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Expander Families And Their Applications
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Book Synopsis Expander Families and Their Applications by :
Download or read book Expander Families and Their Applications written by and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is to provide a brief introduction to the mathematical theory of expander families and their applications. Throughout this paper we mainly deal with graphs with finitely many vertices and edges. The central notion of this thesis is that of expansion roughly meaning the quality of a graph as a communication network where the vertices represent entities and an edge connects two vertices. An ideal communication network is a large graph with large isoperimetric constant, meanwhile the number of the edges are not too large. Cayley graphs are constructed from groups and they play a very important role in expander families. The second largest eigenvalue, the isoperimetric constant, and the diameter are the main measures of the expansion quality of Cayley graphs. The "zig-zag product" provides a straightforward combinatorial method to construct expander families.
Book Synopsis Expander Families and Cayley Graphs by : Mike Krebs
Download or read book Expander Families and Cayley Graphs written by Mike Krebs and published by OUP USA. This book was released on 2011-10-21 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expander families enjoy a wide range of applications in mathematics and computer science, and their study is a fascinating one in its own right. Expander Families and Cayley Graphs: A Beginner's Guide provides an introduction to the mathematical theory underlying these objects. The central notion in the book is that of expansion, which roughly means the quality of a graph as a communications network. Cayley graphs are certain graphs constructed from groups; they play a prominent role in the study of expander families. The isoperimetric constant, the second largest eigenvalue, the diameter, and the Kazhdan constant are four measures of the expansion quality of a Cayley graph. The book carefully develops these concepts, discussing their relationships to one another and to subgroups and quotients as well as their best-case growth rates. Topics include graph spectra (i.e., eigenvalues); a Cheeger-Buser-type inequality for regular graphs; group quotients and graph coverings; subgroups and Schreier generators; the Alon-Boppana theorem on the second largest eigenvalue of a regular graph; Ramanujan graphs; diameter estimates for Cayley graphs; the zig-zag product and its relation to semidirect products of groups; eigenvalues of Cayley graphs; Paley graphs; and Kazhdan constants. The book was written with undergraduate math majors in mind; indeed, several dozen of them field-tested it. The prerequisites are minimal: one course in linear algebra, and one course in group theory. No background in graph theory or representation theory is assumed; the book develops from scatch the required facts from these fields. The authors include not only overviews and quick capsule summaries of key concepts, but also details of potentially confusing lines of reasoning. The book contains ideas for student research projects (for capstone projects, REUs, etc.), exercises (both easy and hard), and extensive notes with references to the literature.
Book Synopsis Operator Algebras and Their Applications by : Robert S. Doran
Download or read book Operator Algebras and Their Applications written by Robert S. Doran and published by American Mathematical Soc.. This book was released on 2016-07-28 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: his volume contains the proceedings of the AMS Special Session Operator Algebras and Their Applications: A Tribute to Richard V. Kadison, held from January 10–11, 2015, in San Antonio, Texas. Richard V. Kadison has been a towering figure in the study of operator algebras for more than 65 years. His research and leadership in the field have been fundamental in the development of the subject, and his influence continues to be felt though his work and the work of his many students, collaborators, and mentees. Among the topics addressed in this volume are the Kadison-Kaplanksy conjecture, classification of C∗-algebras, connections between operator spaces and parabolic induction, spectral flow, C∗-algebra actions, von Neumann algebras, and applications to mathematical physics.
Book Synopsis An Introduction to Expander Graphs by :
Download or read book An Introduction to Expander Graphs written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Emerging Applications of Number Theory by : Dennis A. Hejhal
Download or read book Emerging Applications of Number Theory written by Dennis A. Hejhal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.
Book Synopsis Handbook of Discrete and Computational Geometry by : Csaba D. Toth
Download or read book Handbook of Discrete and Computational Geometry written by Csaba D. Toth and published by CRC Press. This book was released on 2017-11-22 with total page 2354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
Book Synopsis Pseudorandomness by : Salil P. Vadhan
Download or read book Pseudorandomness written by Salil P. Vadhan and published by Foundations and Trends(r) in T. This book was released on 2012 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of pseudorandomness, the theory of efficiently generating objects that look random despite being constructed using little or no randomness. This theory has significance for areas in computer science and mathematics, including computational complexity, algorithms, cryptography, combinatorics, communications, and additive number theory.
Book Synopsis Handbook of Discrete and Combinatorial Mathematics by : Kenneth H. Rosen
Download or read book Handbook of Discrete and Combinatorial Mathematics written by Kenneth H. Rosen and published by CRC Press. This book was released on 2017-10-19 with total page 1612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.
Book Synopsis Expansion in Finite Simple Groups of Lie Type by : Terence Tao
Download or read book Expansion in Finite Simple Groups of Lie Type written by Terence Tao and published by American Mathematical Soc.. This book was released on 2015-04-16 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expander graphs are an important tool in theoretical computer science, geometric group theory, probability, and number theory. Furthermore, the techniques used to rigorously establish the expansion property of a graph draw from such diverse areas of mathematics as representation theory, algebraic geometry, and arithmetic combinatorics. This text focuses on the latter topic in the important case of Cayley graphs on finite groups of Lie type, developing tools such as Kazhdan's property (T), quasirandomness, product estimates, escape from subvarieties, and the Balog-Szemerédi-Gowers lemma. Applications to the affine sieve of Bourgain, Gamburd, and Sarnak are also given. The material is largely self-contained, with additional sections on the general theory of expanders, spectral theory, Lie theory, and the Lang-Weil bound, as well as numerous exercises and other optional material.
