalientes, Department of Chemical Engineering, Aguascalientes, México

RESEARCH SUMMARY Applied thermodynamic calculations are relevant for process design. These thermodynamic calculations include: phase equilibrium calculations, chemical equilibrium calculations, simultaneous phase and chemical equilibrium calculations, phase stability analysis, calculation of critical points, calculation of azeotropes, and parameter estimation of thermodynamic models, among others. These thermodynamic calculations can be solved as global optimization problems. In particular, Simulated Annealing (AS) has shown a promising performance in solving these thermodynamic problems. This manuscript overviews the application of AS and its variants, including hybrid method, in applied thermodynamic calculations for process design.

#

This chapter was previously published in Simulated Annealing: Strategies, Potential Uses and Advantages, edited by Marcos de Sales Guerra Tsuzuki and Thiago de Castro Martins, New York: Nova Publishers Inc., 2014.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 43

SA OPTIMIZATION OF TWO-CHAMBER MUFFLERS EQUIPPED WITH MULTIPLE PARALLEL PERFORATED TUBES WITHIN A CONSTRAINED SPACE #

Min-Chie Chiu Department of Mechanical and Automation Engineering, Chung Chou University of Science and Technology, Taiwan, R.O.C.

RESEARCH SUMMARY Recently, research on mufflers hybridized with a single perforated tube has been addressed; however, the research work on mufflers conjugated with multiple parallel perforated tubes which may disperse the venting fluid and reduce secondary flowing noise has been neglected. Therefore, the main purpose of this paper is not only to analyze the sound transmission loss (STL) of two-chamber mufflers equipped with multiple parallel perforated tubes but also to optimize the best design shape within a limited space. In this paper, the fourpole system matrix for evaluating acoustic performance ― sound transmission loss (STL) ― is derived by using a decoupled numerical method. Moreover, a simulated annealing (SA) method, a robust scheme used to search for the global optimum by imitating a physical annealing process, has been used during the optimization process. Before dealing with a broadband noise, the STL’s maximization with respect to a one-tone noise (300Hz) is introduced for a reliability check on the SA method. Additionally, an accuracy check of the mathematical model is performed. To appreciate the acoustical ability of two-chamber mufflers equipped with multiple parallel perforated tubes, three kinds of two-chamber mufflers hybridized with one, two, and four perforated tubes have been assessed and # 

This chapter was previously published in Simulated Annealing: Strategies, Potential Uses and Advantages, edited by Marcos de Sales Guerra Tsuzuki and Thiago de Castro Martins, New York: Nova Publishers Inc., 2014. Corresponding author: Min-Chie Chiu. E-mail: [email protected]. Mailing address: Department of Mechanical and Automation Engineering, Chung Chou University of Science and Technology, 6, Lane 2, Sec.3, Shanchiao Rd., Yuanlin, Changhua 51003, Taiwan, R.O.C.

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compared. Results reveal that the maximal STL is precisely located at the desired tone. In addition, the acoustical performance of two-chamber mufflers conjugated with more perforated tubes will decrease due to the decrement of the acoustical function for acoustical elements (II) and (III). Consequently, to design a more efficient muffler, the maximum (allowable) flowing velocity within the muffler must be determined in advance before choosing the appropriate number of perforated tubes and performing the muffler’s shape optimization.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 44

A SIMULATED ANNEALING ALGORITHM TO SOLVE THE LOG-TRUCK SCHEDULING PROBLEM #

Mauricio Acuna1* and John Sessions2 1

AFORA, University of the Sunshine Coast, Hobart, TAS, Australia 2 Department of Forest Engineering, Resources and Management, Oregon State University, Corvallis, OR, US

RESEARCH SUMMARY In this paper, we present a simulated annealing (SA) approach for solving the log-truck scheduling problem, which is an extension of the timber transport vehicle routing problem with time windows (TTVRPTW). The problem is characterized by a heterogeneous fleet of trucks that depart from their corresponding depots and must perform a number of daily transport tasks to move log products between wood pickup (harvest areas) locations and industrial customers, such as pulpmills and sawmills. Commencing at their depots, each truck must perform a number of successive transport tasks, each one characterized by a trip between a designated harvest area and an industrial customer, until the number of daily working hours is completed. The objective of the model is to minimize total empty travel time for the whole fleet as well as waiting times at wood pickup locations. In addition, time windows and accessibility to harvest areas and customers, must be taken into account. Our solution approach consists of three main steps: determination of a cooling scheme, search for a random feasible initial solution, and application of the simulation annealing procedure with a random neighborhood that features various types of moves, including single and multiple insertions and swaps between trucks. The efficiency of the heuristics was evaluated and validated with real-life data for two problem instances, each consisting of 30 transport tasks and a fleet of 10 trucks. Considering all the scenarios evaluated, our best SA solutions

#

This chapter was previously published in Simulated Annealing: Strategies, Potential Uses and Advantages, edited by Marcos de Sales Guerra Tsuzuki and Thiago de Castro Martins, New York: Nova Publishers Inc., 2014. * Corresponding author: Tel.: +61-03-62375622; fax: +61-03-62267942 E-mail address: [email protected].

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resulted in maximum deviations of 3% in comparison with the optimal solutions obtained with commercial optimization solvers.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 45

POTENTIAL APPLICATIONS OF SIMULATED ANNEALING TO MULTI-SPECIES FISH HABITAT CONSERVATION IN THE GULF OF MAINE #

Rosamonde R. Cook1,* and Peter J. Auster1,2 1

Northeast Underwater Research, Technology & Education Center, University of Connecticut at Avery Point, Groton, CT, US 2 Sea Research Foundation - Mystic Aquarium, Mystic, CT, US

RESEARCH SUMMARY Simulated annealing has been used successfully in spatial land use planning and nature reserve system design in many parts of the world for more than a decade. While the methods are similar, the underlying data vary in kind and quality. In this chapter, we use standardized fisheries independent survey data from a long term monitoring program to demonstrate the effectiveness of simulated annealing for identifying efficient design scenarios for marine protected areas intended to satisfy the Essential Fish Habitat requirements of the U.S. Sustainable Fisheries Act for 15 economically valuable demersal fish species in the Gulf of Maine on the U.S. Eastern Continental Shelf. Results that ensure minimum total area requirements for conservation targets stated in terms of percent of total regional abundance of individual species from research trawl surveys achieve the goal of capturing those locations where most species occur at their highest region-wide abundances, and by inference, their highest quality habitats, under a range of spatial design scenarios. Significantly, these scenarios also represent the diversity of the wider demersal fish community and capture some of the highest local densities of many species not targeted in fishery operations, and would therefore help ensure the conservation of marine fish biodiversity overall. Using this approach #

This chapter was previously published in Simulated Annealing: Strategies, Potential Uses and Advantages, edited by Marcos de Sales Guerra Tsuzuki and Thiago de Castro Martins, New York: Nova Publishers Inc., 2014. * Corresponding author: Rosamonde Cook, Western Riverside County Biological Monitoring Program, 4500 Glenwood Drive Bldg. C, Riverside, California, 92501. Phone: 951-320-2168. Fax: 951-782-4847. Email: [email protected].

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can aid in developing options to solve a range of important and controversial management issues, described in this chapter. We conclude that simulated annealing is a valuable and vital tool for marine fisheries management on the Eastern Continental Shelf of the U.S., and likely in other parts of the world where systematic time series survey data exist.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 46

SECOND-ORDER PERTURBATIONS IN ENCKE’S METHOD FOR SPACECRAFT FLYBYS #

L. Acedo* Instituto Universitario de Matemática Multidisciplinar, Universitat Politécnica de Valéncia, Valencia, Spain

RESEARCH SUMMARY In this work we consider a generalization of traditional Encke’s method for the computation of perturbed orbits by including second order effects arising by the interaction of the main body with the first order perturbed orbit of a spacecraft in hyperbolic orbit.

#

This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 47

COMMON-RAIL DIESEL INJECTORS BOND GRAPH MODELLING THROUGH THE AMESIM PLATFORM

#

F. J. Salvador1*, M. Carreres1, J. V. Romero2 and M. D. Roselló2 1

CMT-Motores Térmicos, Universitat Politècnica de València, Spain 2 Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Spain

RESEARCH SUMMARY A methodology to mathematically model a common-rail injection system by using a Bond Graph approach is described in the present chapter. All the physical components of a last generation injector have been graphically represented by block diagrams whose union makes it possible to exchange information between them when the associated equations are solved. The implementation of the model has been carried out through the AMESim commercial software, which contains several libraries that make it possible to easily establish the causality relations between elements. Modelled elements include mechanical components (such as masses, springs, dampers, pistons, etc.) and hydraulic lines and orifices. In this chapter, special attention is given to the equations that represent the physics behind these elements and how they interact with each other. On the other hand, each of these elements requires a complete characterization in order to obtain the relevant parameters that need to be included as the coefficients of the equations. An extensive validation against mass flow rate experimental data is finally performed in order to ensure the model capabilities.

#

This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected], Address: CMT-Motores Térmicos, Universitat Politècnica de València, Camino de Vera s/n, E-46022 Spain, Tel: +34-963879659, Fax: +34-963877659 (Corresponding author)

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 48

MATHEMATICAL MODELLING OF FILTRATION AND CATALYTIC OXIDATION OF DIESEL PARTICULATES IN FILTER POROUS MEDIA #

N. V. Vernikovskaya1,2,3,*, T. L. Pavlova1, N. A. Chumakova1,2 and A. S. Noskov1,3 1

Boreskov Institute of Catalysis SB RAS, Novosibirsk, Russia 2 Novosibirsk State University, Novosibirsk, Russia 3 Novosibirsk State Technical University, Novosibirsk, Russia

RESEARCH SUMMARY The soot abatement in diesel exhaust is a very important task in particular because fine soot particles inhaled by humans do serious damage to their health. The mathematical modelling of soot filtration and catalytic oxidation in diesel particulate filters can help in finding more promising filter design, filter porous materials, running regime, and so on. The used mathematical model consists of nonlinear partial and ordinary differential equations. The nonlinearities can cause rather steep non-stationary profiles of concentrations and temperature which propagate (rather slowly move) along the filter. So the standard numerical schemes are not appropriate here. The new modelling methodology is proposed which is based on the three existing methods and takes advantages of each of them: the method of lines, the running scheme, and the second-order Rosenbrock method with stepsize adjustment algorithm. Verification of the mathematical model and numerical method is done by means of comparison of the numerical results with the experimental data. The mathematical modelling is realized with taking into account the mass transport of soot particles of each diameter from a log-normal particle size distribution. For estimating the

#

This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

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kinetic parameters the method of Errorsin-Variables Model with numerical integration is applied.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 49

WATER DEMAND SIMPLIFICATIONS USED TO BUILD MATHEMATICAL MODELS FOR HYDRAULIC SIMULATIONS #

J. Izquierdo*, E. Campbell, I. Montalvo, R. Pérez-García and D. Ayala-Cabrera Instituto Universitario de Matemática Multidisciplinar, I.M.M. Fluing, Universitat Politècnica de València, Valencia, Spain

RESEARCH SUMMARY Mathematical models that describe the complex behavior of water distribution systems are bound to use various simplifications. Simplified models are used systematically in management, monitoring, and understanding of water utilities, sometimes without any awareness of the implications of the assumptions used. One of the reasons for that complexity stems from the vast spatial distribution characteristic of water supply. Thus, some simplifications are derived from the different levels of granularity at which a network can be considered. This chapter addresses the specific question: to what extent can consumptions associated with a line be allocated to the ends of the line? We present examples of situations where certain simplifications produce models that are very unrealistic. Moreover, we develop guidelines that enable to establish whether some simplifications are acceptable or, on the contrary, produce information that differs substantially from reality. We also develop formulae easy to implement that enable to distribute inner line demand between the line ends with minimal error.

#

This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 50

DYNAMIC PREDICTION OF FAILURES: A COMPARISON OF METHODOLOGIES FOR A WIND TURBINE #

S. Carlos1*, A. Sanchez2, I. Marton1 and S. Martorell1 Departament d’Enginyeria Química i Nuclear, Universitat Politécnica de València, Valencia, Spain 2 Departament d’Estadística i Investigació Operativa Aplicades i Qualitat, Universitat Politécnica de València, Valencia, Spain 1

RESEARCH SUMMARY Nowadays, there is an increasing demand for Condition Based Maintenance (CBM) activities as time-directed maintenance is observed to be inefficient in many situations. CBM is a maintenance strategy based on collecting information concerning the working condition of equipment, such as vibration intensity, temperature, pressure, etc., related to the system degradation or status in order to prevent its failure and to determine the optimal maintenance. Prognosis is an important part of CBM. Different methodologies can be used to perform prognosis and can be classified as: model-based or data-driven. Data-driven methods make use of the available monitoring data to train a learning algorithm. Two kinds of data driven methods are Principal component analysis-Partial least Squares and Neural Networks. Mathematical models based on these two methodologies are constructed, and from data monitored for a wind turbine the failure of this kind of systems can be detected and predicted. A discussion of the strength and weakness of each one of the methodologies is presented.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 51

ADVANCES IN MATHEMATICAL MODELING OF SUPERCRITICAL EXTRACTION PROCESSES #

Florian Meyer1,*, Marko Stamenic2†,, Irena Zizovic2,‡ and Rudolf Eggers1,§ 1

Institute of Thermal Separation Processes, Heat and Mass Transfer, Hamburg University of Technology, Hamburg, Germany 2 Faculty of Technology and Metallurgy, University of Belgrade, Belgrade, Serbia

RESEARCH SUMMARY A new trend in mathematical modeling of supercritical extraction process from plant material is presented. The most of the previously published models considered properties of the fixed bed of plant material during the extraction to be constant. This assumption might be quite true in the case of plant materials with relatively low quantity of extractables. However, the fixed bed property change may occur in the case of extraction from material with high quantities of extractables. Recently, mathematical model which took into account particle density, bed porosity and particle diameter as variables was derived. In this chapter, the model is further improved by introducing variable solubility of the extract in supercritical fluid. On the basis of new experimental results on the binary equilibrium of the system supercritical fluid – extract present in solid, a relationship between solubility in supercritical fluid and oil content in solid was established. The new model was derived which took into account particle density, bed porosity, particle diameter and solubility in supercritical fluid as #

This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]. † E-mail address: [email protected]. ‡ E-mail address: [email protected] § E-mail address: [email protected].

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variables. The model was verified on results from experiments in which the kinetics of supercritical extraction from rapseed was analyzed. Parameters of the model showed expected behaviour with respect to the change of particle size. Further analysis, shown in this chapter, showed that, if the dependency of solubility from the concentration in the solid phase is not accounted for, the model tends to overestimate the yield of the extraction. The new model is so far, the most realistic model and one of the most demanding models regarding experimental work and mathematical tools for the description of mass transfer in fixed beds.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 52

PIPE DATABASE ANALYSIS TRANSDUCTION TO ASSESS THE SPATIAL VULNERABILITY TO BIOFILM DEVELOPMENT IN DRINKING WATER DISTRIBUTION SYSTEMS #

E. Ramos-Martínez1,*, J. A. Gutíerrez-Pérez1, M. Herrera2, J. Izquierdo1 and R. Pérez-García1 1

Instituto Universitario de Matemática Multidisciplinar I.M.M. Fluing, Universitat Politècnica de València, Valencia, Spain 2 BATir Department, Université libre de Bruxelles, Brussels, Belgium

RESEARCH SUMMARY Biofilm develops in drinking water distribution systems (DWDSs) as complex communities of microorganisms bound by a matrix of organic polymers and attached to pipe walls. Biofilm can lead to various undesirable problems such as deterioration of bacterial water quality, generation of bad tastes and odors, and biocorrosion, among others. Biofilm formation in DWDSs is dependent on a complex interaction of water quality, infrastructure, and operational factors. However, all these factors have not been studied to the same extent, those associated with the design and operation of DWDS being the most forgotten. Several studies have shown the influence that various physical and hydraulic characteristics of DWDSs have on biofilm. However, due to the complexity of the community and the environment under study, their joint influence, apart from few exceptions, has been scarcely studied. To help bridge this gap an agent-based label propagation technique is applied to a previously obtained database to detect in a given DWDS significant pre-relationships among the characteristics of the pipes related to design and operation, their location, and biofilm #

This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

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development. Besides, the edge betweenness algorithm, which is one of the standard measures of centrality and is able to quantify the importance of a pipe in a network, is implemented. This algorithm enable us to know, according to the design and operation of the DWDS (physical and hydraulic aspects), which are the hot spots of the network, where management efforts must be focused to reduce biofilm formation.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 53

ON KERNEL SPECTRAL CLUSTERING FOR IDENTIFYING AREAS OF BIOFILM DEVELOPMENT IN WATER DISTRIBUTION SYSTEMS #

M. Herrera1,*, E. Ramos-Martínez2, J. A. Gutíerrez-Pérez2, J. Izquierdo2 and R. Pérez-García2 1

Brussels School of Engineering, Université libre de Bruxelles, Belgium 2 Instituto Universitario de Matemática Multidisciplinar, Fluing-IMM, Universitat Politècnica de València, Spain

RESEARCH SUMMARY Nowadays biofilm develops in all drinking water distribution systems (DWDSs) and leads to various undesirable problems, representing a paradigm in management of these systems. Biofilm formation is dependent on a complex interaction of various factors, those associated with the DWDSs infrastructure being the most flexible and adaptable to minimize biofilm development in the inner pipe walls. One of the main objectives in the quality control of DWDSs is the analysis of biofilm development in the network, discovering areas more prone to it. This chapter proposes spectral clustering to achieve these issues after a kernel abstraction of the available data. The theoretical approach is enriched by both: an entropy based ranking to select the eigenvectors to work with, and a full tuning process that automatizes the proposal. Finally, a real case-study is introduced to check the performance of this division of the network. The results are promising, showing the relative trend to biofilm development for each sector. Using this information, managers can carry out, if necessary, changes in the DWDS infrastructure to minimize biofilm development and perform biofilm control policies more efficiently. #

This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 54

UNSUPERVISED METHODOLOGY FOR SECTORIZATION OF TRUNK DEPENDING WATER SUPPLY NETWORKS #

E. Campbell*, R. Pérez-García, J. Izquierdo and D. Ayala-Cabrera Instituto Universitario de Matemática Multidisciplinar, I.M.M. Fluing, Universitat Politècnica de València, Valencia, Spain

RESEARCH SUMMARY The increasing pressure over water resources has raised the need to establish procedures to efficiently control water losses in water supply networks (WSN). An example of such procedures is the segmentation of the networks (also known as sectorization), either by installing valves (closed) or by sectioning pipes. WSN division into sectors implies an improvement of active leakage control by comparing the metered demand (domestic and industrial) vs. the flow inlet in each sector. It also allows water companies to have better control over pressure, consumption and water quality, due to an implicit areal reduction. In most cases, sectorization projects are carried out using empirical criteria, following trial and error techniques. This work presents a novel combination of hydraulic, social, and economic aspects of WSNs, in order to establish sectorization layouts in WSNs with a reduced number of water sources. The methodology uses machine learning-based techniques. Through hierarchical clustering, an initial exploration of the natural clusters in the WSN is conducted. Then, by means of spectral clustering, the WSN is subdivided considering two aspects: the importance of the different partitioning criteria and the minimization of the number of pipes that should be closed. The connection points of the clusters in the distribution network to the trunk are established through an energy analysis aimed to minimize the pressure drop after #

This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

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sectorization. The methodology entails several advantages over other sectorization methodologies. First, it is one of the few that may be applied to WSNs depending on a trunk. Also, the procedure only considers the distribution networks, which offer two important advantages. One advantage is that it translates to a reduction of implementation costs as the closing valves are allocated in low diameter lines; additionally, the resulting active leakages control can be performed more effectively as the sectors are centered in the zones with highest incidence of sectorization, power, supply, leaks, networks, clustering

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 55

QUANTIFYING THE BEHAVIOR OF THE ACTORS IN THE SPREAD OF ANDROID MALWARE INFECTION #

J. Alegre1,*, J. C. Cortés1, F. J. Santonja2 and R. J. Villanueva1 1

Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain 2 Departamento de Estadística e Investigación Operativa, Universitat de València, Burjassot, Valencia, Spain

RESEARCH SUMMARY The ubiquity of smart-phones for personal and business use has increased the spread of mobile malware caused by malware applications that the user downloads to the smart-phone. In this chapter, we analyze the actors involved in the Android malware infection, markets, users and Apps, quantifying the number and type of Apps in each market where a user may download Apps and the behavior of the users when downloading. This quantification will be focused in the Community of Valencia, Spain.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 56

A STOCHASTIC AGENT-BASED APPROACH TO INTERREGIONAL MIGRATION IN QUANTITATIVE SOCIODYNAMICS #

Minoru Tabata1,*, Nobuoki Eshima2, Keiko Kanenoo1 and Ichiro Takagi3 1

Department of Mathematical Sciences, Osaka Prefecture University, Sakai, Osaka, Japan 2 Department of Statistics, Oita University, Oita, Japan 3 Department of Business Management, School of Business Studies, Tokai University, Kumamoto, Japan

RESEARCH SUMMARY In order to describe interregional migration we construct an agent-based model whose agents relocate stochastically to obtain higher utility in a bounded discrete domain. By making use of numerical solutions of the discrete master equation, we will describe the behavior of the agent-based model in order to study how the concentration of agents changes with the cost incurred in moving.

#

This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected], Fax: +81 72 254 9916.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 57

A BAYESIAN MATHEMATICAL MODEL TO ANALYSE RELIGIOUS BEHAVIOR IN SPAIN #

R. Cervelló-Royo1,*, A. Sánchez-Sánchez2,†, F. Guerrero3,‡, F. J. Santonja4,§ and R. J. Villanueva2,¶ 1

Departamento de Economía y Ciencias Sociales. Universitat Politècnica de València, Spain 2 Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Spain 3 Departament de Matemática Aplicada, Universitat de València, Spain 4 Departament d’Estadística i Investigació Operativa, Universitat de València, Spain

RESEARCH SUMMARY In order to study religious behaviors in Spain, two conceptions are studied by a mathematical modelling approach: (a) the religious ideas are transmitted (by social contacts) versus (b) the agent transmitted are the non-believers ideas. A mathematical model based on ordinary differential equations is presented to understand it. Approximate Bayesian Computation scheme (ABC scheme) for parameters estimation and model selection is used. Prediction of the evolution of Catholics, non-believers and believers of other religions are presented for the next few years.

