Fred S. Roberts - Böcker

This book provides an introduction to measurement theory for non-specialists and puts measurement in the social and behavioural sciences on a firm mathematical foundation. Results are applied to such topics as measurement of utility, psychophysical scaling and decision-making about pollution, energy, transportation and health. The results and questions presented should be of interest to both students and practising mathematicians since the author sets forth an area of mathematics unfamiliar to most mathematicians, but which has many potentially significant applications.

Mathematical psychology is an interdisciplinary area of research in which methods of mathematics, operations research, and computer science in psychology are used. Now more than thirty years old, the field has continued to grow rapidly and has taken on a life of its own. This volume summarizes recent progress in mathematical psychology as seen by some of the leading figures in the field as well as some of its leading young researchers. The papers presented in this volume reflect the most important current directions of research in mathematical psychology. They cover topics in measurement, decision and choice, psychophysics and psychometrics, knowledge representation, neural nets and learning models, and cognitive modeling. Some of the major ideas included are new applications of concepts of measurement theory to social phenomena, new directions in the theory of probabilistic choice, surprising results in nonlinear utility theory, applications of boolean methods in the theory of knowledge spaces, applications of neural net ideas to concept learning, developments in the theory of parallel processing models of response time, new results in inhibition theory, and new concepts about paired associate learning.

Explores modern topics in graph theory and its applications to problems in transportation, genetics, pollution, perturbed ecosystems, urban services, and social inequalities. The author presents both traditional and relatively atypical graph-theoretical topics to best illustrate applications.

The original goal of writing this book was to introduce the reader to the tools of combinatorics from an applied point of view. This third edition of Applied Combinatorics was substantially rewritten. There are many new examples and exercises. References throughout the book to modern literature and real applications, a key feature of the book, have been updated and expanded. The exposition continues to be updated with each new edition, as the first edition was published 40 years ago.The emphasis on applications from computer science, genetics, experimental design, chemistry, scheduling, voting, and other topics remains a central feature of the book. Unique to the literature is that entire sections focus on applications such as switching functions, the use of enzymes to uncover unknown RNA chains, searching and sorting problems of information retrieval, construction of error-correcting codes, counting of chemical compounds, calculation of power in voting situations, and uses of Fibonacci numbers. There are entire sections on applications of recurrences involving convolutions, applications of eulerian chains, and applications of generating functions.The book continues to be based on the authors’ philosophy that the best way to learn mathematics is through problem solving. Combinatorics can be a wonderful mechanism for introducing students to proofs. However, the book is not designed for an introduction to proofs course. The authors treat proofs as rather informal, and many of the harder proofs in the book are optional.Applied Combinatorics, Third Edition is divided into four parts. The first part introduces the basic tools of combinatorics and their applications. The remaining three parts are organized around the three basic problems of combinatorics: the counting problem, the existence problem, and the optimization problem.Most of the book is written for a first course on the topic at the undergraduate level. On the other hand, at a fast pace, there is more than enough material for a challenging graduate course. This book first appeared when courses on combinatorics were rare. We are pleased to think that, through its use, the book has helped to establish a key course in many colleges and universities throughout the world. We hope that this new edition will remain a valuable tool for instructors and students alike.

Mathematical psychology is an interdisciplinary area of research in which methods of mathematics, operations research, and computer science in psychology are used. Now more than thirty years old, the field has continued to grow rapidly and has taken on a life of its own. This volume summarizes recent progress in mathematical psychology as seen by some of the leading figures in the field as well as some of its leading young researchers. The papers presented in this volume reflect the most important current directions of research in mathematical psychology. They cover topics in measurement, decision and choice, psychophysics and psychometrics, knowledge representation, neural nets and learning models, and cognitive modeling. Some of the major ideas included are new applications of concepts of measurement theory to social phenomena, new directions in the theory of probabilistic choice, surprising results in nonlinear utility theory, applications of boolean methods in the theory of knowledge spaces, applications of neural net ideas to concept learning, developments in the theory of parallel processing models of response time, new results in inhibition theory, and new concepts about paired associate learning.

