اطلاعيه

به دعوت انجمن آمار ايران و خانه رياضيات اصفهان آقاي پرفسور حسام محمود استاد گروه آمار جورج واشينگتن از25 فروردين ماه لغايت 15 ارديبهشت ماه 90 در ايران خواهند بود.

به منظور بهره­گيري از حضور ايشان در ايران

-         با همكاري قطب داده های ترتیبی و فضایی گروه آمار دانشگاه فردوسي مشهد، نامبرده يك سخنراني در روز چهارشنبه 31/01/90 از ساعت 10 الي 11 تحت عنوان زير ايراد خواهند كرد.

Perpetuities in the Analysis of Algorithms for order statistics 

-         با همكاري خانه رياضيات اصفهان، نامبرده يك سخنراني در روز شنبه 3/02/1390 از ساعت 18 الي 19 تحت عنوان زير در محل خانه رياضيات اصفهان ايراد خواهند كرد.

The class of tenable zero Balanced Polya Urn Schemes: Characterization and Gaussian Phases                                                          

-         با همكاري گروه امار دانشگاه شهيد بهشتي، نامبرده يك سخنراني در روز چهارشنبه 07/02/1390 از ساعت 13 الي 14 تحت عنوان زير در آمفي­تأتر دانشکده علوم ریاضی ايراد خواهند كرد.

Phases in urn models for demographic mixing

چکیده سخنرانی های ایشان به شرح ذیل است:

Mashhad talk:

Perpetuities in the Analysis of Algorithms for Order Statistics

Professor Hosam M. Mahmoud
        Department of Statistics, George Washington University

Wednesday, April 20, 2011

10-11 

  We analyze algorithms for finding order statistics and show that "perpetuities," which are entities that appear in mathematical finance, play a central role. Two one-sided algorithms for finding order statistics are considered: Quick Select (a variant of Quick Sort) and Radix Select (a variant of Radix Sort). We analyze these algorithms when they find an element with a randomly selected rank. This kind of grand average provides a smoothing over all individual distributions for specific fixed order statistics. We show in both cases that the number of swaps (suitably scaled) is perpetuity. In the case of radix Select we detect a phase change between biased and unbiased cases.

 

The tools for this proof include Poissonization, the Mellin transform, depossonization and contraction in the Wasserstein metric space, and identifying the limit as the fixed-point solution of a distributional equation.

 

 Isfahan talk:

The class of tenable zero balanced Pólya urn schemes:
characterization and Gaussian phases

Professor Hosam M. Mahmoud
        Department of Statistics, George Washington University

Saturday, Apri 23, 2011

17:30-18:30

We study a class of tenable irreducible nondegenerate zero-balanced Polya urn schemes. We give a full characterization of the class by sufficient and necessary conditions. Only forms with a certain cyclic structure in their replacement matrix are admissible. The scheme has a steady state into proportions governed by the principal (left) eigenvector of the average replacement matrix. We study the gradual change for any such urn containing n (going to infinity) balls from the initial condition to the steady state.
We look at the status of an urn starting with a positive proportion of each color
after j (n) draws. We identify three phases of j (n): The growing sub linear, the linear, and the super linear. In the growing sub linear phase the number of
balls of different colors has an asymptotic joint multivariate normal distribution,
with mean and covariance structure that are influenced by the initial conditions.
In the linear phase a different multivariate normal distribution kicks in, in which the influence of the initial conditions is attenuated. The steady state is not a good approximation until a certain super linear amount of time has elapsed. We give interpretations for how the results in different phases conjoin at the “seam lines”. In fact, these Gaussian phases are all manifestations of one master theorem. The results are obtained via multivariate martingale theory. We conclude with some illustrating examples.

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