#

This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected] § E-mail address: [email protected] ¶ E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 58

MODEL OF PROBLEMS CLEANING IN EDUCATION

#

Jan M. Myszewski, Malgorzata Gromek, and Joanna Oczkowicz Department of Quality Management, Kozminski University, Warsaw, Poland

RESEARCH SUMMARY An educational system of secondary schools is considered. Focus is given to two processes: educational process, which involves students and a teacher in lesson; improvement of the educational process, which involves teachers and administration of the school. It is shown that both can be represented as special cases of a process of eliminating multiple problems, referred to as „problems cleaning”. Consequently, the effectiveness of the processes depends on characteristics: of amount and quality of resources used in the process as well as those of control of the resources. Considerations are illustrated by a case study of improvement initiated by the evaluation procedure in a school. It demonstrates: the relationship of model parameters with characteristics of the educational system and that change of the characteristics depends on the very involvement of the administration in the improvement processes.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014.  E-mail address: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 59

DOES VAT GROWTH IMPACT COMPULSIVE SHOPPING IN SPAIN? #

E. de la Poza1*, I. García2†, L. Jódar3‡ and P. Merello3§ 1

Departamento de Economía y Ciencias Sociales, Universitat Politècnica de València, Spain 2 Departamento de Comunicación Audiovisual y Publicidad, Universidad del País Vasco, Spain 3 Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Spain

RESEARCH SUMMARY Compulsive buying is a mental disorder based on gratifying dissatisfaction through excessive and unplanned purchase behaviours. Thus, a priori, the number of compulsive buyers should be influenced by those factors that enhance or reduce their compulsive behaviour. This chapter uses a dynamic approach by difference equations to model the influence of two events of opposite nature on compulsive shopping in Spain; on one hand the influence of VAT growth and, on the other, the stress the Spaniards suffer as consequence of the bad economic perspectives. The parameters associated with the event will be estimated using the algorithm of Nelder -Mead. The results show that the 41.85 % of the rational buyers with emotional distress but with good economic expectations increase their level of compulsion becoming excessive buyers. The influence of VAT (decrease of the percentage of addicts) was lower than expected since compulsive buying does not respond to rational behaviour. #

This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected] § E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 60

IS FITNESS ACTIVITY AN EMERGENT BUSINESS? ECONOMIC INFLUENCES AND CONSEQUENCES OF MALE FITNESS PRACTICE #

M. S. S. Alkasadi1, E. De la Poza2* and L. Jódar1 1

Instituto Universitario de Matemática Multidisciplinar, Universitat Politécnica de Valéncia, Valencia, Spain 2 Facultad de Administración y Dirección de Empresas, Universitat Politécnica de Valéncia, Valencia, Spain

RESEARCH SUMMARY Males under forty years old increase their gym practice to improve their self-esteem and sexual appeal through their body image. In this chapter we develop a discrete mathematical model to forecast the future loyal fitness customer rate in Spain over the next years. For this purpose, economic, emotional and social contagion variables are taken into account in order to quantify the dynamic behavior of men gym users. Economic consequences of gym customers’ behavior are studied and also future possibilities of business are suggested. Also, the model can be exported without additional effort to other countries where data is available.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]; Tel: +34963877032; Fax: +34963877032

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 61

POPULAR SUPPORT TO TERRORIST ORGANIZATIONS: A SHORT-TERM PREDICTION BASED ON A DYNAMIC MODEL APPLIED TO A REAL CASE# Matthias Ehrhardt1*, Miguel Peco†2, Ana C. Tarazona3‡, Rafael J. Villanueva3§ and Javier Villanueva-Oller4¶ 1

Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Fachbereich C – Mathematik und Naturwissenschaften, Bergische Universität Wuppertal,Wuppertal, Germany 2 PhD in International Security. Independent Researcher. 3 Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Spain 4 Centro de Estudios Superiores Felipe II, Aranjuez, Spain

RESEARCH SUMMARY In this chapter, we apply the Castillo-Chavez and Song’s model to the Basque Country citizens’ attitude towards the terrorist organization ETA (Basque Fatherland and Liberty) after that organization declared the cease of its violent activity, in 2011±. Of course, what we #

This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected] § E-mail address: [email protected] ¶ [email protected] ± ETA communiqué on 08/01/2011. Video clip issued in GARA. Retrieved from: http://www.gara.net/ bideoak/110108 video/. A transcription (in Spanish) is available at: http://www.elpais.com/elpaismedia/ ultimahora/media/201101/10/espana/ 20110110elpepunac 1 Pes PDF.pdf.

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apply here is the version of the model related to people supporting the organization and not to the version related to people belonging to it. Our objective is to analyze any short term dynamics appearing after that event. To do so, we take data from the Euskobarometro survey [Available at http://www.ehu.es/euskobarometro/], one of the best-known independent opinion polls in the region, as well as demographic index. Then, according to those data, we divide the population into the sub populations appearing in the Castillo-Chavez and Song’s model, and we fit the model parameters by least square techniques. After that, we are able to predict in the short term the quantitative evolution of the full-supporting population, which in turn might constitute in our opinion an estimation of the bulk of people able to become new ETA members in upcoming years. This chapter is organized as follows. In Section 2, we retrieve and prepare the necessary data from Euskobarometro. In Section 3, we recall the Castillo-Chavez and Song’s model, scale it in order to adapt to the data magnitudes and assign values to the demographic parameters. In Section 4 we fit the model with the data and predict the evolution of the sub populations over the next few years. Finally, Section 5 is devoted to conclusions.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 62

MATHEMATICAL MODELLING OF THE CONSUMPTION OF HIGH-INVASIVE PLASTIC SURGERY: ECONOMIC INFLUENCES AND CONSEQUENCES #

M. S. S. Alkasadi1, E. De la Poza2* and L. Jódar1 1Instituto Universitario de Matemática Multidisciplinar, Universitat Politécnica de Valéncia, Valencia, Spain 2 Facultad de Administración y Dirección de Empresas, Universitat Politécnica de Valéncia, Valencia, Spain

RESEARCH SUMMARY Plastic surgery among women grows continuously in Western countries due to body image dissatisfaction, the aging anxiety and ideal body image propagated by media. The consumption growth is so important that the plastic surgery is becoming a normal practice among women, like other cosmetic products, with the risk of suffering psychopathology disorders in the sense that plastic surgery could be regarded as an instrument to recover personal self-esteem, or even happiness. In this chapter we develop a mathematical model to forecast the High-Invasive Plastic Surgery (HIPS) consumption in Spain. We simulate possible economic scenarios. Our results show an increasing trend of occasional and regular women HIPS consumers independently of the economic situation.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]; Tel:+34963877032; Fax: +34963877032 (Corresponding author)

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 63

AN OPTIMAL SCHEME FOR SOLVING THE NONLINEAR GLOBAL POSITIONING SYSTEM PROBLEM #

Manuel Abad*, Alicia Cordero† and Juan R. Torregrosa‡ Instituto de Mathemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain

RESEARCH SUMMARY A new eighth-order family of iterative method for solving the nonlinear system obtained in the Global Positioning System problem is presented. We extend the seventh-order scheme for solving nonlinear equations, designed by Soleymani1, to nonlinear systems improving its order of convergence. To generate our class of methods we use the weight functions procedure, with matricial functions. Numerical comparisons are made to confirm the theoretical results.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected] 1 Soleymani, F.; Mousavi, B.S. On Novel Classes of Iterative Methods for Solving Non-linear Equations, Computational Mathematics and Mathematical Physics 2012, 52, 203-210.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 64

HOW TO MAKE A COMPARISON MATRIX IN AHP WITHOUT ALL THE FACTS #

J. Benítez*, L. Carrión, J. Izquierdo and R. Pérez-García Instituto Universitario de Matemática Multidisciplinar I. M. M. Fluing Universitat Politècnica de València, Valencia, Spain

RESEARCH SUMMARY AHP (analytic hierarchy process) is a leading multi-attribute decision-aiding model designed to help make better choices when faced with complex decisions. AHP is a multiple criteria decision analysis that uses hierarchical structured pairwise comparisons. One of the drawbacks of AHP is that a pairwise comparison cannot be completed by an actor or stakeholder not fully familiar with all the aspects of the problem. Here, we characterize when an incomplete, positive, and reciprocal matrix can be completed to become a consistent matrix. We show that this characterization reduces the problem to the solution of a linear system of equations. Some properties of such a completion are also developed using graph theory, including explicit calculation formulas. In real decision-making processes, facilitators conducting the study could use these characterizations to accept an incomplete comparison body given by an actor or to encourage the actor to further develop the comparison for the sake of consistency.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 65

ON OPTIMAL GAUSSIAN PRELIMINARY ORBIT DETERMINATION BY USING A GENERALIZED CLASS OF ITERATIVE METHODS #

Alicia Cordero*, Juan R. Torregrosa† and María P. Vassileva‡ Instituto de Matemáticas Multidisciplinar, Universitat Politècnica de València, Valencia, Spain Instituto Tecnológico de Santo Domingo (INTEC), Santo Domingo, República Dominicana

RESEARCH SUMMARY A class of optimal methods for solving nonlinear equations is extended up to sixteenthorder of convergence. Some numerical test are made to solve the orbit determination problem of artificial satellites in order to confirm the theoretical results and to compare the new methods with other known ones.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 66

SOLVING ENGINEERING MODELS WHICH USE MATRIX HYPERBOLIC SINE AND COSINE FUNCTIONS #

Emilio Defez1, Jorge Sastre2, Javier J. Ibáñez3 and Jesús Peinado3* 1

2

Instituto Universitario de Matemática Multidisciplinar, Instituto de Telecomunicaciones y Aplicaciones Multimedia, 3 Instituto de Instrumentación para Imagen Molecular, Universitat Politècnica de València, Valencia, Spain

RESEARCH SUMMARY Matrix functions have multiple applications in different areas of applied mathematics. Methods to calculate the matrix exponential and the sine and cosine matrix functions in terms of orthogonal matrix polynomials are introduced recently. In this chapter a method for computing hyperbolic matrix cosine and sine, based on Hermite matrix polynomial series expansions, is presented. This approach allows us to approximate both functions simultaneously. An error bound analysis is given. Based on the ideas above, an efficient and highly-accurate Hermite algorithm is presented. A MATLAB implementation of this algorithm has also been developed. This implementation has been compared with MATLAB function funm on a large class of matrices for different dimensions, obtaining higher accuracy and lower computational costs in the majority of cases.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected], [email protected], {jjibanez, jpeinado }@dsic.upv.es

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 67

RSV MODELING USING GENETIC ALGORITHMS IN A DISTRIBUTED COMPUTING ENVIRONMENT BASED ON CLOUD FILE SHARING #

J. Gabriel García Caro1*, Javier Villanueva-Oller2† and J. Ignacio Hidalgo1‡ 1

2

Universidad Complutense de Madrid, Madrid, Spain, CES Felipe II, Universidad Complutense de Madrid, Madrid, Spain

RESEARCH SUMMARY Usually, when dealing with random network models, we find that the search for the best parameters is a difficult computing task. This is because, the usual way of tackling this problem is through an exhaustive evaluation of all solutions. This finding leads to an optimization of this process to reduce the cost in time and resources needed. In this chapter it is presented an alternative which combines evolutionary algorithms, distributed computation and cloud storage which has allowed us to work with elements created independently (computation system, networks model and genetic generator) and for different platforms without any additional modification.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 68

MULTI-AGENT AND CLUSTERING IN DATA ANALYSIS OF GPR IMAGES #

D. Ayala-Cabrera*, E. P. Carreño-Alvarado, S. J. Ocaña-Levario, J. Izquierdo and R. Pérez-García Instituto Universitario de Matemática Multidisciplinar, I.M.M. Fluing, Universitat Politècnica de València, Valencia, Spain

RESEARCH SUMMARY A combination of the multi-agent paradigm and a very well-known clustering technique is used for unsupervised classification of subsoil characteristics working on a collection of ground penetrating radar (GPR) survey files. The main objective is to assess the feasibility of extracting features and patterns from radargrams. By optimizing both the field work and the interpretation of the raw images, our target is to obtain visualizations that are automatic, fast, and reliable so to suitably assess the characteristics of the prospected areas and extract relevant information. The system also helps characterize subsoil properties in a very natural and fast way, favors GPR files interpretation by non-highly qualified personnel, and does not require any assumptions about subsoil parameters.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 69

SEMI-AUTOMATIC SEGMENTATION OF IVUS IMAGES FOR THE DIAGNOSIS OF CARDIAC ALLOGRAFT VASCULOPATHY #

Damián Ginestar1, José L. Hueso1*, Jaime Riera1 and Ignacio Sánchez Lázaro2 1

Instituto Universitario de Matemática Multidisciplinar Universitat Politècnica de València, Valencia, Spain 2 Hospital La Fe Universitari i Politècnic, Valencia, Spain

RESEARCH SUMMARY Cardiac allograft vasculopathy is the leading cause of death after the first year post-heart transplantation. It consists of a proliferation of the intima layer in the coronary arteries of the transplanted heart, which progressively diminishes the supply of oxygen to the heart. Allograft vasculopathy is difficult to be detected by a standard coronariography and only using an intravascular ultrasound (IVUS) image can be accurately diagnosed. IVUS is a medical imaging technique that produces cross-sectional images as a catheter is pulled-back inside blood vessels and it provides quantitative assessment of the wall, information about the nature of atherosclerotic lesions as well as the plaque shape and size. In this work, a supervised technique for the IVUS images segmentation is proposed. This method consists of two steps. First the media-adventitia contour of the coronary artery is obtained and the second step consists of detecting the lumen contour using a classifying tool. To test the performance of the method, some IVUS images have been segmented and the obtained results have been compared with the segmentation performed manually by an expert.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] (Corresponding author)

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 70

ANALYSIS AND DETECTION OF V-FORMATIONS AND CIRCULAR FORMATIONS IN A SET OF MOVING ENTITIES #

Francisco Javier Moreno Arboleda*, Jaime Alberto Guzmán Luna and Sebastián Alonso Gómez Arias† Universidad Nacional de Colombia, Bogota, Colombia

RESEARCH SUMMARY Diverse movement patterns are identifiable when a set of moving entities is studied. One of these patterns is known as a V-formation for it is shaped like the letter V. Informally, a set of entities presents a V-formation if the entities are located on one of their two characteristic lines. Another movement pattern is known as a circular formation for it is shaped like a circle. Informally, circular formations present a set of individuals grouped around a center in which the distance from these individuals to the center is less than a given threshold. In this chapter, we present a model to identify V-formations and circular formations with outliers. An outlier is an entity which is part of a formation but is distant from the formation. We present formal rules for our models and an algorithm for the detection of outliers. Our models were validated via NetLogo, a programming and modeling environment for the simulation of natural and social phenomena.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]. † E-mail address: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 71

ANALYSIS OF NOISE FOR THE SPARSE GIVENS METHOD IN CT MEDICAL IMAGE RECONSTRUCTION #

A. Iborra1*, M. J. Rodríguez-Álvarez2, A. Soriano2, F. Sánchez2, M. D. Roselló, P. Bellido2, P. Conde2, E. Crespo2, A. J. González2, L. Hernández2, F. Martos2, L. Moliner2, J. P. Rigla2, M. Seimetz2, L. F. Vidal2 and J. M. Benlloch2 1

Instituto de Matemática Multidisciplinar (IM2), Universitat Politècnica de València, Valencia, Spain 2 Instituto de Instrumentación para Imagen Molecular (I3M), Centro Mixto CSIC - Universitat Politècnica de València - CIEMAT, Valencia, Spain

RESEARCH SUMMARY The analytical methods like Filtered Back-projection (FBP) have dominated the image reconstruction in Computed Tomography (CT) because they generate images of a reasonable quality with low cost in terms of computing time. Considering that image reconstruction in CT can be modelled by a large sparse linear system of equations such as Ax = b, direct methods like QR decomposition might also be suitable but they are not commonly used because such kind of methods present various drawbacks with a great difficulty in resolution. The reconstruction of high resolution images requires very large systems of equations and a large amount of computer memory. But these methods let us speed up image reconstruction because heavy computational cost operations are precalculated once and each image reconstruction only involves a backward substitution process. #

This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

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The previous mentioned model has to take into account the geometry of the scanner and the physical processes involved on the measurement. In order to reduce computational costs x-ray scattering is often disregarded and monoenergetic x-ray assumption is made. The numerical stability depends on the method used to solve the system. Unavoidable errors as finite precision arithmetic errors and electronic noise occur. The accumulation of these effects often renders Ax = b a system of equations with no exact solutions. QR decomposition is a good choice to solve this kind of systems of equations because its solution is equivalent to the least squares solution. In this chapter we analyze the noise in the reconstructed image x, as we increase the error assumed in the linear system. Noise analysis is made for simulated and real data from Albira μCT. The results obtained with both the simulated and real data show that the ratio between the number of pixels in the detector and the desired image resolution is the main factor related to the error in the reconstructed images, so the number of projections (radiation dose received by the patient) can be lowered without loss of image quality.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 72

AGENT-BASED MODEL TO DETERMINE THE EVOLUTION OF THE SEROPROTECTION AGAINST MENINGOCOCAL C OVER THE NEXT YEARS #

L. Pérez-Breva1,*, R. J. Villanueva2,†, J. Villanueva-Oller3,‡, L. Acedo2,§, F. J. Santonja4,¶, J. A. Moraño2,ǁ, R. Abad5,±, J. A. Vázquez5,†† and J. Díez-Domingo1,‡‡ 1

Centro Superior de Investigación en Salud Pública Fundación para el Fomento de la Investigación Sanitaria y Biomédica de la Comunidad Valenciana (CSISP-FISABIO), Valencia, Spain 2 Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Spain 3 Centro de Estudios Superiores Felipe II, Aranjuez, Spain 4 Departamento de Estadística e Investigación Operativa, Universitat de València, Spain 5 Instituto de Salud Carlos III, Majadahonda, Madrid, Spain

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: perez [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected] § E-mail address: [email protected] ¶ [email protected] ǁ E-mail address: [email protected] ± E-mail address: [email protected] †† E-mail address: [email protected] ‡‡ E-mail address: diez [email protected]

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RESEARCH SUMMARY Neisseria meningitidis is a major cause of morbidity and mortality during childhood in industrialized countries and has been responsible for epidemics in Africa and in Asia. This bacterium is the main cause of meningitis type C (MenC), an infection of the brain and spinal cord that can even infect the blood. Neisseria meningitidis is transmitted exclusively among humans, mainly during adolescence, by healthy carriers. Men C, even properly treated with specific antibiotics, there is up to 10% of mortality and 10% of survivors have sequelae. From 2000 the Conjugate Vaccine C (MCC) is used in campaigns with different strategies in the Community of Valencia (Spain). In 2006 is fixed the current vaccination schedule with three doses: 2, 6 and 18 months of age. Recent studies on the MCC-vaccination have determined that levels of protection provided by this vaccine are lower than expected, in particular, in toddles. Doctors conjecture that, in 5 − 10 years, there will be an increase of cases in children younger than a year because the herd immunity provided among the adolescents by the current vaccination schedule will disappear. Because of this, health experts in UK and Spain have decided to change the current vaccination schedule removing a dose in infants and adding it in adolescence. In this work, we describe a seroprevalence study and present a dynamic agent-based model to analyse the evolution of the population protection given by the MCC vaccine in order to find out if the doctor’s conjecture is correct. The chapter is structured as follows. In Section 2, we describe the seroepidemiological study. In Section 3 we present the agent-based model. In Section 4, we present the prediction over the next few years and discuss the Doctor’s conjecture.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 73

APPLYING CLUSTERING BASED ON RULES FOR FINDING PATTERNS OF FUNCTIONAL DEPENDENCY IN SCHIZOPHRENIA #

Karina Gibert1* and Luis Salvador Carulla2 1

Knowledge Engineering and Machine Learning group Dpt. Statistics and Operations Research, Universitat Politècnica de Catalunya, Barcelona, Spain 2 PSICOST Research Association, Spain 3 Center for Disability Research and Policy, Faculty of Health Sciences University of Sydney, Australia

RESEARCH SUMMARY In 1996 Fayyad described the Knowledge Discovery process as an integral process including prior expert knowledge, preprocessing, data mining and knowledge production to produce understandable patterns from data. Clustering based on rules (ClBR) is a particular data mining method suitable for profiles discovery. ClBR is a hybrid AI and Statistics technique, which combines some Inductive Learning (from AI) with hierarchical clustering (from Statistics) to extract knowledge from complex domains in form of typical profiles. It has the particularity to embed the prior expert knowledge existent about the target domain in the clustering process itself, guaranteeing more comprehensible profiles. In this paper, the results of applying this technique to a sample of patients with mental disorders are presented and their advantages with regards to other more classical analysis approaches are discussed. The final step of knowledge production is supported by post–processing tools, like Class panel graphs (CPG) and Traffic Lights panels (TLP), which were appreciated by domain

#

This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

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experts as powerful, friendly and useful tools to transform raw clustering results into understandable patterns suitable for later decision-making. It was confirmed that functional impairment (FI) in schizophrenia and other severe mental disorders show a different pattern than FI in physical disability or in ageing population. Understanding the patterns of dependency in schizophrenia and getting criteria to recognize them is a key step to develop both eligibility criteria and services for functional dependency in this particular population. This research was related with the implantation of the Spanish Dependency Low, in Catalonia, acting from 2007.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 74

MODELING MATHEMATICAL FLOWGRAPH MODELS IN RECURRENT EVENTS: AN APPLICATION TO BLADDER CARCINOMA #

B. García-Mora*, C. Santamaría†, G. Rubio‡ and J. Camacho§ Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain

RESEARCH SUMMARY Mathematical Flowgraph models have proven to be very useful in providing an efficient approach for the analysis of time–to–event data. They essentially provide time-to-event distributions and also data for intermediate events to the final event of interest. This technique is able to model complex systems with large number of states. Solving a Flowgraph model we use a mixture of parametric distributions. An integral transform allows us to reduce a complicated problem to a much simpler one in algebraic equations. We apply this methodology to the evolution of bladder carcinoma in a three–state illness model of a recurrence–progression process. The probability of being free of progression at a given time is determined and applied to different risk groups of patients according to common characteristics.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected] § E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 75

NUMERICAL SOLUTION OF AMERICAN OPTION PRICING MODELS USING FRONT-FIXING METHOD

#

V. Egorova*, R. Company† and L. Jódar‡ Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain

RESEARCH SUMMARY This chapter deals with the numerical solution of the American option valuation problem formulated as a parabolic partial differential equation. The opportunity of early exercise for American options leads to a free boundary problem that has an additional difficulty derived by the moving computational domain. By using the front-fixing method the free boundary is involved to a transformed equation that results non-linear. An explicit finite difference scheme is proposed for the numerical solution. Numerical examples showing the conditional stability as well as comparison with other authors are included.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] (Corresponding author) † E-mail address: [email protected] ‡ E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 76

ESTIMATION OF THE COST OF ACADEMIC UNDERACHIEVEMENT IN HIGH SCHOOL IN SPAIN OVER THE NEXT FEW YEARS #

J. Camacho1*, R. Cervelló-Royo2†, J. M. Colmenar3‡ and A. Sánchez-Sánchez1§ 1

Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain 2 Departmento de Económicas y Ciencias Sociales, Universitat Politècnica de València, Valencia,Spain 3 Centro de Estudios Superiores Felipe II, Universidad Complutense de Madrid, Campus de Aranjuez, Madrid, Spain

RESEARCH SUMMARY High rates of academic underachievement have strong negative effects on the economic situation of families and the Spanish Government, mainly, in the current economic crisis which is affecting especially to Spain. We quantify the large costs that would entail for the Spanish society the high rates of academic underachievement in the Spanish Bachillerato in the coming years based on the predictions given with 95% confidence intervals in Cortés, J.C. et al¶. These predictions allow to provide an estimation of the investment could be made in #

This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected] § E-mail address: [email protected] ¶ Cortés, J.C. & Sánchez-Sánchez, A. & Santonja, F.J. & Villanueva, R.-J. (2013). Nonparametric probabilistic forecasting of academic performance in Spanish high school using an epidemiological modelling approach. Applied Mathematics and Computation, 221, 648-661.

