An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science.

Capturing the state of the art of the interplay between positivity, noncommutative analysis, and related areas including partial differential equations, harmonic analysis, and operator theory, this volume was initiated on the occasion of the Delft conference in honour of Ben de Pagter's 65th birthday. It will be of interest to researchers in positivity, noncommutative analysis, and related fields. Contributions by Shavkat Ayupov, Amine Ben Amor, Karim Boulabiar, Qingying Bu, Gerard Buskes, Martijn Caspers, Jurie Conradie, Garth Dales, Marcel de Jeu, Peter Dodds, Theresa Dodds, Julio Flores, Jochen Gluck, Jacobus Grobler, Wolter Groenevelt, Markus Haase, Klaas Pieter Hart, Francisco Hernandez, Jamel Jaber, Rien Kaashoek, Turabay Kalandarov, Anke Kalauch, Arkady Kitover, Erik Koelink, Karimbergen Kudaybergenov, Louis Labuschagne, Yongjin Li, Nick Lindemulder, Emiel Lorist, Qi Lu, Miek Messerschmidt, Susumu Okada, Mehmet Orhon, Denis Potapov, Werner Ricker, Stephan Roberts, Pablo Roman, Anton Schep, Claud Steyn, Fedor Sukochev, James Sweeney, Guido Sweers, Pedro Tradacete, Jan Harm van der Walt, Onno van Gaans, Jan van Neerven, Arnoud van Rooij, Freek van Schagen, Dominic Vella, Mark Veraar, Anthony Wickstead, Marten Wortel, Ivan Yaroslavtsev, and Dmitriy Zanin.

An encompassing socio-historical survey of the political and sociological nature of groups, communities and societies. A transdisciplinary study of crowds, masses and groups as historical, sociological, psychological and psychosocial phenomena. A unique combination of sociology, psychoanalysis and group analysis in the study of social formations. An inquiry into the enigma of crowds and mass psychology with the history of group analytic and group relations' advances in England, especially the study of large groups in the research on group processes. A comprehensive presentation of the social unconscious theory in association with the study of large groups and the Incohesion theory as new group analytic tools for understanding contemporary crowds and masses. In today's world, flooded by social conflicts and polarizations and the mass impact of social media, this book enables the reader to map out the field of the unconscious life of crowds illuminating the darkness of twenty-first century collective movements.

Working out solutions to polynomial equations is a mathematical problem that dates from antiquity. Galois developed a theory in which the obstacle to solving a polynomial equation is an associated collection of symmetries. Obtaining a root requires "breaking" that symmetry. When the degree of an equation is at least five, Galois Theory established that there is no formula for the solutions like those found in lower degree cases. However, this negative result doesn't mean that the practice of equation-solving ends. In a recent breakthrough, Doyle and McMullen devised a solution to the fifth-degree equation that uses geometry, algebra, and dynamics to exploit icosahedral symmetry. Polynomials, Dynamics, and Choice: The Price We Pay for Symmetry is organized in two parts, the first of which develops an account of polynomial symmetry that relies on considerations of algebra and geometry. The second explores beyond polynomials to spaces consisting of choices ranging from mundane decisions to evolutionary algorithms that search for optimal outcomes. The two algorithms in Part I provide frameworks that capture structural issues that can arise in deliberative settings. While decision-making has been approached in mathematical terms, the novelty here is in the use of equation-solving algorithms to illuminate such problems. Features Treats the topic-familiar to many-of solving polynomial equations in a way that's dramatically different from what they saw in school Accessible to a general audience with limited mathematical background Abundant diagrams and graphics.

