Complexity and Approximability Properties

This book documents the state of the art in combinatorial optimization, presenting approximate solutions of virtually all relevant classes of NP-hard optimization problems. The wealth of problems, alg

An overview of current developments in research on feasible computations. Defines and discusses efficient reductions between problems and considers the families and corresponding complete languages of

Emergence and complexity refer to the appearance of higher-level properties and behaviours of a system that obviously comes from the collective dynamics of that system's components. These properties a

This book aims to assess the nature of morphological complexity, and the properties that distinguish it from the complexity manifested in other components of language. Of the many ways languages have

Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book approaches descriptive complexity from the angle of modern structural graph theory, specifically graph minor theory. It develops a 'definable structure theory' concerned with the logical definability of graph theoretic concepts such as tree decompositions and embeddings. The first part starts with an introduction to the background, from logic, complexity, and graph theory, and develops the theory up to first applications in descriptive complexity theory and graph isomorphism testing. It may serve as the basis for a graduate-level course. The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decid

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

This book explores questions about the nature of an interlanguage grammar, i.e. the grammar of a bilingual. John Archibald approaches these questions within a cognitive science perspective that draws upon abstract representational structures in demonstrating that phonological knowledge underlies the surface phonetic properties of L2 speech. Specifically, he proposes that interlanguage grammars are not 'impaired', 'fundamentally different', or 'shallow' (as some have argued); the phonological grammars are complex, hierarchically-structured, mental representations that are governed by the principles of linguistic theory, including those of Universal Grammar. The book outlines a model that addresses Plato's problem (learning in the absence of evidence) and Orwell's problem (resistance to learning in the face of abundant evidence). Furthermore, the study of grammatical interfaces--phonetics/phonology; phonology/morphology; phonology/syntax--reveals the necessary design conditions foran int

Our understanding of the rheological and seismic properties of the Earth’s interior relies on interpreting geophysical observations using mineral physics data. The complexity of natural materials comp

The interaction between light and electrons in semiconductors forms the basis for many interesting and practically significant properties. This book examines the fundamental physics underlying this rich complexity of photoelectronic properties of semiconductors, and will familiarise the reader with the relatively simple models that are useful in describing these fundamentals. The basic physics is also illustrated with typical recent examples of experimental data and observations. Following introductory material on the basic concepts, the book moves on to consider a wide range of phenomena, including photoconductivity, recombination effects, photoelectronic methods of defect analysis, photoeffects at grain boundaries, amorphous semiconductors, photovoltaic effects and photoeffects in quantum wells and superlattices. The author is Professor of Materials Science and Electrical Engineering at Stanford University, and has taught this material for many years. He is an experienced author, his

The science of rheology and its applications have grown steadily. Although polymers dominated in the past, the applications to foods have become increasingly important over the last four decades. The complexity of food rheology has not only generated increased interest among academics, but it has also led to an increased recognition of its importance in the food industry. Emphasizing physics rather than mathematics, Polymer and Food Rheology: Volume 1, Applications to Single-Phase Systems focuses on rheological characteristics and properties of single substances and homogeneous mixtures. It introduces fundamental principles, types of flows, types of instruments, their theory, capabilities, limitations, and sources of error. Both sophisticated rheometers and simple devices and their uses are considered.- Discusses the types of material functions (properties) obtained from the different types of measurements and techniques: shear viscosity, normal stress differences, dynamic mechanical p

Discover all the fascinating things there are to know about mushrooms with this perfect book for autumn and fungi enthusiasts.The world is a treasure trove of fungi. There are over 1.5 million known fungus species on our planet; we use them for food and medicine, they can be found in every ecosystem and on all continents, and they're even more closely related to animals than plants. They can also be as deadly as they are beautiful.Unearth the scientific, cultural and fantastical properties of mushrooms, and explore the world of mushrooms beyond what's in a kitchen, from a ballerina waxcap and barbie pagodas to a snowy disco and stinkhorns.This book celebrates their beauty, complexity and significance, and gives an insight into this fascinating kingdom of fungi.

From the physiology and acoustics to their patterning across human languages, tone is one of the fundamental constructs in human languages that is also among the hardest to apprehend. Drawing upon a large number of languages around the world, this volume explores the concept of tone starting from its physical properties of articulation and acoustics to its manifestation in phonology. Designed as a comprehensive study accessible to the novice and useful for the expert, each chapter covers a particular aspect of tone in increasing depth and complexity, weaving together key concepts and theories that provide complementing or competing accounts of tone's phonological intricacies. In the process, one uncovers the underlying laws and principles that inform today's understanding of the subject to form a more synthesized view that also allows us to explore the relation of tone to other important areas of humanity such as literature, history, music and cognition.

