On Monotonicity Testing And The 2 To 2 Games Conjecture

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On Monotonicity Testing and the 2-to-2 Games Conjecture

Author : Dor Minzer
Publisher : Morgan & Claypool
ISBN 13 : 145039969X
Total Pages : 233 pages
Book Rating : 4.4/5 (53 download)

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Book Synopsis On Monotonicity Testing and the 2-to-2 Games Conjecture by : Dor Minzer

Download or read book On Monotonicity Testing and the 2-to-2 Games Conjecture written by Dor Minzer and published by Morgan & Claypool. This book was released on 2022-12-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses two questions in Complexity Theory: the Monotonicity Testing problem and the 2-to-2 Games Conjecture. Monotonicity testing is a problem from the field of property testing, first considered by Goldreich et al. in 2000. The input of the algorithm is a function, and the goal is to design a tester that makes as few queries to the function as possible, accepts monotone functions and rejects far-from monotone functions with a probability close to 1. The first result of this book is an essentially optimal algorithm for this problem. The analysis of the algorithm heavily relies on a novel, directed, and robust analogue of a Boolean isoperimetric inequality of Talagrand from 1993. The probabilistically checkable proofs (PCP) theorem is one of the cornerstones of modern theoretical computer science. One area in which PCPs are essential is the area of hardness of approximation. Therein, the goal is to prove that some optimization problems are hard to solve, even approximately. Many hardness of approximation results were proved using the PCP theorem; however, for some problems optimal results were not obtained. This book touches on some of these problems, and in particular the 2-to-2 games problem and the vertex cover problem. The second result of this book is a proof of the 2-to-2 games conjecture (with imperfect completeness), which implies new hardness of approximation results for problems such as vertex cover and independent set. It also serves as strong evidence towards the unique games conjecture, a notorious related open problem in theoretical computer science. At the core of the proof is a characterization of small sets of vertices in Grassmann graphs whose edge expansion is bounded away from 1.

Prophets of Computing

Author : Dick van Lente
Publisher : Morgan & Claypool
ISBN 13 : 1450398189
Total Pages : 556 pages
Book Rating : 4.4/5 (53 download)

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Book Synopsis Prophets of Computing by : Dick van Lente

Download or read book Prophets of Computing written by Dick van Lente and published by Morgan & Claypool. This book was released on 2022-12-14 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: When electronic digital computers first appeared after World War II, they appeared as a revolutionary force. Business management, the world of work, administrative life, the nation state, and soon enough everyday life were expected to change dramatically with these machines’ use. Ever since, diverse prophecies of computing have continually emerged, through to the present day. As computing spread beyond the US and UK, such prophecies emerged from strikingly different economic, political, and cultural conditions. This volume explores how these expectations differed, assesses unexpected commonalities, and suggests ways to understand the divergences and convergences. This book examines thirteen countries, based on source material in ten different languages—the effort of an international team of scholars. In addition to analyses of debates, political changes, and popular speculations, we also show a wide range of pictorial representations of "the future with computers."

Current Index to Statistics, Applications, Methods and Theory

Author :
Publisher :
ISBN 13 :
Total Pages : 878 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Current Index to Statistics, Applications, Methods and Theory by :

Download or read book Current Index to Statistics, Applications, Methods and Theory written by and published by . This book was released on 1985 with total page 878 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.

Analysis of Boolean Functions

Author : Ryan O'Donnell
Publisher : Cambridge University Press
ISBN 13 : 1107038324
Total Pages : 445 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Analysis of Boolean Functions by : Ryan O'Donnell

Download or read book Analysis of Boolean Functions written by Ryan O'Donnell and published by Cambridge University Press. This book was released on 2014-06-05 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.

Art Gallery Theorems and Algorithms

Author : Joseph O'Rourke
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 312 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Art Gallery Theorems and Algorithms by : Joseph O'Rourke

Download or read book Art Gallery Theorems and Algorithms written by Joseph O'Rourke and published by Oxford University Press, USA. This book was released on 1987 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Art gallery theorems and algorithms are so called because they relate to problems involving the visibility of geometrical shapes and their internal surfaces. This book explores generalizations and specializations in these areas. Among the presentations are recently discovered theorems on orthogonal polygons, polygons with holes, exterior visibility, visibility graphs, and visibility in three dimensions. The author formulates many open problems and offers several conjectures, providing arguments which may be followed by anyone familiar with basic graph theory and algorithms. This work may be applied to robotics and artificial intelligence as well as other fields, and will be especially useful to computer scientists working with computational and combinatorial geometry.

