Algebraic Geometry Modeling In Information Theory

Author by : Edgar Martínez-Moro
Languange : en
Publisher by : World Scientific
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Total Read : 35
Total Download : 163
File Size : 41,6 Mb
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Description : Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.


Algebraic Geometry Modeling In Information Theory

Author by : Edgar Martinez-Moro
Languange : en
Publisher by : World Scientific
Format Available : PDF, ePub, Mobi
Total Read : 27
Total Download : 111
File Size : 47,9 Mb
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Description : Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.


Singularities Algebraic Geometry Commutative Algebra And Related Topics

Author by : Gert-Martin Greuel
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 54
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Description : This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra. The motivation for this collection comes from the wide-ranging research of the distinguished mathematician, Antonio Campillo, in these and related fields. Besides his influence in the mathematical community stemming from his research, Campillo has also endeavored to promote mathematics and mathematicians' networking everywhere, especially in Spain, Latin America and Europe. Because of his impressive achievements throughout his career, we dedicate this book to Campillo in honor of his 65th birthday. Researchers and students from the world-wide, and in particular Latin American and European, communities in singularities, algebraic geometry, commutative algebra, coding theory, and other fields covered in the volume, will have interest in this book.


Algebra For Secure And Reliable Communication Modeling

Author by : Mustapha Lahyane
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 10
Total Download : 870
File Size : 50,5 Mb
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Description : This volume contains the proceedings of the CIMPA Research School and Conference on Algebra for Secure and Reliable Communication Modeling, held from October 1-13, 2012, in Morelia, State of Michoacán, Mexico. The papers cover several aspects of the theory of coding theory and are gathered into three categories: general theory of linear codes, algebraic geometry and coding theory, and constacyclic codes over rings. The aim of this volume is to fill the gap between the theoretical part of algebraic geometry and the applications to problem solving and computational modeling in engineering, signal processing and information theory. This book is published in cooperation with Real Sociedad Matemática Española (RSME).


Interactions Between Group Theory Symmetry And Cryptology

Author by : María Isabel González Vasco
Languange : en
Publisher by : MDPI
Format Available : PDF, ePub, Mobi
Total Read : 39
Total Download : 115
File Size : 50,6 Mb
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Description : Cryptography lies at the heart of most technologies deployed today for secure communications. At the same time, mathematics lies at the heart of cryptography, as cryptographic constructions are based on algebraic scenarios ruled by group or number theoretical laws. Understanding the involved algebraic structures is, thus, essential to design robust cryptographic schemes. This Special Issue is concerned with the interplay between group theory, symmetry and cryptography. The book highlights four exciting areas of research in which these fields intertwine: post-quantum cryptography, coding theory, computational group theory and symmetric cryptography. The articles presented demonstrate the relevance of rigorously analyzing the computational hardness of the mathematical problems used as a base for cryptographic constructions. For instance, decoding problems related to algebraic codes and rewriting problems in non-abelian groups are explored with cryptographic applications in mind. New results on the algebraic properties or symmetric cryptographic tools are also presented, moving ahead in the understanding of their security properties. In addition, post-quantum constructions for digital signatures and key exchange are explored in this Special Issue, exemplifying how (and how not) group theory may be used for developing robust cryptographic tools to withstand quantum attacks.


Stochastic Models Information Theory And Lie Groups Volume 1

Author by : Gregory S. Chirikjian
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 26
Total Download : 123
File Size : 51,7 Mb
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Description : This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.


Geometries Codes And Cryptography

Author by : G. Longo
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 45
Total Download : 620
File Size : 54,8 Mb
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Description : The general problem studied by information theory is the reliable transmission of information through unreliable channels. Channels can be unreliable either because they are disturbed by noise or because unauthorized receivers intercept the information transmitted. In the first case, the theory of error-control codes provides techniques for correcting at least part of the errors caused by noise. In the second case cryptography offers the most suitable methods for coping with the many problems linked with secrecy and authentication. Now, both error-control and cryptography schemes can be studied, to a large extent, by suitable geometric models, belonging to the important field of finite geometries. This book provides an update survey of the state of the art of finite geometries and their applications to channel coding against noise and deliberate tampering. The book is divided into two sections, "Geometries and Codes" and "Geometries and Cryptography". The first part covers such topics as Galois geometries, Steiner systems, Circle geometry and applications to algebraic coding theory. The second part deals with unconditional secrecy and authentication, geometric threshold schemes and applications of finite geometry to cryptography. This volume recommends itself to engineers dealing with communication problems, to mathematicians and to research workers in the fields of algebraic coding theory, cryptography and information theory.