Working out solutions to polynomial equations is a mathematical problem that dates from antiquity. Galois developed a theory in which the obstacle to solving a polynomial equation is an associated collection of symmetries. Obtaining a root requires "breaking" that symmetry. When the degree of an equation is at least five, Galois Theory established that there is no formula for the solutions like those found in lower degree cases. However, this negative result doesn't mean that the practice of equation-solving ends. In a recent breakthrough, Doyle and McMullen devised a solution to the fifth-degree equation that uses geometry, algebra, and dynamics to exploit icosahedral symmetry. Polynomials, Dynamics, and Choice: The Price We Pay for Symmetry is organized in two parts, the first of which develops an account of polynomial symmetry that relies on considerations of algebra and geometry. The second explores beyond polynomials to spaces consisting of choices ranging from mundane decisions to evolutionary algorithms that search for optimal outcomes. The two algorithms in Part I provide frameworks that capture structural issues that can arise in deliberative settings. While decision-making has been approached in mathematical terms, the novelty here is in the use of equation-solving algorithms to illuminate such problems. Features Treats the topic-familiar to many-of solving polynomial equations in a way that's dramatically different from what they saw in school Accessible to a general audience with limited mathematical background Abundant diagrams and graphics.

The once esoteric idea of embedding scientific computing into a probabilistic framework, mostly along the lines of the Bayesian paradigm, has recently enjoyed wide popularity and found its way into numerous applications. This book provides an insider's view of how to combine two mature fields, scientific computing and Bayesian inference, into a powerful language leveraging the capabilities of both components for computational efficiency, high resolution power and uncertainty quantification ability. The impact of Bayesian scientific computing has been particularly significant in the area of computational inverse problems where the data are often scarce or of low quality, but some characteristics of the unknown solution may be available a priori. The ability to combine the flexibility of the Bayesian probabilistic framework with efficient numerical methods has contributed to the popularity of Bayesian inversion, with the prior distribution being the counterpart of classical regularization. However, the interplay between Bayesian inference and numerical analysis is much richer than providing an alternative way to regularize inverse problems, as demonstrated by the discussion of time dependent problems, iterative methods, and sparsity promoting priors in this book. The quantification of uncertainty in computed solutions and model predictions is another area where Bayesian scientific computing plays a critical role. This book demonstrates that Bayesian inference and scientific computing have much more in common than what one may expect, and gradually builds a natural interface between these two areas.

This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.

Presenting diverse perspectives from eminent scholars and contemporary researchers, The Handbook of Impression Formation contextualizes current and future areas of research in the social psychology of impression formation within a rich historic framework. Affirming that impression formation is at the core of human experience, chapters explore how and why people form snap judgments about others and when those impressions update. They examine the processes through which people infer the reasons for the events they encounter, allowing people to plan for appropriate behavioral responses to social contexts. The research reviewed is informed by the foundational theory of unconscious automatic processes involved in making judgements of other people, pioneered by Professor Jim Uleman who contributes a chapter that suggests important new directions, and concludes the volume by reflecting on the state of the field more broadly. The book explores how certain attributes stimulate categorization, examining current issues around implicit bias, stereotypes, and social media. Chapters cover a range of approaches, featuring personal narratives, presentation of new data and discoveries, comprehensive literature reviews, and contemplations on where the field must go and what questions require focus for progress to be made, calling for even the most advanced scholars to contribute more to the collective investigation of impression formation. This fascinating work provides a solid foundation from which all researchers can build a new and unique program of research, and arms the reader with the intellectual tools they need to chart new theoretical territory and discover aspects of the human experience we have yet to even wonder about. It is essential reading for students and academics in social psychology, and the social sciences more broadly.

Professor Xihua Cao (1920-2005) was a leading scholar at East China Normal University (ECNU) and a famous algebraist in China. His contribution to the Chinese academic circle is particularly the formation of a world-renowned 'ECNU School' in algebra, covering research areas include algebraic groups, quantum groups, algebraic geometry, Lie algebra, algebraic number theory, representation theory and other hot fields. In January 2020, in order to commemorate Professor Xihua Cao's centenary birthday, East China Normal University held a three-day academic conference. Scholars at home and abroad gave dedications or delivered lectures in the conference. This volume originates from the memorial conference, collecting the dedications of scholars, reminiscences of family members, and 16 academic articles written based on the lectures in the conference, covering a wide range of research hot topics in algebra. The book shows not only scholars' respect and memory for Professor Xihua Cao, but also the research achievements of Chinese scholars at home and abroad.