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this educational level by both, the Spanish Government and families, paying special attention on the groups of students who abandon and do not promote. According to our estimations over the next few years, these amounts of money, on average, would have been ranging between 47,348,373.89 and 83,499,397.50 euros for both, the Spanish Government and families investment.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 77

A FINITE DIFFERENCE SCHEME FOR OPTIONS PRICING MODELED BY LÉVY PROCESSES #

R. Company*, M. Fakharany and L. Jódar Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain

RESEARCH SUMMARY In this chapter, we use a new discretization strategy to generate schemes for option pricing modeled by Lévy process of finite and infinite activity. The aim of this discretization is to improve the accuracy of the numerical solutions and guarantees that these solutions are nonnegative. We focus on two models; first Merton’s model (option price with finite jump activity) and the second is the CGMY model (option price with infinite activity). These models are governed by partial-integro differential equations. We apply an explicit discretization for the differential part and the trapezoidal rule for the integral part. To make these discretizations compatible, the double discretization has been used. The associated error for this technique has been calculated. Moreover, the numerical analysis such as stability and consistency have been studied.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 78

PORTFOLIO COMPOSITION TO REPLICATE STOCK MARKET INDEXES. APPLICATION TO THE SPANISH INDEX IBEX-35 #

J. C. Cortés1*, A. Debón2† and C. Moreno1‡ 1

Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain 2 Departamento de Estadística e Investigación Operativa Aplicadas y Calidad, Universitat Politècnica de València, Valencia, Spain

RESEARCH SUMMARY The main goal of this contribution is to provide a methodology to replicate the Spanish stock market index IBEX-35 using the assets of a few companies which perform this index. This will allow us to build up investment portfolios and predictions for this stock market index. The methodology is based in the application of different statistical techniques, namely, linear regression, the principal component analysis, simulation of random variables using Monte Carlo sampling, optimization and stochastic differential equations. In order to determine the weights of the replicating portfolio, a measure of the risk of investment portfolios, usually referred to as Tracking Error Variance, has been used. The period used to apply the proposed methodology is 2 011 and 2 012. After selecting the companies that make up the replicating portfolio, the Log-normal model and sampling Monte Carlo are applied to estimate the value of the shares of each one of these companies. In this way, we are able to estimate the value of the IBEX-35 during the first week of 2 013.

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This chapter was previously published in Mathematical Modeling in Social Sciences and Engineering, edited by Juan Carlos Cortés López, Lucas Antonio Jódar Sánchez and Rafael Jacinto Villanueva Micó, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 79

CURRENT RESEARCH TOPICS IN GALOIS GEOMETRY #

Leo Storme and Jan De Beule Ghent University, Ghent, Belgium

RESEARCH SUMMARY Galois geometry is in our mind a field of mathematics that deals with structures living in projective spaces over a finite field. This is a very rough description, but as with any field in mathematics, its borders and contents are not clearly defined. Several facts have influenced the list of topics that are covered by the chapters in this volume. A wide list of topics are fundamental in the sense that many results in Galois geometry rely on them, not only in the field itself, but also in the wider field of finite (incidence) geometry. We especially think of those structures living in a projective space that are used to build models of interesting (non-classical) incidence structures. Topics that are related to Galois geometry and the study of some of its substructures, but that can also be seen as research topics in algebra, have been included. This brings us to the list of related topics. Two fields play a special role: coding theory and cryptography. The reason, for us, that they play a special role, is that research in these fields does not only use results from Galois geometry, but is also inspiring and influencing research in Galois geometry. Therefore, the list of covered topics has a rather large intersection with these two fields, but we took care that the links with Galois geometry were always undoubtedly present. With these ideas in mind, we can survey the list of topics present in the different chapters. The first two chapters each discuss a variety of substructures in Galois geometry. They are specifically intended for readers wishing to obtain a broad overview of Galois geometry. In particular, Chapter 1 presents results on classical objects in the projective space PG(n,q), such as arcs, ovals, ovoids and unitals, and Chapter 2 presents results on substructures of classical polar spaces. Polar spaces are incidence structures described by different axioms than #

This chapter was previously published as a book: Current Research Topics in Galois Geometry, by Leo Storme and Jan De Beule, New York: Nova Publishers Inc., 2014.

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projective spaces, but the classical ones are represented completely by symplectic, quadratic and sesquilinear forms on a projective space, and as such, their study fits completely in the field of Galois geometry. Results on (partial) ovoids, (partial) spreads, covers and blocking sets are presented. The next two chapters discuss specific substructures in projective spaces. Chapter 3 discusses results on blocking sets in projective spaces. Blocking sets occur within many problems in Galois geometry, thus giving them a central place within Galois geometry. Chapter 4 presents results on large caps in projective spaces; here a topic is discussed which has a well-known link to coding theory, i.e., to the cap-codes. The next two chapters diverge a bit from the four preceding chapters to introduce two important related topics. Chapter 5 is entitled The polynomial method in Galois geometries, discusses a powerful technique within Galois geometry, and presents results that have a strong algebraic nature, but that have immediate consequences for some of the mentioned structures in projective spaces, especially blocking sets of projective spaces. Chapter 6 presents results on finite semifields; these are algebraic structures that are related to e.g. spreads of projective spaces. Also this chapter has a more algebraic nature, but its connections with Galois geometry are clearly described. These first 6 chapters can be thought of as the part of the collection that deals with fundamentals of Galois geometry. Chapter 7 presents results on codes over ring geometries. Chapter 8 presents results on linear codes, and in particular on those geometric objects related to linear codes. Similarly, Chapter 9 presents applications of Galois Geometry to Cryptology. Finally, Chapter 10 presents results on LDPC codes and on their links to Galois geometry. These last four chapters can be thought of as the part of the collection that deals with applications, but as we explained, many of the topics presented here have influenced and inspired research in Galois geometry, and this fact can be found throughout these chapters. Undoubtedly, (many) more topics could have been included in this volume. During the editorial process, cross references between chapters originated, but each chapter of this volume is a self contained paper, and it can be read independently of the others. We assume that the reader is familiar with the basic concepts of Galois Geometry. A thorough introduction to Galois geometry can be found in the three fundamental volumes of Hirschfeld on Galois geometry, of which Thas is the co-author for the third volume; [1–3]. The aim and hope of this collected volume on Galois geometry is to give the readers a survey of current important research topics in Galois geometry, describing to them the main results, main techniques and ideas that led to these results, and to present them open problems for future research. We hope that the chapters of this collected work inspire and motivate the readers to contribute to Galois geometry, and encourage them to continue or initiate research on Galois geometry. There is something for everybody’s taste in Galois geometry! References [1] J. W. P. Hirschfeld, Finite projective spaces of three dimensions, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1985. Oxford Science Publications. [2] ___ Projective geometries over finite fields, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, second ed., 1998. [3] J. W. P. Hirschfeld and J. A. Thas, General Galois geometries, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1991. Oxford Science Publications.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 80

PLANNING AND SCHEDULING AN EMERGENCY ROOM WORKFORCE USING LINEAR PROGRAMMING *

Ciro Alberto Amaya*, Nubia Velasco and Silebis Aguirre Department of Industrial Engineering, University of Los Andes, Bogotá, Colombia

RESEARCH SUMMARY Service congestion, bottlenecks, long waiting times, and unbalanced working hours are common problems in many hospitals. This project proposes new staffing and scheduling “policies” of qualified workers considering patient daily demand. Three main work stages have been proposed. In the first, the objective is to determine optimal staffing levels for all type of medical workers in each area. In the second phase, workers are assigned to different activities and shifts according to legal and institutional policies. Finally, at a third level, personnel programming is updated in real time according to daily demand behavior. Obtained results show an optimal combination of different types of physicians and nurses needed in the emergency room and their weekly scheduling.

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This chapter was previously published in Linear Programming: Theory, Algorithms and Applications, edited by Yaromir Truma, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected], Address: Kr 1E 19A 40. Bogotá. Colombia (Corresponding Author)

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 81

NEURODYNAMIC SOLVERS, ROBOTIC APPLICATIONS AND SOLUTION NONUNIQUENESS OF LINEAR PROGRAMMING #

Yunong Zhang*, Ying Wang, Dechao Chen, Chen Peng and Qing Xie School of Information Science and Technology, Sun Yat-sen University, Guangzhou, Guangdong, China

RESEARCH SUMMARY Linear programming (LP), as a specific case of mathematical programming, has been widely encountered in a broad class of scientific disciplines and engineering applications. In view of its fundamental role, the solution of LP has been investigated extensively for the past decades. Due to the parallel-distributed processing nature and circuit-implementation convenience, the neurodynamic solvers based on recurrent neural network (RNN) have been regarded as powerful alternatives to online computation. In this chapter, three special kinds of RNNs [namely, traditional primal-dual neural network (T-PDNN), improved primal-dual neural network (I-PDNN), and linear variational inequality based primal-dual neural network (LVI-PDNN)] are presented and investigated for the LP problem solving. Moreover, as a robotic application to inverse-kinematic control, the minimum infinity-norm redundancy resolution, also known as the minimum-effort resolution (MER), explicitly minimizes the largest component of joint variable vectors (e.g., joint velocity, acceleration or torque). It is useful in situations where focuses are on low individual magnitude, even distribution of workload, and analysis of motion diversity. Computer-simulation results based on planar, PA10 and PUMA560 robot manipulators well substantiate the feasibility and effectiveness of the MER schemes and the neurodynamic solvers. At last, for handling the discontinuity #

This chapter was previously published in Linear Programming: Theory, Algorithms and Applications, edited by Yaromir Truma, New York: Nova Publishers Inc., 2014. * E-mail addresses: [email protected]; [email protected]; [email protected]

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problem of minimum-effort inverse-kinematic resolution, the nonuniqueness condition of LP is investigated, and a system of one inequality and two equations is presented for online effective nonuniqueness-checking.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 82

MATHEMATICAL EQUIVALENCE OF SIMPLE RECOURSE AND CHANCE CONSTRAINTS IN LINEAR STOCHASTIC PROGRAMMING #

Masatoshi Sakawa1*, Hitoshi Yano2† and Ichiro Nishizaki1‡ 1

Department of System Cybernetics, Hiroshima University, Higashi-Hiroshima, Japan 2 Department of Social Sciences, Nagoya City University, Nagoya, Japan

RESEARCH SUMMARY There are two different approaches to stochastic linear programming; two-stage programming and chance constrained programming. In two-stage programming, a shortage or an excess arising from the violation of the constraints is penalized, and then the expectation of the amount of the penalties for the constraint violation is minimized. In contrast, chance constrained programming admits random data variations and permits constraint violations up to specified probability limits. In this chapter, we consider the mathematical equivalence between stochastic programming problems with simple recourse and those with chance constraints. As a result, two main theorems are presented. In the first theorem, it is shown that the optimal solution of the chance constrained problem coincides that of the simple recourse problem when the satisficing probability levels are specified in connection with the penalty costs to violating the constraints. As the opposite result, in the second theorem, it is also shown that the optimal solution of the simple recourse problem coincides that of the chance constrained problem when the penalty costs to violating the constraints are specified in connection with the satisficing probability levels. These results give the corresponding relationship between stochastic programming problems with simple recourse and those with

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This chapter was previously published in Linear Programming: Theory, Algorithms and Applications, edited by Yaromir Truma, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected]

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Masatoshi Sakawa, Hitoshi Yano and Ichiro Nishizaki

chance constraints, and then to make this relation more easily understood we illustrate it with a simple numerical example.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 83

A DECOMPOSABLE LINEAR PROGRAMMING MODEL FOR ENERGY SUPPLY CHAINS #

Tsan Sheng Ng1*, Buse Aras1†, Charlle Lee Sy2‡ and Wu Biao1 1

Department of Industrial & Systems Engineering, National University of Singapore, Singapore 2 Department of Industrial Engineering, De La Salle University, Manila, Philippines

RESEARCH SUMMARY This chapter presents an application of linear programming to an energy supply chain problem. The energy supply chain is composed of the fuel supply market, electricity generators and electricity consumers. A linear programming model is developed to determine the optimal fuel mix for the system under the constraints of suppliers’ and generators’ capacities, CO2 emission quota, generators’ profit targets and other technical issues. In particular, the Berger Parker Index is considered to measure the fuel diversity index of the supply chain. Then, the model is solved using the Dantzig-Wolfe Decomposition algorithm. The performance of the algorithm, with respect to its computational speed and efficiency, is investigated using various sizes of the energy supply chain model. Numerical studies have also been performed on a case study concerning four suppliers, four electricity generators, four consumers and four fuel types. The case study shows the capability of the energy supply chain model to determine the best aggregate strategy of fuel mix that would generate electricity according to changing fuel prices, customer demands and profit targets. The model is also used to provide Pareto frontiers, which illustrate tradeoffs between diversity index, profit and emission quota. Finally, it is found that the model can be #

This chapter was previously published in Linear Programming: Theory, Algorithms and Applications, edited by Yaromir Truma, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected]

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Tsan Sheng Ng, Buse Aras, Charlle Lee Sy et al.

applied for any areas of energy planning and could also be easily extended to meet specific scenarios.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 84

HIGH ORDER BOUNDARY VALUE PROBLEMS: EXISTENCE, LOCALIZATION AND MULTIPLICITY RESULTS #

João Fialho1 and Feliz Minhós2 1

College of the Bahamas, Nassau, Bahamas 2 Universidade de Évora, Évora, Portugal

RESEARCH SUMMARY The motto for all the results presented in this book is the lower and upper solution method. In short, this method can guarantee not only the existence of a solution for a given boundary value problem but also the location of the solution in a strip defined by the lower and the upper solutions. Therefore, the challenge of finding a solution for a boundary value problem is replaced by the search of two functions (well-ordered, in reversed order or nonordered) satisfying adequate differential inequalities and boundary conditions. The freedom to choose such functions is at the same time its weakness: lower and upper solutions must be defined and exhibited. For first and second order problems, some techniques were disperse in several papers and systematized in the book1. However, in the existent literature, those tasks were not made yet for higher order boundary value problems, neither the location tool was explored to estimate the corresponding derivatives and from them, extract qualitative information about solution properties. Therefore, the goals of this book are: • Adapt lower and upper solutions method to higher order boundary value problems, with different boundary conditions. Part I is dedicated to standard ones such as periodic, mixed, #

This chapter was previously published as a book: High Order Boundary Value Problems: Existence, Localization and Multiplicity Results, by João Fialho and Feliz Minhós, New York: Nova Publishers Inc., 2014. 1 C. de Coster, P. Habets, Two-Point Boundary Value Problems: Lower and Upper Solutions, Mathematics in Science and Engineering, 205, Elsevier, 2006.

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Dirichlet, Neumann,. . . and Part II is dedicated to functional boundary conditions, which include a huge range of applications of problems, such as nonlinear, non local, with delays or advances, with maximum or minimum arguments, etc., and fully functional boundary value problems. • Explore the under used location part of the lower and upper solutions method, applying it to the derivatives of the unknown function. With these arguments, some data is provided on the type of solution, like variation, positivity, monotonicity or convexity. • Present new trends in lower and upper solutions method, for instance: that for some order greater than two the relation of order between lower and upper solutions is not relevant; transfer the assumptions on the nonlinearity to lower and upper solutions definition, allowing more general problems with weaker nonlinearities. These contents have of wide scope amongst researchers as they offer: • Arguments to a general approach for nonlinear and functional problems with functional dependence on the differential equation and in boundary conditions as well. In this way it can be applied to integro-differential equations, problems with deviating and max or min arguments. • Applications to theoretical problems, like Lidstone problems, conjugate problems or others, as well as sharper estimations for the involved parameters; • Methods to transfer some hypothesis on the nonlinear for lower and upper functions, obtaining more general propositions and extending the scope of the results; • Techniques to build and define lower and upper solutions for higher order problems even in the functional case. But it is also useful for non expert readers in those fields as it provides: • Arguments based on elementary and basic concepts, without “deep mathematics tools”, appropriate for undergraduate students or non-mathematics experts; • A “quasi numerical” construction of lower and upper solution, allowing approximation of the solution and its derivatives, as sharp as lower and upper functions can be defined and modeled; • A graphic idea of the localization of the solution and its derivatives, which can be useful to obtain as many data on the solution behavior, as long as lower and upper solutions are properly defined.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 85

MAPPING DATA PROCESSING NEURAL NETWORKS ONTO DISTRIBUTED COMPUTER SYSTEMS WITH REGULAR STRUCTURES #

Mikhail S. Tarkov* Institute of Semiconductor Physics SB RAS, Novosibirsk, Russia

RESEARCH SUMMARY The methods for efficient mapping data processing neural networks onto robust distributed computer systems (CS) are proposed. Cellular neural networks are mapped onto the graphs of parallel programs with structures "mesh" and "line". The efficiency of the proposed methods for neural networks with global connections (Hopfield network, Kohonen network, and multilayer perceptron) is based on a butterfly scheme and mapping this scheme onto hypercube with subsequent embedding of the hypercube onto a torus. This networks are mapped onto regular graphs of parallel programs ("line", "ring", "mesh", "hypercube", "torus") intended for implementation on distributed computer systems.

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This chapter was previously published in Parallel Programming: Practical Aspects, Models and Current Limitations, edited by Mikhail S. Tarkov, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 86

MAPPING PARALLEL PROGRAM GRAPHS ONTO GRAPHS OF DISTRIBUTED COMPUTER SYSTEMS BY NEURAL NETWORK ALGORITHMS

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Mikhail S. Tarkov * Institute of Semiconductor Physics SB RAS, Novosibirsk, Russia

RESEARCH SUMMARY The problem of mapping a parallel program with weighed vertices (processes) and edges (interprocess exchanges) onto a weighed graph of the distributed computer system is considered. An algorithm for solving this problem based on the use of Hopfield networks is proposed. The algorithm is tested on mapping a number of graphs of parallel programs onto a multicore computer. Experiments have shown that the proposed algorithm provides wellbalanced sub-optimal mappings. Optimal solutions are found for mapping a “line”-graph onto a two-dimensional torus. To increase the probability of finding an optimal mapping, a method for splitting the mapping is proposed. The method’s essence is reducing the solution matrix to a block-diagonal form. The Wang recurrent neural network is used to exclude incorrect solutions of the problem of mapping the line-graph onto a three-dimensional torus. An algorithm based on a recurrent neural Wang network and the WTA (“Winner takes all”) principle is proposed for the construction of Hamiltonian cycles in graphs of distributed computer systems.

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This chapter was previously published in Parallel Programming: Practical Aspects, Models and Current Limitations, edited by Mikhail S. Tarkov, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 87

LARGE-SCALE AND FINE-GRAIN PARALLELISM IN PLASMA SIMULATION

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A. Snytnikov* Institute of Computational Mathematics and Mathematical Geophysics, The Siberian Branch of the RAS, Novosibirsk, Russia

RESEARCH SUMMARY A 3D kinetic study of the relaxation processes caused by the propagation of an electron beam in high-temperature plasma was carried out. This problem has two different spatial scales: the plasma Debye length and the beam-plasma interaction wavelength, that is some 10 or 100 times larger, thus one needs high-performance computing to observe the two lengths at once. A mathematical model is built on the basis of the Particle-in-Cell (PIC) method. In order to achieve the highest possible computation performance, both large-scale and finegrain parallel techniques are employed. The large-scale part is presented by the domain decomposition and is performed by cluster supercomputers. The parallelisation efficiency is presented as well as the performance of the program achieved with different clusters. The performance tests show that it is necessary to provide a good memory bandwidth for the cluster if one wants to achieve good performance on real physical problems. The fine-grain part is presented by pushing each particle with a separate thread of a GPU (Graphics Processing Unit). Hybrid (GPU-equipped) supercomputers have reached very high performance level recently. Unfortunately, the solution of real physical problems with such supercomputers is restricted by complexity of the GPU programming. In order to simplify the development of high-performance plasma physics codes for hybrid supercomputers a template implementation of the PIC method was created. The template parameters are the problem-

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This chapter was previously published in Parallel Programming: Practical Aspects, Models and Current Limitations, edited by Mikhail S. Tarkov, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

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specific implementations of "particles" and "cells" (as C++ classes). Thus, it is possible to develop a PIC code for a new plasma physics problem without studying the GPU programming by a plasma physicist. Instead the new physical features are just included into the existing code as new implementations of "particle" and "cell" classes.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 88

NUMERICAL MODELLING OF ASTROPHYSICAL FLOW ON HYBRID ARCHITECTURE SUPERCOMPUTERS #

I. Kulikov1,2,3, I. Chernykh1,2, A. Snytnikov1,2, V. Protasov3, A. Tutukov4, and B. Glinsky1,2,* 1

Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch RAS, Novosibirsk, Russia 2 Novosibirsk State University, Novosibirsk, Russia 3 Novosibirsk State Technical University, Novosibirsk, Russia 4 Institute of Astronomy of the Russian Academy of Sciences, Moscow, Russia

RESEARCH SUMMARY This chapter describes a comprehensive computer technology of numerical modeling of astrophysical flows on hybrid supercomputer equipped with computations accelerators (NVIDIA and/or Intel accelerators). The design of parallel computing algorithms for modeling the gas-dynamic, magnetic gas dynamic, collisionless component of astrophysical objects with consideration of chemical processes is presented. There are three software packages described in this chapter: GPUPEGAS code designed for simulation of astrophysics objects on hybrid supercomputers; AstroPhi code which is used for the dynamics of stars and molecular clouds simulation on hybrid supercomputers equipped with Intel Xeon Phi accelerators; PADME code for simulation of planetary systems formation on hybrid supercomputers.

