Boolean Function Complexity

Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive descrip

Incorporates state-of-the-art interpretations of complex pulmonary physiology revealed by high-resolution or -magnification studies into current concepts of lung mechanics, gas exchange, and pulmonary

This book explains the relationship between intelligence and environmental complexity, and in so doing links philosophy of mind to more general issues about the relations between organisms and environments, and to the general pattern of 'externalist' explanations. The author provides a biological approach to the investigation of mind and cognition in nature. In particular he explores the idea that the function of cognition is to enable agents to deal with environmental complexity. The history of the idea in the work of Dewey and Spencer is considered, as is the impact of recent evolutionary theory on our understanding of the place of mind in nature.

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

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.

Inflectional morphology plays a paradoxical role in language. On the one hand it tells us useful things, for example that a noun is plural or a verb is in the past tense. On the other hand many languages get along perfectly well without it, so the baroquely ornamented forms we sometimes find come across as a gratuitous over-elaboration. This is especially apparent where the morphological structures operate at cross purposes to the general systems of meaning and function that govern a language, yielding inflection classes and arbitrarily configured paradigms. This is what we call morphological complexity. Manipulating the forms of words requires learning a whole new system of structures and relationships. This book confronts the typological challenge of characterising the wildly diverse sorts of morphological complexity we find in the languages of the world, offering both a unified descriptive framework and quantitative measures that can be applied to such heterogeneous systems.

This collection of papers presents a series of in-depth examinations of a variety of advanced topics related to Boolean functions and expressions. The chapters are written by some of the most prominent experts in their respective fields and cover topics ranging from algebra and propositional logic to learning theory, cryptography, computational complexity, electrical engineering, and reliability theory. Beyond the diversity of the questions raised and investigated in different chapters, a remarkable feature of the collection is the common thread created by the fundamental language, concepts, models, and tools provided by Boolean theory. Many readers will be surprised to discover the countless links between seemingly remote topics discussed in various chapters of the book. This text will help them draw on such connections to further their understanding of their own scientific discipline and to explore new avenues for research.

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

Presents a large number of recent research results previously unavailable in book form. Initially deals with the wee-known computation models, and goes on to special types of circuits, parallel comput

There has been a rapid expansion of academic interest and publications on polycentricity. In the contemporary world, nearly all governance situations are polycentric, but people are not necessarily used to thinking this way. Governing Complexity provides an updated explanation of the concept of polycentric governance. The editors provide examples of it in contemporary settings involving complex natural resource systems, as well as a critical evaluation of the utility of the concept. With contributions from leading scholars in the field, this book makes the case that polycentric governance arrangements exist and it is possible for polycentric arrangements to perform well, persist for long periods, and adapt. Whether they actually function well, persist, or adapt depends on multiple factors that are reviewed and discussed, both theoretically and with examples from actual cases.

Spared by the Arab revolts, Bouteflika's Algeria continues to intrigue observers. How does its political system function? Who really governs? Who are behind the protests? How strong are the Islamists?

In recent years, there has been a new understanding of how cities evolve and function, which reflects the emergent paradigm of complexity. The crux of this view is that cities are created by different

The rapidly increasing complexity of societal systems increases the need for professionalism in management—one must be able to function reliably regardless of increasing management complexity in the

The discipline of silviculture is at a crossroads. Silviculturists are under increasing pressure to develop practices that sustain the full function and dynamics of forested ecosystems and maintain ec

This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then treated, including polynomial simulations and conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, direct independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the method of Boolean valuations, the issue of hard tautologies and optimal proof systems, combinatorics and

For modeling the transport of carriers in nanoscale devices, a Green-function formalism is the most accurate approach. Due to the complexity of the formalism, one should have a deep understanding of t

The world of work has changed, no longer fitting the traditional, vertical lines of function and geography. Today, work is much more horizontal - cutting across silos and extending beyond the organiza

The astounding diversity of the immune system and the complexity of its regulatory pathways makes immunology a combinatorial science. Computational analysis has therefore become an essential element o

The groundbreaking first book by a major evolutionary biologist, published in 1912, that anticipated current thinking about organismal complexity. Julian Huxley’s The Individual in the Animal Kingdom, published in 1912, is a concise and groundbreaking work that is almost entirely unknown today. In it, Huxley analyzes the evolutionary advances in life’s organizational complexity, anticipating many of today’s ideas about changes in individuality. Huxley’s overarching system of concepts and his coherent logical principles were so far ahead of their time that they remain valid to this day. In part, this is because his explicitly Darwinian approach carefully distinguished between the integrated form and function of hierarchies within organisms and loosely defined, nonorganismal ecological communities. In The Individual in the Animal Kingdom, we meet a youthful Huxley who uses his commanding knowledge of natural history to develop a nonreductionist account of life’s complexity that aligns

