Hosam M. Mahmoud

Bio: Hosam M. Mahmoud is an academic researcher from George Washington University. The author has contributed to research in topics: Random variable & Random binary tree. The author has an hindex of 23, co-authored 135 publications receiving 2485 citations.

Evolution of random search trees

Abstract: Time Series: The Asymptotic Distribution of Auto-Correlation Coefficients On a Test of Serial Correlation for Regression Models with Lagged Dependent Variables Directional Data Analysis: Optimal Robust Estimators for the Concentration Parameter of a Von Mises-Fisher Distribution On Watson's Anova for Directions Compositional and Shape Data Analysis: Spherical Triangles Revisited New Directions in Shape Analysis Technical Problems in Inference: Tests of Fit for Logistic Models A Class of Nearly Exact Saddlepoint Approximations Spatial Statistics: A Comparison of Variogram Estimation with Covariogram Estimation Statistics and Genetics: Stochastic Comparisons Between Means and Medians for Random Variables Case Studies on Issues of Public Policy: Parameter Estimation in the Operational Modelling of HIV/AIDS. @20 Intermediate @21 E2 @12 0471 93110 1 approx 400pp approx $106.30 #49.95 @13 A Wiley UK Title. @15 PR15 @16 Mardia @17 Watson @18 Chichester P&R

Polya Urn Models

Abstract: Incorporating a collection of recent results, Plya Urn Models deals with discrete probability through the modern and evolving urn theory and its numerous applications. The book first substantiates the realization of distributions with urn arguments and introduces several modern tools, including exchangeability and stochastic processes via urns. It reviews classical probability problems and presents dichromatic Plya urns as a basic discrete structure growing in discrete time. The author then embeds the discrete Plya urn scheme in Poisson processes to achieve an equivalent view in continuous time, provides heuristical arguments to connect the Plya process to the discrete urn scheme, and explores extensions and generalizations. He also discusses how functional equations for moment generating functions can be obtained and solved. The final chapters cover applications of urns to computer science and bioscience. Examining how urns can help conceptualize discrete probability principles, this book provides information pertinent to the modeling of dynamically evolving systems where particles come and go according to governing rules.

Sorting: A Distribution Theory

Abstract: Sorting and associated concepts insertion sort shell sort bubble sort selection sort sorting by counting quick sort sample sort heap sort merge sort bucket sorts sorting non-random data epilogue answers to exercises a notation and standard results from probability theory.

On the distribution for the duration of a randomized leader election algorithm

Abstract: We investigate the duration of an elimination process for identifying a winner by coin tossing or, equivalently, the height of a random incomplete trie Applications of the process include the election of a leader in a computer network Using direct probabilistic arguments we obtain exact expressions for the discrete distribution and the moments of the height Elementary approximation techniques then yield asymptotics for the distribution We show that no limiting distribution exists, as the asymptotic expressions exhibit periodic fluctuations In many similar problems associated with digital trees, no such exact expressions can be derived We therefore outline a powerful general approach, based on the analytic techniques of Mellin transforms, Poissonization and de-Poissonization, from which distributional asymptotics for the height can also be derived In fact, it was this complex variables approach that led to our original discovery of the exact distribution Complex analysis methods are indispensable for deriving asymptotic expressions for the mean and variance, which also contain periodic terms of small magnitude

On the structure of random plane‐oriented recursive trees and their branches

Abstract: This paper is an investigation of the structural properties of random plane-oriented recursive trees and their branches. We begin by an enumeration of these trees and some general properties related to the outdegrees of nodes. Using generalized Polya urn models we study the exact and limiting distributions of the size and the number of leaves in the branches of the tree. The exact distribution for the leaves in the branches is given by formulas involving second-order Eulerian numbers. A martingale central limit theorem for a linear combination of the number of leaves and the number of internal nodes is derived. The distribution of that linear combination is a mixture of normals with a beta distribution as its mixing density. The martingale central limit theorem allows easy determination of the limit laws governing the leaves in the branches. Furthermore, the asymptotic joint distribution of the number of nodes of outdegree 0, 1 and 2 is shown to be trivariate normal. © 1993 John Wiley & Sons, Inc.

Convergence of Probability Measures

Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Analytic Combinatorics

Abstract: Analytic Combinatorics is a self-contained treatment of the mathematics underlying the analysis of discrete structures, which has emerged over the past several decades as an essential tool in the understanding of properties of computer programs and scientific models with applications in physics, biology and chemistry. Thorough treatment of a large number of classical applications is an essential aspect of the presentation. Written by the leaders in the field of analytic combinatorics, this text is certain to become the definitive reference on the topic. The text is complemented with exercises, examples, appendices and notes to aid understanding therefore, it can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study.

A Brief History of Generative Models for Power Law and Lognormal Distributions

Abstract: Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a lognormal distribution. In trying to learn enough about these distributions to settle the question, I found a rich and long history, spanning many fields. Indeed, several recently proposed models from the computer science community have antecedents in work from decades ago. Here, I briefly survey some of this history, focusing on underlying generative models that lead to these distributions. One finding is that lognormal and power law distributions connect quite naturally, and hence, it is not surprising that lognormal distributions have arisen as a possible alternative to power law distributions across many fields.

Optimizing Semantic Coherence in Topic Models

Abstract: Latent variable models have the potential to add value to large document collections by discovering interpretable, low-dimensional subspaces. In order for people to use such models, however, they must trust them. Unfortunately, typical dimensionality reduction methods for text, such as latent Dirichlet allocation, often produce low-dimensional subspaces (topics) that are obviously flawed to human domain experts. The contributions of this paper are threefold: (1) An analysis of the ways in which topics can be flawed; (2) an automated evaluation metric for identifying such topics that does not rely on human annotators or reference collections outside the training data; (3) a novel statistical topic model based on this metric that significantly improves topic quality in a large-scale document collection from the National Institutes of Health (NIH).