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 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

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

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

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

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

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,

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

Integrates traditional statistical data analysis with new computational experimentation capabilities and concepts of algorithmic complexity and chaotic behavior in nonlinear dynamic systems, offering

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.

The book is a collection of papers of experts in the fields of information and complexity. Information is a basic structure of the world, while complexity is a fundamental property of systems and proc

Introduction to Statistical Investigations leads students to learn about the process of conducting statistical investigations from data collection, to exploring data, to statistical inference, to

Introduction to Statistical Investigations, 1st Edition leads readers to learn about the process of conducting statistical investigations from data collection, to exploring data, to statistical i

This book examines the question of whether languages can differ in grammatical complexity and, if so, how relative complexity differences might be measured. The volume differs from others devoted to t

This textbook on statistical modeling and statistical inference will assist advanced undergraduate and graduate students. Statistical Modeling and Computation provides a unique introduction to modern

Because statistical confidentiality embraces the responsibility for both protecting data and ensuring its beneficial use for statistical purposes, those working with personal and proprietary data can

In this provocative and informative book, Don Norman writes that the complexity of our technology must mirror the complexity and richness of our lives. It’s not complexity that’s the problem; it’s bad

Models in Statistical Social Research provides a comprehensive insight of models used in statistical social research based on statistical data and methods. While traditionally understood statistical m

In response to the explosion in both the quantity and the complexity of data collections early in the 21st century, the Center for Statistical Research at the Chinese Academy of Science initiated the

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 textbook systematically presents fundamental methods of statistical analysis, from probability and statistical distributions, through basic concepts of statistical inference, to a collection of m

Global Complexity is a path-breaking book, which examines how the ideas of chaos and complexity can help us to analyse global processes. Urry argues that there are major advantages in thinking about g

Global Complexity is a path-breaking book, which examines how the ideas of chaos and complexity can help us to analyse global processes. Urry argues that there are major advantages in thinking about g

Statistical Parameters is a unique new guide to current statistical methods and research. Based on a series of interdisciplinary lectures for users of statistical methods in research and development,

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.

The twin themes of computational complexity and information pervade this 1998 book. It starts with an introduction to the computational complexity of continuous mathematical models, that is, information-based complexity. This is then used to illustrate a variety of topics, including breaking the curse of dimensionality, complexity of path integration, solvability of ill-posed problems, the value of information in computation, assigning values to mathematical hypotheses, and new, improved methods for mathematical finance. The style is informal, and the goals are exposition, insight and motivation. A comprehensive bibliography is provided, to which readers are referred for precise statements of results and their proofs. As the first introductory book on the subject it will be invaluable as a guide to the area for the many students and researchers whose disciplines, ranging from physics to finance, are influenced by the computational complexity of continuous problems.

The first unified introduction and reference for the field of computational complexity. Virtually non-existent only 25 years ago, computational complexity has expanded tremendously and now comprises a

Communication Complexity describes a new intuitive model for studying circuit networks that captures the essence of circuit depth. Although the complexity of boolean functions has been studied for alm

In Complexity Economics for Environmental Governance, Jean-François Mercure reframes environmental policy and provides a rigorous methodology necessary to tackle the complexity of environmental policy and the transition to sustainability. The book offers a detailed account of the deficiencies of environmental economics and then develops a theory of innovation and macroeconomics based on complexity theory. It also develops a new foundation for evidence-based policy-making using a Risk-Opportunity Analysis applied to the sustainability transition. This multidisciplinary work was developed in partnership with prominent natural scientists and economists as well as active policy-makers with the aim to revolutionize thinking in the face of the full complexity of the sustainability transition, and to show how it can best be governed to minimize its distributional impacts. The book should be read by academics and policy-makers seeking new ways to think about environmental policy-making.

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

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

S-PLUS is the statistical software of choice for many applied researchers in disciplines ranging from finance to medicine. This book focuses on statistical techniques, applies them to one or more data

This clear and pedagogical text delivers a concise overview of classical and quantum statistical physics. Essential Statistical Physics shows students how to relate the macroscopic properties of physical systems to their microscopic degrees of freedom, preparing them for graduate courses in areas such as biophysics, condensed matter physics, atomic physics and statistical mechanics. Topics covered include the microcanonical, canonical, and grand canonical ensembles, Liouville's Theorem, Kinetic Theory, non-interacting Fermi and Bose systems and phase transitions, and the Ising model. Detailed steps are given in mathematical derivations, allowing students to quickly develop a deep understanding of statistical techniques. End-of-chapter problems reinforce key concepts and introduce more advanced applications, and appendices provide a detailed review of thermodynamics and related mathematical results. This succinct book offers a fresh and intuitive approach to one of the most challenging

Communication complexity is the mathematical study of scenarios where several parties need to communicate to achieve a common goal, a situation that naturally appears during computation. This introduction presents the most recent developments in an accessible form, providing the language to unify several disjoint research subareas. Written as a guide for a graduate course on communication complexity, it will interest a broad audience in computer science, from advanced undergraduates to researchers in areas ranging from theory to algorithm design to distributed computing. The first part presents basic theory in a clear and illustrative way, offering beginners an entry into the field. The second part describes applications including circuit complexity, proof complexity, streaming algorithms, extension complexity of polytopes, and distributed computing. Proofs throughout the text use ideas from a wide range of mathematics, including geometry, algebra, and probability. Each chapter contain

Statistical Concepts-A Second Course presents the last 10 chapters from An Introduction to Statistical Concepts, Fourth Edition. Designed for second and upper-level statistics courses, this book highl

Statistical Programming in SAS Second Edition provides a foundation for programming to implement statistical solutions using SAS, a system that has been used to solve data analytic problems for more t

The Process of Research and Statistical Analysis in Psychology presents integrated coverage of psychological research methods and statistical analysis to illustrate how these two crucial processes wor

This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per Martin-Löf in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exerc