Network thinking and network analysis are rapidly expanding features of ecological research. Network analysis of ecological systems include representations and modelling of the interactions in an ecosystem, in which species or factors are joined by pairwise connections. This book provides an overview of ecological network analysis including generating processes, the relationship between structure and dynamic function, and statistics and models for these networks. Starting with a general introduction to the composition of networks and their characteristics, it includes details on such topics as measures of network complexity, applications of spectral graph theory, how best to include indirect species interactions, and multilayer, multiplex and multilevel networks. Graduate students and researchers who want to develop and understand ecological networks in their research will find this volume inspiring and helpful. Detailed guidance to those already working in network ecology but looking

Mathematical and numerical modelling of the human cardiovascular system has attracted remarkable research interest due to its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. This book addresses the two principal components of the cardiovascular system: arterial circulation and heart function. It systematically describes all aspects of the problem, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, reviewing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiovascular system and the need for computational methods that are stable, reliable and efficient. The final part is devoted to control and inverse problems, including parameter estimation, uncertainty quantification and the developmen

This book approaches post-truth and relativism in a multidisciplinary fashion. Researchers from astrophysics, philosophy, psychology, media studies, religious studies, anthropology, social epistemology and sociology discuss and analyse the impact of relativism and post-truth both within the academy and in society at large. The motivation for this multidisciplinary approach is that relativism and post-truth are multifaceted phenomena with complex histories that have played out differently in different areas of society and different academic disciplines. There is hence a multitude of ways in which to use and understand the concepts and the phenomena to which they refer, and a multitude of critiques and defenses as well. No single volume can capture the ongoing discussions in different areas in all their complexity, but the different chapters of the book can function as exemplifications of the ramifications these phenomena have had.

Presenting new approaches to studying food webs, this book uses practical management and policy examples to demonstrate the theory behind ecosystem management decisions and the broader issue of sustainability. All the information that readers need to use food web analyses as a tool for understanding and quantifying transition processes is provided. Advancing the idea of food webs as complex adaptive systems, readers are challenged to rethink how changes in environmental conditions affect these systems. Beginning with the current state of thinking about community organisation, complexity and stability, the book moves on to focus on the traits of organisms, the adaptive nature of communities and their impacts on ecosystem function. The final section of the book addresses the applications to management and sustainability. By helping to understand the complexities of multispecies networks, this book provides insights into the evolution of organisms and the fate of ecosystems in a changing

Property relations are such a common feature of social life that the complexity of the web of laws, practices, and ideas that allow a property regime to function smoothly are often forgotten. But we a

Cephalopods are generally regarded as the most intelligent group among the invertebrates. Despite their popularity, relatively little is known about the range and function of their cognitive abilities. This book fills that gap, accentuating the varied and fascinating aspects of cognition across the group. Starting with the brain, learning and memory, Part I looks at early learning, memory acquisition and cognitive development in modern cephalopods. An analysis of the chambered nautilus, a living fossil, is included, providing insight into the evolution of behavioural complexity. Part II surveys environmental responses, especially within the active and learning-dependent coleoids. The ever-intriguing camouflage abilities of octopus and cuttlefish are highlighted, alongside bioluminescence, navigation and other aspects of visual and cognitive competence. Covering the range of cognitive function, this text underscores the importance of the cephalopods within the field of comparative cogni

Aberrant expression and function of microRNAs (miRNAs) in cancer have added a new layer of complexity to the understanding of development and progression of the disease state. It has been demonstrated

Along with almost 200 fascinating open problems, this updated edition covers most of what we know about Boolean cardinal invariants, and includes detailed studies of 21 cardinal number valued function

In competitive and contested democratic elections, insuring integrity is critical. Evaluating Elections shows why systematic analysis and reporting of election performance is important and how data-driven performance management can be used by election officials to improve elections. The authors outline how performance management systems can function in elections and their benefits for voters, candidates and political parties. Journalists, election administrators and even candidates often ask whether recent elections were run well, whether there were problems in the administration of a particular state's elections and how well elections were run across the country. The authors explain that such questions are difficult to answer because of the complexity of election administration and because there is currently no standard or accepted framework to assess the general quality of an election.

Due to the complexity of the mitochondrial system and the myriad genes involved in their function, the clinical manifestations of mitochondrial diseases are remarkably variable and heterogeneous. The

The complexity of human uterine function and regulation is one of the great wonders of nature and represents a daunting challenge to unravel. This book is dedicated to the biomechanical modeling of th

Memory is a universal function of organized matter. What is the mathematics of memory? How does memory affect the space-time behaviour of spatially extended systems? Does memory increase complexity? T

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

This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theo

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.

Life occurs, as far as we know, only as part of the earthly biosphere. Yet the earth's biotic resources are experiencing a spreading crisis that is leading not only to the most rapid loss of species in the last 65 million years, but also causing abrupt changes in the structure and function of natural communities. This disturbance, unfortunately, is the result of human carelessness in the name of advancing civilisation. As our technologies and societies continue to improve and grow, we remove ourselves more and more from our natural habitat; as a consequence, we destroy countless numbers of species of every style and complexity. To identify and begin rectifying this dangerous situation, a group of outstanding environmental scientists has compiled a collection of case studies that illustrate the changes being wrought on the biosphere by the human presence.

The images gathered in this volume function as a paranamic cartography of contemporary Mexico. The photographers have captured the complexity and diversity of the country, renewing our perceptions of