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This chapter was previously published in Parallel Programming: Practical Aspects, Models and Current Limitations, edited by Mikhail S. Tarkov, New York: Nova Publishers Inc., 2015. * Corresponding author: B. Glinsky. E-mail: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 89

EFFICIENT COMPUTATIONAL APPROACHES FOR PARALLEL STOCHASTIC SIMULATION ON SUPERCOMPUTERS #

Mikhail A. Marchenko* Institute of Computational Mathematics and Mathematical Geophysics of the SB RAS, Novosibirsk State University, Novosibirsk, Russian Federation

RESEARCH SUMMARY The Monte Carlo method (or the method of stochastic simulation) is often used to solve real-life problems. But the main issue of the Monte Carlo simulation is usually the value of its computational cost. Nevertheless, using parallel high performance computers it is possible to get results of simulation in a reasonable time. A question is how to develop justified and effective parallel algorithms and programs. In this chapter, we provide some computational approaches for effective parallel stochastic simulation. As an example, we apply these approaches to study stochastic evolution of electron avalanches in gases.

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This chapter was previously published in Parallel Programming: Practical Aspects, Models and Current Limitations, edited by Mikhail S. Tarkov, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 90

LATTICE GAS CELLULAR AUTOMATA FOR A FLOW SIMULATION AND THEIR PARALLEL IMPLEMENTATION #

Yury G. Medvedev* Supercomputer Software Department, Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, Russia

RESEARCH SUMMARY This chapter presents some directions of the development of gas flows cellular automata models. The transitions from Boolean to integer models, from two-dimensional to threedimensional models, and from the gas-stream to flow models in multiphase media are traced. A software implementation of a two-dimensional model of gas-powder flow with integer alphabet FHP-GP is proposed. A mechanism for parallel execution of the model on a cluster using the library MPI is described. The need for dynamic load balancing of cluster cores in the implementation of models with integer alphabet is shown. A diffusion balancing implemented for this model is argued. Also, some results of computational experiments on modeling the flows obtained using the above software are presented. A problem of dynamic load balancing application for gas and fluid flows simulation by lattice gas automata (LGA) is considered. The choice of a diffusion balancing method is justified. The results of testing both balanced and imbalanced cases are presented. The efficiency of the realizations for LGA simulation is presented and the PIC-method is compared.

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This chapter was previously published in Parallel Programming: Practical Aspects, Models and Current Limitations, edited by Mikhail S. Tarkov, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 91

PARALLEL SIMULATION OF ASYNCHRONOUS CELLULAR AUTOMATA #

Konstantin Kalgin* Institute of Computational Mathematics and Mathematical Geophysics, SB RAS, Novosibirsk, Russia

RESEARCH SUMMARY Overview and experimental comparative study of parallel algorithms of asynchronous cellular automata simulation is presented. The algorithms are tested for the model of physicochemical process of surface CO + O2 reaction over the supported Pd nanoparticles on different parallel computers. For testing we use shared memory computers, distributed memory computers (i.e. clusters), and graphical processing unit. Characterization of these algorithms in respect of methods of parallelism maintenance is given. A new domain specific language CACHE and its translator into C and Processing are presented, where the domain is a set of cellular automata models of physicochemical processes.

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This chapter was previously published in Parallel Programming: Practical Aspects, Models and Current Limitations, edited by Mikhail S. Tarkov, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]. The author was supported by the Grant of the President of the Russian Federation for Young Russian Researchers (project no. MK-3644.2014.9).

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 92

XPU: A C++ METAPROGRAMMING APPROACH TO EASE PARALLELISM EXPRESSION: PARALLELIZATION METHODOLOGY, INTERNAL DESIGN AND PRACTICAL APPLICATION #

Nader Khammassi and Jean-Christophe Le Lann† Lab-STICC UMR CNRS 6285, ENSTA-Bretagne, Brest Cedex, France

RESEARCH SUMMARY The continuous proliferation of multicore architectures has placed developers under great pressure to parallelize their applications in order to take advantage of such platforms. Unfortunately, traditional low-level programming models exacerbate the difficulties of building large and complex parallel applications. Consequently, programmers are facing a complex productivity performance trade-off where they should extract enough parallelism to justify the use of a dedicated parallel programming library. High-level parallel programming models are in high-demand as they reduce the burdens on developers significantly and provide enough abstraction to accommodate hardware heterogeneity. In this chapter, we present a task-based parallel programming model named XPU which aims to ease parallelism expression without sacrificing performances. Contrary to many parallel programming models which introduce new languages, extend existing language or define compiler annotations and thus require specialized compilers, virtual machines or extrahardware... XPU is a pure software technology entirely based on the traditional C++ language and requires nothing more than a standard C++ compiler to be used, and therefore, improves learning curve steepness and is easily portable to many systems. #

This chapter was previously published in Parallel Programming: Practical Aspects, Models and Current Limitations, edited by Mikhail S. Tarkov, New York: Nova Publishers Inc., 2015.  E-mail address: [email protected]; Address: Lab-STICC UMR CNRS 6285, ENSTA-Bretagne, 29806 Brest Cedex 9, France † E-mail address: [email protected].

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Nader Khammassi and Jean-Christophe Le Lann

We show how XPU exploits C++ metaprogramming techniques to ease expression of several types of parallelism including task, data and temporal parallelism at all levels of granularity inside a single structured and homogeneous programming model. We describe the XPU parallelization methodology and we show through a practical signal processing application how we can apply this methodology to parallelize a sequential program at the cost of a little amount of parallel paradigms-related extra-code while reusing the sequential legacy code without significant alteration. This case study demonstrates the ability of the XPU programming model to provide high programmability to improve programmer productivity while delivering high performances.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 93

AN APPROACH TO THE CONSTRUCTION OF ROBUST SYSTEMS OF INTERACTING PROCESSES

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Igor N. Skopin* Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk State University, Novosibirsk, Russia

RESEARCH SUMMARY The problems of distributed computing associated with the reliability of network interactions are discussed. Sequential solutions of some problems that are naturally interpreted as systems of interacted processes are considered. Descriptions of traditional problems solutions as systems of interacting processes are applicable for decomposition of computing task and increase the computations robustness.

#

This chapter was previously published in Parallel Programming: Practical Aspects, Models and Current Limitations, edited by Mikhail S. Tarkov, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]. The chapter presents the work that is supported by grant RF RSF № 14 – 11 00485 “High-performance methods and technologies of electrophysical processes and devices modeling”.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 94

EARLY LEARNING IN PARALLEL PROGRAMMING

#

Igor N. Skopin* Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk State University, Novosibirsk, Russia

RESEARCH SUMMARY The current approach to teaching programming is analyzed. We underline its problems related to training in parallelism. An alternative approach based on rejection of thinking patterns in teaching is presented. The main idea of the approach is separation of two types of activity in the program construction: development of the program sketch, which does not take into account the resource constraints, and mapping the sketch to a real computer. We show the advantages of this approach for the development of thinking and, in particular, when teaching parallelism.

#

This chapter was previously published in Parallel Programming: Practical Aspects, Models and Current Limitations, edited by Mikhail S. Tarkov, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]. The chapter presents the work that is supported by grant RF RSF № 14 – 11 00485 “High-performance methods and technologies of electrophysical processes and devices modeling”

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 95

SUB-INDEPENDENCE: A USEFUL CONCEPT

#

G. G. Hamedani* and Mehdi Maadooliat Statistics and Computer Science, Marquette University, WI, US

RESEARCH SUMMARY The concept of sub-independence is defined in terms of the convolution of the distributions of random variables, providing a stronger sense of dissociation between random variables than that of uncorrelatedness. If statistical tests reject independence but not lack of correlation, a model with sub-independent components can be appropriate to determine the distribution of the sum of the random variables. This monograph presents most of the important classical results in probability and statistics based on the concept of subindependence. This concept is much weaker than that of independence and yet can replace independence in most limit theorems as well as well-known results in probability and statistics. This monograph, the first of its kind on the concept of sub-independence, should appeal to researchers in applied sciences where the lack of independence of the uncorrelated random variables may be apparent but the distribution of their sum may not be tractable.

#

This chapter was previously published as a book: Sub-Independence: A Useful Concept, by G. G. Hamedani and Mehdi Maadooliat, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 96

MINIMIZATION OF QUADRATIC FORMS AND GENERALIZED INVERSES #

ć

Predrag S. Stanimirović1*, Dimitrios Pappas2† and Vasilios N. Katsikis3‡ 1

University of Niš, Faculty of Sciences and Mathematics, Niš, Serbia 2 Athens University of Economics and Business Department of Statistics, Athens, Greece 3 National and Kapodistrian University of Athens, Department of Economics Division of Mathematics and Informatics, Athens, Greece

RESEARCH SUMMARY Minimization of a quadratic form 〈𝑥, 𝑇𝑥〉 + 〈𝑝, 𝑥〉 + a under constraints defined by a linear system is a common optimization problem. It is assumed that the operator T is symmetric positive definite or positive semidefinite. Several extensions to different sets of linear matrix constraints are investigated. Solutions of this problem may be given using the Moore-Penrose inverse and/or the Drazin inverse. In addition, several new classes of generalized inverses are defined minimizing the seminorm defined by the quadratic forms, depending on the matrix equation that is used as a constraint. A number of possibilities for further investigation are considered.

#

This chapter was previously published in Advances in Linear Algebra Research, edited by Ivan Kyrchei, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 97

THE STUDY OF THE INVARIANTS OF HOMOGENEOUS MATRIX POLYNOMIALS USING THE EXTENDED HERMITE EQUIVALENCE 𝜺𝒓𝒉 # Grigoris I. Kalogeropoulos1, Athanasios D. Karageorgos1 and Athanasios A. Pantelous2, 3,* 1

Department of Mathematics, University of Athens, Greece 2 Department of Mathematical Sciences, University of Liverpool, United Kingdom 3 Institute for Risk and Uncertainty, University of Liverpool, United Kingdom

RESEARCH SUMMARY In systems and control theory, Linear Time Invariant (LTI) descriptor (DifferentialAlgebraic) systems are intimately related to the matrix pencil theory. Actually, a large number of systems are reduced to the study of differential (difference) systems S (F,G) of the form: S (F,G) : F𝑥̇ (t) = Gx(t) (or the dual Fx = G𝑥̇ (t)), and S (F,G) : 𝐹𝑥𝑘+1 = 𝐺𝑥𝑘 (or the dual 𝐹𝑥𝑘 = 𝐺𝑥𝑘+1), F,G ∈

m×n

and their properties can be characterized by the homogeneous pencil sF − ŝG. An essential problem in matrix pencil theory is the study of invariants of sF − ŝG under the bilinear strict equivalence. This problem is equivalent to the study of complete Projective Equivalence (PE), 𝜀𝑝 , defined on the set r of complex homogeneous binary polynomials of fixed homogeneous degree r. For a f (s, ˆs) ∈ #

r,

the study of invariants of the PE class 𝜀𝑝 is

This chapter was previously published in Advances in Linear Algebra Research, edited by Ivan Kyrchei, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

194 Grigoris I. Kalogeropoulos, Athanasios D. Karageorgos and Athanasios A. Pantelous reduced to a study of invariants of matrices of the set k×2 (for k ≥ 3 with all 2 × 2-minors non-zero) under the Extended Hermite Equivalence (EHE), 𝜀𝑟ℎ . In this chapter, we present a review of the most interesting properties of the PE and the EHE classes. Moreover, the appropriate projective transformation d ∈ RGL(1, / ) is provided analytically1.

1

A.D. Karageorgos, A.A. Pantelous, G.I. Kalogeropoulos, The study of invariants of matrices under the notion of extended Hermite equivalence (EHE), Report – University of Athens, 2014.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 98

CRAMER’S RULE FOR GENERALIZED INVERSE SOLUTIONS #

Ivan I. Kyrchei* Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Lviv, Ukraine

RESEARCH SUMMARY By a generalized inverse of a given matrix, we mean a matrix that exists for a larger class of matrices than the nonsingular matrices, that has some of the properties of the usual inverse, and that agrees with inverse when given matrix happens to be nonsingular. In theory, there are many different generalized inverses that exist. We shall consider the Moore Penrose, weighted Moore-Penrose, Drazin and weighted Drazin inverses. New determinantal representations of these generalized inverse based on their limit representations are introduced in this chapter. Application of this new method allows us to obtain analogues classical adjoint matrix. Using the obtained analogues of the adjoint matrix, we get Cramer’s rules for the least squares solution with the minimum norm and for the Drazin inverse solution of singular linear systems. Cramer’s rules for the minimum norm least squares solutions and the Drazin inverse solutions of the matrix equations AX = D, XB = D and AXB = D are also obtained, where A, B can be singular matrices of appropriate size. Finally, we derive determinantal representations of solutions of the differential matrix equations, Xˊ+ AX = B and Xˊ+XA = B, where the matrix A is singular.

#

This chapter was previously published in Advances in Linear Algebra Research, edited by Ivan Kyrchei, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 99

FEEDBACK ACTIONS ON LINEAR SYSTEMS OVER VON NEUMANN REGULAR RINGS #

Andrés Sáez-Schwedt* Departamento de Matemáticas, Universidad de León, Campus de Vegazana, León, Spain

RESEARCH SUMMARY Many physical systems in science and engineering can be described at time t in terms of an n-dimensional state vector x(t) and an m-dimensional input vector u(t), governed by an evolution equation of the form xˊ(t) = A∙ x(t)+B ∙u(t), if the time is continuous, or x(t + 1) = A∙ x(t)+B ∙u(t) in the discrete case. Thus, the system is completely described by the pair of matrices (A,B) of sizes n × n and n × m respectively. In two instances feedback is used to modify the structure of a given system (A,B): first, A can be replaced by A+ BF, with some characteristic polynomial that ensures stability of the new system (A + BF,B); and second, combining changes of bases with a feedback action A ↦ A+BF one obtains an equivalent system with a simpler structure. Given a system (A,B), let ℛ(A,B) denote the set of states reachable at finite time when starting with initial condition x(0) = 0 and varying u(t), i.e., ℛ(A,B) is the right image of the matrix [B|AB|A2B| · · · ]. Also, let Pols(A,B) denote the set of characteristic polynomials of all possible matrices A + BF, as F varies. Classically, (A,B) have their entries in the field of real or complex numbers, but the concept of discrete-time system is generalized to matrix pairs with coefficients in an arbitrary commutative ring R. Therefore, techniques from Linear Algebra over commutative rings are needed. In this chapter, the following problems are studied and solved when R is a commutative von Neumann regular ring: #

This chapter was previously published in Advances in Linear Algebra Research, edited by Ivan Kyrchei, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

198

Andrés Sáez-Schwedt • A canonical form is obtained for the feedback equivalence of systems (combination of basis changes with a feedback action). • Given a system (A, B), it is proved that there exist a matrix F and a vector u such that the single-input system (A + BF, Bu) has the same reachable states and the same assignable polynomials as the original system, i.e., ℛ(A + BF, Bu) = ℛ(A, B) and Pols(A + BF,Bu) = Pols(A,B).

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 100

HOW TO CHARACTERIZE PROPERTIES OF GENERAL HERMITIAN QUADRATIC MATRIX-VALUED FUNCTIONS BY RANK AND INERTIA #

Yongge Tian* China Economics and Management Academy, Central University of Finance and Economics, Beijing, China

RESEARCH SUMMARY This chapter gives a comprehensive investigation to behaviors of a general Hermitian quadratic matrix-valued function

ϕ (X) = (AXB + C) M (AXB + C)* + D by using ranks and inertias of matrices. The author first establishes a group of analytical formulas for calculating the global maximal and minimal ranks and inertias of ϕ(X). Based on the formulas, the author derives necessary and sufficient conditions for ϕ(X) to be a positive definite, positive semi-definite, negative definite, negative semi-definite function, respectively, and then solves two optimization problems of finding two matrices 𝑋̂ or 𝑋̃ such that ϕ(X) ≽ ϕ(𝑋̂) and ϕ(X) ≼ (𝑋̃) hold for all X, respectively. As extensions, the author considers definiteness and optimization problems in the Löwner sense of the following two types of multiple Hermitian quadratic matrix-valued function ∗

ϕ(𝑋1 , ⋯ , 𝑋𝑘 ) = (∑𝑘𝑖=1 𝐴𝑖 𝑋𝑖 𝐵𝑖 + 𝐶)𝑀(∑𝑘𝑖=1 𝐴𝑖 𝑋𝑖 𝐵𝑖 + 𝐶) + 𝐷, ∗ ψ(𝑋1 , ⋯ , 𝑋𝑘 ) = ∑𝑘𝑖=1(𝐴𝑖 𝑋𝑖 𝐵𝑖 + 𝐶𝑖 ) 𝑀𝑖 (𝐴𝑖 𝑋𝑖 𝐵𝑖 + 𝐶𝑖 ) + 𝐷.

#

This chapter was previously published in Advances in Linear Algebra Research, edited by Ivan Kyrchei, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

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Yongge Tian

Some open problems on algebraic properties of these matrix-valued functions are mentioned at the end of the chapter.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 101

INTRODUCTION TO THE THEORY OF TRIANGULAR MATRICES (TABLES)# Roman Zatorsky* Precarpathian Vasyl Stefanyk National University, Ivano-Frankivsk, Ukraine

RESEARCH SUMMARY We consider elements of linear algebra based on triangular tables with entries in some number field and their functions, analogical to the classical notions of a matrix, determinant and permanent. Some properties are investigated and applications in various areas of mathematics are given.

#

This chapter was previously published in Advances in Linear Algebra Research, edited by Ivan Kyrchei, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 102

RECENT DEVELOPMENTS IN ITERATIVE ALGORITHMS FOR SOLVING LINEAR MATRIX EQUATIONS #

Masoud Hajarian* Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, General Campus, Evin, Tehran, Iran

RESEARCH SUMMARY The aim of this chapter is to present the latest developments in iterative methods for solving linear matrix equations. The iterative methods are obtained by extending the methods presented to solve the linear system Ax = b. Numerical examples are investigated to confirm the efficiency of the methods.

#

This chapter was previously published in Advances in Linear Algebra Research, edited by Ivan Kyrchei, New York: Nova Publishers Inc., 2015. * E-mail addresses: m [email protected]; [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 103

SIMULTANEOUS TRIANGULARIZATION OF A PAIR OF MATRICES OVER A PRINCIPAL IDEAL DOMAIN WITH QUADRATIC MINIMAL POLYNOMIALS #

Volodymyr M. Prokip* Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Lviv, Ukraine

RESEARCH SUMMARY The problems of existence of common eigenvectors and simultaneous triangularization of a pair of matrices over a principal ideal domain with quadratic minimal polynomials are investigated. The necessary and sufficient conditions of simultaneous triangularization of a pair of matrices with quadratic minimal polynomials are obtained. As a result, the approach offered provides the necessary and sufficient conditions of simultaneous triangularization of pairs of idempotent matrices and pairs of involutory matrices over a principal ideal domain.

#

This chapter was previously published in Advances in Linear Algebra Research, edited by Ivan Kyrchei, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 104

RELATION OF ROW-COLUMN DETERMINANTS WITH QUASI-DETERMINANTS OF MATRICES OVER A QUATERNION ALGEBRA #

Aleks Kleyn1,* and Ivan I. Kyrchei2,† 1

American Mathematical Society, USA Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Lviv, Ukraine 2

RESEARCH SUMMARY Since product of quaternions is noncommutative, there is a problem how to determine a determinant of a matrix with noncommutative elements (it’s called a noncommutative determinant). We consider two approaches to define a noncommutative determinant. Primarily, there are row – column determinants that are an extension of the classical definition of the determinant; however we assume predetermined order of elements in each of the terms of the determinant. In the chapter we extend the concept of an immanant (permanent, determinant) to a split quaternion algebra using methods of the theory of the row and column determinants. Properties of the determinant of a Hermitian matrix are established. Based on these properties, analogs of the classical adjoint matrix over a quaternion skew field have been obtained. As a result we have a solution of a system of linear equations over a quaternion division algebra according to Cramer’s rule by using row–column determinants. Quasi-determinants appeared from the analysis of the procedure of a matrix inversion. By using quasi-determinants, solving of a system of linear equations over a quaternion division algebra is similar to the Gauss elimination method.

