Boolean Function Complexity

Over the past two decades, no field of scientific inquiry has had a more striking impact across a wide array of disciplines–from biology to physics, computing to meteorology–than that known as chaos and complexity, the study of complex systems. Now astrophysicist John Gribbin draws on his expertise to explore, in prose that communicates not only the wonder but the substance of cutting-edge science, the principles behind chaos and complexity. He reveals the remarkable ways these two revolutionary theories have been applied over the last twenty years to explain all sorts of phenomena–from weather patterns to mass extinctions.Grounding these paradigm-shifting ideas in their historical context, Gribbin also traces their development from Newton to Darwin to Lorenz, Prigogine, and Lovelock, demonstrating how–far from overturning all that has gone before–chaos and complexity are the triumphant extensions of simple scientific laws. Ultimately, Gribbin illustrates how chaos and complexity perme

Proteins: Structure and Function is a comprehensive introduction to the study of proteins and their importance to modern biochemistry. Each chapter addresses the structure and function of proteins wi

This undergraduate-level describes the mathematics most needed in computer science. Bender and Williamson (both mathematics, U. of California, San Diego) cover Boolean functions and computer arithmeti

A central problem in the design of programming systems is to provide methods for verifying that computer code performs to specification. This book presents a rigorous foundation for defining Boolean categories, in which the relationship between specification and behaviour can be explored. Boolean categories provide a rich interface between program constructs and techniques familiar from algebra, for instance matrix- or ideal-theoretic methods. The book's distinction is that the approach relies on only a single program construct (the first-order theory of categories), the others being derived mathematically from four axioms. Development of these axioms (which are obeyed by an abundance of program paradigms) yields Boolean algebras of 'predicates', loop-free constructs, and a calculus of partial and total correctness which is shown to be the standard one of Hoare, Dijkstra, Pratt, and Kozen. The book is based in part on courses taught by the author, and will appeal to graduate students a

We live in a moment of unprecedented complexity, an era in which change and information can move faster than our ability to comprehend them. With The Moment of Complexity, Mark C. Taylor offers a map

Mathematics for Electrical Engineering and Computing embraces many applications of modern mathematics, such as Boolean Algebra and Sets and Functions, and also teaches both discrete and continuous sys

The science of complexity is concerned with the study of complex, adaptive systems. Its insights have in recent decades been applied with gusto by social scientists and other thinkers.As research in a

An up-to-date and critical analysis of how archaeologists study past societies, Archaeologies of Complexity addresses the nature of contemporary archaeology and the study of social change, and debates

The two internationally renowned authors elucidate the structure of "fast" parallel computation. Its complexity is emphasised through a variety of techniques ranging from finite combinatorics, probabi

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

Here is an accessible, algorithmically oriented guide to some of the most interesting techniques of complexity theory. The book shows that simple algorithms are at the heart of complexity theory. The

Fully Tuned Radial Basis Function Neural Networks for Flight Control presents the use of the Radial Basis Function (RBF) neural networks for adaptive control of nonlinear systems with emphasis on flig

Neurotransmitters, Drugs and Brain Function aims to link basic aspects of the activity of neurotransmitters at the receptor and synaptic level with their role in normal brain function, disease states,

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

Skeletal Muscle Mechanics: From Mechanisms to Function summarises the variety of approaches used by today's scientist to understand muscle function and the mechanisms of contraction. This book contain

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 describes representations of Boolean functions that have small size for many important functions and which allow efficient work with the represented functions. Efficient algorithms for opera

Boolean algebras have historically played a special role in the development of the theory of general or "universal" algebraic systems, providing important links between algebra and analysis, set theor

Extensively rewritten and long-awaited update of the standard text on insect structure and function.

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"

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

This book gives an introduction to theories of computability from a mathematically sophisticated point of view. It treats not only 'the' theory of computability (created by Alan Turing and others in the 1930s), but also a variety of other theories (of Boolean functions, automata and formal languages). These are addressed from the classical perspective of their generation by grammars and from the modern perspective as rational cones. The treatment of the classical theory of computable functions and relations takes the form of a tour through basic recursive function theory, starting with an axiomatic foundation and developing the essential methods in order to survey the most memorable results of the field. This authoritative account by one of the leading lights of the subject will prove exceptionally useful reading for graduate students, and researchers in theoretical computer science and mathematics.

