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.
Boolean functions are essential to systems for secure and reliable communication. This comprehensive survey of Boolean functions for cryptography and coding covers the whole domain and all important results, building on the author's influential articles with additional topics and recent results. A useful resource for researchers and graduate students, the book balances detailed discussions of properties and parameters with examples of various types of cryptographic attacks that motivate the consideration of these parameters. It provides all the necessary background on mathematics, cryptography, and coding, and an overview on recent applications, such as side channel attacks on smart cards, cloud computing through fully homomorphic encryption, and local pseudo-random generators. The result is a complete and accessible text on the state of the art in single and multiple output Boolean functions that illustrates the interaction between mathematics, computer science, and telecommunications.
Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the "modern biology" skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution. - Examines significant questions in modern biology and their mathematical treatments - Presents important mathematical concepts and tools in the context of essential biology - Features material of interest to students in both mathematics and biology - Presents chapters in modular format so coverage need not follow the Table of Contents - Introduces projects appropriate for undergraduate research - Utilizes freely accessible software for visualization, simulation, and analysis in modern biology - Requires no calculus as a prerequisite - Provides a complete Solutions Manual - Features a companion website with supplementary resources
This two volume set LNCS 8634 and LNCS 8635 constitutes the refereed conference proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014, held in Budapest, Hungary, in August 2014. The 95 revised full papers presented together with 6 invited talks were carefully selected from 270 submissions. The focus of the conference was on following topics: Logic, Semantics, Automata, Theory of Programming, Algorithms, Complexity, Parallel and Distributed Computing, Quantum Computing, Automata, Grammars and Formal Languages, Combinatorics on Words, Trees and Games.
Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.
This book constitutes the proceedings of the Second International Conference on Codes, Cryptology and Information Security, C2SI 2017, held in Rabat, Morocco, in April 2017. The 19 regular papers presented together with 5 invited talks were carefully reviewed and selected from 72 submissions. The first aim of this conference is to pay homage to Claude Carlet for his valuable contribution in teaching and disseminating knowledge in coding theory and cryptography worldwide, especially in Africa. The second aim of the conference is to provide an international forum for researchers from academia and practitioners from industry from all over the world for discussion of all forms of cryptology, coding theory and information security.
This book constitutes the thoroughly refereed proceedings of the 10th International Symposium on Automated Technology for Verification and Analysis, ATVA 2012, held at Thiruvananthapuram, Kerala, India, in October 2012. The 25 regular papers, 3 invited papers and 4 tool papers presented were carefully selected from numerous submissions. Conference papers are organized in 9 technical sessions, covering the topics of automata theory, logics and proofs, model checking, software verification, synthesis, verification and parallelism, probabilistic verification, constraint solving and applications, and probabilistic systems.
Using Bishop's work on constructive analysis as a framework, this monograph gives a systematic, detailed and general constructive theory of probability theory and stochastic processes. It is the first extended account of this theory: almost all of the constructive existence and continuity theorems that permeate the book are original. It also contains results and methods hitherto unknown in the constructive and nonconstructive settings. The text features logic only in the common sense and, beyond a certain mathematical maturity, requires no prior training in either constructive mathematics or probability theory. It will thus be accessible and of interest, both to probabilists interested in the foundations of their speciality and to constructive mathematicians who wish to see Bishop's theory applied to a particular field.
Neuronal dendritic trees are complex structures that endow the cell with powerful computing capabilities and allow for high neural interconnectivity. Studying the function of dendritic structures has a long tradition in theoretical neuroscience, starting with the pioneering work by Wilfrid Rall in the 1950s. Recent advances in experimental techniques allow us to study dendrites with a new perspective and in greater detail. The goal of this volume is to provide a résumé of the state-of-the-art in experimental, computational, and mathematical investigations into the functions of dendrites in a variety of neural systems. The book first looks at morphological properties of dendrites and summarizes the approaches to measure dendrite morphology quantitatively and to actually generate synthetic dendrite morphologies in computer models. This morphological characterization ranges from the study of fractal principles to describe dendrite topologies, to the consequences of optimization principles for dendrite shape. Individual approaches are collected to study the aspects of dendrite shape that relate directly to underlying circuit constraints and computation. The second main theme focuses on how dendrites contribute to the computations that neurons perform. What role do dendritic morphology and the distributions of synapses and membrane properties over the dendritic tree have in determining the output of a neuron in response to its input? A wide range of studies is brought together, with topics ranging from general to system-specific phenomena—some having a strong experimental component, and others being fully theoretical. The studies come from many different neural systems and animal species ranging from invertebrates to mammals. With this broad focus, an overview is given of the diversity of mechanisms that dendrites can employ to shape neural computations.