Originally published in 1982, Time Resources, Society and Ecology examines and seeks to examine the time dimension in terms of the ecology, technology, social organization and spatial structure of the human habitat. Approaches to time resources - sociological time-budget studies, anthropological activity analysis, and economic analysis of money allocation - have been limited by their sectoral scope or their failure to relate effectively to the processes of social interaction, technological change and environmental structure. In this book, the book's articulation of time resources is developed in a general theoretical framework of action and interaction in time and space. The book examines constraints and possibilities facing preindustrial societies and throws light on the impact of technology on modern societies. Basic models of time allocation are presented, and, finally, a cross-cultural comparison is made of the mobilization of time resources in preindustrial societies. Geographers, social anthropologists and human ecologists should find this work directly relevant to their interest in understanding the interactions between man and environment.

Hyperidentities are important formulae of second-order logic, and research in hyperidentities paves way for the study of second-order logic and second-order model theory.This book illustrates many important current trends and perspectives for the field of hyperidentities and their applications, of interest to researchers in modern algebra and discrete mathematics. It covers a number of directions, including the characterizations of the Boolean algebra of n-ary Boolean functions and the distributive lattice of n-ary monotone Boolean functions; the classification of hyperidentities of the variety of lattices, the variety of distributive (modular) lattices, the variety of Boolean algebras, and the variety of De Morgan algebras; the characterization of algebras with aforementioned hyperidentities; the functional representations of finitely-generated free algebras of various varieties of lattices and bilattices via generalized Boolean functions (De Morgan functions, quasi-De Morgan functions, super-Boolean functions, super-De Morgan functions, etc); the structural results for De Morgan algebras, Boole-De Morgan algebras, super-Boolean algebras, bilattices, among others.While problems of Boolean functions theory are well known, the present book offers alternative, more general problems, involving the concepts of De Morgan functions, quasi-De Morgan functions, super-Boolean functions, and super-De Morgan functions, etc. In contrast to other generalized Boolean functions discovered and investigated so far, these functions have clearly normal forms. This quality is of crucial importance for their applications in pure and applied mathematics, especially in discrete mathematics, quantum computation, quantum information theory, quantum logic, and the theory of quantum computers.

Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.

This book attempts to 'shake up' the current complacency around therapy and 'mental health' behaviours by putting therapy fully into context using Social Contextual Analysis; showing how changes to our social, discursive, and societal environments, rather than changes to an individual's 'mind', will reduce suffering from the 'mental health' behaviours. Guerin challenges many assumptions about both current therapy and psychology, and offers alternative approaches, synthesized from sociology, social anthropology, sociolinguistics, and elsewhere. The book provides a way of addressing the 'mental health' behaviours including actions, talking, thinking, and emotions, by taking people's external life situations into account, and not relying on an imagined 'internal source'. Guerin describes the broad contexts for current Western therapies, referring to social, discursive, cultural, societal, and economic contexts, and suggests that we need to research the components of therapies and stop treating therapies as units. He reframes different types of therapy away from their abstract jargons, offering an alternative approach grounded in our real social worlds, aligning with new thinking that challenges the traditional methods of therapy, and also providing a better framework for rethinking psychology itself. The book ultimately suggests more emphasis should be put on 'mental health' behaviours as arising from social issues including the modern contexts of extreme capitalism, excessive bureaucracy, weakened discursive communities, and changing forms of social relationships. Practical guidelines are provided for building the reimagined therapies into clinics and institutions where labelling and pathologizing the 'mental health' behaviours will no longer be needed. By putting 'mental health' behaviours and therapy into a naturalistic or ecological social sciences framework, this book will be practical and fascinating reading for professional therapists, counsellors, social workers, and mental health nurses, as well as academics interested in psychology and the social sciences more generally.

