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Here Professor Paterson brings together papers from the 1990 Durham symposium on Boolean function complexity. The participants include many well known figures in the field.
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 description of basic lower bound arguments, covering many of the gems of this “complexity Waterloo” that have been discovered over the past several decades, right up to results from the last year or two. Many open problems, marked as Research Problems, are mentioned along the way. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science. The book will be of interest to graduate students and researchers in the fields of computer science and discrete mathematics.
This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.
This is the first book to cover the theory of noise sensitivity of Boolean functions with particular emphasis on critical percolation.
Systems Biology Modelling and Analysis Describes important modelling and computational methods for systems biology research to enable practitioners to select and use the most suitable technique Systems Biology Modelling and Analysis provides an overview of state-of-the-art techniques and introduces related tools and practices to formalize models and automate reasoning for systems biology. The authors present and compare the main formal methods used in systems biology for modelling biological networks, including discussion of their advantages, drawbacks, and main applications. Each chapter includes an intuitive presentation of the specific formalism, a brief history of the formalism and of its applications in systems biology, a formal description of the formalism and its variants, at least one realistic case study, some applications of formal techniques to validate and make deep analysis of models encoded with the formalism, and a discussion on the kind of biological systems for which the formalism is suited, along with concrete ideas on its possible evolution. Edited by a highly qualified expert with significant experience in the field, some of the methods and techniques covered in Systems Biology Modelling and Analysis include: Petri nets, an important tool for studying different aspects of biological systems, ranging from simple signaling pathways to metabolic networks and beyond Pathway Logic, a formal, rule-based system and interactive viewer for developing executable models of cellular processes Boolean networks, a mathematical model which has been widely used for decades in the context of biological regulation networks Answer Set Programming (ASP), which has proven to be a strong logic programming paradigm to deal with the inherent complexity of biological models For systems biologists, biochemists, bioinformaticians, molecular biologists, pharmacologists, and computer scientists, Systems Biology Modelling and Analysis is a comprehensive all-in-one resource to understand and harness the field’s current models and techniques while also preparing for their potential developments in coming years with the help of the author’s expert insight.
"Et moi ..., si j'avait Sll comment en revenir. One sennce mathematics has rendered the human race. It has put common sense back je n'y serais point alle.' Jules Verne whe", it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be smse'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'!ltre of this series
Written by prominent experts in the field, this monograph provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations) and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form for the first time. Because of the depth and breadth and its emphasis on algorithms and applications, this monograph will have special appeal for researchers and graduate students in discrete mathematics, operations research, computer science, engineering and economics.
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".