Proceedings 1995 Ieee International Symposium On Information Theory Held In British Columbia Canada On 17 22 September 1995

Author by : Anonim
Languange : en
Publisher by : Unknown
Format Available : PDF, ePub, Mobi
Total Read : 43
Total Download : 320
File Size : 55,8 Mb
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Description : PARTIAL CONTENTS: Shannon theory; Universal lossless source coding; Code division multiple access; Turbo codes; Broadband networks and protocols; Signal processing and coding; Coded modulation; Information theory and applications; Algebraic geometry codes; Modeling analysis and stability in networks; Channel capacity.


Information Geometry

Author by : Nihat Ay
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 56
Total Download : 571
File Size : 53,6 Mb
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Description : The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems.


Stochastic Models Information Theory And Lie Groups Volume 2

Author by : Gregory S. Chirikjian
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 18
Total Download : 423
File Size : 42,5 Mb
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Description : This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises, motivating examples, and real-world applications make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.


Algebraic Geometry And Geometric Modeling

Author by : Mohamed Elkadi
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 27
Total Download : 148
File Size : 50,8 Mb
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Description : This book spans the distance between algebraic descriptions of geometric objects and the rendering of digital geometric shapes based on algebraic models. These contrasting points of view inspire a thorough analysis of the key challenges and how they are met. The articles focus on important classes of problems: implicitization, classification, and intersection. Combining illustrative graphics, computations and review articles this book helps the reader gain a firm practical grasp of these subjects.


Information Theory Models Of Instabilities In Critical Systems

Author by : Rodrick Wallace
Languange : en
Publisher by : World Scientific
Format Available : PDF, ePub, Mobi
Total Read : 51
Total Download : 969
File Size : 50,6 Mb
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Description : The book is a unique exploration of a spectrum of unexpected analogs to psychopathologies likely to afflict real-time critical systems, written by a specialist in the epidemiology of mental disorders. The purpose of this book is to develop a set of information-theoretic statistical tools for analyzing the instabilities of real-time cognitive systems at those varying scales and levels of organization, with special focus on high level machine function. The book should be of particular interest to both industry and academic scientists, and government regulators, concerned with driverless cars on intelligent roads. Many of the same concerns also afflict high-end automated weapons systems. The book should appeal to students, researchers, and industrial and governmental administrators facing the design, operation, and maintenance of real time critical systems ranging across manufacturing facilities, transportation, finance, and military operations.


Forward Error Correction Based On Algebraic Geometric Theory

Author by : Jafar A. Alzubi
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 32
Total Download : 965
File Size : 53,7 Mb
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Description : This book covers the design, construction, and implementation of algebraic-geometric codes from Hermitian curves. Matlab simulations of algebraic-geometric codes and Reed-Solomon codes compare their bit error rate using different modulation schemes over additive white Gaussian noise channel model. Simulation results of Algebraic-geometric codes bit error rate performance using quadrature amplitude modulation (16QAM and 64QAM) are presented for the first time and shown to outperform Reed-Solomon codes at various code rates and channel models. The book proposes algebraic-geometric block turbo codes. It also presents simulation results that show an improved bit error rate performance at the cost of high system complexity due to using algebraic-geometric codes and Chase-Pyndiah’s algorithm simultaneously. The book proposes algebraic-geometric irregular block turbo codes (AG-IBTC) to reduce system complexity. Simulation results for AG-IBTCs are presented for the first time.