The Probabilistic Method

Author : Noga Alon
Publisher : John Wiley & Sons
ISBN 13 : 1119062071
Total Pages : 400 pages
Book Rating : 4.1/5 (19 download)

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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 2015-11-02 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 1884 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1884 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Twenty Lectures on Algorithmic Game Theory

Author : Tim Roughgarden
Publisher : Cambridge University Press
ISBN 13 : 1316781178
Total Pages : 356 pages
Book Rating : 4.3/5 (167 download)

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Book Synopsis Twenty Lectures on Algorithmic Game Theory by : Tim Roughgarden

Download or read book Twenty Lectures on Algorithmic Game Theory written by Tim Roughgarden and published by Cambridge University Press. This book was released on 2016-08-30 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer science and economics have engaged in a lively interaction over the past fifteen years, resulting in the new field of algorithmic game theory. Many problems that are central to modern computer science, ranging from resource allocation in large networks to online advertising, involve interactions between multiple self-interested parties. Economics and game theory offer a host of useful models and definitions to reason about such problems. The flow of ideas also travels in the other direction, and concepts from computer science are increasingly important in economics. This book grew out of the author's Stanford University course on algorithmic game theory, and aims to give students and other newcomers a quick and accessible introduction to many of the most important concepts in the field. The book also includes case studies on online advertising, wireless spectrum auctions, kidney exchange, and network management.

Prediction, Learning, and Games

Author : Nicolo Cesa-Bianchi
Publisher : Cambridge University Press
ISBN 13 : 113945482X
Total Pages : 4 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Prediction, Learning, and Games by : Nicolo Cesa-Bianchi

Download or read book Prediction, Learning, and Games written by Nicolo Cesa-Bianchi and published by Cambridge University Press. This book was released on 2006-03-13 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important text and reference for researchers and students in machine learning, game theory, statistics and information theory offers a comprehensive treatment of the problem of predicting individual sequences. Unlike standard statistical approaches to forecasting, prediction of individual sequences does not impose any probabilistic assumption on the data-generating mechanism. Yet, prediction algorithms can be constructed that work well for all possible sequences, in the sense that their performance is always nearly as good as the best forecasting strategy in a given reference class. The central theme is the model of prediction using expert advice, a general framework within which many related problems can be cast and discussed. Repeated game playing, adaptive data compression, sequential investment in the stock market, sequential pattern analysis, and several other problems are viewed as instances of the experts' framework and analyzed from a common nonstochastic standpoint that often reveals new and intriguing connections.

Noise Sensitivity of Boolean Functions and Percolation

Author : Christophe Garban
Publisher : Cambridge University Press
ISBN 13 : 1107076439
Total Pages : 223 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Noise Sensitivity of Boolean Functions and Percolation by : Christophe Garban

Download or read book Noise Sensitivity of Boolean Functions and Percolation written by Christophe Garban and published by Cambridge University Press. This book was released on 2015 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to cover the theory of noise sensitivity of Boolean functions with particular emphasis on critical percolation.

Optimal Transport for Applied Mathematicians

Author : Filippo Santambrogio
Publisher : Birkhäuser
ISBN 13 : 3319208284
Total Pages : 353 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Optimal Transport for Applied Mathematicians by : Filippo Santambrogio

Download or read book Optimal Transport for Applied Mathematicians written by Filippo Santambrogio and published by Birkhäuser. This book was released on 2015-10-17 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource.

