This book contains select chapters on support vector algorithms from different perspectives, including mathematical background, properties of various kernel functions, and several applications. The main focus of this book is on orthogonal kernel functions, and the properties of the classical kernel functions-Chebyshev, Legendre, Gegenbauer, and Jacobi-are reviewed in some chapters. Moreover, the fractional form of these kernel functions is introduced in the same chapters, and for ease of use for these kernel functions, a tutorial on a Python package named ORSVM is presented. The book also exhibits a variety of applications for support vector algorithms, and in addition to the classification, these algorithms along with the introduced kernel functions are utilized for solving ordinary, partial, integro, and fractional differential equations. On the other hand, nowadays, the real-time and big data applications of support vector algorithms are growing. Consequently, the Compute Unified Device Architecture (CUDA) parallelizing the procedure of support vector algorithms based on orthogonal kernel functions is presented. The book sheds light on how to use support vector algorithms based on orthogonal kernel functions in different situations and gives a significant perspective to all machine learning and scientific machine learning researchers all around the world to utilize fractional orthogonal kernel functions in their pattern recognition or scientific computing problems.

"Game Theory for Economists" introduces economists to the game-theoretic approach of modelling economic behaviour and interaction, focusing on concepts and ideas from the vast field of game-theoretic models which find commonly used applications in economics. This careful selection of topics allows the reader to concentrate on the parts of the game which are the most relevant for the economist who does not want to become a specialist. Written at a level appropriate for a student or researcher with a solid microeconomic background, the book should provide the reader with skills necessary to formalize economic games and to make them accessible for game theoretic analysis. It offers a concise introduction to game theory which provides economists with the techniques and results necessary to follow the literature in economic theory; helps the reader formalize economic problems; and, concentrates on equilibrium concepts that are most commonly used in economics.

This book defines and studies a combinatorial object called the pedigree and develops the theory for optimising a linear function over the convex hull of pedigrees (the Pedigree polytope). A strongly polynomial algorithm implementing the framework given in the book for checking membership in the pedigree polytope is a major contribution. This book challenges the popularly held belief in computer science that a problem included in the NP-complete class may not have a polynomial algorithm to solve. By showing STSP has a polynomial algorithm, this book settles the P vs NP question. This book has illustrative examples, figures, and easily accessible proofs for showing this unexpected result. This book introduces novel constructions and ideas previously not used in the literature. Another interesting feature of this book is it uses basic max-flow and linear multicommodity flow algorithms and concepts in these proofs establishing efficient membership checking for the pedigree polytope. Chapters 3-7 can be adopted to give a course on Efficient Combinatorial Optimization. This book is the culmination of the author's research that started in 1982 through a presentation on a new formulation of STSP at the XIth International Symposium on Mathematical Programming at Bonn.

The primary aim of this book is to present notions of convex analysis which constitute the basic underlying structure of argumentation in economic theory and which are common to optimization problems encountered in many applications. The intended readers are graduate students, and specialists of mathematical programming whose research fields are applied mathematics and economics. The text consists of a systematic development in eight chapters, with guided exercises containing sometimes significant and useful additional results. The book is appropriate as a class text, or for self-study.

This book features mathematical and formal philosophers' efforts to understand philosophical questions using mathematical techniques. It offers a collection of works from leading researchers in the area, who discuss some of the most fascinating ways formal methods are now being applied. It covers topics such as: the uses of probable and statistical reasoning, rational choice theory, reasoning in the environmental sciences, reasoning about laws and changes of rules, and reasoning about collective decision procedures as well as about action. Utilizing mathematical techniques has been very fruitful in the traditional domains of formal philosophy - logic, philosophy of mathematics and metaphysics - while formal philosophy is simultaneously branching out into other areas in philosophy and the social sciences. These areas particularly include ethics, political science, and the methodology of the natural and social sciences. Reasoning about legal rules, collective decision-making procedures, and rational choices are of interest to all those engaged in legal theory, political science and economics. Statistical reasoning is also of interest to political scientists and economists.

In trying to make a satisfactory decision when imprecise and multicriteria situations are involved, a decision maker has to use a fuzzy multicriteria decision making method. "Fuzzy Multi-Criteria Decision Making" (MCDM) presents fuzzy multiattribute and multiobjective decision-making methodologies by distinguished MCDM researchers.

In summarizing the concepts and results of the most popular fuzzy multicriteria methods, using numerical examples, this work examines all the fuzzy multicriteria methods recently developed, such as fuzzy AHP, fuzzy TOPSIS, interactive fuzzy multiobjective stochastic linear programming, fuzzy multiobjective dynamic programming, grey fuzzy multiobjective optimization, fuzzy multiobjective geometric programming, and more. Each of the 22 chapters includes practical applications along with new developments/results.