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

The concepts of form and function have traditionally been defined in terms of biology and then extended to other disciplines. Stephen T. Asma examines the various interpretations of form and function

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

In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illu

The book offers an interpretation of Euripides' The Trojan Women which issues from the argument that the function of Greek tragedy was to educate. The author demonstrates that the play performs its function by examining Athenian ideology. By making the didactic function of tragedy the basis of interpretation, he is able to offer a coherent view of a number of long-standing problems in Euripidean criticism, for instance, the relation of Euripides to the Sophists.

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

Computational Complexity and Natural Language heralds an entirely new way of looking at grammatical systems. It applies the recently developed computer science tool of complexity theory to the study o

The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects of

The perfect text, on-the-job reference and certification exam review, MANUAL OF PULMONARY FUNCTION TESTING, 9th Edition includes a wealth of information on pulmonary function tests, techniques, pathop

Organisational Development in Practice: A Complexity Approach draws on conventional, critical and complexity thinking in relation to organisational development with a view to exploring what's useful and what's not.This book proffers an approach to organisational development that helps to develop, support, and maintain more democratic, collaborative, inclusive and sustainable ways of learning, working, and living. The author explores the practicalities of working with the frustrations and inconsistencies involved in coping with the patterns of human interaction that inevitably make up organisations, where planned and emergent approaches co-exist, whether we would like them to or not. Woven in between the substantive chapters are vignettes from a range of international practitioners reflecting on their own experiences in the field.This book is a radically different approach to organisational development suitable for advanced students and researchers of organisation and organisational dev

Gain a solid foundation in A&P with this easy-to-understand text! Clear and straightforward, Structure & Function of the Body, 17th Edition introduces the typical structure and function of the human body and describes what the body does to maintain homeostasis. The book shows how structure fits function, using clinical examples to reinforce A&P concepts and featuring hundreds of photos and micrographs for realistic visual detail. Written by a team of experts led by Kevin Patton, this text includes an Evolve website packed with animations, audio pronunciations, review questions, and other interactive learning resources.NEW! Updated content is added, and new line art and photos ensure wider representation of skin color, sex, age, body type, and cultural diversity.NEW! Inclusive terminology reduces the emphasis on eponyms - for example, the term "normal" is more carefully used to avoid implying that healthy conditions outside the average are "abnormal."NEW! The latest scientific thinking

This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling–Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges–Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the i

Constraint Satisfaction Problems (CSPs) are natural computational problems that appear in many areas of theoretical computer science. Exploring which CSPs are solvable in polynomial time and which are NP-hard reveals a surprising link with central questions in universal algebra. This monograph presents a self-contained introduction to the universal-algebraic approach to complexity classification, treating both finite and infinite-domain CSPs. It includes the required background from logic and combinatorics, particularly model theory and Ramsey theory, and explains the recently discovered link between Ramsey theory and topological dynamics and its implications for CSPs. The book will be of interest to graduate students and researchers in theoretical computer science and to mathematicians in logic, combinatorics, and dynamics who wish to learn about the applications of their work in complexity theory.

This reference work provides an authoritative single source for understanding and applying the concepts of complexity theory together with the tools and measures for analyzing complex systems in all f

Fascia, Function, and Medical Applications is essential reading for medical and allied health practitioners who want to bring scientific insights of the importance of fascia to human health into

Fascia, Function, and Medical Applications is essential reading for medical and allied health practitioners who want to bring scientific insights of the importance of fascia to human health into

This book explores noun phrase (NP) complexity in English, showing that it is best accounted for both by a linear and a hierarchical parameter: its length and its type of postmodifier(s). The study is methodologically unique in that it combines univariate and multivariate analyses in an investigation of four different syntactic variables. Drawing on more than three billion words of British and American data, Eva Berlage shows that the length and the structure of the NPs, along with language-external factors such as the regional variety of English, work as powerful determinants of the variation. On a theoretical level, the book reveals that the structural complexity of NPs cannot be sufficiently captured by (phrasal) node counts but that we need to incorporate the degree to which NPs are sentential. The book is designed for researchers and students interested in syntax, language variation, sociolinguistics, structural complexity and the history of English.