Statistical Complexity

Statistical mechanics is the theoretical apparatus used to study the properties of macroscopic systems - systems made up of many atoms or molecules - and relates those properties to the system's microscopic constitution. This book is an introduction to statistical mechanics, intended to be used either by advanced undergraduates or by beginning graduate students. The first chapter deals with statistical thermodynamics and aims to quickly derive the most commonly used formulas in the subject. The remainder of the book then illustrates the application of these formulas in traditional areas such as the ideal gas and less traditional areas such as the quantum ideal gas. Highly illustrated with numerous exercises and worked solutions, it provides a concise treatise of statistical mechanics ideal for use on an 8-12 lecture course.

Statistical mechanics is the theoretical apparatus used to study the properties of macroscopic systems - systems made up of many atoms or molecules - and relates those properties to the system's microscopic constitution. This book is an introduction to statistical mechanics, intended to be used either by advanced undergraduates or by beginning graduate students. The first chapter deals with statistical thermodynamics and aims to quickly derive the most commonly used formulas in the subject. The remainder of the book then illustrates the application of these formulas in traditional areas such as the ideal gas and less traditional areas such as the quantum ideal gas. Highly illustrated with numerous exercises and worked solutions, it provides a concise treatise of statistical mechanics ideal for use on an 8-12 lecture course.

An incomparably useful examination of statistical methods for comparisonThe nature of doing science, be it natural or social, inevitably calls for comparison. Statistical methods are at the heart of s

The discrepancy method is the glue that binds randomness and complexity. It is the bridge between randomized computation and discrepancy theory, the area of mathematics concerned with irregularities in distributions. The discrepancy method has played a major role in complexity theory; in particular, it has caused a mini-revolution of sorts in computational geometry. This book tells the story of the discrepancy method in a few short independent vignettes. It is a varied tale which includes such topics as communication complexity, pseudo-randomness, rapidly mixing Markov chains, points on the sphere and modular forms, derandomization, convex hulls, Voronoi diagrams, linear programming and extensions, geometric sampling, VC-dimension theory, minimum spanning trees, linear circuit complexity, and multidimensional searching. The mathematical treatment is thorough and self-contained. In particular, background material in discrepancy theory is supplied as needed. Thus the book should appeal t

"The Moment of Complexity is a profoundly original work. In remarkable and insightful ways, Mark Taylor traces an entirely new way to view the evolution of our culture, detailing how information theor

This book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniqu

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

A groundbreaking look at complexity theory and its implications in the world of finance Complexity theory tells us that processes with a large number of seemingly independent agents-such as free marke

Probabilistic and Statistical Methods in Computer Science

Presents statistical principles in a simple fashion, and develops an awareness of the abuses and misuses of statistics, combining coverage of research and statistical practices. Early chapters centere

Thermodynamics and Statistical Mechanics provides undergraduate chemistry students with a grounding in both classical and statistical thermodynamics. Thermodynamic quantities and relationships are int

The discrepancy method is the glue that binds randomness and complexity. It is the bridge between randomized computation and discrepancy theory, the area of mathematics concerned with irregularities in distributions. The discrepancy method has played a major role in complexity theory; in particular, it has caused a mini-revolution of sorts in computational geometry. This book tells the story of the discrepancy method in a few short independent vignettes. It is a varied tale which includes such topics as communication complexity, pseudo-randomness, rapidly mixing Markov chains, points on the sphere and modular forms, derandomization, convex hulls, Voronoi diagrams, linear programming and extensions, geometric sampling, VC-dimension theory, minimum spanning trees, linear circuit complexity, and multidimensional searching. The mathematical treatment is thorough and self-contained. In particular, background material in discrepancy theory is supplied as needed. Thus the book should appeal t

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 clear book presents a critical and modern analysis of the conceptual foundations of statistical mechanics as laid down in Boltzmann's works. The author emphasises the relation between microscopic

A thorough understanding of statistical mechanics depends strongly on the insights and manipulative skills that are acquired through the solving of problems. Problems on Statistical Mechanics provides

Many of the exciting new developments in microscale engineering are based on the application of traditional principles of statistical thermodynamics. This book offers a modern view of thermodynamics, interweaving classical and statistical thermodynamic principles and applying them to current engineering systems. It begins with coverage of microscale energy storage mechanisms from a quantum mechanics perspective and develops the fundamentals of classical and statistical thermodynamics. Next, applications of equilibrium statistical thermodynamics to solid, liquid, and gas phase systems are discussed. The remainder of the book discusses nonequilibrium thermodynamics of transport phenomena and introduces nonequilibrium effects and noncontinuum behaviour at the microscale. Although the text emphasizes mathematical development, it includes many examples and exercises illustrating how the theoretical concepts are applied to systems of scientific and engineering interest. It offers a fresh vie

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

Clearly written and free of statistical jargon, this invaluable guide concentrates on the practicalities of statistical analysis for anyone involved with agricultural research. Each section starts wi

This 1998 book describes the sampling and statistical methods used most often by behavioral ecologists and field biologists. Written by a biologist and two statisticians, it provides a rigorous discussion together with worked examples of statistical concepts and methods that are generally not covered in introductory courses, and which are consequently poorly understood and applied by field biologists. The first section reviews important issues such as defining the statistical population and the sampling plan when using non-random methods for sample selection, bias, interpretation of statistical tests, confidence intervals and multiple comparisons. After a detailed discussion of sampling methods and multiple regression, subsequent chapters discuss specialized problems such as pseudoreplication, and their solutions. It will quickly become the statistical handbook for all field biologists.