#

This chapter was previously published in Advances in Linear Algebra Research, edited by Ivan Kyrchei, New York: Nova Publishers Inc., 2015. * E-mail address: Aleks [email protected] † E-mail address: [email protected]

208

Aleks Kleyn and Ivan I. Kyrchei

The common feature in definition of row and column determinants and quasideterminants is that we have not one determinant of a quadratic matrix of order n with noncommutative entries, but certain set (there are n2 quasi-determinants, n row determinants, and n column determinants). We have obtained a relation of row-column determinants with quasi-determinants of a matrix over a quaternion division algebra.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 105

FIRST ORDER CHEMICAL KINETICS MATRICES AND STABILITY OF O.D.E. SYSTEMS #

Victor Martinez-Luaces* Electrochemistry Engineering Multidisciplinary Research Group, Udelar, Uruguay

RESEARCH SUMMARY First order chemical reaction mechanisms are modeled through Ordinary Differential Equations (O.D.E.) systems of the form: 𝑋̇ = 𝐴𝑋, 𝑋 being the chemical species concentrations vector, 𝑋̇ its time derivative, and 𝐴 A the associated system matrix. A typical example of these reactions, which involves two species, is the Mutarotation of Glucose1, which has a corresponding matrix with a null eigenvalue whereas the other one is negative. A very simple example with three chemical compounds is grape juice, when it is converted into wine and then transformed into vinegar2. A more complicated example, also involving three species, is the adsorption of Carbon Dioxide over Platinum surfaces3. Although, in these examples the chemical mechanisms are very different, in both cases the O.D.E. system matrix has two negative eigenvalues and the other one is zero. Consequently, in all these cases that involve two or three chemical species, solutions show a weak stability (i.e., they are stable but not asymptotically). This fact implies that small errors due to measurements in the initial concentrations will remain bounded, but they do not tend to vanish as the reaction proceeds. #

This chapter was previously published in Advances in Linear Algebra Research, edited by Ivan Kyrchei, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]. 1 Guerasimov, Y.A. et al. (1995), Physical Chemistry, 2nd Ed., Houghton-Mifflin, Boston 2 Martinez-Luaces, V. (2005), Engaging secondary school and university teachers in modelling: some experiences in South American countries, International Journal of Mathematical Education in Science and Technology, Vol. 36, N° 2–3, 193–205. 3 Martinez-Luaces, V. (2012), Chemical Kinetics and Inverse Modelling Problems, in Chemical Kinetics, In Tech Open Science Eds., Rijeka, Croatia.

210

Victor Martinez-Luaces

In order to know if these results can be extended or not to other chemical mechanisms, a possible general result is studied through an inverse modeling approach, like in previous papers3,4,5. For this purpose, theoretical mechanisms involving two or more species are proposed and a general type of matrices – so-called First Order Chemical Kinetics Mechanisms (F.O.C.K.M.) matrices – is studied from the eigenvalues and eigenvectors view point. This chapter shows that in an F.O.C.K.M. matrix all columns add to zero, all the diagonal elements are non-positive and all the other matrix entries are non-negative. Because of this particular structure, the Gershgorin Circles Theorem6 can be applied to show that all the eigenvalues are negative or zero. Moreover, it can be proved that in the case of the null eigenvalues – under certain conditions – algebraic and geometric multiplicities give the same number. As an application of these results, several conclusions about the stability of the O.D.E. solutions are obtained for these chemical reactions, and its consequences on the propagation of concentrations and/or surface concentration measurement errors, are analyzed.

4

Martinez-Luaces, V. (2009), Modelling and Inverse Modelling: Experiences with O.D.E. linear systems in engineering courses, International Journal of Mathematical Education in Science and Technology,Vol. 40, N° 2, 259-268. 5 Martinez-Luaces, V. (2012), Problemas inversos y de modelado inverso en Matemática Educativa, Editorial Académica Española, Saarbrücken, Germany. 6 Varga, R.S. (2004),Geršgorin and His Circles. Springer-Verlag, Berlin.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 106

STOCHASTIC MODELLING AND SIMULATIONS OF STRUCTURED INVESTMENT PLANS #

Ling Feng1, Yile Li2, Xuerong Mao2* and Zhigang Huang1 1

School of Economics and Management, Fuzhou University, Fuzhou, China 2 Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK

RESEARCH SUMMARY Structured investment plans (also known as the FTSE 100 Index linked savings accounts) have become more and more popular. The returns of these accounts are random so the returns, even the initial capital, are not guaranteed. The aim of this chapter is to show how to perform the stochastic modelling and numerical analysis on the structured investment plans. The numerical analysis with R-codes will provide the user with a tool to compute the approximate mean percentage of return for the plan so that the user will be able to compare the plan with the familiar fixed-term-fixed-rated savings accounts.

#

This chapter was previously published in Brownian Motion: Elements, Dynamics and Applications, edited by Mark A. McKibben and Micah Webster, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 107

LIMITATION OF THE LEAST SQUARE METHOD IN THE EVALUATION OF DIMENSION OF FRACTAL BROWNIAN MOTIONS #

Siming Liu* and Bingqiang Qiao Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, China Yunnan University, Kunming, China

RESEARCH SUMMARY To model a given time series F(t) with fractal Brownian motions (fBms), it is necessary to have an appropriate error assessment for related quantities. Usually, the fractal dimension D is derived from the Hurst exponent H via the relation D = 2−H, and the Hurst exponent can be evaluated by analyzing the dependence of the rescaled range 〈|𝐹(𝑡 + 𝜏) − 𝐹(𝜏)|〉 on the time span 𝜏. For fBms, the standard deviation of the rescaled range not only depends on data sampling but also varies with H due to the presence of long term memory. This error for a given time series then cannot be assessed without knowing the fractal dimension. We carry out extensive numerical simulations to explore the standard deviation of rescaled range of fBms and find that for 0 < H ≤ 0.5, |F(t + 𝜏) − F(t)| can be treated as independent for time spans without overlap; for 0.5 < H < 1, the long term memory makes |F(t + 𝜏) − F(t)| correlated and an approximate method is given to evaluate the standard deviation of 〈|𝐹(𝑡 + 𝜏) − 𝐹(𝜏)|〉 for several sampling methods. The method of least squares is then adopted to determine the slope, S, and intercept, I, of the log(〈|𝐹(𝑡 + 𝜏) − 𝐹(𝜏)|〉) vs log(𝜏) plot to investigate the limitation of this procedure. It is found that the reduced χ2 of the fitting decreases with the increase of H (the expectation value of S), which may be attributed to the

#

This chapter was previously published in Brownian Motion: Elements, Dynamics and Applications, edited by Mark A. McKibben and Micah Webster, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

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Siming Liu and Bingqiang Qiao

correlation among the rescaled range. Similarly, it is found that the errors of the fitting parameters S and I are usually smaller than their corresponding standard deviations. These results show the limitation of using the simple least square method to determine the dimension of a fractal time series. More self-consistent interpretation of the fitting results is discussed.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 108

PARAMETER ESTIMATION FOR WEIGHTED FRACTIONAL ORNSTEIN-UHLENBECK PROCESSES WITH DISCRETE OBSERVATIONS #

Xiuwei Yin, Guangjun Shen* and Longjuan Deng Anhui Normal University, Wuhu, China

RESEARCH SUMMARY In this chapter, we consider an Ornstein-Uhlenbeck process 𝑑𝑋𝑡 = −𝜃𝑋𝑡 𝑑𝑡 + 𝑑𝐵𝑡𝑎,𝑏 ,

𝑡≥0

driven by a weighted fractional Brownian motion 𝐵𝑎,𝑏 with known parameters −1 < a < 0, 0 < b < 1, a+b > 0, but for which the parameter 𝜃 > 0 is unknown. Assume that the process is observed at discrete time ti = iΔn, i = 0, ..., n. We construct a least squares estimator 𝜃̂n of 𝜃 which is consistent, namely, 𝜃̂n converges to 𝜃 in probability as 𝑛 → ∞.

#

This chapter was previously published in Brownian Motion: Elements, Dynamics and Applications, edited by Mark A. McKibben and Micah Webster, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]. This work was supported by National Natural Science Foundation of China (11271020, 11401010).

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 109

COMPARING TRADITIONAL PROOFS OF THE MODULUS OF CONTINUITY AND THE LAW OF THE ITERATED LOGARITHM TO A NEW METHOD WHICH YIELDS RATES OF CONVERGENCE #

Lisa Marano* West Chester University, Pennsylvania, US

RESEARCH SUMMARY Traditional proofs of the modulus of continuity and the law of the iterated logarithm require using the Borel-Cantelli lemma and are therefore asymptotic results. The author compares these proofs to ones that find non-asymptotic estimates for the maximal deviation of increments of a Brownian motion process (𝑊𝑡 )𝑡≥0 normalized by the global and local modulus function, for all positive 𝜀 and uniformly over 𝛿.

#

This chapter was previously published in Brownian Motion: Elements, Dynamics and Applications, edited by Mark A. McKibben and Micah Webster, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 110

TRANSPORTING A MACROSCOPIC OBJECT BY BROWNIAN MOTION - AN OBJECT AS A POLLEN PARTICLE, ROBOTS AS LIQUID MOLECULES #

Teturo Itami* Robotics Industry Development Council, Japan

RESEARCH SUMMARY Brownian motion inspires us to design a new transportation system in the macroscopic world. We take an object to be transported as a pollen particle and robots as liquid molecules. Both the robots and the object are classical in the understanding that it is Newton mechanics that governs the motion. Controlling the Brownian motion of the object in a plane region by multiple collisions with robots can maneuver the object along a required path. In a physical example each robot with a battery moves by its motor driven wheels. We control the motion according to appropriate acceleration values sent to it by way of a communication module. Collision-free performance is usually an important goal when coordinating a group of robots. On the contrary, both collision among the robots and that of the robot with the object are expected in our group robot system. It is the collision of the object with the robots that makes the object move and the collision among the robots that causes energy exchange among them. Our robots have neither external sensors nor apparatuses to communicate with other robots to avoid collisions. In this chapter, we first show, in detail, the concepts of this transportation system according to macroscopic Brownian motion. Methods to describe the system appropriate to examine control strategies are subsequently presented. To overcome essential difficulties in applying methods of molecular dynamics to our system without periodicity and to lessen computational burden, we develop a continuum mechanical description of group robots. We introduce a distribution function according to canonical mechanics where, from the outset, #

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Teturo Itami

friction proportional to robot velocity is taken into account. Development of a number of robots with specified interval of coordinates and that of momenta is calculated in time. We work with an equilibrium distribution characterized by “temperature” parameter. We derive that the temperature is determined by an ordinary differential equation in time. After analysis of the collision process, we use simulations to show validity of the methods. Then, we examine how to track the object path to the required one is examined. We give control input as a sum of a component of feedforward and that of feedback. The feedforward is a solution that satisfies the equilibrium distribution when the object follows the required path. The feedback component is given as only a proportional one. If an appropriate prediction of relaxation time of our distribution function to the equilibrium one is obtained, a way of control becomes more satisfactory.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 111

MAXIMUM PRINCIPLE FOR STOCHASTIC DISCRETE-TIME ITO EQUATIONS #

N. I. Mahmudov* Eastern Mediterranean University Gazimagusa, Mersin, Turkey

RESEARCH SUMMARY In this chapter, a new version of maximum principle for discrete-time stochastic optimal control problem governed by stochastic a difference Ito equation is established. A new backward stochastic difference Ito equation is introduced, and it is shown that stochastic the discrete-time maximum principle is associated with the solution of a backward stochastic difference Ito equation. Based on the backward stochastic difference Ito equation discretetime stochastic maximum principle for the stochastic discrete optimal control problem is obtained. A sufficient condition for the problem is also given, and the solution of discrete time stochastic linear-quadratic optimal control problem is presented.

#

This chapter was previously published in Brownian Motion: Elements, Dynamics and Applications, edited by Mark A. McKibben and Micah Webster, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 112

ON THE CONTROLLABILITY FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS DRIVEN BY A FRACTIONAL BROWNIAN MOTION IN A HILBERT SPACE #

El Hassan Lakhel* National School of Applied Sciences, Cadi Ayyad University, Safi, Morocco

RESEARCH SUMMARY In this chapter we study the controllability results of neutral stochastic functional differential equations with time varying delays driven by fractional Brownian motion in a real separable Hilbert space. The controllability results are obtained using stochastic analysis and a fixed-point strategy. Finally, an illustrative example is provided to demonstrate the effectiveness of the theoretical result.

#

This chapter was previously published in Brownian Motion: Elements, Dynamics and Applications, edited by Mark A. McKibben and Micah Webster, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 113

CONTROLLABILITY OF IMPULSIVE NEUTRAL STOCHASTIC FUNCTIONAL INTEGRO-DIFFERENTIAL EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION #

El Hassan Lakhel* and Mark A. McKibben† National School of Applied Sciences, Cadi Ayyad University, Safi, Morocco West Chester University, Pennsylvania, US

RESEARCH SUMMARY This chapter focuses on the controllability of impulsive neutral stochastic delay partial functional integro-differential equations perturbed by a fractional Brownian motion with 1

Hurst parameter 𝐻 ∈ ( , 1). Sufficient conditions are established using the theory of 2

resolvent operators developed by R. Grimmer1 combined with a fixed point approach for achieving the required result. An example is provided to illustrate the applicability of the abstract theory.

#

This chapter was previously published in Brownian Motion: Elements, Dynamics and Applications, edited by Mark A. McKibben and Micah Webster, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected] † E-mail address: [email protected] 1 R. Grimmer, Resolvent operators for integral equations in Banach spaces, Trans. Amer. Math. Soc, 273, 33-349 (1982).

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 114

SPECIFIC FEATURES OF BROWNIAN DIFFUSION OF NANOPARTICLES IN MICRO-NANODROPLETS #

Sergey P. Fisenko* and Yuliya A. Khodyko† A.V. Luikov Heat and Mass Transfer, Institute of National Academy of Sciences of Belarus, Minsk, Belarus

RESEARCH SUMMARY The Brownian diffusion of nanoparticles in a liquid micron size droplet is considered. For an equilibrium distribution function of nanoparticles the mean radius-vector of all nanoparticles is calculated. Numerically and analytically the relaxation of arbitrary initial distribution function to the equilibrium distribution function is studied. Simulation of the Brownian diffusion of nanoparticles in evaporating droplet helps to explain the formation of hollow structures in low pressure spray experiments. Brownian diffusion of nanoparticles in 2D circle is studied also.

#

This chapter was previously published in Brownian Motion: Elements, Dynamics and Applications, edited by Mark A. McKibben and Micah Webster, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected] † E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 115

BROWNIAN MOTION AND THE FORMATION OF DARK MATTER HALOES #

N. Hiotelis* 1st Lyceum of Athens, Athens, Greece

RESEARCH SUMMARY The density δ around a point of an initial snapshot of the Universe, smoothed at scale R, exhibits a random walk for varying R. The nature of this random walk depends on the form of the particular filter used to smooth the density field. In the case when the filter is a k-sharp one, δ executes a Brownian motion. We use a combination of a path integral approach with the model of the Brownian motion in order to estimate two important characteristics of dark matter haloes, multiplicity functions and number densities. In our analysis we include the role of the extended environment of haloes and the results are compared with the predictions of numerical simulations. A satisfactory agreement is found. More data, available from the predictions of N-body simulations, are needed in order to improve our understanding about the process of structure formation, is necessary.

#

This chapter was previously published in Brownian Motion: Elements, Dynamics and Applications, edited by Mark A. McKibben and Micah Webster, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 116

LITERATURE AS A DIFFUSION PROCESS

#

Agamirza E. Bashirov1,2* and Gunash Bashirova3† 1

Eastern Mediterranean University, Gazimagusa, Turkey Institute of Control Systems, ANAS, Baku, Azerbaijan 3 Institute of Manuscripts, ANAS, Baku, Azerbaijan

2

RESEARCH SUMMARY In the second half of the 20th century a new viewpoint to literature was established. This viewpoint presents literature as a reflection of nature in the narrative form transmitted through humans. Unlike the traditional viewpoint, which considers literature as an invention of humans for cultural needs, this new viewpoint is open for study of literature by use of mathematical methods. In this chapter we demonstrate similarities between literature and diffusion, and present some ideas about how to model the structure of literary texts as a specific diffusion process. The chapter is addressed not only to mathematicians but also to literary philosophers. Therefore, a speculative form is used with a minimum number of mathematical formulae, and necessary information from related fields is included in an effort to make the chapter self-contained.

#

This chapter was previously published in Brownian Motion: Elements, Dynamics and Applications, edited by Mark A. McKibben and Micah Webster, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected] † E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 117

ALMOST PERIODIC SOLUTION OF SOME STOCHASTIC DIFFERENCE EQUATIONS #

Mamadou Moustapha Mbaye* Université Gaston Berger de Saint-Louis, Saint-Louis, Sénégal

RESEARCH SUMMARY In this chapter, we study and obtain the existence of almost periodic solutions of some stochastic difference equations. We recall the basic theory of random mean almost periodic sequences on ℤ+. Using dichotomy techniques, and some appropriate assumptions, we establish the existence of a globally attracting almost periodic solution of a semilinear system of difference equations. To apply our abstract results, we consider the discrete reproducing populations with overlapping generations.

#

This chapter was previously published in Brownian Motion: Elements, Dynamics and Applications, edited by Mark A. McKibben and Micah Webster, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 118

IMPULSIVE STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY G-BROWNIAN MOTION #

Lanying Hu* and Yong Ren† Department of Mathematics, Anhui Normal University, Wuhu, China

RESEARCH SUMMARY In this chapter, we prove the existence and uniqueness of a solution to stochastic differential equations driven by G-Brownian motion with nonlinear impulsive effects (IGSDEs, for short). The results are established using an equivalent relation between the solution of IGSDEs and that of the stochastic differential equations driven by G-Brownian motion (GSDEs, for short) without nonlinear impulsive effects.

#

This chapter was previously published in Brownian Motion: Elements, Dynamics and Applications, edited by Mark A. McKibben and Micah Webster, New York: Nova Publishers Inc., 2015. * [email protected] † [email protected] and [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 119

FRACTIONAL STOCHASTIC DIFFERENTIAL EQUATIONS

#

P. Balasubramaniam* and P. Tamilalagan Gandhigram Rural Institute-Deemed University, Tamil Nadu, India

RESEARCH SUMMARY In this chapter, we discuss the existence of mild solutions for semilinear fractional stochastic differential equations [FSDEs] using various methods. While studying FSDEs, the question, “What is its solution,” naturally arises. As of yet there is no accurate solution representation for FSDEs. Semigroup theory is used to study the existence of a mild solution for FSDEs of two types: the one-sided probability density function is used for one type and Mainardi’s function is used for the second. Since the Riemann- Liouville and the Caputo fractional operators possess neither semigroup nor commutative properties, which are inherent to the derivatives of integer order, the solution representation using semigroup theory is incorrect. Rather, resolvent operators should be used. Accordingly, we discuss the existence of a mild solution for FSDEs using analytic resolvent operators.

#

This chapter was previously published in Brownian Motion: Elements, Dynamics and Applications, edited by Mark A. McKibben and Micah Webster, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 120

ABSTRACT SECOND-ORDER DAMPED STOCHASTIC EVOLUTION EQUATIONS IN A HILBERT SPACE DRIVEN BY FRACTIONAL BROWNIAN MOTION #

Mark A. McKibben* and Micah Webster† West Chester University, Pennsylvania, US Goucher College, Maryland, US

RESEARCH SUMMARY We investigate two classes of abstract second-order stochastic evolution equations driven by a fractional Brownian motion (fBm) in a separable Hilbert space. The first is an abstract functional stochastic evolution equation and the second class allows for nonlinearities at a given time t to depend on not only on the state of the solution at time t, but also on the corresponding probability distribution at time t. We establish the existence and uniqueness of mild solutions and illustrate the applicability of the theory through two examples.

#

This chapter was previously published in Brownian Motion: Elements, Dynamics and Applications, edited by Mark A. McKibben and Micah Webster, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected] † E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 121

ABSTRACT CONVEX FUNCTIONALS DEFINED ON ℝ𝓷 AND THEIR SUBDIFFERENTIABILITY #

Seyedalireza Seyedi1,*, Iraj Sadegh Amiri2,† and Sara Chaghervand3,‡ 1

Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran 2 Photonics Research Centre, University of Malaya, Kuala Lumpur, Malaysia 3 Department of Electrical Engineering, Borujerd Branch, Islamic Azad University, Borujerd, Iran

RESEARCH SUMMARY Convexity as a main field of Euclidean geometry has its proof, in the language of algebra and analysis. This study proposes abstract convex functionals and investiagtes the existence of their subdifferentiability which is defined on ℝ𝓃 based on the Inheritance and Generalizability of function properties on functionals.

#

This chapter was previously published in A Note on Inheritance and Generalizability Properties in Optimal Control Problems, edited by Iraj Sadegh Amiri, New York: Nova Publishers Inc., 2017. * [email protected]. † Corresponding Author address. E-mail: [email protected]. ‡ [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 122

CONVEX-ALONG-RAYS FUNCTIONALS DEFINED ON ℝ𝓷 AND THEIR SUBDIFFERENTIABILITY #

Seyedalireza Seyedi1,, Iraj Sadegh Amiri2,† and Sara Chaghervand3,‡ 1

Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran 2 Photonics Research Centre, University of Malaya, Kuala Lumpur, Malaysia 3 Department of Electrical Engineering, Borujerd Branch, Islamic Azad University, Borujerd, Iran

RESEARCH SUMMARY As a major branch of Euclidean geometry, convexity has its proof in the field of algebra and analysis. This study investigates convex-along-rays functionals and based on the Inheritance and Generalizability of function properties on functionals it analyses the existence of their subdifferentiability which is defined on ℝ𝓃 .

#

This chapter was previously published in A Note on Inheritance and Generalizability Properties in Optimal Control Problems, edited by Iraj Sadegh Amiri, New York: Nova Publishers Inc., 2017.  Seyedalireza Seyedi: E-mail: [email protected]. † Corresponding author: Iraj Sadegh Amiri. E-mail: [email protected]. ‡ Sara Chaghervand: E-mail: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 123

INCREASING POSITIVELY HOMOGENEOUS FUNCTIONAL DEFINED ON ℝ𝓷 AND THEIR SUBDIFFERENTIABILITY #

Seyedalireza Seyedi1,*, Iraj Sadegh Amiri2,† and Sara Chaghervand3,‡ 1

Department of Mathematics, Hamedan Branch, Islamic Azad University,Hamedan, Iran 2 Photonics Research Centre, University of Malaya, Kuala Lumpur, Malaysia 3 Department of Electrical Engineering, Borujerd Branch, Islamic Azad University, Borujerd, Iran

RESEARCH SUMMARY The homogeneous functionals which are defined on the cone ℝ𝓃 are well presented and developed. This paper discusses increasing positively homogeneous (IPH) functionals and based on the Inheritance and Generalizability of function properties on functionals, it investigates the existence of their sub differentiability on ℝ𝓃 .