Information is central to the evolution of biological complexity, a physical system relying on a continuous supply of energy. Biology provides superb examples of the consequent Darwinian selection of mechanisms for efficient energy utilisation. Genetic information, underpinned by the Watson-Crick base-pairing rules is largely encoded by DNA, a molecule uniquely adapted to its roles in information storage and utilisation.This volume addresses two fundamental questions. Firstly, what properties of the molecule have enabled it to become the predominant genetic material in the biological world today and secondly, to what extent have the informational properties of the molecule contributed to the expansion of biological diversity and the stability of ecosystems. The author argues that bringing these two seemingly unrelated topics together enables Schrödinger's What is Life?, published before the structure of DNA was known, to be revisited and his ideas examined in the context of our current

Information is central to the evolution of biological complexity, a physical system relying on a continuous supply of energy. Biology provides superb examples of the consequent Darwinian selection of mechanisms for efficient energy utilisation. Genetic information, underpinned by the Watson-Crick base-pairing rules is largely encoded by DNA, a molecule uniquely adapted to its roles in information storage and utilisation.This volume addresses two fundamental questions. Firstly, what properties of the molecule have enabled it to become the predominant genetic material in the biological world today and secondly, to what extent have the informational properties of the molecule contributed to the expansion of biological diversity and the stability of ecosystems. The author argues that bringing these two seemingly unrelated topics together enables Schrödinger's What is Life?, published before the structure of DNA was known, to be revisited and his ideas examined in the context of our current

Biological systems are extremely complex and have emergent properties that cannot be explained or even predicted by studying their individual parts in isolation. The reductionist approach, although successful in the early days of molecular biology, underestimates this complexity. As the amount of available data grows, so it will become increasingly important to be able to analyse and integrate these large data sets. This book introduces novel approaches and solutions to the Big Data problem in biomedicine, and presents new techniques in the field of graph theory for handling and processing multi-type large data sets. By discussing cutting-edge problems and techniques, researchers from a wide range of fields will be able to gain insights for exploiting big heterogonous data in the life sciences through the concept of 'network of networks'.

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.

From the physiology and acoustics to their patterning across human languages, tone is one of the fundamental constructs in human languages that is also among the hardest to apprehend. Drawing upon a large number of languages around the world, this volume explores the concept of tone starting from its physical properties of articulation and acoustics to its manifestation in phonology. Designed as a comprehensive study accessible to the novice and useful for the expert, each chapter covers a particular aspect of tone in increasing depth and complexity, weaving together key concepts and theories that provide complementing or competing accounts of tone's phonological intricacies. In the process, one uncovers the underlying laws and principles that inform today's understanding of the subject to form a more synthesized view that also allows us to explore the relation of tone to other important areas of humanity such as literature, history, music and cognition.

This volume collects the proceedings of the conference 'Topological methods in group theory', held at Ohio State University in 2014 in honor of Ross Geoghegan's 70th birthday. It consists of eleven peer-reviewed papers on some of the most recent developments at the interface of topology and geometric group theory. The authors have given particular attention to clear exposition, making this volume especially useful for graduate students and for mathematicians in other areas interested in gaining a taste of this rich and active field. A wide cross-section of topics in geometric group theory and topology are represented, including left-orderable groups, groups defined by automata, connectivity properties and Σ-invariants of groups, amenability and non-amenability problems, and boundaries of certain groups. Also included are topics that are more geometric or topological in nature, such as the geometry of simplices, decomposition complexity of certain groups, and problems in shape theory.

Traditional approaches have reduced Caesar's Bellum Civile to a tool for teaching Latin or to one-dimensional propaganda, thereby underestimating its artistic properties and ideological complexity. Reading strategies typical of scholarship on Latin poetry, like intertextuality, narratology, semantic, rhetorical and structural analysis, cast a new light on the Bellum Civile: Ciceronian language advances Caesar's claim to represent Rome; technical vocabulary reinforces the ethical division between 'us' and the 'barbarian' enemy; switches of focalization guide our perception of the narrative; invective and characterization exclude the Pompeians from the Roman community, according to the mechanisms of rhetoric; and the very structure of the work promotes Caesar's cause. As a piece of literature interacting with its cultural and socio-political world, the Bellum Civile participates in Caesar's multimedia campaign of self-fashioning. A comprehensive approach, such as has been productively ap

This reference summarizes the properties and techniques of conceptual modeling and provides analyses of many examples of existing software. It examines the complexity and scale of software systems, in

The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.

