Mathematics Motivated By The Social And Behavioral Sciences

Author : Donald G. Saari
Publisher : SIAM
Page : 182 pages
File Size : 55,6 Mb
Release : 2018-02-06
Category : Mathematics
ISBN : 9781611975178

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Mathematics Motivated by the Social and Behavioral Sciences by Donald G. Saari Pdf

The mathematical challenges coming from the social and behavioral sciences differ significantly from typical applied mathematical concerns. ?Change,? for instance, is ubiquitous, but without knowing the fundamental driving force, standard differential and iterative methods are not appropriate. Although differing forms of aggregation are widely used, a general mathematical assessment of potential pitfalls is missing. These realities provide opportunities to create new mathematical approaches. These themes are described in an introductory, expository, and accessible manner by exploring new ways to handle dynamics and evolutionary game theory, to identify subtleties of decision and voting methods, to recognize unexpected modeling concerns, and to introduce new approaches with which to examine game theory. Applications range from avoiding undesired consequences when designing policy to identifying unanticipated voting (where the ?wrong? person could win), nonparametric statistical, and economic ?supply and demand? properties.

Author : Donald G. Saari
Publisher : SIAM
Page : 171 pages
File Size : 47,9 Mb
Release : 2018-02-06
Category : Mathematics
ISBN : 9781611975185

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Mathematics Motivated by the Social and Behavioral Sciences by Donald G. Saari Pdf

The mathematical challenges coming from the social and behavioral sciences differ significantly from typical applied mathematical concerns. “Change,” for instance, is ubiquitous, but without knowing the fundamental driving force, standard differential and iterative methods are not appropriate. Although differing forms of aggregation are widely used, a general mathematical assessment of potential pitfalls is missing. These realities provide opportunities to create new mathematical approaches. These themes are described in an introductory, expository, and accessible manner by exploring new ways to handle dynamics and evolutionary game theory, to identify subtleties of decision and voting methods, to recognize unexpected modeling concerns, and to introduce new approaches with which to examine game theory. Applications range from avoiding undesired consequences when designing policy to identifying unanticipated voting (where the “wrong” person could win), nonparametric statistical, and economic “supply and demand” properties.

Author : Anatol Rapoport
Publisher : John Wiley & Sons
Page : 528 pages
File Size : 54,9 Mb
Release : 1983
Category : Psychology
ISBN : UOM:39015005899631

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Mathematical Models in the Social and Behavioral Sciences by Anatol Rapoport Pdf

Author : Šárka Hošková-Mayerová,Fabrizio Maturo,Janusz Kacprzyk
Publisher : Springer
Page : 437 pages
File Size : 42,5 Mb
Release : 2017-06-20
Category : Technology & Engineering
ISBN : 9783319548197

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Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences by Šárka Hošková-Mayerová,Fabrizio Maturo,Janusz Kacprzyk Pdf

This book presents a broad spectrum of problems related to statistics, mathematics, teaching, social science, and economics as well as a range of tools and techniques that can be used to solve these problems. It is the result of a scientific collaboration between experts in the field of economic and social systems from the University of Defence in Brno (Czech Republic), G. d’Annunzio University of Chieti-Pescara (Italy), Pablo de Olavid eUniversity of Sevilla (Spain), and Ovidius University in Constanţa, (Romania). The studies included were selected using a peer-review process and reflect heterogeneity and complexity of economic and social phenomena. They and present interesting empirical research from around the globe and from several research fields, such as statistics, decision making, mathematics, complexity, psychology, sociology and economics. The volume is divided into two parts. The first part, “Recent trends in mathematical and statistical models for economic and social sciences”, collects papers on quantitative matters, which propose mathematical and statistical models for social sciences, economics, finance, and business administration. The second part, “Recent trends in qualitative theories for economic and social sciences”, includes papers on qualitative matters, which discuss social, economic, and teaching issues. It is an ideal reference work for all those researchers interested in recent quantitative and qualitative tools. Covering a wide range of topics, it appeals in equal measure to mathematicians, statisticians, sociologists, philosophers, and specialists in the fields of communication, social and political sciences.

