Combinatorics, Paul Erdös is Eighty
Author:
Publisher:
Published: 1996
Total Pages:
ISBN-13: 9789638022752
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Matroid Theory
Author: D. J. A. Welsh
Publisher: Courier Corporation
Published: 2010-01-01
Total Pages: 450
ISBN-13: 0486474399
DOWNLOAD EBOOKThe theory of matroids connects disparate branches of combinatorial theory and algebra such as graph and lattice theory, combinatorial optimization, and linear algebra. This text describes standard examples and investigation results, and it uses elementary proofs to develop basic matroid properties before advancing to a more sophisticated treatment. 1976 edition.
Random Walks and Electric Networks
Author: Peter G. Doyle
Publisher: American Mathematical Soc.
Published: 1984-12-31
Total Pages: 174
ISBN-13: 1614440220
DOWNLOAD EBOOKProbability theory, like much of mathematics, is indebted to physics as a source of problems and intuition for solving these problems. Unfortunately, the level of abstraction of current mathematics often makes it difficult for anyone but an expert to appreciate this fact. Random Walks and electric networks looks at the interplay of physics and mathematics in terms of an example—the relation between elementary electric network theory and random walks —where the mathematics involved is at the college level.
Random Walks on Infinite Graphs and Groups
Author: Wolfgang Woess
Publisher: Cambridge University Press
Published: 2000-02-13
Total Pages: 350
ISBN-13: 0521552923
DOWNLOAD EBOOKThe main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Author: Moses Charikar
Publisher: Springer
Published: 2007-08-28
Total Pages: 636
ISBN-13: 3540742085
DOWNLOAD EBOOKThis volume presents the refereed proceedings of the 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and the 11th International Workshop on Randomization and Computation. The papers cover design and analysis of approximation algorithms, hardness of approximation, small space and data streaming algorithms, sub-linear time algorithms, embeddings and metric space methods, and much more.
Probability on Graphs
Author: Geoffrey Grimmett
Publisher: Cambridge University Press
Published: 2018-01-25
Total Pages: 279
ISBN-13: 1108542999
DOWNLOAD EBOOKThis introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Computing and Combinatorics
Author: Hung Q. Ngo
Publisher: Springer Science & Business Media
Published: 2009-07-11
Total Pages: 552
ISBN-13: 3642028829
DOWNLOAD EBOOKThe papers in this volume were selected for presentation at the 15th Annual InternationalComputing and CombinatoricsConference (COCOON 2009), held during July 13-15, 2009 in Niagara Falls, New York, USA. Previous meetings of this conference were held in Xian (1995), Hong Kong (1996), Shanghai (1997), Taipei(1998), Tokyo(1999), Sydney(2000), Guilin(2001), Singapore(2002), Big Sky (2003), Jeju Island (2004), Kunming (2005), Taipei (2006), Alberta (2007), and Dalian (2008). In response to the Call for Papers, 125 extended abstracts (not counting withdrawn papers) were submitted from 28 countries and regions, of which 51 were accepted. Authors of the submitted papers were from Cyprus (1), The Netherlands (1), Bulgaria (1), Israel (1), Vietnam (2), Finland (1), Puerto Rico (2), Australia (4), Norway (4), Portugal (1) Spain (2), France (16), Republic of Korea(3), Singapore(2), Italy(6), Iran, (4), Greece(7), Poland(4), Switzerland (8), Hong Kong (10), UK (12), India (7), Taiwan (18), Canada (23), China (19), Japan (39), Germany (44), and the USA (77). The submitted papers were evaluated by an international Technical P- gram Committee (TPC) consisting of Srinivas Aluru (Iowa State University, USA), Lars Arge (University of Aarhus, Denmark), Vikraman Arvind (Ins- tute of Mathematical Sciences, India), James Aspnes (Yale University, USA), Mikhail Atallah (Purdue University, USA), Gill Barequet (Technion - Israel - stitute of Technology, Israel), Michael Brudno (University of Toronto, Canada), Jianer Chen (Texas A & M, USA), Bhaskar DasGupta (University of Illinois at Chicago, USA), Anupam Gupta (Carnegie Mellon University, USA), Lane A.
Combinatorial Algorithms
Author: Zsuzsanna Lipták
Publisher: Springer
Published: 2016-03-09
Total Pages: 377
ISBN-13: 3319295160
DOWNLOAD EBOOKThis book constitutes the thoroughly refereed post-workshop proceedings for the 26 International Workshop on combinatorial Algorithms, IWOCA 2015, held in Verona, Italy, in October 2015. The 29 revised full papers presented were carefully reviewed and selected from a total of 90 submissions. The topics of the papers include algorithms and data structures (including sequential, parallel, distributed, approximation, probabilistic, randomised, and on-line algorithms), algorithms on strings and graphs; applications (bioinformatics, music analysis, networking, and others); combinatorics on words; combinatorial enumeration; combinatorial optimization; complexity theory; computational biology; compression and information retrieval; cryptography and information security; decompositions and combinatorial designs; discrete and computational geometry; graph drawing and labeling; graph theory.
Foundations of Data Science
Author: Avrim Blum
Publisher: Cambridge University Press
Published: 2020-01-23
Total Pages: 433
ISBN-13: 1108617360
DOWNLOAD EBOOKThis 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.
Matrix Inequalities for Iterative Systems
Author: Hanjo Taubig
Publisher: CRC Press
Published: 2017-02-03
Total Pages: 219
ISBN-13: 1498777791
DOWNLOAD EBOOKThe book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.