This book may be used as a textbook in graduate operations research, industrial engineering, and economics courses. It will also be an excellent resource, providing new suggestions and directions for further research, for computer programmers, mathematicians, and scientists in a variety of disciplines where multicriteria decision making is needed.

This book describes concepts and tools needed for water resources management, including methods for modeling, simulation, optimization, big data analysis, data mining, remote sensing, geographical information system, game theory, conflict resolution, System dynamics, agent-based models, multiobjective, multicriteria, and multiattribute decision making and risk and uncertainty analysis, for better and sustainable management of water resources and consumption, thus mitigating the present and future global water shortage crisis. It presents the applications of these tools through case studies which demonstrate its benefits of proper management of water resources systems. This book acts as a reference for students, professors, industrial practitioners, and stakeholders in the field of water resources and hydrology.

This book presents mathematical models of demand-side management programs, together with operational and control problems for power and renewable energy systems. It reflects the need for optimal operation and control of today's electricity grid at both the supply and demand spectrum of the grid. This need is further compounded by the advent of smart grids, which has led to increased customer/consumer participation in power and renewable energy system operations. The book begins by giving an overview of power and renewable energy systems, demand-side management programs and algebraic modeling languages. The overview includes detailed consideration of appliance scheduling algorithms, price elasticity matrices and demand response incentives. Furthermore, the book presents various power system operational and control mathematical formulations, incorporating demand-side management programs. The mathematical formulations developed are modeled and solved using the Advanced Interactive Multidimensional Modeling System (AIMMS) software, which offers a powerful yet simple algebraic modeling language for solving optimization problems. The book is extremely useful for all power system operators and planners who are concerned with optimal operational procedures for managing today's complex grids, a context in which customers are active participants and can curb/control their demand. The book details how AIMMS can be a useful tool in optimizing power grids and also offers a valuable research aid for students and academics alike.

The COVID-19 pandemic has vividly and dramatically demonstrated the importance of supply chains to the functioning of societies and our economies. The discussion in this timely book explores prominent issues concerning supply chain networks and labor. The readership is aimed to include students, researchers, practitioners, and policy-makers, interested in the wide range of topics presented in these pages. Labor has a particular focus as the driver behind supply chains, whether associated with food products, life-saving medicines and supplies, or high tech products that make innovation possible, just to name a few. The impacts of policy interventions, in the form of wage bounds, and their ramifications, in terms of volume of attracted labor, product prices, product volumes, as well as profits, are explored. Profit-maximizing firms are considered (with relevant associated issues such as waste management in the case of the food sector, for example), but also non-profits, as in blood services, as well as humanitarian organizations engaged in disaster relief. The book is filled with many network figures, graphs, and tables with data, both input and output and includes an appendix that provides the foundations of the underlying mathematical methodologies used. The book offers strong evidence for the need to provide a holistic, system-wide perspective for the modeling, analysis, and solution of supply chain problems with the inclusion of the critical labor resources. A formalism using the prism of supply chain networks, which yields a graphic representation of supply chains, consisting of multiple stakeholders, is constructed. Models that capture the behaviors and interactions of single decision-makers as well as multiple decision-makers engaged in supply chain activities of production, transportation, storage, and distribution, are considered. The models capture many realistic constraints faced by firms today, as they seek to produce and deliver products, while dealing with competition, various constraints on labor, a variety of disruptions, labor shortages, challenges associated with proper wage-determination, plus the computation of optimal investments in labor productivity subject to budget constraints. The book provides prescriptive suggestions in terms of how to ameliorate negative impacts of labor disruptions and demonstrate benefits of appropriate wage determination.

This book presents a modern perspective on the modelling, analysis, and synthesis ideas behind convex-optimisation-based control of nonlinear systems: it embeds them in models with convex structures. Analysis and Synthesis of Nonlinear Control Systems begins with an introduction to the topic and a discussion of the problems to be solved. It then explores modelling via convex structures, including quasi-linear parameter-varying, Takagi-Sugeno models, and linear fractional transformation structures. The authors cover stability analysis, addressing Lyapunov functions and the stability of polynomial models, as well as the performance and robustness of the models. With detailed examples, simulations, and programming code, this book will be useful to instructors, researchers, and graduate students interested in nonlinear control systems.

