Algebraic Geometry Modeling in Information Theory

Algebraic Geometry Modeling in Information Theory
Author: Edgar Martinez-Moro
Publisher: World Scientific
Total Pages: 334
Release: 2013
Genre: Computers
ISBN: 9814335754

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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 and Geometric Modeling

Algebraic Geometry and Geometric Modeling
Author: Mohamed Elkadi
Publisher: Springer Science & Business Media
Total Pages: 252
Release: 2006-11-02
Genre: Mathematics
ISBN: 3540332758

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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.

Model Theory and Algebraic Geometry

Model Theory and Algebraic Geometry
Author: Elisabeth Bouscaren
Publisher:
Total Pages: 236
Release: 2014-09-01
Genre:
ISBN: 9783662194478

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Stochastic Models, Information Theory, and Lie Groups, Volume 1

Stochastic Models, Information Theory, and Lie Groups, Volume 1
Author: Gregory S. Chirikjian
Publisher: Springer Science & Business Media
Total Pages: 397
Release: 2009-09-02
Genre: Mathematics
ISBN: 0817648038

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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.

Geometry and Codes

Geometry and Codes
Author: Goppa
Publisher: Springer Science & Business Media
Total Pages: 174
Release: 1988-09-30
Genre: Mathematics
ISBN: 9789027727763

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Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day. that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering: and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Applications of Algebraic Geometry to Coding Theory, Physics and Computation

Applications of Algebraic Geometry to Coding Theory, Physics and Computation
Author: Ciro Ciliberto
Publisher: Springer Science & Business Media
Total Pages: 364
Release: 2001-08-31
Genre: Computers
ISBN: 9781402000041

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Proceedings of the NATO Advanced Research Workshop, held in Eilat, Israel, from 25th February to 1st March 2001

Algebraic Geometry and Geometric Modeling

Algebraic Geometry and Geometric Modeling
Author: Mohamed Elkadi
Publisher: Springer
Total Pages: 0
Release: 2010-11-19
Genre: Mathematics
ISBN: 9783642069932

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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.

Topics in Algebraic Geometry and Geometric Modeling

Topics in Algebraic Geometry and Geometric Modeling
Author: Ron Goldman
Publisher: American Mathematical Soc.
Total Pages: 378
Release: 2003
Genre: Mathematics
ISBN: 0821834207

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Algebraic geometry and geometric modeling both deal with curves and surfaces generated by polynomial equations. Algebraic geometry investigates the theoretical properties of polynomial curves and surfaces; geometric modeling uses polynomial, piecewise polynomial, and rational curves and surfaces to build computer models of mechanical components and assemblies for industrial design and manufacture. The NSF sponsored the four-day ''Vilnius Workshop on Algebraic Geometry and Geometric Modeling'', which brought together some of the top experts in the two research communities to examine a wide range of topics of interest to both fields. This volume is an outgrowth of that workshop. Included are surveys, tutorials, and research papers. In addition, the editors have included a translation of Minding's 1841 paper, ''On the determination of the degree of an equations obtained by elimination'', which foreshadows the modern application of mixed volumes in algebraic geometry. The volume is suitable for mathematicians, computer scientists, and engineers interested in applications of algebraic geometry to geometric modeling.

Model Theory and Algebraic Geometry

Model Theory and Algebraic Geometry
Author: Elisabeth Bouscaren
Publisher: Springer
Total Pages: 223
Release: 2009-03-14
Genre: Mathematics
ISBN: 3540685219

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This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.