Statistical Complexity

Statistical mechanics is our tool for deriving the laws that emerge from complex systems. Sethna's text distills the subject to be accessible to those in all realms of science and engineering - avoidi

These notes are based on a series of lectures given at the Advanced Research Institute of Discrete Applied Mathematics held at Rutgers University. Their aim is to link together algorithmic problems arising in knot theory, statistical physics and classical combinatorics. Apart from the theory of computational complexity concerned with enumeration problems, introductions are given to several of the topics treated, such as combinatorial knot theory, randomised approximation algorithms, percolation and random cluster models. To researchers in discrete mathematics, computer science and statistical physics, this book will be of great interest, but any non-expert should find it an appealing guide to a very active area of research.

Complexity science is the study of systems with many interdependent components. Such systems - and the self-organization and emergent phenomena they manifest - lie at the heart of many challenges of global importance. This book is a coherent introduction to the mathematical methods used to understand complexity, with plenty of examples and real-world applications. It starts with the crucial concepts of self-organization and emergence, then tackles complexity in dynamical systems using differential equations and chaos theory. Several classes of models of interacting particle systems are studied with techniques from stochastic analysis, followed by a treatment of the statistical mechanics of complex systems. Further topics include numerical analysis of PDEs, and applications of stochastic methods in economics and finance. The book concludes with introductions to space-time phases and selfish routing. The exposition is suitable for researchers, practitioners and students in complexity sci

This book concerns the use of concepts from statistical physics in the description of financial systems. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully developed turbulent fluids. These concepts are then applied to financial time series. The authors also present a stochastic model that displays several of the statistical properties observed in empirical data. Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling permit an understanding of the global behaviour of economic systems without first having to work out a detailed microscopic description of the system. Physicists will find the application of statistical physics concepts to economic systems interesting. Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number o

The environmental sciences are undergoing a revolution in the use of models and data. Facing ecological data sets of unprecedented size and complexity, environmental scientists are struggling to under

Complex behaviour can occur in any system made up of large numbers of interacting constituents, be they atoms in a solid, cells in a living organism, or consumers in a national economy. Analysis of this behaviour often involves making important assumptions and approximations, the exact nature of which vary from subject to subject. Foundations of Complex-system Theories begins with a description of the general features of complexity and then examines a range of important concepts, such as theories of composite systems, collective phenomena, and stochastic processes. Each topic is discussed with reference to the fields of statistical physics, evolutionary biology, and economics, thereby highlighting recurrent themes in the study of complex systems. This detailed yet nontechnical book will appeal to anyone who wants to know more about complex systems and their behaviour. It will also be of great interest to specialists studying complexity in the physical, biological, and social sciences.

Switching parties is arguably the most important decision a politician will ever make. This book is the first-ever systematic study of the causes and consequences of legislative party switching in the United States. The author argues that re-election alone does not explain party switching. He proposes an ambition-based theory that accounts for multiple goals (including higher office aspirations and the desire for influence in the legislature) with a focus on the electoral costs and the institutional benefits of the decision. The book combines the statistical analysis of electoral data and legislative careers in the US Congress and state legislatures with elite interviews of party switchers, non-switchers, and a party leader. The case study of a party switcher's decision in 'real time' documents the complexity of the decision in a politician's own words prior to and following the switch. The book raises important questions regarding the meaning of a party label.

The complexity of social problems necessitates that social work researchers understand and apply multivariate statistical methods in their investigations. In this pocket guide, the authors introduce r

As one of the most comprehensive machine learning texts around, this book does justice to the field's incredible richness, but without losing sight of the unifying principles. Peter Flach's clear, example-based approach begins by discussing how a spam filter works, which gives an immediate introduction to machine learning in action, with a minimum of technical fuss. Flach provides case studies of increasing complexity and variety with well-chosen examples and illustrations throughout. He covers a wide range of logical, geometric and statistical models and state-of-the-art topics such as matrix factorisation and ROC analysis. Particular attention is paid to the central role played by features. The use of established terminology is balanced with the introduction of new and useful concepts, and summaries of relevant background material are provided with pointers for revision if necessary. These features ensure Machine Learning will set a new standard as an introductory textbook.

