Mathematical Foundations of Information Flow
Mathematical Foundations of Information Flow

Author: Samson Abramsky

Publisher: American Mathematical Soc.

Published: 2012

Total Pages: 282

ISBN-13: 0821849239

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This volume is based on the 2008 Clifford Lectures on Information Flow in Physics, Geometry and Logic and Computation, held March 12-15, 2008, at Tulane University in New Orleans, Louisiana. The varying perspectives of the researchers are evident in the topics represented in the volume, including mathematics, computer science, quantum physics and classical and quantum information. A number of the articles address fundamental questions in quantum information and related topics in quantum physics, using abstract categorical and domain-theoretic models for quantum physics to reason about such systems and to model spacetime. Readers can expect to gain added insight into the notion of information flow and how it can be understood in many settings. They also can learn about new approaches to modeling quantum mechanics that provide simpler and more accessible explanations of quantum phenomena, which don't require the arcane aspects of Hilbert spaces and the cumbersome notation of bras and kets.

Mathematical Foundations and Applications of Graph Entropy
Mathematical Foundations and Applications of Graph Entropy

Author: Matthias Dehmer

Publisher: John Wiley & Sons

Published: 2017-09-12

Total Pages: 298

ISBN-13: 3527339094

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This latest addition to the successful Network Biology series presents current methods for determining the entropy of networks, making it the first to cover the recently established Quantitative Graph Theory. An excellent international team of editors and contributors provides an up-to-date outlook for the field, covering a broad range of graph entropy-related concepts and methods. The topics range from analyzing mathematical properties of methods right up to applying them in real-life areas. Filling a gap in the contemporary literature this is an invaluable reference for a number of disciplines, including mathematicians, computer scientists, computational biologists, and structural chemists.

Information Flow
Information Flow

Author: Jon Barwise

Publisher: Cambridge University Press

Published: 1997-07-28

Total Pages: 292

ISBN-13: 1316582663

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Information is a central topic in computer science, cognitive science and philosophy. In spite of its importance in the 'information age', there is no consensus on what information is, what makes it possible, and what it means for one medium to carry information about another. Drawing on ideas from mathematics, computer science and philosophy, this book addresses the definition and place of information in society. The authors, observing that information flow is possible only within a connected distribution system, provide a mathematically rigorous, philosophically sound foundation for a science of information. They illustrate their theory by applying it to a wide range of phenomena, from file transfer to DNA, from quantum mechanics to speech act theory.

Foundations of Data Science
Foundations of Data Science

Author: Avrim Blum

Publisher: Cambridge University Press

Published: 2020-01-23

Total Pages: 433

ISBN-13: 1108617360

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This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.

Quantum Information Theory and the Foundations of Quantum Mechanics
Quantum Information Theory and the Foundations of Quantum Mechanics

Author: Christopher G. Timpson

Publisher: Oxford Philosophical Monograph

Published: 2013-04-25

Total Pages: 308

ISBN-13: 0199296464

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Christopher G. Timpson provides the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. He argues for an ontologically deflationary account of the nature of quantum information, which is grounded in a revisionary analysis of the concepts of information.

Quantitative Graph Theory
Quantitative Graph Theory

Author: Matthias Dehmer

Publisher: CRC Press

Published: 2014-10-27

Total Pages: 530

ISBN-13: 1466584513

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The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as: Comparative approaches (graph similarity or distance) Graph measures to characterize graphs quantitatively Applications of graph measures in social network analysis and other disciplines Metrical properties of graphs and measures Mathematical properties of quantitative methods or measures in graph theory Network complexity measures and other topological indices Quantitative approaches to graphs using machine learning (e.g., clustering) Graph measures and statistics Information-theoretic methods to analyze graphs quantitatively (e.g., entropy) Through its broad coverage, Quantitative Graph Theory: Mathematical Foundations and Applications fills a gap in the contemporary literature of discrete and applied mathematics, computer science, systems biology, and related disciplines. It is intended for researchers as well as graduate and advanced undergraduate students in the fields of mathematics, computer science, mathematical chemistry, cheminformatics, physics, bioinformatics, and systems biology.