Algebraic Shift Register Sequences

Author by : Mark Goresky
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 13
Total Download : 797
File Size : 52,7 Mb
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Description : Pseudo-random sequences are essential ingredients of every modern digital communication system including cellular telephones, GPS, secure internet transactions and satellite imagery. Each application requires pseudo-random sequences with specific statistical properties. This book describes the design, mathematical analysis and implementation of pseudo-random sequences, particularly those generated by shift registers and related architectures such as feedback-with-carry shift registers. The earlier chapters may be used as a textbook in an advanced undergraduate mathematics course or a graduate electrical engineering course; the more advanced chapters provide a reference work for researchers in the field. Background material from algebra, beginning with elementary group theory, is provided in an appendix.


P Adic Deterministic And Random Dynamics

Author by : Andrei Y. Khrennikov
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 67
Total Download : 604
File Size : 48,6 Mb
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Description : This book provides an overview of the theory of p-adic (and more general non-Archimedean) dynamical systems. The main part of the book is devoted to discrete dynamical systems. It presents a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. Coverage also details p-adic neural networks and their applications to cognitive sciences: learning algorithms, memory recalling.


Algebraic Geometry And Statistical Learning Theory

Author by : Sumio Watanabe
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 28
Total Download : 593
File Size : 43,7 Mb
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Description : Sure to be influential, Watanabe's book lays the foundations for the use of algebraic geometry in statistical learning theory. Many models/machines are singular: mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.


Spatial Information Theory A Theoretical Basis For Gis

Author by : Pa.) COSIT'97 (1997 : Hidden Valley
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 17
Total Download : 705
File Size : 55,9 Mb
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Description : This book constitutes the refereed proceedings of the 1997 International Conference on Spatial Information Theory, COSIT'97, held in Laurel Highlands, Pennsylvania, USA, in October 1997. The 31 revised full papers presented were carefully selected from a total of 66 submissions. Also included are seven posters. The volume is divided into sections on representations of change, structuring of space, boundaries and gradations, topological models of space, formal models of space, cognitive aspects of spatial acquisition, novel use of spatial information, wayfinding and map interpretation, representations of spatial concepts, new approaches to spatial information.


Information Theory In Computer Vision And Pattern Recognition

Author by : Francisco Escolano Ruiz
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 14
Total Download : 553
File Size : 45,9 Mb
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Description : Information theory has proved to be effective for solving many computer vision and pattern recognition (CVPR) problems (such as image matching, clustering and segmentation, saliency detection, feature selection, optimal classifier design and many others). Nowadays, researchers are widely bringing information theory elements to the CVPR arena. Among these elements there are measures (entropy, mutual information...), principles (maximum entropy, minimax entropy...) and theories (rate distortion theory, method of types...). This book explores and introduces the latter elements through an incremental complexity approach at the same time where CVPR problems are formulated and the most representative algorithms are presented. Interesting connections between information theory principles when applied to different problems are highlighted, seeking a comprehensive research roadmap. The result is a novel tool both for CVPR and machine learning researchers, and contributes to a cross-fertilization of both areas.


Theory And Applications Of Models Of Computation

Author by : Jin-Yi Cai
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 36
Total Download : 760
File Size : 49,5 Mb
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Description : This book constitutes the refereed proceedings of the 4th International Conference on Theory and Applications of Models of Computation, TAMC 2007, held in Shanghai, China in May 2007. The 67 revised full papers presented together with 2 plenary lectures were carefully reviewed and selected from over 500 submissions. All major areas in computer science, mathematics (especially logic) and the physical sciences particularly with regard to computation and computability theory are addressed. The papers particularly focus on algorithms, complexity and computability theory, giving the conference a special flavor and distinction.


Modeling Paradigms And Analysis Of Disease Transmission Models

Author by : Abba B. Gumel
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 77
Total Download : 507
File Size : 49,6 Mb
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Description : This volume stems from two DIMACS activities, the U.S.-Africa Advanced Study Institute and the DIMACS Workshop, both on Mathematical Modeling of Infectious Diseases in Africa, held in South Africa in the summer of 2007. It contains both tutorial papers and research papers. Students and researchers should find the papers on modeling and analyzing certain diseases currently affecting Africa very informative. In particular, they can learn basic principles of disease modeling and stability from the tutorial papers where continuous and discrete time models, optimal control, and stochastic features are introduced.