This book establishes an important mathematical connection between cooperative control problems and network optimization problems. It shows that many cooperative control problems can in fact be understood, under certain passivity assumptions, using a pair of static network optimization problems. Merging notions from passivity theory and network optimization, it describes a novel network optimization approach that can be applied to the synthesis of controllers for diffusively-coupled networks of passive (or passivity-short) dynamical systems. It also introduces a data-based, model-free approach for the synthesis of network controllers for multi-agent systems with passivity-short agents. Further, the book describes a method for monitoring link faults in multi-agent systems using passivity theory and graph connectivity. It reports on some practical case studies describing the effectivity of the developed approaches in vehicle networks. All in all, this book offers an extensive source of information and novel methods in the emerging field of multi-agent cooperative control, paving the way to future developments of autonomous systems for various application domains

Control Theory for Linear Systems deals with the mathematical theory of feedback control of linear systems. It treats a wide range of control synthesis problems for linear state space systems with inputs and outputs. The book provides a treatment of these problems using state space methods, often with a geometric flavour. Its subject matter ranges from controllability and observability, stabilization, disturbance decoupling, and tracking and regulation, to linear quadratic regulation, H2 and H-infinity control, and robust stabilization. Each chapter of the book contains a series of exercises, intended to increase the reader's understanding of the material. Often, these exercises generalize and extend the material treated in the regular text.

FROM THE REVIEWS:
"...The book covers quite a broad range of material and gives the student a solid introduction to the field of systems and control theory ... I found this book to be well written and rigorous in its approach. It provides a good introduction to the mathematical theory of linear systems and control system design. I would recommend it as a good choice for a first-year graduate course covering these topics."
-IEEE TRANSACTIONS ON AUTOMATIC CONTROL

MATHEMATICAL REVIEWS
"...it is no small task to produce a book that presents the essential ingredients of the theory in a manner suitable for graduate students who are learning it for the first time. However, this is precisely the objective of the book under review and, in the opinion of this reviewer, the authors have succeeded admirably...Each chapter concludes with a set of exercises and historical notes and references. Also included in a fairly extensive bibliography with 232 references. These features and the lucid writing style of the authors make this book ideally suited for any graduate course in linear control theory aimed at students of applied mathematics or mathematically inclined students of engineering."

This book includes up-to-date contributions in the broadly defined area of probabilistic analysis of voting rules and decision mechanisms. Featuring papers from all fields of social choice and game theory, it presents probability arguments to allow readers to gain a better understanding of the properties of decision rules and of the functioning of modern democracies. In particular, it focuses on the legacy of William Gehrlein and Dominique Lepelley, two prominent scholars who have made important contributions to this field over the last fifty years. It covers a range of topics, including (but not limited to) computational and technical aspects of probability approaches, evaluation of the likelihood of voting paradoxes, power indices, empirical evaluations of voting rules, models of voters' behavior, and strategic voting. The book gathers articles written in honor of Gehrlein and Lepelley along with original works written by the two scholars themselves.

This monograph introduces a novel multiset-based conceptual, mathematical and knowledge engineering paradigm, called multigrammatical framework (MGF), used for planning and scheduling in resource-consuming, resource-producing (industrial) and resource-distributing (economical) sociotechnological systems (STS). This framework is meant to enable smart operation not only in a "business-as-usual" mode, but also in extraordinary, highly volatile or hazardous environments. It is the result of convergence and deep integration into a unified, flexible and effectively implemented formalism operating on multisets of several well-known paradigms from classical operations research and modern knowledge engineering, such as: mathematical programming, game theory, optimal scheduling, logic programming and constraint programming. The mathematical background needed for MGF, its algorithmics, applications, implementation issues, as well as its nexus with known models from operations research and theoretical computer science areas are considered. The resilience and recovery issues of an STS are studied by applying the MGF toolkit and on paying special attention to the multigrammatical assessment of resilience of energy infrastructures. MGF-represented resource-based games are introduced, and directions for further development are discussed. The author presents multiple applications to business intelligence, critical infrastructure, ecology, economy and industry. This book is addressed to scholars working in the areas of theoretical and applied computer science, artificial intelligence, systems analysis, operations research, mathematical economy and critical infrastructure protection, to engineers developing software-intensive solutions for implementation of the knowledge-based digital economy and Industry 4.0, as well as to students, aspirants and university staff. Foundational knowledge of set theory, mathematical logic and routine operations on data bases is needed to read this book. The content of the monograph is gradually presented, from simple to complex, in a well-understandable step-by-step manner. Multiple examples and accompanying figures are included in order to support the explanation of the various notions, expressions and algorithms.

