Valiant Transcript Final with Timestamps
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Efficient Algorithms with Asymmetric Read and Write Costs
Efficient Algorithms with Asymmetric Read and Write Costs Guy E. Blelloch1, Jeremy T. Fineman2, Phillip B. Gibbons1, Yan Gu1, and Julian Shun3 1 Carnegie Mellon University 2 Georgetown University 3 University of California, Berkeley Abstract In several emerging technologies for computer memory (main memory), the cost of reading is significantly cheaper than the cost of writing. Such asymmetry in memory costs poses a fun- damentally different model from the RAM for algorithm design. In this paper we study lower and upper bounds for various problems under such asymmetric read and write costs. We con- sider both the case in which all but O(1) memory has asymmetric cost, and the case of a small cache of symmetric memory. We model both cases using the (M, ω)-ARAM, in which there is a small (symmetric) memory of size M and a large unbounded (asymmetric) memory, both random access, and where reading from the large memory has unit cost, but writing has cost ω 1. For FFT and sorting networks we show a lower bound cost of Ω(ωn logωM n), which indicates that it is not possible to achieve asymptotic improvements with cheaper reads when ω is bounded by a polynomial in M. Moreover, there is an asymptotic gap (of min(ω, log n)/ log(ωM)) between the cost of sorting networks and comparison sorting in the model. This contrasts with the RAM, and most other models, in which the asymptotic costs are the same. We also show a lower bound for computations on an n × n diamond DAG of Ω(ωn2/M) cost, which indicates no asymptotic improvement is achievable with fast reads. -
Computational Learning Theory: New Models and Algorithms
Computational Learning Theory: New Models and Algorithms by Robert Hal Sloan S.M. EECS, Massachusetts Institute of Technology (1986) B.S. Mathematics, Yale University (1983) Submitted to the Department- of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 1989 @ Robert Hal Sloan, 1989. All rights reserved The author hereby grants to MIT permission to reproduce and to distribute copies of this thesis document in whole or in part. Signature of Author Department of Electrical Engineering and Computer Science May 23, 1989 Certified by Ronald L. Rivest Professor of Computer Science Thesis Supervisor Accepted by Arthur C. Smith Chairman, Departmental Committee on Graduate Students Abstract In the past several years, there has been a surge of interest in computational learning theory-the formal (as opposed to empirical) study of learning algorithms. One major cause for this interest was the model of probably approximately correct learning, or pac learning, introduced by Valiant in 1984. This thesis begins by presenting a new learning algorithm for a particular problem within that model: learning submodules of the free Z-module Zk. We prove that this algorithm achieves probable approximate correctness, and indeed, that it is within a log log factor of optimal in a related, but more stringent model of learning, on-line mistake bounded learning. We then proceed to examine the influence of noisy data on pac learning algorithms in general. Previously it has been shown that it is possible to tolerate large amounts of random classification noise, but only a very small amount of a very malicious sort of noise. -
Four Results of Jon Kleinberg a Talk for St.Petersburg Mathematical Society
Four Results of Jon Kleinberg A Talk for St.Petersburg Mathematical Society Yury Lifshits Steklov Institute of Mathematics at St.Petersburg May 2007 1 / 43 2 Hubs and Authorities 3 Nearest Neighbors: Faster Than Brute Force 4 Navigation in a Small World 5 Bursty Structure in Streams Outline 1 Nevanlinna Prize for Jon Kleinberg History of Nevanlinna Prize Who is Jon Kleinberg 2 / 43 3 Nearest Neighbors: Faster Than Brute Force 4 Navigation in a Small World 5 Bursty Structure in Streams Outline 1 Nevanlinna Prize for Jon Kleinberg History of Nevanlinna Prize Who is Jon Kleinberg 2 Hubs and Authorities 2 / 43 4 Navigation in a Small World 5 Bursty Structure in Streams Outline 1 Nevanlinna Prize for Jon Kleinberg History of Nevanlinna Prize Who is Jon Kleinberg 2 Hubs and Authorities 3 Nearest Neighbors: Faster Than