The explosive growth and increasing complexity of global financial markets are defining characteristics of the contemporary world economy. Unfortunately, financial globalization has been accompanied by a marked increase in the frequency and severity of financial crises. The International Monetary Fund (IMF) has taken a central role in managing these crises through its loans to developing countries. Despite extensive analysis and criticism of the IMF in recent years, key questions remain unanswered. Why does the Fund treat some countries more generously than others? To what extent is IMF lending driven by political factors rather than economic concerns? In whose interests does the IMF act? In this book, Mark Copelovitch offers novel answers to these questions. Combining statistical analysis with detailed case studies, he demonstrates how the politics and policies of the IMF have evolved over the last three decades in response to fundamental changes in the composition of international ca

The theory of empirical processes provides valuable tools for the development of asymptotic theory in (nonparametric) statistical models, and makes possible the unified treatment of a number of them. This book reveals the relation between the asymptotic behaviour of M-estimators and the complexity of parameter space. Virtually all results are proved using only elementary ideas developed within the book; there is minimal recourse to abstract theoretical results. To make the results concrete, a detailed treatment is presented for two important examples of M-estimation, namely maximum likelihood and least squares. The theory also covers estimation methods using penalties and sieves. Many illustrative examples are given, including the Grenander estimator, estimation of functions of bounded variation, smoothing splines, partially linear models, mixture models and image analysis. Graduate students and professionals in statistics as well as those with an interest in applications, to such area

This book describes theoretical advances in the study of artificial neural networks. It explores probabilistic models of supervised learning problems, and addresses the key statistical and computational questions. Research on pattern classification with binary-output networks is surveyed, including a discussion of the relevance of the Vapnik–Chervonenkis dimension, and calculating estimates of the dimension for several neural network models. A model of classification by real-output networks is developed, and the usefulness of classification with a 'large margin' is demonstrated. The authors explain the role of scale-sensitive versions of the Vapnik–Chervonenkis dimension in large margin classification, and in real prediction. They also discuss the computational complexity of neural network learning, describing a variety of hardness results, and outlining two efficient constructive learning algorithms. The book is self-contained and is intended to be accessible to researchers and gradua

Macroeconomics is evolving in an almost dialectic fashion. The latest evolution is the development of a new synthesis that combines insights of new classical, new Keynesian and real business cycle traditions into a dynamic, stochastic general equilibrium (DSGE) model that serves as a foundation for thinking about macro policy. That new synthesis has opened up the door to a new antithesis, which is being driven by advances in computing power and analytic techniques. This new synthesis is coalescing around developments in complexity theory, automated general to specific econometric modeling, agent-based models, and non-linear and statistical dynamical models. This book thus provides the reader with an introduction to what might be called a Post Walrasian research program that is developing as the antithesis of the Walrasian DSGE synthesis.

This 2002 book presents the reader with mathematical tools taken from matrix calculus and zero-one matrices and demonstrates how these tools greatly facilitate the application of classical statistical procedures to econometric models. The matrix calculus results are derived from a few basic rules that are generalizations of the rules of ordinary calculus. These results are summarized in a useful table. Well-known zero-one matrices, together with some newer ones, are defined, their mathematical roles explained, and their useful properties presented. The basic building blocks of classical statistics, namely the score vector, the information matrix, and the Cramer-Rao lower bound, are obtained for a sequence of linear econometric models of increasing statistical complexity. From these are obtained interactive interpretations of maximum likelihood estimators, linking them with efficient econometric estimators. Classical test statistics are also derived and compared for hypotheses of intere

Statistical techniques and theories have become widely applied in the physical, biological and social sciences. The enormous increase in their scope and complexity has led to much philosophical discussion of their significance, and of the meaning in non-mathematical terms of the methods and concepts they employ. This book deals not so much with statistical methods as with the central concept of chance, or statistical probability, which statistical theories apply to nature. Examples range from the chance of a tossed coin falling heads to that of a man dying or a radioactive atom decaying in a fixed period of time. Chances seem, however, to be peculiar properties, and to belong to peculiar entitles, to events rather than to things.

This is a comprehensive discussion of complexity as it arises in physical, chemical, and biological systems, as well as in mathematical models of nature. Common features of these apparently unrelated fields are emphasised and incorporated into a uniform mathematical description, with the support of a large number of detailed examples and illustrations. The quantitative study of complexity is a rapidly developing subject with special impact in the fields of physics, mathematics, information science, and biology. Because of the variety of the approaches, no comprehensive discussion has previously been attempted. This book will be of interest to graduate students and researchers in physics (nonlinear dynamics, fluid dynamics, solid-state, cellular automata, stochastic processes, statistical mechanics and thermodynamics), mathematics (dynamical systems, ergodic and probability theory), information and computer science (coding, information theory and algorithmic complexity), electrical engi

Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the

This textbook integrates traditional statistical data analysis with new computational experimentation capabilities and concepts of algorithmic complexity and chaotic behavior in nonlinear dynamic syst