Traditional approaches have reduced Caesar's Bellum Civile to a tool for teaching Latin or to one-dimensional propaganda, thereby underestimating its artistic properties and ideological complexity. Reading strategies typical of scholarship on Latin poetry, like intertextuality, narratology, semantic, rhetorical and structural analysis, cast a new light on the Bellum Civile: Ciceronian language advances Caesar's claim to represent Rome; technical vocabulary reinforces the ethical division between 'us' and the 'barbarian' enemy; switches of focalization guide our perception of the narrative; invective and characterization exclude the Pompeians from the Roman community, according to the mechanisms of rhetoric; and the very structure of the work promotes Caesar's cause. As a piece of literature interacting with its cultural and socio-political world, the Bellum Civile participates in Caesar's multimedia campaign of self-fashioning. A comprehensive approach, such as has been productively ap

Since first described, multiple properties of classical conditioning have been discovered, establishing the need for mathematical models to help explain the defining features. The mathematical complexity of the models puts our understanding of their workings beyond the ability of our intuitive thinking and makes computer simulations irreplaceable. The complexity of the models frequently results in function redundancy, a natural property of biologically evolved systems that is much desired in technologically designed products. Experts provide the latest advancements in the field and present detailed descriptions of how the models simulate conditioned behaviour and its physiological bases. It offers advanced students and researchers examples of how the models are used to analyse existing experimental results and design future experiments. This volume is of great interest to psychologists and neuroscientists, as well as computer scientists and engineers searching for ideas applicable to t

This collaborative volume presents trends arising from the fruitful interaction between the themes of combinatorics on words, automata and formal language theory, and number theory. Presenting several important tools and concepts, the authors also reveal some of the exciting and important relationships that exist between these different fields. Topics include numeration systems, word complexity function, morphic words, Rauzy tilings and substitutive dynamical systems, Bratelli diagrams, frequencies and ergodicity, Diophantine approximation and transcendence, asymptotic properties of digital functions, decidability issues for D0L systems, matrix products and joint spectral radius. Topics are presented in a way that links them to the three main themes, but also extends them to dynamical systems and ergodic theory, fractals, tilings and spectral properties of matrices. Graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, numbe

In this study Terence McKay demonstrates how the principles of the theory of Government and Binding apply to German syntax and in particular to an aspect that has exposed especially problematic and interesting issues: the properties of the infinitival constructions with lassen, scheinen and the verbs of perception. Previous attempts to account for the syntactic ambivalence between mono- and bisententiality of these constructions have been demonstrably inadequate or incomplete. Here Dr McKay argues convincingly for a bisentential approach, which is compatible not only with standard constituency tests but also with the Projection Principle. Such an approach, interacting with government, binding, theta and case theories, successfully accounts for the specific facts concerning relativisation, extraposition, topicalisation, quantifier movement and negative scope interpretation. The book not only offers important insights into the structural complexity of German but also makes a valuable con

Entropy quantities are connected with the 'degree of compactness' of compact or precompact spaces, and so are appropriate tools for investigating linear and compact operators between Banach spaces. The main intention of this Tract is to study the relations between compactness and other analytical properties, e.g. approximability and eigenvalue sequences, of such operators. The authors present many generalized results, some of which have not appeared in the literature before. In the final chapter, the authors demonstrate that, to a certain extent, the geometry of Banach spaces can also be developed on the basis of operator theory. All mathematicians working in functional analysis and operator theory will welcome this work as a reference or for advanced graduate courses.