Brute Force 2 / 43 5 Bursty Structure in Streams Outline 1 Nevanlinna Prize for Jon Kleinberg History of Nevanlinna Prize Who is Jon Kleinberg 2 Hubs and Authorities 3 Nearest Neighbors: Faster Than Brute Force 4 Navigation in a Small World 2 / 43 Outline 1 Nevanlinna Prize for Jon Kleinberg History of Nevanlinna Prize Who is Jon Kleinberg 2 Hubs and Authorities 3 Nearest Neighbors: Faster Than Brute Force 4 Navigation in a Small World 5 Bursty Structure in Streams 2 / 43 Part I History of Nevanlinna Prize Career of Jon Kleinberg 3 / 43 Nevanlinna Prize The Rolf Nevanlinna Prize is awarded once every 4 years at the International Congress of Mathematicians, for outstanding contributions in Mathematical Aspects of Information Sciences including: 1 All mathematical aspects of computer science, including complexity theory, logic of programming languages, analysis of algorithms, cryptography, computer vision, pattern recognition, information processing and modelling of intelligence. -
January 2011 Prizes and Awards
January 2011 Prizes and Awards 4:25 P.M., Friday, January 7, 2011 PROGRAM SUMMARY OF AWARDS OPENING REMARKS FOR AMS George E. Andrews, President BÔCHER MEMORIAL PRIZE: ASAF NAOR, GUNTHER UHLMANN American Mathematical Society FRANK NELSON COLE PRIZE IN NUMBER THEORY: CHANDRASHEKHAR KHARE AND DEBORAH AND FRANKLIN TEPPER HAIMO AWARDS FOR DISTINGUISHED COLLEGE OR UNIVERSITY JEAN-PIERRE WINTENBERGER TEACHING OF MATHEMATICS LEVI L. CONANT PRIZE: DAVID VOGAN Mathematical Association of America JOSEPH L. DOOB PRIZE: PETER KRONHEIMER AND TOMASZ MROWKA EULER BOOK PRIZE LEONARD EISENBUD PRIZE FOR MATHEMATICS AND PHYSICS: HERBERT SPOHN Mathematical Association of America RUTH LYTTLE SATTER PRIZE IN MATHEMATICS: AMIE WILKINSON DAVID P. R OBBINS PRIZE LEROY P. S TEELE PRIZE FOR LIFETIME ACHIEVEMENT: JOHN WILLARD MILNOR Mathematical Association of America LEROY P. S TEELE PRIZE FOR MATHEMATICAL EXPOSITION: HENRYK IWANIEC BÔCHER MEMORIAL PRIZE LEROY P. S TEELE PRIZE FOR SEMINAL CONTRIBUTION TO RESEARCH: INGRID DAUBECHIES American Mathematical Society FOR AMS-MAA-SIAM LEVI L. CONANT PRIZE American Mathematical Society FRANK AND BRENNIE MORGAN PRIZE FOR OUTSTANDING RESEARCH IN MATHEMATICS BY AN UNDERGRADUATE STUDENT: MARIA MONKS LEONARD EISENBUD PRIZE FOR MATHEMATICS AND OR PHYSICS F AWM American Mathematical Society LOUISE HAY AWARD FOR CONTRIBUTIONS TO MATHEMATICS EDUCATION: PATRICIA CAMPBELL RUTH LYTTLE SATTER PRIZE IN MATHEMATICS M. GWENETH HUMPHREYS AWARD FOR MENTORSHIP OF UNDERGRADUATE WOMEN IN MATHEMATICS: American Mathematical Society RHONDA HUGHES ALICE T. S CHAFER PRIZE FOR EXCELLENCE IN MATHEMATICS BY AN UNDERGRADUATE WOMAN: LOUISE HAY AWARD FOR CONTRIBUTIONS TO MATHEMATICS EDUCATION SHERRY GONG Association for Women in Mathematics ALICE T. S CHAFER PRIZE FOR EXCELLENCE IN MATHEMATICS BY AN UNDERGRADUATE WOMAN FOR JPBM Association for Women in Mathematics COMMUNICATIONS AWARD: NICOLAS FALACCI AND CHERYL HEUTON M. -
Navigability of Small World Networks
Navigability of Small World Networks Pierre Fraigniaud CNRS and University Paris Sud http://www.lri.fr/~pierre Introduction Interaction Networks • Communication networks – Internet – Ad hoc and sensor networks • Societal networks – The Web – P2P networks (the unstructured ones) • Social network – Acquaintance – Mail exchanges • Biology (Interactome network), linguistics, etc. Dec. 19, 2006 HiPC'06 3 Common statistical properties • Low density • “Small world” properties: – Average distance between two nodes is small, typically O(log n) – The probability p that two distinct neighbors u1 and u2 of a same node v are neighbors is large. p = clustering coefficient • “Scale free” properties: – Heavy tailed probability distributions (e.g., of the degrees) Dec. 19, 2006 HiPC'06 4 Gaussian vs. Heavy tail Example : human sizes Example : salaries µ Dec. 19, 2006 HiPC'06 5 Power law loglog ppk prob{prob{ X=kX=k }} ≈≈ kk-α loglog kk Dec. 19, 2006 HiPC'06 6 Random graphs vs. Interaction networks • Random graphs: prob{e exists} ≈ log(n)/n – low clustering coefficient – Gaussian distribution of the degrees • Interaction networks – High clustering coefficient – Heavy tailed distribution of the degrees Dec. 19, 2006 HiPC'06 7 New problematic • Why these networks share these properties? • What model for – Performance analysis of these networks – Algorithm design for these networks • Impact of the measures? • This lecture addresses navigability Dec. 19, 2006 HiPC'06 8 Navigability Milgram Experiment • Source person s (e.g., in Wichita) • Target person t (e.g., in Cambridge) – Name, professional occupation, city of living, etc. • Letter transmitted via a chain of individuals related on a personal basis • Result: “six degrees of separation” Dec. -