The Science of Quantitative Information Flow
The Science of Quantitative Information Flow

Author: Mário S. Alvim

Publisher: Springer Nature

Published: 2020-09-23

Total Pages: 478

ISBN-13: 3319961314

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This book presents a comprehensive mathematical theory that explains precisely what information flow is, how it can be assessed quantitatively – so bringing precise meaning to the intuition that certain information leaks are small enough to be tolerated – and how systems can be constructed that achieve rigorous, quantitative information-flow guarantees in those terms. It addresses the fundamental challenge that functional and practical requirements frequently conflict with the goal of preserving confidentiality, making perfect security unattainable. Topics include: a systematic presentation of how unwanted information flow, i.e., "leaks", can be quantified in operationally significant ways and then bounded, both with respect to estimated benefit for an attacking adversary and by comparisons between alternative implementations; a detailed study of capacity, refinement, and Dalenius leakage, supporting robust leakage assessments; a unification of information-theoretic channels and information-leaking sequential programs within the same framework; and a collection of case studies, showing how the theory can be applied to interesting realistic scenarios. The text is unified, self-contained and comprehensive, accessible to students and researchers with some knowledge of discrete probability and undergraduate mathematics, and contains exercises to facilitate its use as a course textbook.

Formal Techniques for Distributed Objects, Components, and Systems
Formal Techniques for Distributed Objects, Components, and Systems

Author: Jorge A. Pérez

Publisher: Springer

Published: 2019-06-03

Total Pages: 308

ISBN-13: 3030217590

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This book constitutes the proceedings of the 39th IFIP WG 6.1 International Conference on Formal Techniques for Distributed Objects, Components, and Systems, FORTE 2019, held in Copenhagen, Denmark, in June 2019, as part of the 14th International Federated Conference on Distributed Computing Techniques, DisCoTec 2019. The 15 full and 3 short papers presented were carefully reviewed and selected from 42 submissions. The conference is dedicated to fundamental research on theory, models, tools, and applications for distributed systems.

Mathematical Foundations of Computer Networking
Mathematical Foundations of Computer Networking

Author: Srinivasan Keshav

Publisher: Pearson Education

Published: 2012

Total Pages: 496

ISBN-13: 0321792106

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Mathematical techniques pervade current research in computer networking, yet are not taught to most computer science undergraduates. This self-contained, highly-accessible book bridges the gap, providing the mathematical grounding students and professionals need to successfully design or evaluate networking systems. The only book of its kind, it brings together information previously scattered amongst multiple texts. It first provides crucial background in basic mathematical tools, and then illuminates the specific theories that underlie computer networking. Coverage includes: * Basic probability * Statistics * Linear Algebra * Optimization * Signals, Systems, and Transforms, including Fourier series and transforms, Laplace transforms, DFT, FFT, and Z transforms * Queuing theory * Game Theory * Control theory * Information theory

Foundations of Security, Protocols, and Equational Reasoning
Foundations of Security, Protocols, and Equational Reasoning

Author: Joshua D. Guttman

Publisher: Springer

Published: 2019-05-17

Total Pages: 250

ISBN-13: 3030190528

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This Festschrift volume is published in honor of Catherine A. Meadows and contains essays presented at the Catherine Meadows Festschrift Symposium held in Fredericksburg, VA, USA, in May 2019. Catherine A. Meadows has been a pioneer in developing symbolic formal verification methods and tools. Her NRL Protocol Analyzer, a tool and methodology that embodies symbolic model checking techniques, has been fruitfully applied to the analysis of many protocols and protocol standards and has had an enormous influence in the field. She also developed a new temporal logic to specify protocol properties, as well as new methods for analyzing various kinds of properties beyond secrecy such as authentication and resilience under Denial of Service (DoS) attacks and has made important contributions in other areas such as wireless protocol security, intrusion detection, and the relationship between computational and symbolic approaches to cryptography. This volume contains 14 contributions authored by researchers from Europe and North America. They reflect on the long-term evolution and future prospects of research in cryptographic protocol specification and verification.