Random Walks in Colored Graphs PDF Download
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Author: University of California, Berkeley. Computer Science Division
Publisher:
ISBN:
Category : Graph theory
Languages : en
Pages : 15
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Book Description
We give tight upper and lower bounds on the expected cover time of a random walk in an undirected graph with colored edges. We show that for graphs with two colors the expected cover time is exponential, and that for three or more colors it is double exponential. In addition, we give polynomial bounds in a number of interesting special cases. We describe applications of these results to understanding the eigenvalues of products and weighted averages of matrices, and to problems on time-inhomogeneous Markov chains.
Author: University of California, Berkeley. Computer Science Division
Publisher:
ISBN:
Category : Graph theory
Languages : en
Pages : 15
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Book Description
We give tight upper and lower bounds on the expected cover time of a random walk in an undirected graph with colored edges. We show that for graphs with two colors the expected cover time is exponential, and that for three or more colors it is double exponential. In addition, we give polynomial bounds in a number of interesting special cases. We describe applications of these results to understanding the eigenvalues of products and weighted averages of matrices, and to problems on time-inhomogeneous Markov chains.
Author: Diane Hernek
Publisher:
ISBN:
Category :
Languages : en
Pages : 142
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Book Description
Author: Alan Frieze
Publisher: Cambridge University Press
ISBN: 1107118506
Category : Mathematics
Languages : en
Pages : 483
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Book Description
The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.
Author: Peter G. Doyle
Publisher: American Mathematical Soc.
ISBN: 1614440220
Category : Electric network topology
Languages : en
Pages : 159
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Book Description
Probability 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.
Author: Philipp Blanchard
Publisher: Springer Science & Business Media
ISBN: 364219592X
Category : Science
Languages : en
Pages : 271
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Book Description
Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks.
Author: Steven L. Salzberg
Publisher: Springer Science & Business Media
ISBN: 3642042406
Category : Science
Languages : en
Pages : 440
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Book Description
These proceedings contain papers from the 2009 Workshop on Algorithms in Bioinformatics (WABI), held at the University of Pennsylvania in Philadelphia, Pennsylvania during September 12–13, 2009. WABI 2009 was the ninth annual conference in this series, which focuses on novel algorithms that address imp- tantproblemsingenomics,molecularbiology,andevolution.Theconference- phasizes research that describes computationally e?cient algorithms and data structures that have been implemented and tested in simulations and on real data. WABI is sponsored by the European Association for Theoretical C- puter Science (EATCS) and the International Society for Computational Bi- ogy (ISCB). WABI 2009 was supported by the Penn Genome Frontiers Institute and the Penn Center for Bioinformatics at the University of Pennsylvania. For the 2009 conference, 90 full papers were submitted for review by the Program Committee, and from this strong ?eld of submissions, 34 papers were chosen for presentation at the conference and publication in the proceedings. The ?nal programcovered a wide range of topics including gene interaction n- works, molecular phylogeny, RNA and protein structure, and genome evolution.
Author: Rick Durrett
Publisher: Cambridge University Press
ISBN: 1139460889
Category : Mathematics
Languages : en
Pages : 203
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Book Description
The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.
Author: Leszek Antoni Gąsieniec
Publisher: Springer
ISBN: 303025027X
Category : Computers
Languages : en
Pages : 372
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Book Description
This book constitutes the proceedings of the 22nd International Symposium on Fundamentals of Computation Theory, FCT 2019, held in Copenhagen, Denmark, in August 2019. The 21 full papers included in this volume were carefully reviewed and selected from 45 submissions. In addition, the book contains 3 invited talks in full-paper length. The papers were organized in topical sections named: formal methods, complexity, and algorithms.
Author: Rajeev Motwani
Publisher: Cambridge University Press
ISBN: 9780521474658
Category : Computers
Languages : en
Pages : 496
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Book Description
This book presents basic tools from probability theory used in algorithmic applications, with concrete examples.
Author: Oliver C. Ibe
Publisher: John Wiley & Sons
ISBN: 1118617932
Category : Mathematics
Languages : en
Pages : 280
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Book Description
Presents an important and unique introduction to random walk theory Random walk is a stochastic process that has proven to be a useful model in understanding discrete-state discrete-time processes across a wide spectrum of scientific disciplines. Elements of Random Walk and Diffusion Processes provides an interdisciplinary approach by including numerous practical examples and exercises with real-world applications in operations research, economics, engineering, and physics. Featuring an introduction to powerful and general techniques that are used in the application of physical and dynamic processes, the book presents the connections between diffusion equations and random motion. Standard methods and applications of Brownian motion are addressed in addition to Levy motion, which has become popular in random searches in a variety of fields. The book also covers fractional calculus and introduces percolation theory and its relationship to diffusion processes. With a strong emphasis on the relationship between random walk theory and diffusion processes, Elements of Random Walk and Diffusion Processes features: Basic concepts in probability, an overview of stochastic and fractional processes, and elements of graph theory Numerous practical applications of random walk across various disciplines, including how to model stock prices and gambling, describe the statistical properties of genetic drift, and simplify the random movement of molecules in liquids and gases Examples of the real-world applicability of random walk such as node movement and node failure in wireless networking, the size of the Web in computer science, and polymers in physics Plentiful examples and exercises throughout that illustrate the solution of many practical problems Elements of Random Walk and Diffusion Processes is an ideal reference for researchers and professionals involved in operations research, economics, engineering, mathematics, and physics. The book is also an excellent textbook for upper-undergraduate and graduate level courses in probability and stochastic processes, stochastic models, random motion and Brownian theory, random walk theory, and diffusion process techniques.