#

This chapter was previously published in A Note on Inheritance and Generalizability Properties in Optimal Control Problems, edited by Iraj Sadegh Amiri, New York: Nova Publishers Inc., 2017. * [email protected] † Corresponding Author address: [email protected]. ‡ [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 124

THE CUTTING ANGLE METHOD AND A LOCAL SEARCH ON OPTIMAL CONTROL PROBLEMS #

Seyedalireza Seyedi1,, Iraj Sadegh Amiri2,†, Sara Chaghervand3,‡, Rohanin Ahmad4,§ and Mohd Ismail abd Aziz4,║ 1

Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran 2 Photonics Research Centre, University of Malaya, Kuala Lumpur, Malaysia 3 Department of Electrical Engineering, Borujerd Branch, Islamic Azad University, Borujerd, Iran 4 Department of Mathematics, Faculty Science, UniversitiTeknologi Malaysia, Skudai, Johor, Malaysia

RESEARCH SUMMARY Optimal control is a study on way of choosing the best set of decisions to accomplish a particular objective. The paper mainly concerns the combinations of the Cutting Angle Method (CAM) with a local search in global optimization for solving functionals. Based on using the unit vector, a new technique is proposed to employ the CAM directly on optimal control problems. The numerical findings indicated that the proposed approach is very beneficial in the search for a global minimum. #

This chapter was previously published in A Note on Inheritance and Generalizability Properties in Optimal Control Problems, edited by Iraj Sadegh Amiri, New York: Nova Publishers Inc., 2017.  E-mail: [email protected]. † Email: [email protected]. ‡ E-mail: [email protected]. § E-mail: [email protected], ║ [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 125

THE CUTTING ANGLE METHOD FOR SOLVING OF VARIATIONAL PROBLEMS

#

Seyedalireza Seyedi1,, Iraj Sadegh Amiri2,†, Sara Chaghervand3,‡, Rohanin Ahmad4,§ and Mohd Ismail abd Aziz4,║ 1

Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran 2 Photonics Research Centre, University of Malaya, Kuala Lumpur, Malaysia 3 Department of Electrical Engineering, Borujerd Branch, Islamic Azad University, Borujerd, Iran 4 Department of Mathematics, Faculty Science, UniversitiTeknologi Malaysia, Skudai, Johor, Malaysia

RESEARCH SUMMARY Calculus of variations which is a field of mathematics deals with functionals. This study puts forward an application of the cutting angle method on a class of problems referred to as the variational problems. The solution approach is based on a recent technique which is called the unit vectors combinations. At the end of the study the numerical findings will be presented.

#

This chapter was previously published in A Note on Inheritance and Generalizability Properties in Optimal Control Problems, edited by Iraj Sadegh Amiri, New York: Nova Publishers Inc., 2017.  E-mail: [email protected]. † E-mail: [email protected]. ‡ E-mail: [email protected]. § E-mail: [email protected]. ║ E-mail: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 126

THE CUTTING ANGLE METHOD ON OPTIMAL CONTROL PROBLEMS

#

Seyedalireza Seyedi1,, Iraj Sadegh Amiri2,†, Sara Chaghervand3,‡, Rohanin Ahmad4,§ and Mohd Ismail abd Aziz4,¶ 1

Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran 2 Photonics Research Centre, University of Malaya, Kuala Lumpur, Malaysia 3 Department of Electrical Engineering, Borujerd Branch, Islamic Azad University, Borujerd, Iran 4 Department of Mathematics, Faculty Science, UniversitiTeknologi Malaysia, Skudai, Johor, Malaysia

RESEARCH SUMMARY A study of optimal control is a way of taking a best set of decisions to accomplish a particular objective which deals with functionals. This paper focuses on an application of the cutting angle method to a class of problems referred to as the optimal control problems. The solution approach is based on a new technique called unit vector combinations. At the end of this study the numerical findings are put forward.

#

This chapter was previously published in A Note on Inheritance and Generalizability Properties in Optimal Control Problems, edited by Iraj Sadegh Amiri, New York: Nova Publishers Inc., 2017.  [email protected]. † [email protected]. ‡ [email protected]. § [email protected]. ¶ [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 127

PRESERVER PROBLEMS OVER FINITE FIELDS

#

Marko Orel1,2,3,* 1

Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, Koper, Slovenia 2 Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia 3 Andrej Marušič Institute, University of Primorska, Koper, Slovenia

RESEARCH SUMMARY Solving preserver problems represents an active research area in matrix theory. Typically it demands a characterization of all maps between two given sets of matrices that fulfill certain additional criteria. When preserver problems are studied on matrices with coefficients from a finite field, a mixture of various mathematical subdisciplines can be used to attack the problem. These include graph theory, matrix theory, theory of finite fields, and finite geometry. Since these methods are not yet widely known and did not yet reach their fully potential, we survey them in this chapter along a list of selected results. To make the content accessible as much as possible, we include basic definitions and results from the mathematical areas mentioned above, which one encounters when dealing with preserver problems. In particular, the chapter contains: an introduction to preserver problems; normal forms of various types of matrices, with a special emphasis on matrices over a finite field; a description of the connection between preserver problems over finite fields and graph homomorphisms/ chromatic graph theory; basic properties of several types of graphs that arise from various mathematical structures over a finite field, with an emphasis on their spectrum.

#

This chapter was previously published in Finite Fields: Theory, Fundamental Properties and Applications, edited by Janet Simmon, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 128

CLASSICAL COHERENT STATE TRANSFORMS OVER FINITE FIELDS #

Arash Ghaani Farashahi* Numerical Harmonic Analysis Group (NuHAG), Faculty of Mathematics, University of Vienna, Austria

RESEARCH SUMMARY Over the last decades, the mathematical theory of coherent state transforms over finite algebraic structures have achieved significant popularity in the framework of finite quantum systems, computational (numerical), and applied harmonic analysis. This theory is commonly used in science and engineering to synthesize finite size signals/data from, or to decompose finite size signals/data into, building blocks (elements of a dictionary). This chapter contains a basic and self-contained introduction to classical coherent state transforms, namely classical wavelet and classical wave-packet transforms, on finite fields. In this setting, we shall present a systematic study of the essential results on classical wavelet and wave-packet transforms in the greatest possible generality; that is, we consider coherent state transforms corresponding to the action of the classical dilations in arbitrary finite fields.

#

This chapter was previously published in Finite Fields: Theory, Fundamental Properties and Applications, edited by Janet Simmon, New York: Nova Publishers Inc., 2017. * E-mail addresses: [email protected], [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 129

THE STRUCTURE OF FINITE mΘ FIELD INTRINSIC ANATOMY #

Ayissi Etémé* Higher Teacher’s Training College, Department of Mathematics, Yaounde, Cameroon

RESEARCH SUMMARY This short chapter proposes an intrinsic representation of finite mΘ extension as this is a tradition for finite extension fields.

#

This chapter was previously published in Finite Fields: Theory, Fundamental Properties and Applications, edited by Janet Simmon, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 130

MΘ CYCLIC CODES ON A mΘ FIELD# Fidèle Ayissi Etémé1,* and Jean Armand Tsimi2† 1

University of Yaounde 1, Higher Teacher’s Training College, Department of Mathematics, Yaounde, Cameroon 2 University of Douala, Faculty of Sciences, Department of Mathematics and Computer Sciences, Douala, Cameroon

RESEARCH SUMMARY F. Ayissi Eteme and Jean Armand Tsimi define the notion of mΘ code in [Etémé and Tsimi, 2011]1. In [F Etémé and Tsimi, 2011]2 they define and characterize that of mΘ linear ℤ𝑝ℤ

codes on (pℤ , 𝐹∞ ). The purpose of this note is to define and characterize the notion of mΘ 𝑝ℤ

cyclic codes on a mΘ finite field (

ℤ𝑝ℤ

pℤ𝑝ℤ

#

, 𝐹∞ ).

This chapter was previously published in Finite Fields: Theory, Fundamental Properties and Applications, edited by Janet Simmon, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected] † E-mail address: [email protected] 1 F.A. Etémé and J.A. Tsimi: A modal Θ-approach of the notion of code, Journal of Discrete Mathematical Sciences & Cryptography, Vol. 14, No.5, pp. 445 − 473, 2011. 2 F.A. Etémé and J.A. Tsimi: A modal Θ-approach of the algebraic theory of linear codes, Journal of Discrete Mathematical Sciences & Cryptography, Vol. 14, No. 6, pp. 559 − 581, 2011.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 131

ON TWO PROBLEMS OF CARLITZ AND THEIR GENERALIZATIONS #

Ioulia N. Baoulina* Department of Mathematics, Moscow State Pedagogical University Moscow, Russia

RESEARCH SUMMARY Let Nq be the number of solutions to the equation 𝑚

𝑚

𝑘

𝑘

𝑘

(𝑎1 𝑥1 1 + ⋯ + 𝑎𝑛 𝑥𝑛 𝑛 ) = 𝑏𝑥1 1 ⋯ 𝑥𝑛 𝑛 over the finite field q = ps. Carlitz found formulas for Nq when k1 = ⋯ = kn = m1 = ⋯ = mn = 1, k = 2, n = 3 or 4, p > 2; and when m1 = ⋯ = mn = 2, k = k1 = ⋯ = kn = 1, n = 3 or 4, p > 2. In earlier papers, we studied the above equation with k1 = ⋯ = kn = 1 and obtained some generalizations of Carlitz’s results. Recently, Pan, Zhao and Cao considered the case of arbitrary positive integers k1, ⋯ , kn and proved the formula Nq = qn−1 + (−1)n−1, provided that gcd(∑𝑛𝑗=1(𝑘𝑗 𝑚1 ⋯ 𝑚𝑛 /𝑚𝑗 ) − 𝑘𝑚1 ⋯ 𝑚𝑛 , 𝑞 − 1) = 1. In this chapter, we determine Nq explicitly in some other cases.

#

This chapter was previously published in Finite Fields: Theory, Fundamental Properties and Applications, edited by Janet Simmon, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 132

COMPACTONS IN CARBON NANOTUBE ARRAYS #

Raïssa S. Noule# and Victor K. Kuetche† National Advanced School of Engineering, University of Yaounde I, Cameroon Centre d’Excellence en Technologies de l’Information et de la Communication (CETIC), University of Yaounde I, Cameroon Department of Physics, Faculty of Science, University of Yaounde I, Cameroon The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera, Trieste, Italy

RESEARCH SUMMARY In this work, we investigate the formation of ultrashort spatiotemporal optical compactons waveforms in arrays of carbon nanotubes modeled by an evolution equation derived by using a rigorous application of the reductive perturbation formalism for the Maxwell equations and for the corresponding Boltzmann kinetic equation of the distribution function of electrons in such nanomaterials. As a result, we find that the interactions between the above waveguide channels are elastic/nonelastic. We also discuss the physical applications of the results.

#

This chapter was previously published in Advances in Nonlinear Dynamics Research, edited by Margaret Palmer, New York: Nova Publishers Inc., 2017. # Email address: [email protected] † Email address: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 133

ELASTIC AND PLASTIC TYPE BEHAVIOURS IN THE FRACTAL THEORY OF MOTION AT NANOSCALE #

Maricel Agop1, Alina Gavriluţ2, Gabriel Gavriluţ2, Irina Butuc2 and Dan Dezideriu Iacob2 1

Gh. Asachi Technical University, Department of Physics, Iaşi, Romania 2 Al.I. Cuza University, Faculty of Mathematics, Iaşi, Romania

RESEARCH SUMMARY Besides the usual quantum mechanics approach of physical issues, approach from which the Newton-Ehrenfast solution results, there is a more direct approach, meaning that it starts from the interpretation of the wavefunction that results from an already existing probability density and which is given as a time and position function. We are talking about the so called hydrodynamics model of quantum mechanics. Its formalism, although a summary and one limited only to strictly intuitive correlations, brings forward some unusual notions, but through which the problems of the solid bodies’ deformations are solved. In the present chapter, considering that the solid fractal body's ''structural units'' (particles) movements take place on continuous but non-differentiable curves (fractal curves), a fractal equilibrium equation is obtained in the framework of the Scale Relativity Theory with arbitrary constant fractal dimension. Such a result is important because it allows the defining of ''fractal material constitutive laws'' at any scale resolution. Let us note that the knowledge of a constitutive law material at any scale is of great importance in understanding the mechanics that take place along any kind of interface (residual tensions, chemical composition etc.).

#

This chapter was previously published in Advances in Nonlinear Dynamics Research, edited by Margaret Palmer, New York: Nova Publishers Inc., 2017.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 134

MALIGNANT INVASION MODEL WITH A SMALL AMOUNT OF DIFFUSION IN THE FRAMEWORK OF A FRACTAL THEORY: IMPLICATIONS OF DRUG RELEASE FROM THE POLYMERIC MATRIX PROCESS #

Decebal Vasincu1, Daniel Timofte2, Lăcrămioara Ochiuz3, Maricel Agop4 and Alina Gavriluţ5, 1

Surgery Department, Biophysical Section, “Gr.T. Popa” University of Medicine and Pharmacy, Iaşi, Romania 2 Surgery Department., Hospital Sf. Spiridon, “Gr.T. Popa” University of Medicine and Pharmacy, Iaşi, Romania 3 Faculty of Pharmacy, Department of Pharmaceutical Technology, “Gr.T. Popa” University of Medicine and Pharmacy, Iaşi, Romania 4 Department of Physics, “Gh. Asachi” Technical University, Iaşi, Romania 5 Faculty of Mathematics, “Al.I. Cuza” University, Iaşi, Romania

RESEARCH SUMMARY A particular model of tumour progression (extended Perumpanani's model), assuming that the invasive cells, the connective tissue and the proteases are moving through a nondifferential medium governed by the Non-Standard Scale Relativity Theory (NSRT) (Scale Relativity Theory with arbitrary constant fractal dimension) is analyzed. In such context an action-reaction type law acting on the complex system formed by the extra cellular matrix and the non-differential medium is considered. As a result, artificial cancer cell proliferation satisfies a logistic law accounting for the competition for space with the non-differential #

This chapter was previously published in Advances in Nonlinear Dynamics Research, edited by Margaret Palmer, New York: Nova Publishers Inc., 2017.  Corresponding Author: [email protected].

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Decebal Vasincu, Daniel Timofte, Lăcrămioara Ochiuz et al.

medium. Moreover, the connective tissues concentration increases proportionally to the real fractal velocity, squared. Over small distances, it results that even in avascular stages, malignant tumours might propagate and invade healthy tissues. Exact solutions for malignant invasion model with a small amount of diffusion in the framework of the Non-Standard Scale Relativity Theory using the factorization and the Tanh methods are obtained. For small diffusion coefficients, we may conclude that there is a gap between the invasive cells front and the degraded connective tissue, the extra cellular matrix is not continuously degraded by the concentration of proteases and the latter one shows amplified followed by amortized oscillations and jumps between distinct levels. Finally, implications of drug release from the polymeric matrix process in correspondence with extended Perumpanani’s model are also provided.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 135

NON-LINEARITIES IN DRUG RELEASE PROCESSES FROM POLYMERIC MICROPARTICLES: IMPLICATIONS IN THE FRACTAL MORPHO-FUNCTIONAL STRUCTURE OF BIOLOGICAL SYSTEMS #

Lăcrămioara Ochiuz1, Daniel Timofte2, Decebal Vasincu3, Alina Gavriluţ4,, Gabriel Gavriluţ5 and Maricel Agop6 Department of Pharmaceutical Technology, Faculty of Pharmacy, “Gr. T. Popa” University of Medicine and Pharmacy, Iaşi, Romania 2 Surgery Dept., “Gr. T. Popa” University of Medicine and Pharmacy, Hospital Sf. Spiridon, Iaşi, Romania 3 Surgery Dept., Biophysical Section, “Gr. T. Popa” University of Medicine and Pharmacy, Iaşi, Romania 4 Faculty of Mathematics, Al. I. Cuza University, Iaşi, Romania 5 Faculty of Physics, Al. I. Cuza University, Iaşi, Romania 6 Department of Physics, Gh. Asachi Technical University, Iaşi, Romania 1

RESEARCH SUMMARY The adequate description of real, natural and artificial objects is restricted by the mere use of Euclidean geometry, that is, the description of integer-dimensional objects. In such perspective, this happens because numerous objects with non-integer dimensions such as, plants, galaxies, population patterns and crystal growth, are left beyond analytical purpose. The characteristics of such objects can be described by means of fractal geometry. Natural # 

This chapter was previously published in Advances in Nonlinear Dynamics Research, edited by Margaret Palmer, New York: Nova Publishers Inc., 2017. Corresponding author: Alina Gavriluţ. Faculty of Mathematics, Al.I. Cuza University, 11 Carol I Bd., Iaşi, Romania. E-mail: [email protected].

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and synthetic polymers considered as fractal objects are also included in the above category. Their main structural unit, the macromolecular coil, is known to be a fractal with typical fractal behaviour. The main idea of this chapter focuses on this type of process in which polymer fractality is responsible for drug release from various polymer matrixes. In what follows, we shall produce arguments to sustain the above statement. The present chapter analyzes the process of drug release from polymer matrix. This process has been considered as fractal polymer process. Since complexity of physical processes is replaced by fractality, the chapter studies the process through fractal approach. In drug dynamics, fractal “diffusion” equation can be obtained through fractal approximation of motion. All experimental release curves have been best demonstrated by Weibull relation (which was, in its turn, also demonstrated). Weibull parameters are related to the fractal dimension of drug release kinetics from a polymer matrix. Such a dimension can characterize and measure the complexity of the system. In the above-mentioned context, some experimental results of our researches are presented and analyzed by comparing them with Peppas relation, a basic law in the description of drug release kinetics. Consequently, experimental data for Weibull relation are better correlated with certain resulting factors. At the same time, some conclusions regarding the phenomena involved in the process are considered as being based on the approach. Some implications of the drug release processes in the fractal morpho-functional structure of the biological systems are analyzed.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 136

CHAOS AND SELF-STRUCTURING BEHAVIORS IN THE DYNAMICS OF BIOLOGICAL STRUCTURES: IMPLICATIONS OF DRUG RELEASE FROM THE POLYMERIC MATRIX PROCESS #

Daniel Timofte1, Lăcrămioara Ochiuz2, Decebal Vasincu3, Gabriel Crumpei4, Alina Gavriluţ5,* and Maricel Agop6 Surgery Department, Hospital Sf. Spiridon, “Gr.T. Popa” University of Medicine and Pharmacy, Iaşi, Romania 2 Faculty of Pharmacy, Department of Pharmaceutical Technology, “Gr.T. Popa” University of Medicine and Pharmacy, Iaşi, Romania 3 Surgery Department, Biophysical Section, “Gr.T. Popa” University of Medicine and Pharmacy, Iaşi, Romania 4 Catharsis Psychiatry, Psychotherapy and Counseling Center Iaşi, Romania 5 Faculty of Mathematics, “Al.I. Cuza” University, Iaşi, Romania 6 Department of Physics, “Gh. Asachi” Technical University, Iaşi, Romania

1

RESEARCH SUMMARY In the most general representation, the biological systems can be divided into three different categories such as open, dissipative and non-linear systems. In our opinion, the “specialization” process of any biological structure (for instance, differentiation process) is based on the legitimate alternation between chaos and order of mutual states. This behavior is defined by the living matter multivalent logic and its communication codes. Further to this representation, we can say now that this visible interdisciplinary work aims to explain how mathematical knowledge can be used to describe, predict and control the phenomena

#

This chapter was previously published in Advances in Nonlinear Dynamics Research, edited by Margaret Palmer, New York: Nova Publishers Inc., 2017. * Corresponding Author: [email protected].

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observed in some biological systems. From a functional point of view and not only, we understand here the biological systems in the particular sense of the discipline known under a variety of names such as: “complexity theory”, self-organization theory”, “chaos theory” or “non-linear dynamics”. Our choice was not easy but in what follows we will use the latter name, non-linear dynamics, respectively. Assuming that the biological systems are fractal systems, a few aspects of natural dynamics in biological structures are studied. The “non-linear dynamics” analysis in an arbitrary space with constant fractal dimension, using an extended version of the Scale Relativity Theory, has been performed. Additionally, a dedicated mathematical model of biological non-linear system by association with stochastic Levy type processes was developed. Finally, some implications of the drug release from polymeric matrix process are given.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 137

BEHAVIORS OF TRAVELLING WAVES AND SHAPIRO STEPS TYPES IN A TUMOUR-GROWTH MODEL #

Cipriana Ştefănescu1, Daniel Timofte2, Decebal Vasincu3, Dan Tesloianu4, Maricel Agop5 and Alina Gavriluţ6, 1

Faculty of Medicine, Biophysics and Medical Physics Department, “Gr.T. Popa” University of Medicine and Pharmacy, Iaşi, Romania 2 Surgery Department, Hospital Sf. Spiridon, “Gr.T. Popa” University of Medicine and Pharmacy, Iaşi, Romania 3 Surgery Department, Biophysical Section, “Gr.T. Popa” University of Medicine and Pharmacy, Iaşi, Romania 4 IV Internal Medicine Department, “Gr.T. Popa” University of Medicine and Pharmacy, Iaşi, Romania 5 Department of Physics, “Gh. Asachi” Technical UniversityIaşi, Romania 6 Faculty of Mathematics, “Al.I. Cuza” University, Iaşi, Romania

RESEARCH SUMMARY Distinct from simple genetic diseases where an inherited mutation in a single gene is sufficient to determine the pathological phenotype, cancer, among pathogenetic diseases, has the most complex mechanism where typically numerous mutations are present. Current medical theory views the pathology of cancer as an example of a complex adaptive system whose behaviour expresses the interplay between order and chaos. With some cancers, tumorigenesis is driven by chaotic behaviour, while other cancers show more order in their formation. Accompanying the transformation from normal to neoplastic tissue is an overall decrease in the complexity of the cell.