Download or read book Erdös Centennial written by László Lovász and published by Springer Science & Business Media. This book was released on 2014-01-24 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paul Erdös was one of the most influential mathematicians of the twentieth century, whose work in number theory, combinatorics, set theory, analysis, and other branches of mathematics has determined the development of large areas of these fields. In 1999, a conference was organized to survey his work, his contributions to mathematics, and the far-reaching impact of his work on many branches of mathematics. On the 100th anniversary of his birth, this volume undertakes the almost impossible task to describe the ways in which problems raised by him and topics initiated by him (indeed, whole branches of mathematics) continue to flourish. Written by outstanding researchers in these areas, these papers include extensive surveys of classical results as well as of new developments.
Download or read book Index Medicus written by and published by . This book was released on 2002 with total page 1596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vols. for 1963- include as pt. 2 of the Jan. issue: Medical subject headings.
Book Synopsis Computational Complexity by : Sanjeev Arora
Download or read book Computational Complexity written by Sanjeev Arora and published by Cambridge University Press. This book was released on 2009-04-20 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set. The book starts with a broad introduction to the field and progresses to advanced results. Contents include: definition of Turing machines and basic time and space complexity classes, probabilistic algorithms, interactive proofs, cryptography, quantum computation, lower bounds for concrete computational models (decision trees, communication complexity, constant depth, algebraic and monotone circuits, proof complexity), average-case complexity and hardness amplification, derandomization and pseudorandom constructions, and the PCP theorem.
Book Synopsis Mathematical Adventures in Performance Analysis by : Eitan Bachmat
Download or read book Mathematical Adventures in Performance Analysis written by Eitan Bachmat and published by Springer. This book was released on 2014-09-22 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes problems in the field of performance analysis, primarily the study of storage systems and the diverse mathematical techniques that are required for solving them. Topics covered include best practices for scheduling I/O requests to a disk drive, how this problem is related to airplane boarding, and how both problems can be modeled using space-time geometry. Also provided is an explanation of how Riemann's proof of the analytic continuation and functional equation of the Riemann zeta function can be used to analyze express line queues in a minimarket. Overall, the book displays the surprising relevance of abstract mathematics that is not usually associated with applied mathematics topics. Advanced undergraduate students or graduate students with an interest in the applications of mathematics will find this book to be a useful resource. It will also be of interest to professional mathematicians who want exposure to the surprising ways that theoretical mathematics may be applied to engineering problems. To encourage further study, each chapter ends with notes pointing to various related topics that the reader may want pursue. This mathematically rigorous work was noted in the news section of the journal Nature, and in popular media such as New Scientist, The Wall Street Journal, The Guardian, and USA Today.
Author :European Association of Fisheries Economists. Conference Publisher :Editions Quae ISBN 13 :2844331262 Total Pages :313 pages Book Rating :4.8/5 (443 download)
Book Synopsis EAFE 2003 Proceedings by : European Association of Fisheries Economists. Conference
Download or read book EAFE 2003 Proceedings written by European Association of Fisheries Economists. Conference and published by Editions Quae. This book was released on 2004 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Le Centre Ifremer de Brest a hébergé la 15e conférence annuelle de l'Association européenne des économistes des pêches. La conférence a rassemblé plus de 80 participants. Les communications ont traité de thèmes très divers touchant aux aspects économiques des usages et de la gestion des ressources et de l'environnement marin, des industries et des marchés. Les débats sur la réforme de la politique commune de la pêche 2002, abordée en plénière, ont montré l'importance de la gestion des pêches pour la recherche économique. Plusieurs communications et une table ronde se sont centrées sur la filière, la consommation et les marchés des produits de la mer : ces thèmes mobilisent de plus en plus l'attention des économistes européens.
Book Synopsis The Probabilistic Method by : Noga Alon
Download or read book The Probabilistic Method written by Noga Alon and published by John Wiley & Sons. This book was released on 2004-04-05 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The leading reference on probabilistic methods in combinatorics-now expanded and updated When it was first published in 1991, The Probabilistic Method became instantly the standard reference on one of the most powerful and widely used tools in combinatorics. Still without competition nearly a decade later, this new edition brings you up to speed on recent developments, while adding useful exercises and over 30% new material. It continues to emphasize the basic elements of the methodology, discussing in a remarkably clear and informal style both algorithmic and classical methods as well as modern applications. The Probabilistic Method, Second Edition begins with basic techniques that use expectation and variance, as well as the more recent martingales and correlation inequalities, then explores areas where probabilistic techniques proved successful, including discrepancy and random graphs as well as cutting-edge topics in theoretical computer science. A series of proofs, or "probabilistic lenses," are interspersed throughout the book, offering added insight into the application of the probabilistic approach. New and revised coverage includes: * Several improved as well as new results * A continuous approach to discrete probabilistic problems * Talagrand's Inequality and other novel concentration results * A discussion of the connection between discrepancy and VC-dimension * Several combinatorial applications of the entropy function and its properties * A new section on the life and work of Paul Erdös-the developer of the probabilistic method
Book Synopsis Logical Foundations of Mathematics and Computational Complexity by : Pavel Pudlák
Download or read book Logical Foundations of Mathematics and Computational Complexity written by Pavel Pudlák and published by Springer Science & Business Media. This book was released on 2013-04-22 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.
Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Sirakov Boyan
Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Sirakov Boyan and published by World Scientific. This book was released on 2019-02-27 with total page 5396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