This 1998 book describes the sampling and statistical methods used most often by behavioral ecologists and field biologists. Written by a biologist and two statisticians, it provides a rigorous discussion together with worked examples of statistical concepts and methods that are generally not covered in introductory courses, and which are consequently poorly understood and applied by field biologists. The first section reviews important issues such as defining the statistical population and the sampling plan when using non-random methods for sample selection, bias, interpretation of statistical tests, confidence intervals and multiple comparisons. After a detailed discussion of sampling methods and multiple regression, subsequent chapters discuss specialized problems such as pseudoreplication, and their solutions. It will quickly become the statistical handbook for all field biologists.

This advanced handbook presents a broad and up-to-date view of the computational complexity theory of Boolean circuits. It combines the algorithmic and the automata-theoretic approaches, and includes

An advanced textbook giving a broad, modern view of the computational complexity theory of boolean circuits, with extensive references, for theoretical computer scientists and mathematicians.

An approach to complexity theory which offers a means of analysing algorithms in terms of their tractability. The authors consider the problem in terms of parameterized languages and taking "k-slices"

Rescher (philosophy of science, U. of Pittsburgh) explores the nature of complexity, its bearing on the human world, and how people manage their affairs within it. His overall lesson is that as lives

The text is written for technique oriented courses on quality like Introduction to Statistical Quality Control/Process Improvement that stress the use of statistical tools.In addition to the statistic

In Complexity and Postmodernism, Paul Cilliers explores the idea of complexity in the light of contemporary perspectives from philosophy and science. Cilliers offers us a unique approach to understand

Statistical Mechanics reflects the latest techniques and developments in statistical mechanics. Covering a variety of concepts and topics - molecular dynamic methods, renormalization theory, chaos, po

Interpreting statistical data as evidence, Statistical Evidence: A Likelihood Paradigm focuses on the law of likelihood, fundamental to solving many of the problems associated with interpreting data i

Proceedings of the December 1996 symposium, with sections on statistical mechanics of protein and of DNA, biologically inspired physics, statistical mechanics in biology and physics, micromanipulation

Joyce, Chaos, and Complexity studies the manifold relations among twentieth-century mathematics and Science, James Joyce's fiction, and the critical reception of Joyce's work. Calling for profound rea

A computer science text bridging the gap between the perceived impenetrability of computability and complexity theory and practical programming problems. Jones (computer science, U. of Copenhagen) of

A practical guide for multivariate statistical techniques-- now updated and revised In recent years, innovations in computer technology and statistical methodologies have dramatically altered the lan

Explains how scientists who study complexity are convinced that certain constant processes are at work in all kinds of unrelated complex systems.

In this volume, which was originally published in 1996, noisy information is studied in the context of computational complexity; in other words the text deals with the computational complexity of mathematical problems for which information is partial, noisy and priced. The author develops a general theory of computational complexity of continuous problems with noisy information and gives a number of applications; deterministic as well as stochastic noise is considered. He presents optimal algorithms, optimal information, and complexity bounds in different settings: worst case, average case, mixed worst-average and average-worst, and asymptotic. The book integrates the work of researchers in such areas as computational complexity, approximation theory and statistics, and includes many fresh results as well. About two hundred exercises are supplied with a view to increasing the reader's understanding of the subject. The text will be of interest to professional computer scientists, statis

Statistical Factor Analysis and Related Methods Theory and Applications In bridging the gap between the mathematical and statistical theory of factor analysis, this new work represents the first unifi

This text introduces statistical language processing techniques—word tagging, parsing with probabilistic context free grammars, grammar induction, syntactic disambiguation, semantic word classes, word

This is the first comprehensive, yet clearly presented, account of statistical methods for analysing spherical data. The analysis of data, in the form of directions in space or of positions of points on a spherical surface, is required in many contexts in the earth sciences, astrophysics and other fields, yet the methodology required is disseminated throughout the literature. Statistical Analysis of Spherical Data aims to present a unified and up-to-date account of these methods for practical use. The emphasis is on applications rather than theory, with the statistical methods being illustrated throughout the book by data examples.

This work elucidates the structure and complexity of human language in terms of the mathematics of information and computation. It strengthens Chomsky's early work on the mathematics of language, with

This volume focuses on the abuse of statistical inference in scientific and statistical literature, as well as in a variety of other sources, presenting examples of misused statistics to show that man

By considering the size of the logical network needed to perform a given computational task, the intrinsic difficulty of that task can be examined. Boolean function complexity, the combinatorial study of such networks, is a subject that started back in the 1950s and has today become one of the most challenging and vigorous areas of theoretical computer science. The papers in this book stem from the London Mathematical Society Symposium on Boolean Function Complexity held at Durham University in July 1990. The range of topics covered will be of interest to the newcomer to the field as well as the expert, and overall the papers are representative of the research presented at the Symposium. Anyone with an interest in Boolean Function complexity will find that this book is a necessary purchase.