#

This chapter was previously published in Advances in Nonlinear Dynamics Research, edited by Margaret Palmer, New York: Nova Publishers Inc., 2017.  Corresponding Author: [email protected].

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In such context, in the present chapter, in a simplified approach of Ivancevic growth physical model, we show that important features appear. A numerical analysis of this model is performed, involving travelling wave solutions for some choices of parameters. Moreover, a reduced travelling wave equations system results which exhibits an amplitude dependence on the “pseudo-period,” indicating a strong non-linearity and a characteristic increase in Shapiro steps. Finally, a fractal model of the biological system evolution is proposed.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 138

THE ASTONISHING EVOLUTIONARY DYNAMICS OF A CLASS OF NONLINEAR DISCRETE 2D PATTERN FORMATION AND GROWTH MODELS #

Leonid Yaroslavsky* Department of Physical Electronics, School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel

RESEARCH SUMMARY A family of 2D pattern formation and growth nonlinear discrete binary models with feedback are introduced and their evolutionary dynamics is experimentally studied. The models are inspired by the famous mathematical “Game of Life” and act on rectangular arrays (“living space”) of cells, which assume binary states 0 (“dead”) and 1 (“alive”). At each evolutionary step, each cell keeps or inverts its state depending on weighted sum of states of its spatial neighbors at the previous step and on a random binary control signal, which activates or de-activates, with a certain probability, the change of the cell state. The summation weight coefficients specify particular models of the family. A number of new and astonishing phenomena discovered in the evolutionary collective behavior of patterns the models generate is described.

#

This chapter was previously published in Advances in Nonlinear Dynamics Research, edited by Margaret Palmer, New York: Nova Publishers Inc., 2017. * Corresponding Author address Email: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 139

DIRECTED PARTIAL ORDERS ON QUATERNIONS A BRIEF SUMMARY #

Jingjing Ma* Department of Mathematics and Statistics, University of Houston Clear Lake, Houston, TX, US

RESEARCH SUMMARY This paper collects some old problems on lattice orders and directed partial orders on complex numbers and quaternions, and summarizes recent development in answering those questions.

#

This chapter was previously published in Quaternions: Theory and Applications, edited by Sandra Griffin, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 140

SPIN 1 PARTICLE WITH ANOMALOUS MAGNETIC MOMENT IN THE EXTERNAL UNIFORM ELECTRIC FIELD #

E. M. Ovsiyuk1,*, Ya. A. Voynova2,†, V. V. Kisel3,‡, V. Balan4,§ and V. M. Red’kov5¶ 1

Mozyr State Pedagogical University, Belarus 2 Secondary School, Yelsk Region, Belarus 3 BGUIR, Minsk, Belarus 4 University Politehnica of Bucharest, Romania 5 Institute of Physics, NAS, Belarus

RESEARCH SUMMARY Within the matrix 10-dimensional Duffin-Kemmer-Petiau formalism applied to the Shamaly-Capri field, we study the behavior of a vector particle with anomalous magnetic moment in the presence of an external uniform electric field. The separation of variables in the wave equation is performed by using projective operator techniques and the theory of DKP-algebras. The whole wave function is decomposed into the sum of three components Ψ0, Ψ+, Ψ+. It is enough to solve the equation for the main component Φ0, the two remaining ones being uniquely determined by it. Consequently, the problem reduces to three independent differential equations for three functions, which are of the type of one-dimensional Klein– Fock–Gordon equation in the presence of a uniform electric field modified by the nonvanishing anomalous magnetic moment of the particle. The solutions are constructed in terms #

This chapter was previously published in Quaternions: Theory and Applications, edited by Sandra Griffin, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected]. † E-mail address: [email protected]. ‡ E-mail address: [email protected]. § E-mail address: [email protected]. ¶ E-mail address: [email protected].

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of confluent hypergeometric functions. For assigning physical sense for these solutions, one must impose special restrictions on a certain parameter related to the anomalous moment of the particle. The neutral spin 1 particle is considered as well. In this case, the main manifestation of the anomalous magnetic moment consists in the modification of the ordinary plane wave solution along the electric field direction. Again, one must impose special restrictions on a parameter related to the anomalous moment of the particle.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 141

TECHNIQUES OF PROJECTIVE OPERATORS USED TO CONSTRUCT SOLUTIONS FOR A SPIN 1 PARTICLE WITH ANOMALOUS MAGNETIC MOMENT IN THE EXTERNAL UNIFORM MAGNETIC FIELD #

V. V. Kisel1,*, Ya. A. Voynova2,†, E. M. Ovsiyuk3,‡, V. Balan4,§ and V. M. Red'kov5,¶ 1

BGUIR, Minsk, Belarus Secondary School, Yelsk Region, Belarus 3 Mozyr State Pedagogical University, Belarus 4 University Politehnica of Bucharest, Romania 5Institute of Physics, NAS Belarus 2

RESEARCH SUMMARY Within the matrix 10-dimensional Duffin–Kemmer-Petiau formalism applied to the Shamaly–Capri field, we study the behavior of a vector particle with anomalous magnetic moment in presence of an external uniform magnetic field. The separation of variables in the wave equation is performed using projective operator techniques and the theory of DKP-algebras. The problem is reduced to a system of 2-nd order differential equations for three independent functions, which is solved in terms of confluent hypergeometric functions. Three series of energy levels are found, of which two substantially differ from those for spin 1 particles without anomalous magnetic moment. For assigning to #

This chapter was previously published in Quaternions: Theory and Applications, edited by Sandra Griffin, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected]. † E-mail address: [email protected]. ‡ E-mail address: [email protected]. § E-mail address: [email protected]. ¶ E-mail address: [email protected].

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them physical sense for all the values of the main quantum number n = 0, 1, 2, ..., one must impose special restrictions on a parameter related to the anomalous moment. Otherwise, only some part of the energy levels corresponds to bound states. The neutral spin 1 particle is considered as well. In this case no bound states exist in the system, and the main qualitative manifestation of the anomalous magnetic moment consists in the occurrence of a space scaling of the arguments of the wave functions, compared to a particle without such a moment.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 142

A QUATERNION APPROACH IN THE ESTIMATION OF THE ATTITUDE OF AN INDUSTRIAL ROBOT #

Bernardino Benito Salmerón-Quiroz1, PhD, Gerardo Villegas-Medina1, José Fermi Guerrero-Castellanos2, PhD, Elena O. Milhacea3 and Rodolfo Villalobos-Martinez4 1

Instituto Politécnico Nacional (I.P.N.), SEPI ESIME Azcapotzalco, CDMX, México 2 Faculty of Sciences of the Electronics BUAP, Puebla, México 3 Division of Postgraduate Studies and Research, TecNM/Instituto Tecnológico de Morelia, Morelia, Michoacán, México 4 Instituto Politécnico Nacional (I.P.N.), ESIT Zacatenco CDMX, México

RESEARCH SUMMARY Traditionally, the automotive industry has been the largest employer of robots, but their control is inline and programmed to follow planning trajectories. In this case, in the department motor’s test of Volkswagen Mexico a semi-autonomous robot is developed. To date, some critical technical problems must be solved in a number of areas, including in dynamics control. Generally, the attitude estimation and the measurement of the angular velocity are a requirements for the attitude control. As a result, the computational cost and the complexity of the control loop is relatively hight. This chapter deals with the implementation of a cheap Micro AHRS (Attitude and Heading Reference System) using low-cost inertial sensors. In the present chapter, the technique proposed is designed with attitude estimation and the prediction movement via the kinematic of a 4GDL robot. With this approach, only the measurements of at least two non-collinear directional sensors are needed. Since the control

#

This chapter was previously published in Quaternions: Theory and Applications, edited by Sandra Griffin, New York: Nova Publishers Inc., 2017.

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laws are highly simple and a model-based observer for angular velocity reconstruction is not needed, the proposed new strategy is very suitable for embedded implementations. The global convergence of the estimation and prediction techniques is proved. Simulation with some robustness tests is performed.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 143

2D HERMITE-GAUSSIAN AND GAUSS-LAGUERRE CIRCULAR HARMONIC EIGENFUNCTION OF THE QUATERNION AND REDUCED BIQUATERNION FOURIER TRANSFORM #

Soo-Chang Pei and Yu-Zhe Hsiao Graduate Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan

RESEARCH SUMMARY The quaternions, reduced biquaternions (RBs) and their respective Fourier transformations, i.e., discrete quaternion Fourier transform (DQFT) and discrete reduced biquaternion Fourier transform (DRBQFT), are very useful for multi-dimensional signal processing and analysis. In this paper, the basic concepts of quaternion and RB algebra are reviewed, and we introduce the two dimensional Hermite-Gaussian functions (2D-HGF) as the eigenfunction of DQFT/DRBQFT, and the eigenvalues of 2D-HGF for three types of DQFT and two types of DRBQFT. After that, the relation between 2D-HGF and GaussLaguerre circular harmonic function (GLCHF) is given. From the aforementioned relation and some derivations, the GLCHF can be proved as the eigenfunction of DQFT/DRBQFT and its eigenvalues are summarized. These GLCHFs can be used as the basis to perform color image expansion. The expansion coefficients can be used to reconstruct the original color image and as a rotation invariant feature. The GLCHFs can also be applied to color matching applications.

# 

This chapter was previously published in Quaternions: Theory and Applications, edited by Sandra Griffin, New York: Nova Publishers Inc., 2017. Corresponding author: E-mail: [email protected], [email protected]; Address: Graduate Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan R.O.C.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 144

THE QUATERNIONS WITH AN APPLICATION OF QUADROTORS TEAM FORMATION #

Wesam Jasim* and Dongbing Gu† College of Computer Science and Information Technology, University of Anbar, Ramadi, Iraq School of Computer Science and Electronic Engineering, University of Essex, Wivenhoe Park, Colchester, UK

RESEARCH SUMMARY The unit quaternion system was invented in 1843 by William Rowan Hamilton as an extension to the complex number to find an answer to the question (how to multiply triplets?). Yet, quaternions are extensively used to represent the attitude of a rigid body such as quadrotors, which is able to alleviate the singularity problem caused by the Euler angles representation. The singularity is in general a point at which a given mathematical object is not defined and it outcome of the so called gimbal lock. The singularity is occur when the pitch angles rotation is θ = ±90o. In this chapter, a leader-follower formation control problem of quadrotors is investigated. The quadrotor dynamic model is represented by unit quaternion with the consideration of external disturbance. Three different control techniques are proposed for both the leader and the follower robots. First, a nonlinear 𝐻∞ design approach is derived by solving a Hamilton-Jacobi inequality following from a result for general nonlinear affine systems. Second, integral backstepping (IBS) controllers are also addressed for the leader-follower formation control problem. Then, an iterative Linear Quadratic Regulator (iLQR) is derived to solve the problem of leader-follower formation. The simulation results from all types of controllers are compared and robustness performance of the 𝐻∞ controllers,

#

This chapter was previously published in Quaternions: Theory and Applications, edited by Sandra Griffin, New York: Nova Publishers Inc., 2017. * E-mail address: wmj [email protected]. † E-mail address: [email protected]

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fast convergence and small tracking errors of iLQR controllers over the IBS controllers are demonstrated.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 145

DETERMINANTAL REPRESENTATIONS OF THE DRAZIN AND W-WEIGHTED DRAZIN INVERSES OVER THE QUATERNION SKEW FIELD WITH APPLICATIONS #

Ivan Kyrchei* Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine

RESEARCH SUMMARY A generalized inverse of a given quaternion matrix (similarly, as for complex matrices) exists for a larger class of matrices than the invertible matrices. It has some of the properties of the usual inverse, and agrees with the inverse when a given matrix happens to be invertible. There exist many different generalized inverses. In this chapter, we consider determinantal representations of the Drazin and weighted Drazin inverses over the quaternion skew field. Due to the theory of column-row determinants recently introduced by the author, we derive determinantal representations of the Drazin inverse for both Hermitian and arbitrary matrices over the quaternion skew field. Using obtained determinantal representations of the Drazin inverse we get explicit representation formulas (analogs of Cramer’s rule) for the Drazin inverse solutions of the quaternionic matrix equations AXB = D and, consequently, AX = D, XB = D in both cases when A and B are Hermitian and arbitrary, where A, B can be noninvertible matrices of appropriate sizes. We obtain determinantal representations of solutions of the differential quaternionic matrix equations, Xˊ + AX = B and Xˊ + XA = B, where A is noninvertible as well. Also, we obtain new determinantal representations of the W-weighted Drazin inverse over the quaternion skew field. We give determinantal representations of the W-weighted #

This chapter was previously published in Quaternions: Theory and Applications, edited by Sandra Griffin, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected].

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Drazin inverse by using previously obtained determinantal representations of the Drazin inverse, the Moore- Penrose inverse, and the limit representations of the W-weighted Drazin inverse in some special case. Using these determinantal representations of the W-weighted Drazin inverse, we derive explicit formulas for determinantal representations of the Wweighted Drazin inverse solutions of the quaternionic matrix equations WAWX = D, XWAW = D, and W1AW1XW2BW2 = D.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 146

A PROCESS ALGEBRA APPROACH TO QUANTUM ELECTRODYNAMICS: PHYSICS FROM THE TOP UP

#

William Sulis* McMaster University, Hamilton, Canada

RESEARCH SUMMARY The process algebra was developed to study information flow and emergence in complex systems. From this perspective, fundamental phenomena are viewed as emerging from primitive informational elements generated by processes. The process algebra has been shown to successfully reproduce scalar non-relativistic quantum mechanics (NRQM), providing a realist model of quantum mechanics which appears to be free of the usual paradoxes and dualities. NRQM appears as an effective theory which emerges under specific asymptotic limits. Space-time, scalar particle wave functions and the Born rule are all emergent in this framework. In this chapter, the process algebra model is reviewed, extended to the relativistic setting and then applied to the problem of electrodynamics. A semiclassical version is presented in which a Minkowski-like space-time emerges as well as a vector potential that is discrete and photon-like at small scales and near-continuous and wave-like at large scales. QED is viewed as an effective theory at small scales while Maxwell theory becomes an effective theory at large scales. The process algebra version of quantum electrodynamics is intuitive and realist, free from divergences and eliminates the distinction between particle, field and wave. The need for second quantization is eliminated and the particle and field theories rest on a common foundation, clarifying and simplifying the relationship between the two.

#

This chapter was previously published in Complex Systems: Theory and Applications, edited by Rebecca Martine, New York: Nova Publishers Inc., 2017. * Email: [email protected]

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 147

REALIZING SUCCESS FOR COMPLEX CONVERGING SYSTEMS #

Geerten Van de Kaa Faculty of Technology, Policy, and Management, Delft University of Technology, Delft, the Netherlands

RESEARCH SUMMARY In this chapter a specific aspect of complex systems, the fact that they may consist of established subsystems or components that originate from converging industries, will be described. To realize such complex systems, common standards with which the components of such systems can be interconnected are essential. A specific type of standard will be described which can be used to realize such complex systems; subsystem standards. It will be determined which factors affect the success of subsystem standards by studying a specific example of a subsystem standard; USB. This specific case illustrates the importance of flexibility; standards should guarantee a certain amount of flexibility so that it is possible to adapt them to changing requirements that inevitably emerge when components that originate from multiple converging industries are connected. Second, the case illustrates the importance of network diversity in that subsystem standards should be supported by a diverse network in terms of stakeholder representation. The paper concludes with recommendations for future research directions.

#

This chapter was previously published in Complex Systems: Theory and Applications, edited by Rebecca Martine, New York: Nova Publishers Inc., 2017.  Corresponding Author Address: Faculty of Technology, Policy, and Management, Delft University of Technology, Jaffalaan, 5, 2628BX, Delft, the Netherlands. Tel: 31.15. 2786789, Tel: 31.15.2786789, Email: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 148

DEVELOPMENT OF THE GENERALIZED NONLINEAR SCHRÖDINGER EQUATION OF ROTATING COSMOGONICAL BODY FORMATION #

Alexander M. Krot* Laboratory of Self-Organization System Modeling, United Institute of Informatics Problems of National Academy of Sciences of Belarus, Minsk, Belarus

RESEARCH SUMMARY This chapter considers the statistical theory of gravitating spheroidal bodies to derive and develop a new generalized nonlinear Schrödinger equation of a gravitating cosmogonical body formation. Previously, the statistical theory for a cosmogonical body forming (so-called spheroidal body with fuzzy boundaries) has been proposed. As shown, interactions of oscillating particles inside a spheroidal body lead to a gravitational condensation increasing with the time. In this connection, the notions of an antidiffusion mass flow density as well as an antidiffusion particle velocity in a rotating spheroidal body have been introduced. The generalized nonlinear time-dependent Schrödinger equation describing a gravitational formation of a rotating cosmogonical body is derived. This chapter considers different dynamical states of a gravitating spheroidal body and respective forms of the generalized nonlinear time-dependent Schrödinger equation including the virial mechanical equilibrium, the quasi-equilibrium and the gravitational instability cases. Besides, the last case involves the avalanche gravitational compression increasing (when the parameter of gravitational condensation grows exponentially with the time) among them the case of unlimited gravitational compression leading to a collapse of a spheroidal body. Within framework of oscillating interactions of particles, a frequency interpretation of the gravitational potential and the gravitational strength of a forming spheroidal body is #

This chapter was previously published in Complex Systems: Theory and Applications, edited by Rebecca Martine, New York: Nova Publishers Inc., 2017. * Corresponding Author address. Email: [email protected].

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considered in detail. In particular, we explain how Alfvén’s oscillating force modifies the forms of planetary orbits within the framework of the statistical theory of gravitating spheroidal bodies. We find that temporal deviation of the gravitational compression function of a rotating cosmogonical body induces the Alfvén additional periodic force. An oscillating behavior of the derivative of the gravitational compression function implies the special case when the additional periodic force becomes counterbalance to the gravitational force thus realizing the principle of an anchoring mechanism in exoplanetary systems.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

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Chapter 149

THE APPLICATION OF NEURAL NETWORK MODELING IN ORGANIZING A HIERARCHICAL TEACHING SYSTEM BASED ON MENTORSHIP #

A. Dashkina and D. Tarkhov Peter the Great Saint Petersburg Polytechnic University, Saint Petersburg, Russian Federation

RESEARCH SUMMARY In this chapter we consider the application of the hierarchical teaching systems and mentorship. We illustrate that they have many advantages over the conventional system of organizing the learning process within a group of learners with different levels of knowledge. The process of interaction between a teacher and students is complex and non-linear. If the knowledge is transferred not only from a teacher to learners, but also from one student to another, the system can be referred to as a hierarchical one. Neural networks prove to be an appropriate tool for creating models of such systems, so we apply them here. We have conducted a number of practical experiments which involved application of mentorship and the hierarchical teaching systems within some groups of learners. The results of the experiments were processed by neural networks. It allowed us to create a sociodynamic model of the learning process and to forecast and maximize its further results. At the end of this research we formulated the conclusions and gave practical recommendations.

#

This chapter was previously published in Complex Systems: Theory and Applications, edited by Rebecca Martine, New York: Nova Publishers Inc., 2017.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 150

MODELLING ORGANISATION NETWORKS COLLABORATING ON HEALTH AND ENVIRONMENT WITHIN ASEAN #

P. Mazzega* and C. Lajaunie 1

Geosciences Environment Toulouse, CNRS, University of Toulouse, Toulouse, France 2 Ceric - DICE - International, Comparative and European Law, CNRS, Aix-Marseille University, Aix en Provence, France

RESEARCH SUMMARY The emergence of infectious diseases is related to environmental factors such as biodiversity loss, land use and land cover changes, and regional impacts of climate change. The threat of worldwide pandemics led to the development of prevention and mitigation strategies implemented via public policies and national/international legal instruments. These measures involve networks of organisations engaged in a wide range of quite disparate activities. We present two methods to evaluate the collaborative potential of a network of 16 organisations and identify measures to promote their coordination: 1) the first method uses Galois lattices to identify groups of organisations and issues forming a nexus able to tackle with the environment and health challenges. It also allows pointing out the divide between some sub-issues that should be considered together in order to develop an integrated approach of these problems as recommended for example by the One Health initiative; 2) the second method, inspired by the functioning of networks of cerebral cortex areas for the realisation of high-level cognitive functions, analyses the graphs induced by mutual information functions between organisations. Here we evaluate these functions based on the composition of the governing boards (altogether involving 91 organisations) and partnerships (altogether #

This chapter was previously published in Complex Systems: Theory and Applications, edited by Rebecca Martine, New York: Nova Publishers Inc., 2017. * Corresponding Author email: [email protected].

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involving 263 organisations) of these organisations. The approach gives the opportunity to assess a priori the effects induced by a change in the profile of the collaborating organisations. The contributions of these two methods are then discussed and compared to other approaches developed for the analysis of social intelligence or socio-cognitive artificial systems. Both methods are illustrated by the analysis of a network of several organisations involved in the management of health and environmental issues in Southeast Asia (hot spot for emerging infectious diseases and for biodiversity). Taken as a whole, our findings show that regional governance in the health-environment sector is polycentric and entangled, and provide guidance for improving governance on the basis of the competences and collaborations of participating organisations.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 151

THE EVOLUTION EQUATION OF LIE-TYPE FOR FINITE DEFORMATIONS AND ITS TIME-DISCRETE INTEGRATION #

Zdeněk Fiala* Institute of Theoretical and Applied Mechanics CAS, Prague, Czech Republic

RESEARCH SUMMARY The theory of evolution equations of Lie-type analyses a class of systems of timedependent first-order ordinary differential equations on a Lie group (resp. homogeneous space), which are generated by vector fields related to a corresponding finite dimensional Lie algebra. Their interesting geometric features give rise to important tools, and have originated new mathematical techniques and notions used for investigating differential equations. Here, we shall identify such a type of evolution equation within solid mechanics wherein it describes the evolution of finite deformations on the space of all symmetric positive-definite matrices resp. on the general linear group. In fact, while the position and shape of a deformed body take place in the usual three-dimensional Euclidean space ℝ3, a corresponding progress of the deformation tensor C makes up a trajectory in the space of all symmetric positivedefinite matrices – a negatively curved Riemannian symmetric manifold (a specific homogeneous space). We prove that a well-known relation between deformation rate ∂C and symmetric velocity gradient d, via deformation gradient F, can actually be interpreted as an equation of Lie-type describing evolution of the deformation tensor C on the configuration space. The same applies to deformation gradient F, which evolves on the general linear group. As a consequence, this identification leads to geometrically consistent time-discrete integration schemes for finite deformation processes, such as the Runge–Kutta–Munthe-Kaas method, or also briefly mentioned the semi-discrete Magnus and Fer expansion methods. #

This chapter was previously published in Emerging Concepts in Evolution Equations, edited by Carolyn Murphy, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 152

NEW APPLICATIONS OF SYMMETRY ANALYSIS TO NONLINEAR EVOLUTION EQUATIONS #

Renat Zhdanov1,* and Qing Huang2 1

BIO-key International, Eagan, MN, US Department of Mathematics, Northwest University, Xi’an, China

2

RESEARCH SUMMARY In this chapter we present a review of our recent results on group analysis of nonlinear evolution equations in one spatial variable. The main emphasis is on the novel systematic approaches that expand the range of applications of the traditional Lie approach to evolution equations. We analyze two possible ways of expanding the applicability of Lie group methods: considering more general types of symmetries and applying the group approach to more general (fractional) evolution equations.