This contributed volume presents some of the latest research related to model order reduction of complex dynamical systems with a focus on time-dependent problems. Chapters are written by leading researchers and users of model order reduction techniques and are based on presentations given at the 2019 edition of the workshop series Model Reduction of Complex Dynamical Systems - MODRED, held at the University of Graz in Austria. The topics considered can be divided into five categories: system-theoretic methods, such as balanced truncation, Hankel norm approximation, and reduced-basis methods; data-driven methods, including Loewner matrix and pencil-based approaches, dynamic mode decomposition, and kernel-based methods; surrogate modeling for design and optimization, with special emphasis on control and data assimilation; model reduction methods in applications, such as control and network systems, computational electromagnetics, structural mechanics, and fluid dynamics; and model order reduction software packages and benchmarks. This volume will be an ideal resource for graduate students and researchers in all areas of model reduction, as well as those working in applied mathematics and theoretical informatics.

This book presents efficient metaheuristic algorithms for optimal design of structures. Many of these algorithms are developed by the author and his graduate students, consisting of Particle Swarm Optimization, Charged System Search, Magnetic Charged System Search, Field of Forces Optimization, Democratic Particle Swarm Optimization, Dolphin Echolocation Optimization, Colliding Bodies Optimization, Ray Optimization. These are presented together with algorithms which are developed by other authors and have been successfully applied to various optimization problems. These consist of Partical Swarm Optimization, Big Band Big Crunch algorithm, Cuckoo Search Optimization, Imperialist Competitive Algorithm and Chaos Embedded Metaheuristic Algorithm. Finally a multi-objective Optimization is presented to Solve large scale structural problems based on the Charged System Search algorithm, In the second edition seven new chapters are added consisting of Enhance colliding bodies optimization, Global sensitivity analysis, Tug of War Optimization, Water evaporation optimization, Vibrating System Optimization and Cyclical Parthenogenesis Optimization algorithm. In the third edition, five new chapters are included consisting of the recently developed algorithms. These are Shuffled Shepherd Optimization Algorithm, Set Theoretical Shuffled Shepherd Optimization Algorithm, Set Theoretical Teaching-Learning-Based Optimization Algorithm, Thermal Exchange Metaheuristic Optimization Algorithm, and Water Strider Optimization Algorithm and Its Enhancement. The concepts and algorithm presented in this book are not only applicable to optimization of skeletal structure, finite element models, but can equally be utilized for optimal design of other systems such as hydraulic and electrical networks.

This book is about algebraic and differential methods, as well as fractional calculus, applied to diagnose and reject faults in nonlinear systems, which are of integer or fractional order. This represents an extension of a very important and widely studied problem in control theory, namely fault diagnosis and rejection (using differential algebraic approaches), to systems presenting fractional dynamics, i.e. systems whose dynamics are represented by derivatives and integrals of non-integer order. The authors offer a thorough overview devoted to fault diagnosis and fault-tolerant control applied to fractional-order and integer-order dynamical systems, and they introduce new methodologies for control and observation described by fractional and integer models, together with successful simulations and real-time applications. The basic concepts and tools of mathematics required to understand the methodologies proposed are all clearly introduced and explained. Consequently, the book is useful as supplementary reading in courses of applied mathematics and nonlinear control theory. This book is meant for engineers, mathematicians, physicists and, in general, to researchers and postgraduate students in diverse areas who have a minimum knowledge of calculus. It also contains advanced topics for researchers and professionals interested in the area of states and faults estimation.

Praise for the Second Edition:

"This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications."
--Mathematical Reviews of the American Mathematical Society

An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems.

This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel(R), for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel(R) is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications.

Additional features of the Third Edition include:

A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integerprogramming, non-linear programming, and make vs. buy models

Revised proofs and a discussion on the relevance and solution of the dual problem

A section on developing an example in Data Envelopment Analysis

An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games

Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science.

Economic archaeology and ancient economic history have boomed the past decades. The former thanks to greatly enhanced techniques to identify, collect, and interpret material remains as proxies for economic interactions and performance; the latter by embracing the frameworks of new institutional economics. Both disciplines, however, still have great difficulty talking with each other. There is no reliable method to convert ancient proxy-data into the economic indicators used in economic history. In turn, the shared cultural belief-systems underlying institutions and the symbolic ways in which these are reproduced remain invisible in the material record. This book explores ways to bring both disciplines closer together by building a theoretical and methodological framework to evaluate and integrate archaeological proxy-data in economic history research. Rather than the linear interpretations offered by neoclassical or neomalthusian models, we argue that complexity economics, based on system theory, offers a promising way forward.

