“Draft:Hosam Mahmoud (Probabilist)”的意思、由来-开放百科全书

Hosam M. Mahmoud (born April 16, 1954 in Cairo, Eygpt) is an eminent Egyptian-American probabilist best known for his work on Pólya urns and random trees. He received a B.Sc. in Electrical Engineering in 1976, and another B.Sc. in Mathematics in 1979, both from Cairo University, Egypt. Later on, he went to Ohio State University, where he received an M.S. and a Ph.D., both in Computer Science. He has been a faculty member of the Department of Statistics at The George Washington University since 1983. Hse served as department chair from 1998 to 2001. H. Mahmoud has an international reputation as a probabilist as well as a computer scientist. He has made several seminal contributions in the areas of randomized algorithms and random graphs. He is especially well known for his prominent contributions to Pólya urns and random trees. He has published more than 100 research articles in prestigious national and international journals, and has authored four books and edited volumes. He has been a visiting professor at several top institutions and research centers around the world, including Centre de Recerca Matemàtica (Bellaterra, Spain), Institut national de recherche et de sécurité (Rocquencourt, France), Princeton University (Princeton, NJ), Institute of Statistical Mathematics (Tokyo, Japan), and Purdue University (West Lafayette, IN). H. Mahmoud is an elected member of International Statistical Institute.

Contributions to science

H. Mahmoud has worked on the analysis of random networks and random graphs during and after his dissertation at Ohio State University. His research is inspired by a seminal book, The Art of Computer Programming^[1] by Professor Donald E. Knuth from Stanford University. H. Mahmoud is committed to developing rigorous methods to uncover a distributional theory for random structures and algorithms, which form the foundation in computer science and discrete mathematics. It is evident that theoretical analysis of the exact and limiting distributions underlying random structures and algorithms helps applied scientists precisely characterizing the random models and properties of primary interest. Mahmoud's contribution is manifested by a large number of theorems in areas like searching, sorting, random tree models, random graphs and Pólya urn model, mostly are listed and summarized in his books^[2]^[3]^[4].

H. Mahmoud has also made contributions to a rather different methodology for analyzing random structures—analytic methods. The essence of this analytic toolkit is presented in one of his books^[3]. The kit comprises a program that goes in two layers of transformations: the Poisson transform (Poissonization in the jargon) and the Mellin transform, and is followed by their inverse operations. Mahmoud has worked on a large number of problems of this nature and his work led to a series of systematic methods (for example, a novel theory of moving poles ^[5]^[6]^[7]^[8]^[9]^[10]). This series of methods is also discussed in Mahmoud's new book^[11].

Pólya urn model

One of Mahmoud's most significant contributions to science is his work on Pólya urns and extensions. Pólya urn, named after the late Hungarian mathematician George Pólya, is a classic probabilistic model depicted by an urn containing a certain number of marbles of different types (often represented by color). The primary interest is the distribution of the number of marbles of each time as the urn evolves according to some pertinent rules of drawing marbles therein. Precusory applications of Pólya urns are to model disease contagion^[12] and gas diffusion^[13]. In Mahmouds's book^[4], a plethora of urn models are investigated, and a large number of theorems are derived and proved. Several classes of urn models are nonclassic, and made connections to random trees, random graphs, and generally random combinatorial objects; for example, random bucket trees^[14] and generalized random recursive trees^[15].

Selected papers

H. Mahmoud has published more than 100 research articles, many of which were written with his Ph.D. students. Besides, H. Mahmoud has single authored a large amount of papers published on top peer-refereed journals.

Representative papers with students

Representative single-authored papers

Awards, honors and services

H. Mahmoud is an elected member of International Statistical Institute. He serves as associate editor for many internationally reputed journals in applied probability and related fields, including Journal of Applied Probability, Advances in Applied Probability, Methodologies and Computing in Applied Probability, and The Annals of the Institute of Statistical Mathematics. In addition, he has chaired or joined as a member of steering committees or professional committees for a large number of national and international conferences, including International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, International Workshop on Applied Probability, and Meeting on Analytic Algorithmics and Combinatorics.

