The Interface of Three Areas of Computer Science with the Mathematical Sciences

Summary of a Workshop

Dianne P. O'Leary,

Member, and

Scott T. Weidman,

Director

Board on Mathematical Sciences

National Research Council

National Academy Press
Washington, D.C.



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The Interface of Three Areas of Computer Science with the Mathematical Sciences: Summary of a Workshop The Interface of Three Areas of Computer Science with the Mathematical Sciences Summary of a Workshop Dianne P. O'Leary, Member, and Scott T. Weidman, Director Board on Mathematical Sciences National Research Council National Academy Press Washington, D.C.

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The Interface of Three Areas of Computer Science with the Mathematical Sciences: Summary of a Workshop NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competences and with regard for appropriate balance. This summary is based on work supported by the National Research Council and by the National Science Foundation under Grant No. DMS-0084252. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Cover image: Copyright 2000 by Donald Towsley. Used by permission. Copyright2000by the National Academy of Sciences. All rights reserved. Additional copies of this report are available from: Board on Mathematical Sciences National Research Council 2101 Constitution Avenue, N.W. Washington, D.C. 20418 Printed in the United States of America

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The Interface of Three Areas of Computer Science with the Mathematical Sciences: Summary of a Workshop THE NATIONAL ACADEMIES National Academy of Sciences National Academy of Engineering Institute of Medicine National Research Council The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Bruce M. Alberts is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievements of engineers. Dr. William A. Wulf is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Kenneth I. Shine is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy's purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Bruce M. Alberts and Dr. William A. Wulf are chairman and vice chairman, respectively, of the National Research Council.

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The Interface of Three Areas of Computer Science with the Mathematical Sciences: Summary of a Workshop SPONSORING BOARDS Board on Mathematical Sciences Robert MacPherson, Institute for Advanced Study, Chair Lynne Billard, University of Georgia George Casella, Cornell University Jennifer Chayes, Microsoft Research Robert Fefferman, University of Chicago C. William Gear, NEC Research Institute Raymond L. Johnson, University of Maryland Iain M. Johnstone, Stanford University Dianne P. O'Leary, University of Maryland Alan S. Perelson, Los Alamos National Laboratory William R. Pulleyblank, IBM T.J. Watson Research Center Karen E. Smith, University of Michigan Daniel W. Stroock, Massachusetts Institute of Technology De Witt L. Sumners, Florida State University Peter J. Bickel, University of California at Berkeley, Chair, Committee on Applied and Theoretical Statistics Computer Science and Telecommunications Board David D. Clark, Massachusetts Institute of Technology, Chair James Chiddix, Time Warner Cable John M. Cioffi, Stanford University Elaine Cohen, University of Utah Bruce Croft, University of Massachusetts, Amherst Susan L. Graham, University of California at Berkeley Judith Hempel, University of California at San Francisco Jeffrey M. Jaffe, Lucent Technologies Anna Karlin, University of Washington Butler W. Lampson, Microsoft Corporation Edward D. Lazowska, University of Washington David Liddle, U.S. Venture Partners Tom M. Mitchell, WhizBang! Labs, Inc. Donald Norman, UNext.com Raymond Ozzie, Groove Networks David Patterson, University of California at Berkeley Charles Simonyi, Microsoft Corporation Burton Smith, Cray, Inc. Terry Smith, University of California at Santa Barbara Lee Sproull, Boston University

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The Interface of Three Areas of Computer Science with the Mathematical Sciences: Summary of a Workshop Preface On April 28-29, 2000, the Board on Mathematical Sciences (BMS) and the Computer Science and Telecommunications Board of the National Research Council co-sponsored a workshop on the interface between the mathematical sciences and three areas of computer science: network traffic modeling, computer vision, and data mining. The workshop 's goal was to identify some open research questions in the mathematical sciences whose solution would contribute to important unsolved problems in those fields of computer science. The 48 participants (p. 18) engaged in lively discussions, and at least 36 research challenges of a mathematical, statistical, or probabilistic nature were identified. To make those challenges more widely known, Dianne P. O'Leary of the University of Maryland, a member of the BMS and an organizer of the workshop, developed this summary with the help of Scott Weidman, BMS director. This summary represents the viewpoint of its authors only and should not be taken as a consensus report of the BMS or of the National Research Council. We are grateful to the following individuals who reviewed this summary: Ronald Douglas, Texas A&M University; Anna Karlin, University of Washington; Jon Kleinberg, Cornell University; Stanley Osher, University of California at Los Angeles; and Walter Willinger, AT&T-Research. Funding for the workshop was provided by the National Research Council and the National Science Foundation. The workshop organizers were Peter J. Bickel, University of California at Berkeley; Jennifer Chayes, Microsoft Research; C. William Gear, NEC Research Institute; Dianne P. O'Leary, University of Maryland; and William R. Pulleyblank, IBM T.J. Watson Research Center. We thank Don Towsley of the University of Massachusetts for the cover illustration. This report summarizes each of the workshop's three sessions—network traffic modeling, computer vision, and data mining and search. Other workshop materials, including most of the presentations, are available online at http://www.cs.umd.edu/~oleary/nasworkshop.html/ and also through a link at http://www.nas.edu/bms. References for further reading are also listed there.