This textbook provides a comprehensive overview of noncooperative and cooperative dynamic games involving uncertain parameter values, with the stochastic process being described by an event tree. Primarily intended for graduate students of economics, management science and engineering, the book is self-contained, as it defines and illustrates all relevant concepts originally introduced in static games before extending them to a dynamic framework. It subsequently addresses the sustainability of cooperative contracts over time and introduces a range of mechanisms to help avoid such agreements breaking down before reaching maturity. To illustrate the concepts discussed, the book provides various examples of how dynamic games played over event trees can be applied to environmental economics, management science, and engineering.

A long long time ago, echoing philosophical and aesthetic principles that existed since antiquity, William of Ockham enounced the principle of parsimony, better known today as Ockham's razor: "Entities should not be multiplied without neces sity. " This principle enabled scientists to select the "best" physical laws and theories to explain the workings of the Universe and continued to guide scienti?c research, leadingtobeautifulresultsliketheminimaldescriptionlength approachtostatistical inference and the related Kolmogorov complexity approach to pattern recognition. However, notions of complexity and description length are subjective concepts anddependonthelanguage"spoken"whenpresentingideasandresults. The?eldof sparse representations, that recently underwent a Big Bang like expansion, explic itly deals with the Yin Yang interplay between the parsimony of descriptions and the "language" or "dictionary" used in them, and it became an extremely exciting area of investigation. It already yielded a rich crop of mathematically pleasing, deep and beautiful results that quickly translated into a wealth of practical engineering applications. You are holding in your hands the ?rst guide book to Sparseland, and I am sure you'll ?nd in it both familiar and new landscapes to see and admire, as well as ex cellent pointers that will help you ?nd further valuable treasures. Enjoy the journey to Sparseland! Haifa, Israel, December 2009 Alfred M. Bruckstein vii Preface This book was originally written to serve as the material for an advanced one semester (fourteen 2 hour lectures) graduate course for engineering students at the Technion, Israel.

This book covers recent advances in Complex Automated Negotiations as a widely studied emerging area in the field of Autonomous Agents and Multi-Agent Systems. The book includes selected revised and extended papers from the 7th International Workshop on Agent-Based Complex Automated Negotiation (ACAN2014), which was held in Paris, France, in May 2014. The book also includes brief introductions about Agent-based Complex Automated Negotiation which are based on tutorials provided in the workshop, and brief summaries and descriptions about the ANAC'14 (Automated Negotiating Agents Competition) competition, where authors of selected finalist agents explain the strategies and the ideas used by them. The book is targeted to academic and industrial researchers in various communities of autonomous agents and multi-agent systems, such as agreement technology, mechanism design, electronic commerce, related areas, as well as graduate, undergraduate, and PhD students working in those areas or having interest in them.

This book provides an in-depth analysis of the current evolutionary clustering techniques. It discusses the most highly regarded methods for data clustering. The book provides literature reviews about single objective and multi-objective evolutionary clustering algorithms. In addition, the book provides a comprehensive review of the fitness functions and evaluation measures that are used in most of evolutionary clustering algorithms. Furthermore, it provides a conceptual analysis including definition, validation and quality measures, applications, and implementations for data clustering using classical and modern nature-inspired techniques. It features a range of proven and recent nature-inspired algorithms used to data clustering, including particle swarm optimization, ant colony optimization, grey wolf optimizer, salp swarm algorithm, multi-verse optimizer, Harris hawks optimization, beta-hill climbing optimization. The book also covers applications of evolutionary data clustering in diverse fields such as image segmentation, medical applications, and pavement infrastructure asset management.

This book provides a systematic description about the development of Isogeometric Topology Optimization (ITO) method using the density, and then addresses the effectiveness and efficiency of the ITO method on several design problems, including multi-material structures, stress-minimization structures, piezoelectric structures and also with the uniform manufacturability, ultra-lightweight architected materials with extreme bulk/shear moduli, auxetic metamaterials and auxetic meta-composites with the NPRs behavior in microstructures. A detailed MATLAB implementation of the ITO method with an in-house code "IgaTop" is also presented.

Robert J Aumann has received numerous prizes, including the Nobel Memorial Prize in Economic Sciences for 2005.With his 1976 paper, 'Agreeing to Disagree', Robert Aumann pioneered the subject of interactive epistemology: the study of what people know, and what they know about what others know. Since then, the discipline has burgeoned enormously. This book documents Aumann's work leading to the 1976 paper and his subsequent contributions to the discipline. The scientific controversies emanating from his work are also included.