Statistical Complexity

The understanding of electron density as the carrier of all the information of a multielectronic system is implicit in the theorems of density functional theory. Information theoretical based measures

In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this ste

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

The media, scientific researchers, and the Diagnostic and Statistical Manual all refer to "autism" as if it were a single disorder or a single disorder over a spectrum. However, autism is unlike any s

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.

This volume of the Encyclopedia of Complexity and Systems Science, Second Edition, focuses on current challenges in the field from materials and mechanics to applications of statistical and nonlinear physics in the life sciences. Challenges today are mostly in the realm of non-equilibrium systems, although certain equilibrium systems also present serious hurdles. Where possible, pairwise articles focus on a single topic, one from a theoretical perspective and the other from an experimental one, providing valuable insights. In other cases, theorists and experimentalists have collaborated on a single article. Coverage includes both quantum and classical systems, and emphasizes 1) mature fields that are not covered in the current specialist literature, (2) topics that fall through the cracks in disciplinary journals/books, or (3) developing areas where the knowledge base is large and robust and upon which future developments will depend. The result is an invaluable resource for condensed

Complexity theory aims to understand and classify computational problems, especially decision problems, according to their inherent complexity. This book uses new techniques to expand the theory for use with counting problems. The authors present dichotomy classifications for broad classes of counting problems in the realm of P and NP. Classifications are proved for partition functions of spin systems, graph homomorphisms, constraint satisfaction problems, and Holant problems. The book assumes minimal prior knowledge of computational complexity theory, developing proof techniques as needed and gradually increasing the generality and abstraction of the theory. This volume presents the theory on the Boolean domain, and includes a thorough presentation of holographic algorithms, culminating in classifications of computational problems studied in exactly solvable models from statistical mechanics.

This book focuses on recent progress in complexity research based on the fundamental nonlinear dynamical and statistical theory of oscillations, waves, chaos, and structures far from equilibrium. Cele

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 book

This book provides an interdisciplinary and integrative overview of environmental problem-solving using statistical methods. It shows how statistics can be used to solve problems related to food, wate

Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive

The structural mechanics of proteins that fold into functional shapes, polymers that aggregate and form clusters, and organic macromolecules that bind to inorganic matter can only be understood through statistical physics and thermodynamics. This book reviews the statistical mechanics concepts and tools necessary for the study of structure formation processes in macromolecular systems that are essentially influenced by finite-size and surface effects. Readers are introduced to molecular modeling approaches, advanced Monte Carlo simulation techniques, and systematic statistical analyses of numerical data. Applications to folding, aggregation, and substrate adsorption processes of polymers and proteins are discussed in great detail. Particular emphasis is placed on the reduction of complexity by coarse-grained modeling, which allows for the efficient, systematic investigation of structural phases and transitions. Providing insight into modern research at this interface between physics,

Zero-knowledge interactive proofs play a central role in the design and study of cryptographic protocols and are rich objects for complexity-theoretic study. Statistical zero-knowledge (SZK) proofs ac

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

In recent years, interest in developing statistical and computational techniques for applied manufacturing engineering has been increased. Today, due to the great complexity of manufacturing engineeri

Evolutionary genomics is a relatively new research field with the ultimate goal of understanding the underlying evolutionary and genetic mechanisms for the emergence of genome complexity under changi

The complexity, diversity, and random nature of transportation problems necessitates a broad analytical toolbox. Describing tools commonly used in the field, Statistical and Econometric Methods for Tr

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

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.

Presents 20 statistical case studies for the classroom using data sets that have not been simplified for classroom use; that is, they retain the complexity of real-life statistical problems. The stud

This cross-disciplinary volume provides an overview of how complexity theory and the tools of statistical mechanics can be applied to linguistic problems to help reveal language groups, and to model the evolution and competition of languages in space and time. Illustrated with a series of case studies and worked examples, it presents an interdisciplinary framework to enable researchers from the mathematical, physical and social sciences to collaborate on linguistic problems. It demonstrates the complexity of linguistic databases and provides a mathematical toolkit for analyzing and extracting useful information from them - helping to conceptualize empirical facts better than a mere ethnographic view. Providing an important bridge to facilitate collaboration between linguists and mathematical modelers, this book will stimulate new ideas and avenues for research, and will form a valuable resource for advanced students and academics working across complex systems, sociolinguistics, and la

This pedagogical and self-contained text describes the modern mean field theory of simple structural glasses. The book begins with a thorough explanation of infinite-dimensional models in statistical physics, before reviewing the key elements of the thermodynamic theory of liquids and the dynamical properties of liquids and glasses. The central feature of the mean field theory of disordered systems, the existence of a large multiplicity of metastable states, is then introduced. The replica method is then covered, before the final chapters describe important, advanced topics such as Gardner transitions, complexity, packing spheres in large dimensions, the jamming transition, and the rheology of glass. Presenting the theory in a clear and pedagogical style, this is an excellent resource for researchers and graduate students working in condensed matter physics and statistical mechanics.

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.

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.

This engaging introduction to random processes provides students with the critical tools needed to design and evaluate engineering systems that must operate reliably in uncertain environments. A brief review of probability theory and real analysis of deterministic functions sets the stage for understanding random processes, whilst the underlying measure theoretic notions are explained in an intuitive, straightforward style. Students will learn to manage the complexity of randomness through the use of simple classes of random processes, statistical means and correlations, asymptotic analysis, sampling, and effective algorithms. Key topics covered include: • Calculus of random processes in linear systems • Kalman and Wiener filtering • Hidden Markov models for statistical inference • The estimation maximization (EM) algorithm • An introduction to martingales and concentration inequalities. Understanding of the key concepts is reinforced through over 100 worked examples and 300 thoroughly

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.

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.

Describing the relevant detection and estimation theory, this detailed guide provides the background knowledge needed to tackle the design of practical WLAN positioning systems. It sets out key system-level challenges and design considerations in increasing positioning accuracy and reducing computational complexity, and it also examines design trade-offs and experimental results. Radio characteristics in real environments are discussed, as are the theoretical aspects of non-parametric statistical tools appropriate for modeling radio signals, statistical estimation techniques and the model-based stochastic estimators often used for positioning. A historical account of positioning systems in also included, giving graduate students, researchers and practitioners alike the perspective needed to understand the benefits and potential applications of WLAN positioning.

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 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