This book attempts to 'shake up' the current complacency around therapy and 'mental health' behaviours by putting therapy fully into context using Social Contextual Analysis; showing how changes to our social, discursive, and societal environments, rather than changes to an individual's 'mind', will reduce suffering from the 'mental health' behaviours. Guerin challenges many assumptions about both current therapy and psychology, and offers alternative approaches, synthesized from sociology, social anthropology, sociolinguistics, and elsewhere. The book provides a way of addressing the 'mental health' behaviours including actions, talking, thinking, and emotions, by taking people's external life situations into account, and not relying on an imagined 'internal source'. Guerin describes the broad contexts for current Western therapies, referring to social, discursive, cultural, societal, and economic contexts, and suggests that we need to research the components of therapies and stop treating therapies as units. He reframes different types of therapy away from their abstract jargons, offering an alternative approach grounded in our real social worlds, aligning with new thinking that challenges the traditional methods of therapy, and also providing a better framework for rethinking psychology itself. The book ultimately suggests more emphasis should be put on 'mental health' behaviours as arising from social issues including the modern contexts of extreme capitalism, excessive bureaucracy, weakened discursive communities, and changing forms of social relationships. Practical guidelines are provided for building the reimagined therapies into clinics and institutions where labelling and pathologizing the 'mental health' behaviours will no longer be needed. By putting 'mental health' behaviours and therapy into a naturalistic or ecological social sciences framework, this book will be practical and fascinating reading for professional therapists, counsellors, social workers, and mental health nurses, as well as academics interested in psychology and the social sciences more generally.

Presenting diverse perspectives from eminent scholars and contemporary researchers, The Handbook of Impression Formation contextualizes current and future areas of research in the social psychology of impression formation within a rich historic framework. Affirming that impression formation is at the core of human experience, chapters explore how and why people form snap judgments about others and when those impressions update. They examine the processes through which people infer the reasons for the events they encounter, allowing people to plan for appropriate behavioral responses to social contexts. The research reviewed is informed by the foundational theory of unconscious automatic processes involved in making judgements of other people, pioneered by Professor Jim Uleman who contributes a chapter that suggests important new directions, and concludes the volume by reflecting on the state of the field more broadly. The book explores how certain attributes stimulate categorization, examining current issues around implicit bias, stereotypes, and social media. Chapters cover a range of approaches, featuring personal narratives, presentation of new data and discoveries, comprehensive literature reviews, and contemplations on where the field must go and what questions require focus for progress to be made, calling for even the most advanced scholars to contribute more to the collective investigation of impression formation. This fascinating work provides a solid foundation from which all researchers can build a new and unique program of research, and arms the reader with the intellectual tools they need to chart new theoretical territory and discover aspects of the human experience we have yet to even wonder about. It is essential reading for students and academics in social psychology, and the social sciences more broadly.

Psychology of Prejudice and Discrimination provides a comprehensive and compelling overview of what psychological theory and research have to say about the nature, causes, and reduction of prejudice and discrimination. It balances a detailed discussion of theories and selected research with applied examples that ensure the material is relevant to students. This edition has been thoroughly revised and updated and addresses several interlocking themes. It first looks at the nature of prejudice and discrimination, followed by a discussion of research methods. Next come the psychological underpinnings of prejudice: the nature of stereotypes, the conditions under which stereotypes influence responses to other people, contemporary theories of prejudice, and how individuals' values and belief systems are related to prejudice. Explored next are the development of prejudice in children and the social context of prejudice. The theme of discrimination is developed via discussions of the nature of discrimination, the experience of discrimination, and specific forms of discrimination, including gender, gender identity, sexual orientation, age, ability, and appearance. The concluding theme is the reduction of prejudice. The book is accompanied by a comprehensive website featuring an Instructor Manual that contains activities and tools to help with teaching a prejudice and discrimination course; PowerPoint slides for every chapter; and a Test Bank with short answer and multiple-choice exam questions for every chapter. This book is an essential companion for all students of prejudice and discrimination, including those in psychology, education, social work, business, communication studies, ethnic studies, and other disciplines. In addition to courses on prejudice and discrimination, this book will also appeal to those studying racism and diversity.