The Algorithmic Foundations of Differential Privacy

Author : Cynthia Dwork
Publisher :
ISBN 13 : 9781601988188
Total Pages : 286 pages
Book Rating : 4.9/5 (881 download)

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Book Synopsis The Algorithmic Foundations of Differential Privacy by : Cynthia Dwork

Download or read book The Algorithmic Foundations of Differential Privacy written by Cynthia Dwork and published by . This book was released on 2014 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of privacy-preserving data analysis has a long history spanning multiple disciplines. As electronic data about individuals becomes increasingly detailed, and as technology enables ever more powerful collection and curation of these data, the need increases for a robust, meaningful, and mathematically rigorous definition of privacy, together with a computationally rich class of algorithms that satisfy this definition. Differential Privacy is such a definition. The Algorithmic Foundations of Differential Privacy starts out by motivating and discussing the meaning of differential privacy, and proceeds to explore the fundamental techniques for achieving differential privacy, and the application of these techniques in creative combinations, using the query-release problem as an ongoing example. A key point is that, by rethinking the computational goal, one can often obtain far better results than would be achieved by methodically replacing each step of a non-private computation with a differentially private implementation. Despite some powerful computational results, there are still fundamental limitations. Virtually all the algorithms discussed herein maintain differential privacy against adversaries of arbitrary computational power -- certain algorithms are computationally intensive, others are efficient. Computational complexity for the adversary and the algorithm are both discussed. The monograph then turns from fundamentals to applications other than query-release, discussing differentially private methods for mechanism design and machine learning. The vast majority of the literature on differentially private algorithms considers a single, static, database that is subject to many analyses. Differential privacy in other models, including distributed databases and computations on data streams, is discussed. The Algorithmic Foundations of Differential Privacy is meant as a thorough introduction to the problems and techniques of differential privacy, and is an invaluable reference for anyone with an interest in the topic.

Bandit Algorithms

Author : Tor Lattimore
Publisher : Cambridge University Press
ISBN 13 : 1108486827
Total Pages : 537 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Bandit Algorithms by : Tor Lattimore

Download or read book Bandit Algorithms written by Tor Lattimore and published by Cambridge University Press. This book was released on 2020-07-16 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and rigorous introduction for graduate students and researchers, with applications in sequential decision-making problems.

Computational Complexity

Author : Subhash Khot
Publisher :
ISBN 13 : 9781499797503
Total Pages : 98 pages
Book Rating : 4.7/5 (975 download)

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Book Synopsis Computational Complexity by : Subhash Khot

Download or read book Computational Complexity written by Subhash Khot and published by . This book was released on 2014-06-22 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are from a course in Computational Complexity, as offered in Spring 2014 at the Courant Institute of Mathematical Sciences, a school of New York University.The professor for the course was Subhash Khot. Two guest lectures were given by Pratik Worah.The first part of the course includes bread-and-butter complexity. Definitions are given for P and NP, then space complexity, the Polynomial Hierarchy, #P, Interactive Proofs; relations between them will be discussed. The rest of the course consists of some selected topics, including Proof Complexity, Circuit Lower Bounds, Quantum Computation, Communication Complexity, and Probabilistically Checkable Proofs.

Understanding Machine Learning

Author : Shai Shalev-Shwartz
Publisher : Cambridge University Press
ISBN 13 : 1107057132
Total Pages : 415 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Understanding Machine Learning by : Shai Shalev-Shwartz

Download or read book Understanding Machine Learning written by Shai Shalev-Shwartz and published by Cambridge University Press. This book was released on 2014-05-19 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces machine learning and its algorithmic paradigms, explaining the principles behind automated learning approaches and the considerations underlying their usage.

Introduction to Property Testing

Author : Oded Goldreich
Publisher : Cambridge University Press
ISBN 13 : 1107194059
Total Pages : 473 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Introduction to Property Testing by : Oded Goldreich

Download or read book Introduction to Property Testing written by Oded Goldreich and published by Cambridge University Press. This book was released on 2017-11-23 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive and authoritative introduction to property testing, the study of super-fast algorithms for the structural analysis of large quantities of data in order to determine global properties. This book can be used both as a reference book and a textbook, and includes numerous exercises.

Comprehensive Dissertation Index

Author :
Publisher :
ISBN 13 :
Total Pages : 974 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Comprehensive Dissertation Index by :

Download or read book Comprehensive Dissertation Index written by and published by . This book was released on 1984 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vols. for 1973- include the following subject areas: Biological sciences, Agriculture, Chemistry, Environmental sciences, Health sciences, Engineering, Mathematics and statistics, Earth sciences, Physics, Education, Psychology, Sociology, Anthropology, History, Law & political science, Business & economics, Geography & regional planning, Language & literature, Fine arts, Library & information science, Mass communications, Music, Philosophy and Religion.