Author : Michael A. Jones,David McCune,Jennifer M. Wilson
Publisher : American Mathematical Society
Page : 210 pages
File Size : 55,5 Mb
Release : 2024-03-25
Category : Mathematics
ISBN : 9781470469788

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Mathematical Analyses of Decisions, Voting and Games by Michael A. Jones,David McCune,Jennifer M. Wilson Pdf

This volume contains the proceedings of the virtual AMS Special Session on Mathematics of Decisions, Elections and Games, held on April 8, 2022. Decision theory, voting theory, and game theory are three related areas of mathematics that involve making optimal decisions in different contexts. While these three areas are distinct, much of the recent research in these fields borrows techniques from other branches of mathematics such as algebra, combinatorics, convex geometry, logic, representation theory, etc. The papers in this volume demonstrate how the mathematics of decisions, elections, and games can be used to analyze problems from the social sciences.

Author : Yuji Kodama
Publisher : SIAM
Page : 267 pages
File Size : 40,9 Mb
Release : 2018-12-10
Category : Science
ISBN : 9781611975512

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Solitons in Two-Dimensional Shallow Water by Yuji Kodama Pdf

Web-like waves, often observed on the surface of shallow water, are examples of nonlinear waves. They are generated by nonlinear interactions among several obliquely propagating solitary waves, also known as solitons. In this book, modern mathematical tools?algebraic geometry, algebraic combinatorics, and representation theory, among others?are used to analyze these two-dimensional wave patterns. The author?s primary goal is to explain some details of the classification problem of the soliton solutions of the KP equation (or KP solitons) and their applications to shallow water waves. This book is intended for researchers and graduate students.

Author : Douglas N. Arnold
Publisher : SIAM
Page : 120 pages
File Size : 42,8 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9781611975543

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Finite Element Exterior Calculus by Douglas N. Arnold Pdf

Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world—wave propagation, thermodynamics, fluid flow, solid deformation, electricity and magnetism, quantum mechanics, general relativity, and many more—are described by differential equations. We depend on numerical methods for the ability to simulate, explore, predict, and control systems involving these processes. The finite element exterior calculus, or FEEC, is a powerful new theoretical approach to the design and understanding of numerical methods to solve partial differential equations (PDEs). The methods derived with FEEC preserve crucial geometric and topological structures underlying the equations and are among the most successful examples of structure-preserving methods in numerical PDEs. This volume aims to help numerical analysts master the fundamentals of FEEC, including the geometrical and functional analysis preliminaries, quickly and in one place. It is also accessible to mathematicians and students of mathematics from areas other than numerical analysis who are interested in understanding how techniques from geometry and topology play a role in numerical PDEs.

Author : Qiang Du
Publisher : SIAM
Page : 181 pages
File Size : 48,7 Mb
Release : 2019-03-20
Category : Science
ISBN : 9781611975611

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Nonlocal Modeling, Analysis, and Computation by Qiang Du Pdf

Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.

Author : Darren Crowdy
Publisher : SIAM
Page : 456 pages
File Size : 45,9 Mb
Release : 2020-04-20
Category : Mathematics
ISBN : 9781611976151

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Solving Problems in Multiply Connected Domains by Darren Crowdy Pdf

Whenever two or more objects or entities—be they bubbles, vortices, black holes, magnets, colloidal particles, microorganisms, swimming bacteria, Brownian random walkers, airfoils, turbine blades, electrified drops, magnetized particles, dislocations, cracks, or heterogeneities in an elastic solid—interact in some ambient medium, they make holes in that medium. Such holey regions with interacting entities are called multiply connected. This book describes a novel mathematical framework for solving problems in two-dimensional, multiply connected regions. The framework is built on a central theoretical concept: the prime function, whose significance for the applied sciences, especially for solving problems in multiply connected domains, has been missed until recent work by the author. This monograph is a one-of-a-kind treatise on the prime function associated with multiply connected domains and how to use it in applications. The book contains many results familiar in the simply connected, or single-entity, case that are generalized naturally to any number of entities, in many instances for the first time. Solving Problems in Multiply Connected Domains is aimed at applied and pure mathematicians, engineers, physicists, and other natural scientists; the framework it describes finds application in a diverse array of contexts. The book provides a rich source of project material for undergraduate and graduate courses in the applied sciences and could serve as a complement to standard texts on advanced calculus, potential theory, partial differential equations and complex analysis, and as a supplement to texts on applied mathematical methods in engineering and science.

Author : Fioralba Cakoni,David Colton,Houssem Haddar
Publisher : SIAM
Page : 259 pages
File Size : 41,5 Mb
Release : 2022-12-07
Category : Mathematics
ISBN : 9781611977424

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Inverse Scattering Theory and Transmission Eigenvalues by Fioralba Cakoni,David Colton,Houssem Haddar Pdf

Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers—a subset of transmission eigenvalues—using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.