Since its inception in 2013, Mathematics of Planet Earth (MPE) focuses on mathematical issues arising in the study of our planet. Demonstrating the mathematical sciences in action, this book presents real-world challenges for the mathematical sciences, highlighting applications to issues of current concern to society.

Since its inception in 2013, Mathematics of Planet Earth (MPE) focuses on mathematical issues arising in the study of our planet. Demonstrating the mathematical sciences in action, this book presents real-world challenges for the mathematical sciences, highlighting applications to issues of current concern to society.

The growth of a global digital economy has enabled rapid communication, instantaneous movement of funds, and availability of vast amounts of information. With this come challenges such as the vulnerability of digitalized sociotechnological systems (STSs) to destructive events (earthquakes, disease events, terrorist attacks). Similar issues arise for disruptions to complex linked natural and social systems (from changing climates, evolving urban environments, etc.). This book explores new approaches to the resilience of sociotechnological and natural-social systems in a digital world of big data, extraordinary computing capacity, and rapidly developing methods of Artificial Intelligence.Most of the book’s papers were presented at the Workshop on Big Data and Systems Analysis held at the International Institute for Applied Systems Analysis in Laxenburg, Austria in February, 2020. Their authors are associated with the Task Group “Advanced mathematical tools for data-driven applied systems analysis” created and sponsored by CODATA in November, 2018.The world-wide COVID-19 pandemic illustrates the vulnerability of our healthcare systems, supply chains, and social infrastructure, and confronts our notions of what makes a system resilient. We have found that use of AI tools can lead to problems when unexpected events occur. On the other hand, the vast amounts of data available from sensors, satellite images, social media, etc. can also be used to make modern systems more resilient.Papers in the book explore disruptions of complex networks and algorithms that minimize departure from a previous state after a disruption; introduce a multigrammatical framework for the technological and resource bases of today’s large-scale industrial systems and the transformations resulting from disruptive events; and explain how robotics can enhance pre-emptive measures or post-disaster responses to increase resiliency. Other papers explore current directions in data processing and handling and principles of FAIRness in data; how the availability of large amounts of data can aid in the development of resilient STSs and challenges to overcome in doing so. The book also addresses interactions between humans and built environments, focusing on how AI can inform today’s smart and connected buildings and make them resilient, and how AI tools can increase resilience to misinformation and its dissemination.

Peter Fishburn has had a splendidly productive career that led to path-breaking c- tributions in a remarkable variety of areas of research. His contributions have been published in a vast literature, ranging through journals of social choice and welfare, decision theory, operations research, economic theory, political science, mathema- cal psychology, and discrete mathematics. This work was done both on an individual basis and with a very long list of coauthors. The contributions that Fishburn made can roughly be divided into three major topical areas, and contributions to each of these areas are identi?ed by sections of this monograph. Section 1 deals with topics that are included in the general areas of utility, preference, individual choice, subjective probability, and measurement t- ory. Section 2 covers social choice theory, voting models, and social welfare. S- tion 3 deals with more purely mathematical topics that are related to combinatorics, graph theory, and ordered sets. The common theme of Fishburn’s contributions to all of these areas is his ability to bring rigorous mathematical analysis to bear on a wide range of dif?cult problems.

Peter Fishburn has had a splendidly productive career that led to path-breaking c- tributions in a remarkable variety of areas of research. His contributions have been published in a vast literature, ranging through journals of social choice and welfare, decision theory, operations research, economic theory, political science, mathema- cal psychology, and discrete mathematics. This work was done both on an individual basis and with a very long list of coauthors. The contributions that Fishburn made can roughly be divided into three major topical areas, and contributions to each of these areas are identi?ed by sections of this monograph. Section 1 deals with topics that are included in the general areas of utility, preference, individual choice, subjective probability, and measurement t- ory. Section 2 covers social choice theory, voting models, and social welfare. S- tion 3 deals with more purely mathematical topics that are related to combinatorics, graph theory, and ordered sets. The common theme of Fishburn’s contributions to all of these areas is his ability to bring rigorous mathematical analysis to bear on a wide range of dif?cult problems.