Bibliography

References

1. ^{{cite book | last=Knuth | first=D. | authorlink=Donald Knuth | date=1998 | title=The Art of Computer Programming | volume = III | edition = 2 | publisher=Addison-Wesley Professional | isbn= 9780201896855}}
2. ^{{cite book | last=Mahmoud | first=H. | authorlink=Hosam Mahmoud | date=1991 | title=Evolution of Random Search Trees | publisher=Wiley | isbn= 9780471532286}}
3. ^¹{{cite book | last=Mahmoud | first=H. | authorlink=Hosam Mahmoud | date=2000 | title=Sorting: A Distribution Theory | publisher=Wiley | isbn= 9780471327103}}
4. ^¹{{cite book | last=Mahmoud | first=H. | authorlink=Hosam Mahmoud | date=2008 | title=Pólya urn model | publisher=CRC Press | doi=10.1201/9781420059847.ch3 | isbn= 9781420059830}}
5. ^{{cite journal | last1=Christophi | first1=C. |last2=Mahmoud |first2=H. | authorlink2=Hosam Mahmoud | date=2005 |title=The oscillatory distribution of distances in random tries |url=https://projecteuclid.org/download/pdfview_1/euclid.aoap/1115137985 | format=PDF |journal=The Annals of Applied Probability |volume=15 |issue=2 |pages=1536-1564 |doi=10.1214/105051605000000106}}
6. ^{{cite journal | last1=Aguech | first1=R. | last2=Lasmar | first2=N. | last3=Mahmoud |first3=H. | authorlink3=Hosam Mahmoud | date=2006 |title=Limit distribution of distances in biased random tries |url=https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2BF3722794009EBCCF4BB0D1EC30E053/S0021900200001704a.pdf/limit_distribution_of_distances_in_biased_random_tries.pdf | format=PDF |journal=Journal of Applied Probability |volume=43 |issue=2 |pages=377-390 |doi=10.1017/s0021900200001704 }}
7. ^{{cite journal | last1=Aguech | first1=R. | last2=Lasmar | first2=N. | last3=Mahmoud |first3=H. | authorlink3=Hosam Mahmoud | date=2006 |title=Distances in random digital search trees |url=https://link.springer.com/content/pdf/10.1007%2Fs00236-006-0019-7.pdf | format=PDF |journal=Acta Informatica |volume=43 |issue=4 |pages=243-264 |doi=10.1017/s0021900200001704 }}
8. ^{{cite journal | last1=Christophi | first1=C. |last2=Mahmoud |first2=H. | authorlink2=Hosam Mahmoud | date=2007 |title=On climbing tries |url=https://www.cambridge.org/core/services/aop-cambridge-core/content/view/0882E9D1151A8B0ED19858E814E4533D/S0269964808000089a.pdf/on_climbing_tries.pdf | format=PDF |journal=Probability in the Engineering and Informational Sciences |volume=22 |issue=1 |pages=133-149 |doi=10.1017/S0269964808000089}}
9. ^{{cite journal | last=Mahmoud |first=H. | authorlink=Hosam Mahmoud | date=2008 |title=Imbalance in random digital trees |url=https://link.springer.com/content/pdf/10.1007%2Fs11009-008-9087-1.pdf | format=PDF |journal=Methodology and Computing in Applied Probability |volume=11 |issue=2 |pages=231-247 |doi=10.1007/s11009-008-9087-1 }}
10. ^{{cite journal | last1=Gaither | first1=J. | last2=Mahmoud | first2=H. | last3=Ward |first3=M. | authorlink2=Hosam Mahmoud | date=2016 |title=On the variety of shapes in digital trees |url=https://link.springer.com/content/pdf/10.1007%2Fs10959-016-0700-x.pdf | format=PDF |journal=Journal of Theoretical Probability |volume=30 |issue=4 |pages=1225-1254 |doi=10.1007/s10959-016-0700-x }}
11. ^{{cite book | last1=Hofri | first1=M.| last2=Mahmoud | first2=H. | authorlink=Hosam Mahmoud | date=2018 | title=Algorithmics of Nonuniformity—Tools and Paradigms | publisher=CRC Press | isbn= 9781498750721 }}
12. ^{{cite journal |last1=Eggenberger |first1=F. |last2=Pólya |first2=G. | authorlink2=George Pólya | date=1923 |title=Über die Statistik verketteter Vorgänge |url=https://onlinelibrary.wiley.com/doi/pdf/10.1002/zamm.19230030407 |journal=Zeitschrift für Angewandte Mathematik und Mechanik |volume=3 |issue=4 |pages=279-289 |doi=10.1002/zamm.19230030407}}
13. ^{{cite journal |last1=Ehrenfest |first1=P. |last2=Ehrenfest |first2=T. | date=1907 |title=Über zwei bekannte Einwände gegen das Boltzmannsche H-Theorem |journal=Physikalische Zeitschrift | volume=8 | pages=311-314}}
14. ^{{cite journal |last=Mahmoud |first=H. | authorlink=Hosam Mahmoud | date=2002 |title=The size of random bucket trees via urn models |url=https://link.springer.com/article/10.1007/s00236-002-0096-1 |journal=Acta Informatica |volume=38 |issue=11-12 |pages=818-838 |doi=10.1007/s00236-002-0096-1}}
15. ^{{cite journal |last=Mahmoud |first=H. | authorlink=Hosam Mahmoud | date=2012 |title=The degree profile in some classes of random graphs that generalize recursive trees |url=https://link.springer.com/article/10.1007/s11009-012-9312-9 |journal=Methodology and Computing in Applied Probability |volume=16 |issue=3 |pages=527-538 |doi=10.1007/s11009-012-9312-9}}