Based on extensive analysis of real-time, authentic crisis encounters collected in the UK and US, Crisis Talk: Negotiating with Individuals in Crisis sheds light on the relatively hidden world of communication between people in crisis and the professionals whose job it is to help them. The crisis situations explored in this book involve police hostage and crisis negotiators and emergency dispatchers interacting with individuals in crisis who threaten suicide or self-harm. The practitioners face various communicative challenges in these encounters, including managing strong emotions, resistance, hostility, and unresponsiveness. Using conversation analysis, Crisis Talk presents evidence on how practitioners deal with the interactional challenge of negotiating with people in crisis and how what they say shapes outcomes. Each chapter includes recommendations based on the detailed analysis of numerous cases of actual negotiation. Crisis Talk shows readers how every turn taken by negotiators can exacerbate or solve the communicative challenges created by crisis situations, making it a unique and invaluable text for academics in psychology, sociology, linguistic sciences, and related fields, as well as for practitioners engaging in crisis negotiation training or fieldwork.

Primarily concerned with the study of cohomology theories of general topological spaces with "general coefficient systems", the parts of sheaf theory covered here are those areas important to algebraic topology. Among the many innovations in this book, the concept of the "tautness" of a subspace is introduced and exploited; the fact that sheaf theoretic cohomology satisfies the homotopy property is proved for general topological spaces; and relative cohomology is introduced into sheaf theory. A list of exercises at the end of each chapter helps students to learn the material, and solutions to many of the exercises are given in an appendix. This new edition of a classic has been substantially rewritten and now includes some 80 additional examples and further explanatory material, as well as new sections on Cech cohomology, the Oliver transfer, intersection theory, generalised manifolds, locally homogeneous spaces, homological fibrations and p- adic transformation groups. Readers should have a thorough background in elementary homological algebra and in algebraic topology.

Loop groups, the simplest class of infinite dimensional Lie groups, have recently been the subject of intense study. This book gives a complete and self-contained account of what is known about them from a geometrical and analytical point of view, drawing together the many branches of mathematics from which current theory developed--algebra, geometry, analysis, combinatorics, and the mathematics of quantum field theory. The authors discuss Loop groups' applications to simple particle physics and explain how the mathematics used in connection with Loop groups is itself interesting and valuable, thereby making this work accessible to mathematicians in many fields.

Features Written to be self-contained. Ideal as a primary textbook for an undergraduate course in linear algebra. Applications of the general theory which are of interest to disciplines outside of mathematics, such as engineering.

Features Written to be self-contained. Ideal as a primary textbook for an undergraduate course in linear algebra. Applications of the general theory which are of interest to disciplines outside of mathematics, such as engineering.

This book provides a systematic, rigorous and self-contained treatment of positive dynamical systems. A dynamical system is positive when all relevant variables of a system are nonnegative in a natural way. This is in biology, demography or economics, where the levels of populations or prices of goods are positive. The principle also finds application in electrical engineering, physics and computer sciences. "The author has greatly expanded the field of positive systems in surprising ways." - Prof. Dr. David G. Luenberger, Stanford University(USA)

This work deals with the matrix methods of continuous signal and image processing according to which strip-transformation is used. The authors suggest ways to solve a problem of evaluating potential noise immunity and synthesis of an optimal filter for the case of pulse noises, of applying the two-dimensional strip-transformation for storage and noise immune transmission of images. The strip-transformation of images is illustrated by examples and classes of images invariant relative to symmetrical orthogonal transformations. The monograph is intended for scientists and specialists whose activities are connected with computer signals and images processing, instrumentation and metrology. It can also be used by undergraduates, as well as by post-graduates for studying computer methods of signal and image processing.

This new text offers a student-centered approach. It presents groups first approach, offers flexibility, and is aimed at both a one- and two-semester course. The primary difference from key competitors is level and organization. There are many AA texts, offering a wide-range of levels, and this text is written to the precise middle of the market. Abstract Algebra is taught at every four-year university and college throughout the world. It is a course typically required of mathematics majors, yet also of those planning on becoming teachers. The groups-first approach is the most popular.