This book, first published in 2000, explores the exciting field of complexity. It features in-depth coverage of important theoretical areas, including fractals, chaos, non-linear dynamics, artificial life and self-organization. It also provides overviews of complexity in several applied areas, including parallel computation, control systems, neural systems and ecosystems. Some of the properties that best characterize complex systems, including algorithmic richness, non-linearity and abundant interactions between components are examined. In this way the book draws out themes, especially the ideas of connectivity and natural computation, that reveal deep, underlying similarities between phenomena that have formerly been treated as completely distinct. The idea of natural computation is particularly rich in fresh approaches applicable to both biology and computing. Analogies such as the DNA code as life's underlying program, or organisms as automata, are very compelling. Conversely, biolo

Advances in materials science have given rise to novel materials with unique properties, through the manipulation of structure at the atomic level. Elucidating the shape and form of matter at this scale requires the application of mathematical concepts. This 2006 book presents the geometrical ideas that are being developed and integrated into materials science to provide descriptors and enable visualisation of the atomic arrangements in three-dimensional space. Emphasis is placed on the intuitive understanding of geometrical principles, presented through numerous illustrations. Mathematical complexity is kept to a minimum and only a superficial knowledge of vectors and matrices is required, making this an accessible introduction to the area. With a comprehensive reference list, this book will appeal to those working in crystallography, solid state and materials science.

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

Thermal systems are essential features in power, chemical processing, air conditioning, and other industries where heat and power are used. As the cost and complexity of designing thermal systems have increased, the need to understand and improve the design process has also grown. This book describes recent progress in the design of thermal systems. The book begins with a brief history and outline of developments in thermal system design. Chapters then discuss computer design tools for the power and chemical industries, predicting physical properties with computational tools, the use of 'pinch analysis' to improve thermal efficiency, applications of the exergy concept, the emerging concept of thermoeconomics, and the potential for artificial intelligence and expert systems in the design of thermal systems. With chapters written by internationally recognised authorities, the book offers a state-of-the-art review for both researchers and practitioners in mechanical, aerospace, chemical,

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 an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. Three appendices supply basic background information and numerous exercises are provided. Ideal for anyone wanting to learn modern modal logic.

This textbook is an accessible introduction to the theory underlying the many fascinating properties of solids. Assuming only an elementary knowledge of quantum mechanics, it describes the methods by which one can perform calculations and make predictions of some of the many complex phenomena that occur in solids and quantum liquids. The emphasis is on reaching important results by direct and intuitive methods, and avoiding unnecessary mathematical complexity. Designed as a self-contained text that starts at an elementary level and proceeds to more advanced topics, this book is aimed primarily at advanced undergraduate and graduate students in physics, materials science, and electrical engineering. Problem sets are included at the end of each chapter, with solutions available to lecturers. The coverage of some of fascinating developments in condensed matter physics will also appeal to experienced scientists in industry and academia working on electrical properties of materials.

This textbook is an accessible introduction to the theory underlying the many fascinating properties of solids. Assuming only an elementary knowledge of quantum mechanics, it describes the methods by which one can perform calculations and make predictions of some of the many complex phenomena that occur in solids and quantum liquids. The emphasis is on reaching important results by direct and intuitive methods, and avoiding unnecessary mathematical complexity. Designed as a self-contained text that starts at an elementary level and proceeds to more advanced topics, this book is aimed primarily at advanced undergraduate and graduate students in physics, materials science, and electrical engineering. Problem sets are included at the end of each chapter, with solutions available to lecturers. The coverage of some of fascinating developments in condensed matter physics will also appeal to experienced scientists in industry and academia working on electrical properties of materials.

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

This book, first published in 2000, explores the exciting field of complexity. It features in-depth coverage of important theoretical areas, including fractals, chaos, non-linear dynamics, artificial life and self-organization. It also provides overviews of complexity in several applied areas, including parallel computation, control systems, neural systems and ecosystems. Some of the properties that best characterize complex systems, including algorithmic richness, non-linearity and abundant interactions between components are examined. In this way the book draws out themes, especially the ideas of connectivity and natural computation, that reveal deep, underlying similarities between phenomena that have formerly been treated as completely distinct. The idea of natural computation is particularly rich in fresh approaches applicable to both biology and computing. Analogies such as the DNA code as life's underlying program, or organisms as automata, are very compelling. Conversely, biolo

Thermal systems are essential features in power, chemical processing, air conditioning, and other industries where heat and power are used. As the cost and complexity of designing thermal systems have increased, the need to understand and improve the design process has also grown. This book describes recent progress in the design of thermal systems. The book begins with a brief history and outline of developments in thermal system design. Chapters then discuss computer design tools for the power and chemical industries, predicting physical properties with computational tools, the use of 'pinch analysis' to improve thermal efficiency, applications of the exergy concept, the emerging concept of thermoeconomics, and the potential for artificial intelligence and expert systems in the design of thermal systems. With chapters written by internationally recognised authorities, the book offers a state-of-the-art review for both researchers and practitioners in mechanical, aerospace, chemical,

This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all lev