Author : Per-Gunnar Martinsson
Publisher : SIAM
Page : 332 pages
File Size : 49,8 Mb
Release : 2019-12-16
Category : Mathematics
ISBN : 9781611976045

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Fast Direct Solvers for Elliptic PDEs by Per-Gunnar Martinsson Pdf

Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.

Author : Alain Miranville
Publisher : SIAM
Page : 216 pages
File Size : 51,8 Mb
Release : 2019-09-09
Category : Mathematics
ISBN : 9781611975925

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The Cahn–Hilliard Equation: Recent Advances and Applications by Alain Miranville Pdf

This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn–Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn–Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn–Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.

Author : Daniel T. Jessie,Donald G. Saari
Publisher : Springer Nature
Page : 217 pages
File Size : 55,9 Mb
Release : 2019-12-13
Category : Mathematics
ISBN : 9783030358471

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Coordinate Systems for Games by Daniel T. Jessie,Donald G. Saari Pdf

This monograph develops a method of creating convenient coordinate systems for game theory that will allow readers to more easily understand, analyze, and create games at various levels of complexity. By identifying the unique characterization of games that separates the individual’s strategic interests from the group’s collective behavior, the authors construct a single analytical methodology that readers will be able to apply to a wide variety of games. With its emphasis on practicality and approachability, readers will find this book an invaluable tool, and a viable alternative to the ad hoc analytical approach that has become customary for researchers utilizing game theory. The introductory chapters serve two important purposes: they review several games of fundamental importance, and also introduce a dynamic that is inherent in games, but has gone unexplored until now. After this has been established, readers will advance from simple 2 x 2 games to games with more player strategies and dynamics. For interested readers, a rigorous treatment of the underlying mathematics is conveniently gathered at the end of the book. Additional topics of interest, such as extensive form and coalitional games, are presented to help readers visualize more complex settings that will be vital in aiding the understanding of advanced topics, such as coalition-free Nash points, multi-player repeated games, and more. Coordinate Systems for Games is ideal for a wide variety of researchers interested in game theory, including social scientists, economists, mathematicians, computer scientists, and more. The authors' approachable style also makes this accessible to an audience at any scale of experience, from beginning non-specialists to more practiced researchers.

Author : Dan S. Felsenthal,Hannu Nurmi
Publisher : Springer
Page : 92 pages
File Size : 48,6 Mb
Release : 2019-04-02
Category : Business & Economics
ISBN : 9783030126278

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Voting Procedures Under a Restricted Domain by Dan S. Felsenthal,Hannu Nurmi Pdf

This book deals with 20 voting procedures used or proposed for use in elections resulting in the choice of a single winner. These procedures are evaluated in terms of their ability to avoid five important paradoxes in a restricted domain, viz., when a Condorcet winner exists and is elected in the initial profile. Together with the two companion volumes by the same authors, published by Springer in 2017 and 2018, this book aims at giving a comprehensive overview of the most important advantages and disadvantages of voting procedures thereby assisting decision makers in the choice of a voting procedure that would best suit their purposes.

Author : Jian Sun,Fong Peng Chew,Intakhab Alam Khan,Christopher Jenks
Publisher : Springer Nature
Page : 602 pages
File Size : 50,7 Mb
Release : 2023-02-10
Category : Sports & Recreation
ISBN : 9782494069138

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Proceedings of the 2022 International Conference on Sport Science, Education and Social Development (SSESD 2022) by Jian Sun,Fong Peng Chew,Intakhab Alam Khan,Christopher Jenks Pdf

This is an open access book. 2022 International Conference on Sport Science, Education and Social Development(SSESD2022)was held from July 15th to 17th in Kunming China. The objective of SSESD is to promote scientific information interchange by creating a platform to students, researchers, Practitioners, and academicians to present their ongoing researches on diverse themes ranging from Sport Science, Education and Social Development. Under the influence of the current COVID-19 epidemic, people pay more and more attention to physical health, scientific distance education of physical exercise, in the meantime, wisdom education provides a guarantee for people to acquire knowledge. SSESD aims to provide the opportunity for Engineers Academicians, Scientists, Researchers and students to share ideas and knowledge and to network with an international crowd and deliberate the practical challenges encountered and solutions adopted in respective domains worldwide. Thus, organizing committee invites all Industry Professional, delegates and students representing worldwide institutions, Government agencies, and other organizations, to take part in the International Conference on Sport Science, Education and Social Development.