The Homeschooler S Book Of Lists

Author by : Sonya Haskins
Languange : en
Publisher by : Bethany House
Format Available : PDF, ePub, Mobi
Total Read : 83
Total Download : 747
File Size : 49,9 Mb
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Description : With more than 250 lists, home educators, private school teachers, and others will find important facts and essential information in one easy-to-use resource.


Theory And Applications Of Models Of Computation

Author by : Manindra Agrawal
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 40
Total Download : 743
File Size : 53,6 Mb
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Description : This book constitutes the refereed proceedings of the 9th International Conference on Theory and Applications of Models of Computation, TAMC 2012, held in Beijing, China, in May 2012. The conference was combined with the Turing Lectures 2012, dedicated to celebrating Alan Turing’s unique impact on mathematics, computing, computer science, informatics, morphogenesis, philosophy, and the wider scientific world. Eight Turing Lectures were given at the TAMC 2012. The 40 revised full papers presented together with invited talks were carefully reviewed and selected from 86 submissions. The papers address 4 special sessions at TAMC 2012 which were algorithms and information in networks, complexity and cryptography, models of computing and networking, programming and verification.


Stochastic Models Information Theory And Lie Groups Volume 2

Author by : Gregory S. Chirikjian
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 49
Total Download : 825
File Size : 43,6 Mb
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Description : This two-volume set covers stochastic processes, information theory and Lie groups in a unified setting, bridging topics rarely studied together. The emphasis is on using stochastic, geometric, and group-theoretic concepts for modeling physical phenomena.


Introduction To Coding And Information Theory

Author by : Steven Roman
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 78
Total Download : 596
File Size : 51,5 Mb
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Description : This book is intended to introduce coding theory and information theory to undergraduate students of mathematics and computer science. It begins with a review of probablity theory as applied to finite sample spaces and a general introduction to the nature and types of codes. The two subsequent chapters discuss information theory: efficiency of codes, the entropy of information sources, and Shannon's Noiseless Coding Theorem. The remaining three chapters deal with coding theory: communication channels, decoding in the presence of errors, the general theory of linear codes, and such specific codes as Hamming codes, the simplex codes, and many others.


Digital Forensics And Watermarking

Author by : Yun-Qing Shi
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 56
Total Download : 436
File Size : 47,9 Mb
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Description : This book constitutes the thoroughly refereed post-conference proceedings of the 13th International Workshop on Digital-Forensics and Watermarking, IWDW 2014, held in Taipei, Taiwan, during October 2014. The 32 full and 14 poster papers, presented together with 1 keynote speech, were carefully reviewed and selected from 79 submissions. The papers are organized in topical sections on forensics; watermarking; reversible data hiding; visual cryptography; and steganography and steganalysis.


Information Theory

Author by : Defense Documentation Center (U.S.)
Languange : en
Publisher by : Unknown
Format Available : PDF, ePub, Mobi
Total Read : 85
Total Download : 796
File Size : 44,6 Mb
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Description :


Algebraic Statistics

Author by : Seth Sullivant
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 30
Total Download : 434
File Size : 52,5 Mb
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Description : Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.


Finite Fields And Their Applications

Author by : Pascale Charpin
Languange : en
Publisher by : Walter de Gruyter
Format Available : PDF, ePub, Mobi
Total Read : 98
Total Download : 346
File Size : 41,9 Mb
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Description : This book is based on the invited talks of the "RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials" held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2-7, 2012. Finite fields play important roles in many application areas such as coding theory, cryptography, Monte Carlo and quasi-Monte Carlo methods, pseudorandom number generation, quantum computing, and wireless communication. In this book we will focus on sequences, character sums, and polynomials over finite fields in view of the above mentioned application areas: Chapters 1 and 2 deal with sequences mainly constructed via characters and analyzed using bounds on character sums. Chapters 3, 5, and 6 deal with polynomials over finite fields. Chapters 4 and 9 consider problems related to coding theory studied via finite geometry and additive combinatorics, respectively. Chapter 7 deals with quasirandom points in view of applications to numerical integration using quasi-Monte Carlo methods and simulation. Chapter 8 studies aspects of iterations of rational functions from which pseudorandom numbers for Monte Carlo methods can be derived. The goal of this book is giving an overview of several recent research directions as well as stimulating research in sequences and polynomials under the unified framework of character theory.