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1 
Sparse random graphs methods, structure, and heuristicsFernholz, Daniel Turrin, 1976 28 August 2008 (has links)
This dissertation is an algorithmic study of sparse random graphs which are parametrized by the distribution of vertex degrees. Our contributions include: a formula for the diameter of various sparse random graphs, including the ErdösRényi random graphs G[subscript n,m] and G[subscript n,p] and certain powerlaw graphs; a heuristic for the korientability problem, which performs optimally for certain classes of random graphs, again including the ErdösRényi models G[subscript n,m] and G[subscript n,p]; an improved lower bound for the independence ratio of random 3regular graphs. In addition to these structural results, we also develop a technique for reasoning abstractly about random graphs by representing discrete structures topologically.

2 
Sparse random graphs methods, structure, and heuristicsFernholz, Daniel Turrin, January 1900 (has links)
Thesis (Ph. D.)University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

3 
Limit theorems for random measures with applicationsSolomon, Wiremu. January 1985 (has links)
Thesis (Ph. D.)University of WisconsinMadison, 1985. / Typescript. Vita. eContent providerneutral record in process. Description based on print version record. Includes bibliographical references.

4 
Aspects of random matrix theory concentration and subsequence problems /Xu, Hua. January 2008 (has links)
Thesis (Ph.D)Mathematics, Georgia Institute of Technology, 2009. / Committee Chair: Christian Houdre; Committee Member: Heinrich Matzinger; Committee Member: Ionel Popescu; Committee Member: Mikhail Lifshits; Committee Member: Robert Foley; Committee Member: Vladimir I Kolchinskii; Committee Member: Yuri Bakhtin. Part of the SMARTech Electronic Thesis and Dissertation Collection.

5 
Special problems in random graphsRuiz Esparza, Eduardo. January 1900 (has links)
Thesis (Ph. D.)University of California, Berkeley, 1981. / Typescript. eContent providerneutral record in process. Description based on print version record. Includes bibliographical references (p. 4648).

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The theory of L[superscript p]random measures /Revesz, Michael Bela, January 2000 (has links)
Thesis (Ph. D.)University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 208211) and indexes. Available also in a digital version from Dissertation Abstracts.

7 
The inversion method in random variate generation /Yuen, Colleen. January 1982 (has links)
No description available.

8 
The inversion method in random variate generation /Yuen, Colleen. January 1982 (has links)
No description available.

9 
A Simulation Study of Walks in Large Social GraphsAnwar, Shahed 05 November 2015 (has links)
Online Social Networks (OSNs) such as Facebook, Twitter, and YouTube are among the most popular sites on the Internet. Billions of users are connected through these sites, building strong and effective communities to share views and ideas, and make recommendations nowadays. Therefore, by choosing an appropriate userbase from billions of people is required to analyze the structure and key characteristics of the large social graphs to improve current systems and to design new applications. For this reason, node sampling technique plays an important role to study largescale social networks. As a basic requirement, the sampled nodes and their links should possess similar statistical features of the original network, otherwise the conclusion drawn from the sampled network may not be appropriate for the entire population. Hence, good sampling strategies are key to many online social network applications. For instance, before introducing a new product or adding new feature(s) of a product to the online social network community, that specific new product or the additional feature has to be exposed to only a small set of users, who are carefully chosen to represent the complete set of users. As such, different random walkbased sampling techniques have been introduced to produce samples of nodes that not only are internally wellconnected but also capture the statistical features of the whole network. Traditionally, walkbased techniques do not have the restriction on the number of times that a node can be revisited while sampling. This may lead to an inefficient sampling method, because the walk may be "stuck" at a small number of highdegree nodes without being able to reach out to the rest of the nodes. A random walk, even after a large number of hops, may not be able to obtain a sampled network that captures the statistical features of the entire network.
In this thesis, we propose two walkbased sampling techniques to address the above problem, called KAvoiding Random Walk (KARW) and NeighborhoodAvoiding Random Walk (NARW). With KARW, the number of times that a node can be revisited is constrained within a given number K. With NARW, the random walk works in a "jump" fashion, since the walk starts outside of the Nhop neighborhood from the current node chosen randomly. By avoiding the current nodes neighboring area of levelN, NARW is expected to reach out the other nodes within the entire network quickly. We apply these techniques to construct multiple independent subgraphs from a social graph, consisting of 63K users with around a million connections between users collected from a Facebook dataset. By simulating our proposed strategies, we collect performance metrics and compare the results with the current stateoftheart sampling techniques (Uniform Random Sampling, Random Walk, and Metropolis Hastings Random Walk). We also calculate some of the key statistical features (i.e., degree distribution, betweenness centrality, closeness centrality, modularity, and clustering coefficient) of the sampled graphs to get an idea about the network structures that essentially represent the original social graph. / Graduate / 0984 / shahed.anwar@gmail.com

10 
Rapid Prototyping and Design of a Fast Random Number GeneratorFranco, Juan 12 1900 (has links)
Information in the form of online multimedia, bank accounts, or password usage for diverse applications needs some form of security. the core feature of many security systems is the generation of true random or pseudorandom numbers. Hence reliable generators of such numbers are indispensable. the fundamental hurdle is that digital computers cannot generate truly random numbers because the states and transitions of digital systems are well understood and predictable. Nothing in a digital computer happens truly randomly. Digital computers are sequential machines that perform a current state and move to the next state in a deterministic fashion. to generate any secure hash or encrypted word a random number is needed. But since computers are not random, random sequences are commonly used. Random sequences are algorithms that generate a pattern of values that appear to be random but after some time start repeating. This thesis implements a digital random number generator using MATLAB, FGPA prototyping, and custom silicon design. This random number generator is able to use a truly random CMOS source to generate the random number. Statistical benchmarks are used to test the results and to show that the design works. Thus the proposed random number generator will be useful for online encryption and security.

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