Incorporating a collection of recent results, Polya 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 Polya urns as a basic discrete structure growing in discrete time. The author then embeds the discrete Polya urn scheme in Poisson processes to achieve an equivalent view in continuous time, provides heuristical arguments to connect the Polya 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.

Incorporating a collection of recent results, Polya 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 Polya urns as a basic discrete structure growing in discrete time. The author then embeds the discrete Polya urn scheme in Poisson processes to achieve an equivalent view in continuous time, provides heuristical arguments to connect the Polya 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.

Algorithmics of Nonuniformity is a solid presentation about the analysis of algorithms, and the data structures that support them. Traditionally, algorithmics have been approached either via a probabilistic view or an analytic approach. The authors adopt both approaches and bring them together to get the best of both worlds and benefit from the advantage of each approach. The text examines algorithms that are designed to handle general data-sort any array, find the median of any numerical set, and identify patterns in any setting. At the same time, it evaluates "average" performance, "typical" behavior, or in mathematical terms, the expectations of the random variables that describe their operations. Many exercises are presented, which are essential since they convey additional material complementing the content of the chapters. For this reason, the solutions are more than mere answers, but explain and expand upon related concepts, and motivate further work by the reader. Highlights: A unique book that merges probability with analysis of algorithms Approaches analysis of algorithms from the angle of uniformity Non-uniformity makes more realistic models of real-life scenarios possible Results can be applied to many applications Includes many exercises of various levels of difficulty About the Authors: Micha Hofri is a Professor of Computer Science, and former department head at Worcester Polytechnic Institute. He holds a Ph.D. of Industrial Engineering (1972), all from Technion, the Israel Institute of Technology. He has 39 publications in Mathematics. Hosam Mahmoud is a Professor at, the Department of Statistics at George Washington University in Washington D.C., where he used to be the former chair. He holds an Ph.D. in Computer Science from Ohio State University. He is on the editorial board of five academic journals.