#

This chapter was previously published in Emerging Concepts in Evolution Equations, edited by Carolyn Murphy, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected](Corresponding author).

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 153

A METHOD FOR EXPONENTIALLY STABILIZING A CLASS OF 1-D PDES #

Abdelhadi Elharf* and Ahmed Sani† Department of Mathematics, Regional Center of the Education Professions and Formation, Agadir, Morocco Department of Mathematics, Faculty of Sciences Ibn Zohr University, Agadir, Morocco

RESEARCH SUMMARY In this chapter, we address the problem of exponential stabilization of a class of 1-D PDEs with Dirichlet boundary control. We first reformulate the control problem in semigroups context on a suitable state space. We also convert the initial system to an auxiliary one by the use of a Volterra transformation with a kernel satisfying an appropriate PDE. Secondly, we prove the exponential stabilization of the target system and we show some useful spectral properties. Thirdly, we deal with the exponential stability of the initial system. In semigroup context, this corresponds to construct a boundary controller which causes an exponential decay of the semigroup S(·) representing the closed-loop system. Precisely, ‖𝑆(𝑡)‖ = O(e-λt), t → ∞, for some λ > 0. The proposed method provides an explicit solution of the Lyapunov’s equation by means of the kernel PDE and the parameters of the system in consideration. Further, the technics of constructing the feedback law offer operational information about the stabilization mechanism.

#

This chapter was previously published in Emerging Concepts in Evolution Equations, edited by Carolyn Murphy, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected]. † E-mail address: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 154

THE PRINCIPAL COMPONENT ANALYSIS OF OMICS DATA #

Hiroyuki Yamamoto* Human Metabolome Technologies, Inc., Mizukami, Kakuganji, Tsuruoka, Yamagata, Japan

RESEARCH SUMMARY With recent advances in high-throughput technologies, large amounts of transcriptomic, proteomic, metabolomic and other omics data have become available. Biological knowledge can be extracted from these comprehensive datasets by data-driven approaches such as multivariate analysis. Omics data are high-dimensional; that is, the number of variables is much higher than the number of samples. Principal component analysis (PCA) has been widely applied to visualize omics data in low-dimensional subspaces. In this chapter, we review the applications of PCA in different types of omics data. Another important task in PCA is to select variables (e.g., genes, proteins, metabolites) associated with phenotypes such as groups or time series information. After choosing relevant variables by statistical approaches, biologists make biological inferences from the statistically selected variables. In the literature, factor loading is known by a variety of other terms (PC loading, PC coefficient, weights, and eigenvectors), which are frequently interchanged and confused in the literature. Here, we theoretically explain the relationships among these technical terms in the presence and absence of scaling. Finally, we introduce the way to select variables by using statistical hypothesis testing of the factor loading in PCA. We urge that future PCA of omics data be applied in an appropriate manner.

#

This chapter was previously published in Principal Component Analysis: Methods, Applications and Technology, edited by Virginia Gray, New York: Nova Publishers Inc., 2017. * Corresponding Author E-mail: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 155

A FACTOR ANALYSIS OF AN OUTCOME MEASUREMENT SURVEY FOR SCIENCE, TECHNOLOGY AND SOCIETY: A COURSE OF GENERAL EDUCATION BASED ON PCA #

Tzu-Yi Pai1,, Yi-Ti Tung2, Ming-Ray Lin1, Su-Hwa Lin1, Lung-Yi Chan1 and Chia-Fu Lin1 1

Master Program of Environmental Education and Management, Department of Science Education and Application, National Taichung University of Education, Taichung, Taiwan, ROC 2 Department of Social Work, National Taipei University, New Taipei City, Taiwan, ROC

RESEARCH SUMMARY In this study, a factor analysis of outcome measurement survey for “Science, Technology and Society” (STS) course of general education was studied based on principal component analysis (PCA). STS course is mainly designed to familiarize students with knowledge, attitude, and action associated with science, technology and society including nature evolution, information and network, mathematics, nano-technology, global climate change, and sustainable development etc. STS course also intends to develop students’ civil responsibility, information and science accomplishments, and ability for logical thinking and identification. The results showed that the questionnaire for evaluating the outcome of the STS course was edited. The questionnaire was divided into 15 respects. Besides, the construct was divided into three classifications including knowledge, attitude, and action. The construct validity of the outcome measurement survey was calculated using PCA. There were totally 33 PCs extracted from PCA. According to PCA, the previous 19 and 27 PCs could account for #

This chapter was previously published in Principal Component Analysis: Methods, Applications and Technology, edited by Virginia Gray, New York: Nova Publishers Inc., 2017.  Corresponding Author E-mail: [email protected].

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about 70% and 80% of total variance, respectively. Total 33 PCs could account for 86.313% of total variance. The first PC consisted of 37 components, mainly the components of action, i.e., the action dimension explained the most variance. The first PC which was mainly made up of the action dimension accounted for 14.110% of variance alone. The second PCC consisted of 32 components, mainly the components of attitude. The attitude dimension explained as much of the remaining variation. The second PC which was mainly made up of the attitude dimension accounted for 10.250% of variance alone. The third PC consisted of 11 components, mainly the components of attitude. The remaining attitude dimension explained as much of the remaining variation. The third PC which was mainly made up of the attitude dimension accounted for 5.089% of variance alone. The 5th, 6th, 7th, 8th, 9th, 10th, 14th, 15th, 16th, 17th, and 18th PC mainly consisted of the components of knowledge. The knowledge dimension explained as much of the remaining variation.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 156

THE APPLICATION OF PRINCIPAL COMPONENT ANALYSIS (PCA) TO PERFORMANCE ENHANCEMENT OF HYPERSPECTRAL RADIATIVE TRANSFER COMPUTATIONS #

Robert Spurr1,*, Vijay Natraj2, Pushkar Kopparla3 and Matt Christi4 1RT

2Jet

Solutions Inc., Cambridge, MA, US Propulsion Laboratory, California Institute of Technology, Pasadena, CA, US 3California Institute of Technology, Pasadena, CA, US 4Fort Collins, Colorado, CO, US

RESEARCH SUMMARY For retrievals and sensitivity studies with passive Earth- (and planetary-) atmosphere remote-sensing instruments having moderate or high spectral resolution, the major timelimiting step is the forward-model multiple-scatter (MS) radiative transfer (RT) computation. In this paper, we use a principal component analysis (PCA)-based spectral binning technique to enhance RT performance. For a given spectral window, one may apply PCA to a data set of optical profiles (of trace gas absorption and single-scatter albedo, for example) to derive a much smaller set of optical profiles that captures most of the data variability. Further, 2stream (2S) RT calculations, although not accurate, are highly correlated with full MS RT computations. The key to enhanced performance is: (1) to separate the (fast) single-scatter (SS) and (slow) MS computations, and (2) to limit the number of full MS RT calculations to the PCA-reduced data set, and thus develop a series of PC-based correction factors that are applied to the fast hyperspectral calculations made by the 2S and SS RT models. This technique delivers accuracy of 0.1% or better, depending on the number of EOFs selected for

#

This chapter was previously published in Principal Component Analysis: Methods, Applications and Technology, edited by Virginia Gray, New York: Nova Publishers Inc., 2017. * Corresponding Author Email: [email protected].

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the PCA; 2–4 EOFs are usually sufficient. Speed-ups of 1–2 orders of magnitude are possible for a wide range of spectral windows. For global atmospheric chemical and climate modeling studies, performance considerations currently require that RT calculations must be done using fast and analytic 2S RT models; in this regard, 2S fluxes are frequently in error by 10–15% compared with highaccuracy MS RT results, and this uncertainty is a significant source of error in radiative forcing calculations. We have developed a set of hyperspectral PCA-based RT tools that can perform fast radiance and/or flux calculations across the entire solar and thermal regions from 260 nm to 20 microns (including the cross-over region where both solar and thermal sources apply) with an accuracy that is comparable (at the 0.1% level) to that obtained with full MS RT. We show that the fast-PCA method works for RT with polarization, e.g., for the VLIDORT model — multiple-scatter correction factors for the intensity can be derived with the (scalar) 2S model, and the technique can also be applied to fast calculation of Stokes parameters Q and U. The fast-PCA method is also applicable to calculations of analyticallyderived atmospheric profile and total column Jacobians, as well as surface weighting functions; we present an example for ozone profile Jacobians in the UV range from 306–335 nm. The fast-PCA method has been used operationally (in a spectral fitting algorithm requiring total column ozone weighting functions in the forward calculations) to reprocess the long-term global total ozone record from several atmospheric chemistry satellite platforms past and present (GOME, GOME-2, SCIAMACHY). In addition to this application, we present two examples of fast-PCA RT performance enhancement for the O2 A band and the strong and weak CO2 absorption bands that are central to the Orbiting Carbon Observatory (OCO-2) mission, which is being used to generate global maps of CO2 concentrations from space.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 157

RANDOM APPROXIMATIONS IN STOCHASTIC PROGRAMMING: A SURVEY #

Silvia Vogel* Faculty of Mathematics and Natural Sciences Ilmenau University of Technology, Ilmenau, Germany

RESEARCH SUMMARY This chapter considers random approximations of deterministic optimization problems. Such approximations come into play if unknown parameters or probability distributions are replaced with estimates or for numerical reasons. The objective function and the constraint set can be approximated simultaneously. Stochastic programming problems are of special interest in this context. They are deterministic models that heavily depend on the underlying probability distribution. Moreover, many statistical estimators are solutions of random optimization problems to which a deterministic limit problem can be assigned. Hence the approaches can also be applied to statistical estimators. In the first part of the chapter the focus is on qualitative stability results in terms of convergence almost surely and in probability for constraint sets, optimal values, and solution sets. Because in general only a subset of the true solution set can be approximated, one-sided approximations are explained in detail. The statements are supplemented with sufficient conditions for the convergence of the functions involved. Furthermore, it is shown how socalled near-optimal or 𝜀-optimal solutions can be incorporated. In the second part universal confidence sets for constraint sets, optimal values, and solution sets are derived. These quantitative results require stronger convergence properties of the approximating constraint functions and objective functions. Two approaches are presented. One approach employs a convergence notion which is related to KuratowskiPainlevé convergence of sequences of random sets, the second approach relies on ‘relaxation’ #

This chapter was previously published in Stochastic Programming: Theory, Applications and Impacts, edited by Carlos Narciso Bouza Herrera, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected].

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of the constraints or optimality conditions. While the first approach uses some knowledge about the true problem, the second one does not require any knowledge of that kind. Again, sufficient conditions for the necessary convergence properties are provided.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 158

APPROXIMATION AND ESTIMATION OF THE APPROXIMATION ERROR IN STOCHASTIC PROGRAMING PROGRAMS #

Carlos N. Bouza–Herrera1,*, Sira M. Allende Alonso1 and Rajesh Singh2 1

Department of Matemática Aplicada, Facultad de Matemática y Computación, Universidad de La Habana, Ciudad de La Habana, La Habana, Cuba 2 Department of Statistics, Banaras Hindu University, Varanasi, India

RESEARCH SUMMARY Stochastic optimization problems are present in applications in management, engineering and medicine, as well as in environment, physical and social sciences. This chapter is concerned with studying the behavior of the estimation and approximation of the Approximation Error in different types of stochastic problems. Statistical techniques are considered for developing the studies of Two-stage stochastic programming and Chance Constrained models. The estimation of the involved probability density functions is studied and kernel density estimators are proposed. The effectivity of the proposed solutions are analyzed in terms of the convergence of estimated Approximation Errors of the models. The performance of the proposals for estimating the involved probability density functions is evaluated by performing some Monte Carlo simulation experiments. Some applications in managing inventories, constructing strata, are discussed. Simulated problems are also used for evaluating the speed of convergence of the estimated Approximation Errors. #

This chapter was previously published in Stochastic Programming: Theory, Applications and Impacts, edited by Carlos Narciso Bouza Herrera, New York: Nova Publishers Inc., 2017. * Corresponding Author address; Email: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 159

PROBABILISTIC LINEAR PROGRAMMING PROBLEM WITH CAUCHY DISTRIBUTED RANDOM VARIABLES

#

Manas Kumar Pal Birla Global University Bhubaneswar, Odisha, India

RESEARCH SUMMARY The aim of this chapter is to derive a method for solving a probabilistic linear programming problem with cauchy distributed random variables. Assuming that the coefficients are distributed as cauchy random variables, a transformation is presented to convert the probabilistic linear programming to deterministic non-linear programming problem. Then an algorithm can be used to solve the resulting deterministic problem.

#

This chapter was previously published in Stochastic Programming: Theory, Applications and Impacts, edited by Carlos Narciso Bouza Herrera, New York: Nova Publishers Inc., 2017.  Corresponding Author: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 160

STOCHASTIC MODELING OF IMPERFECT MARKETS

#

Tobias Baltensperger1,2 and Ruud Egging2,* 1

ETH Zurich, Switzerland NTNU, Trondheim, Norway

2

RESEARCH SUMMARY Stochastic optimization approaches ignore that the decisions of different actors in markets typically do not lead to a system-wide optimal solution. Suppliers in markets with entrance barriers or other aspects that hinder competition, can use their dominant positions to exert market power and drive up market prices. To represent such gaming behavior, a different modeling approach is needed. Equilibrium models can represent varying market structures, including perfect competition and oligopoly. This chapter presents a multi-stage stochastic equilibrium model for a general commodity market wherein suppliers, transportation agents and storage agents make capacity investment decisions while facing uncertainty in future market circumstances and production and sales decisions in later stages when the uncertainty has been revealed. An illustrative example for the natural gas market is used to show how market power may affect decisions and expected profits, and discuss the value of the stochastic solution for the different agents in our gaming setting.

#

This chapter was previously published in Stochastic Programming: Theory, Applications and Impacts, edited by Carlos Narciso Bouza Herrera, New York: Nova Publishers Inc., 2017. * Corresponding author: ruud.egging-at-iot.ntnu.no.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 161

OPTIMIZING DERIVATIVES THROUGH STOCHASTIC PROGRAMMING #

Carlos N. Bouza-Herrera* and Sira M. Allende Alonso Department of Matemática Aplicada, Facultad de Matemática y Computación, Universidad de La Habana, Ciudad de La Habana, La Habana, Cuba

RESEARCH SUMMARY In many environment applications, the objective of the analysis is not to predict the entire derivative curve of a conditional expectation function at each data point. Instead, it is often sufficient to construct statistics to estimate the Average Derivative. Commonly the analysis is based on a regression function. We will be concerned about the point-wise consistency of an estimator of a probability density function. A common solution is using nonparametric probability density function estimation. Hence many applications need exploring the estimation of a probability density function for working with a good approximation to the underlying model. Under a set of suitable conditions on the objective function we need of the asymptotic convergence of a kernel density estimator. This chapter is concerned with modeling the optimization of the estimation of a derivative using a suitable stochastic programming model. The key problem is that using an estimate of the density poses the need of evaluating “quantitatively” the effect of solving the approximate problem. That is analyzing the behavior of the approximation error. We develop a study of the related issues and establish the bounding of the approximation error. The point-wise convergence of kernel estimator of the density ensures that the involved metrics tend to zero. Therefore having a sufficiently large sample size enable to be confident that the estimated optimal solution is close to the real solution.

#

This chapter was previously published in Stochastic Programming: Theory, Applications and Impacts, edited by Carlos Narciso Bouza Herrera, New York: Nova Publishers Inc., 2017. * Corresponding Author address, Email: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 162

A GUIDE FOR THE USE OF THE STOCHASTIC PROGRAMMING REFERENCES REPORTED IN THE CONTRIBUTIONS OF THIS BOOK #

Carlos N. Bouza-Herrera* and José M. Sautto-Vallejo Department of Matemática Aplicada, Facultad de Matemática y Computación, Universidad de La Habana, Ciudad de La Habana, La Habana, Cuba Coordinador Regional Campurs Costa Chica, Universidad Autnóma de Gerrero. Cruz Grande, Florencio Villarreal, Mexico

RESEARCH SUMMARY This paper is concerned with the organization of the references reported in this book. A classification is made considering whether a paper was devoted to the development of new models, the theoretical support of stochastic issues (probabilistic or statistical) and those dealing with applications, mathematical models providing a framework for stochastic programming theory and computing aspects.

#

This chapter was previously published in Stochastic Programming: Theory, Applications and Impacts, edited by Carlos Narciso Bouza Herrera, New York: Nova Publishers Inc., 2017. * Corresponding Author address: Email: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 163

SYNCHRONIZATION OF CHAOTIC DYNAMIC SYSTEMS VIA NONLINEAR OBSERVERS #

Ricardo Aguilar-López1,, Ricardo Femat2, Santo Banerjee3 and Juan Luis Mata-Machuca4 1

Department of Biotechnology and Bioengineering, Centro de Investigación y de Estudios Avanzados (CINVESTAV), México City, México 2 Division of Applied Mathematics, Instituto Potosino de Investigación Científica y Tecnológica (IPICyT), San Luis Potosí S. L. P., Mexico 3 Laboratory of Cryptography, Analysis and Structure, Institute for Mathematical Research, University Putra Malaysia, Selangor, Malaysia 4 Academy of Mechatronic, Unidad Profesional Interdisciplinaria de Tecnología Avanzada del I.P.N. (UPIITA-IPN), Ciudad de México, Mexico

RESEARCH SUMMARY The main goal of this chapter is to introduce some nonlinear techniques for the synchronization of a class of chaotic oscillator under the framework of observer design from control theory. The proposed methodologies are applied under the assumption of a masterslave synchronization configuration for nonlinear oscillators with the same topological structure. The named slave system is analyzed as a state observer where corresponding measured output injection or feedback tries to cancel the upper bounds of the corresponding nonlinearities and imposing the corresponding trajectories of the master system in order to achieve the synchronization. To illustrate the performance of the considered synchronization

# 

This chapter was previously published in Chaotic Systems: Dynamics, Algorithms and Synchronization, edited by Victor Powell, New York: Nova Publishers Inc., 2017. Corresponding author: Ricardo Aguilar-López. Department of Biotechnology and Bioengineering, Centro de Investigación y de Estudios Avanzados (CINVESTAV), Av. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, Delegación Gustavo A. Madero, 07360. México City, México. E-mail: [email protected].

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methodologies, numerical experiments were carried out to show the performance of the proposal.

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 164

ON MULTI-DOMAIN SPECTRAL RELAXATION METHOD FOR CHAOTIC SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS #

Sandile S. Motsa*, Vusi M. Magagula and Precious Sibanda School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal Scottsville, Pietermaritzburg, South Africa

RESEARCH SUMMARY In this work, we discuss in detail the application of a novel multi-domain spectral collocation approach for finding solutions of ordinary differential equations that exhibit general chaotic behaviour. The proposed approach, termed the multi-domain spectral relaxation method (MD-SRM) is a simple iterative multi-domain spectral collocation algorithm that does not require linearization of the differential equations. Spectral collocation is used to discretize the equations whose solutions are found over a sequence of nonoverlapping sub-intervals of the domain. Continuity conditions are used to advance the solution across the non-overlapping subintervals. Different types of initial boundary value problems that have been solved previously using other numerical methods are used for numerical experimentation to determine the accuracy of the method. These include the Lorenz, Rössler, Chen, Arneodo-Coullet and the Genesio-Tesi chaotic systems. The validity and accuracy of the MD-SRM is tested against Runge-Kutta based numerical scheme. The approximate numerical results indicate that the proposed method is accurate, efficient, reliable and very effective in finding solutions of initial value problems over large time intervals.

#

This chapter was previously published in Chaotic Systems: Dynamics, Algorithms and Synchronization, edited by Victor Powell, New York: Nova Publishers Inc., 2017. * Corresponding author email: [email protected].

In: Mathematical Research Summaries. Volume 2 Editor: Matthew A. Rowe

ISBN: 978-1-53612-022-6 © 2017 Nova Science Publishers, Inc.

Chapter 165

ENCRYPTED REAL-WORLD IMAGE COMMUNICATION DESIGN USING SYNCHRONIZED DISCRETE-TIME HYPER CHAOTIC MAPS #

Sonia Hammami Engineering Sciences and Techniques Department, El Manar Preparatory Institute for Engineering Studies, University of Tunis El Manar, Tunis, Tunisia

RESEARCH SUMMARY Based on aggregation techniques associated with the forced arrow form matrix, to derive the stability property of dynamic discrete-time complex systems, a new strategy of control is formulated for chaos synchronization of two identical 3D Hénon maps. The designed state feedback controller ensures that the state variables of both controlled hyper chaotic slave system globally synchronize with the state variables of the hyper chaotic master one. Numerical simulations are carried out to assess the performance as well as the high level security of the proposed contributions in the important field of secure image communication through hyper chaotic synchronization phenomenon.

# 

This chapter was previously published in Chaotic Systems: Dynamics, Algorithms and Synchronization, edited by Victor Powell, New York: Nova Publishers Inc., 2017. Corresponding author: Sonia Hammami. University of Tunis El Manar, Engineering Sciences and Techniques Department, El Manar Preparatory Institute for Engineering Studies, BP 244, Tunis 2092, Tunisia. E-mail: [email protected].