The Best Nurturers in Computer Science Research
The Best Nurturers in Computer Science Research Bharath Kumar M. Y. N. Srikant IISc-CSA-TR-2004-10 http://archive.csa.iisc.ernet.in/TR/2004/10/ Computer Science and Automation Indian Institute of Science, India October 2004 The Best Nurturers in Computer Science Research Bharath Kumar M.∗ Y. N. Srikant† Abstract The paper presents a heuristic for mining nurturers in temporally organized collaboration networks: people who facilitate the growth and success of the young ones. Specifically, this heuristic is applied to the computer science bibliographic data to find the best nurturers in computer science research. The measure of success is parameterized, and the paper demonstrates experiments and results with publication count and citations as success metrics. Rather than just the nurturer’s success, the heuristic captures the influence he has had in the indepen- dent success of the relatively young in the network. These results can hence be a useful resource to graduate students and post-doctoral can- didates. The heuristic is extended to accurately yield ranked nurturers inside a particular time period. Interestingly, there is a recognizable deviation between the rankings of the most successful researchers and the best nurturers, which although is obvious from a social perspective has not been statistically demonstrated. Keywords: Social Network Analysis, Bibliometrics, Temporal Data Mining. 1 Introduction Consider a student Arjun, who has finished his under-graduate degree in Computer Science, and is seeking a PhD degree followed by a successful career in Computer Science research. How does he choose his research advisor? He has the following options with him: 1. Look up the rankings of various universities [1], and apply to any “rea- sonably good” professor in any of the top universities. -
Prizes and Awards
MathFest 2010 Prizes and Awards Pittsburgh, Pennsylvania August 6, 2010 Program Opening and Closing Remarks David Bressoud, President Mathematical Association of America Carl B. Allendoerfer Awards ..................................... 1 Trevor Evans Awards ............................................... 7 Lester R. Ford Awards ............................................ 12 George Pólya Awards ............................................. 25 Annie and John Selden Prize ................................. 29 Henry L. Alder Awards ........................................... 31 Carl B. Allendoerfer Awards The Carl B. Allendoerfer Awards, established in 1976, are made to authors of expository articles published in Mathematics Magazine. The Awards are named for Carl B. Allendoerfer, a distinguished mathematician at the University of Washington and President of the Mathematical Association of America, 1959-60. Ezra Brown and Keith Mellinger “Kirkman‟s Schoolgirls Wearing Hats and Walking Through Fields of Numbers,” Mathematics Magazine, 82:1 (2009), p. 3-15. The historical basis for this interesting article is a problem in recreational mathematics posed by T. P. Kirkman in 1850. Kirkman‘s problem states: ―Fifteen young ladies of a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk abreast more than once.‖ Using this problem as a springboard, the authors treat the reader to a captivating exploration of the theory and applications of block designs. In the process, solutions to the schoolgirls problem are uncovered in such seemingly unrelated areas as the subfield structure of algebraic number fields and the configuration of ―spreads‖ and ―packings‖ in finite projective geometry. Additional connections to the schoolgirls problem are revealed by the authors‘ extension of Todd Ebert‘s ―Three Hats‖ problem to an analogous problem involving fifteen hats. -
A Memorable Trip Abhisekh Sankaran Research Scholar, IIT Bombay
A Memorable Trip Abhisekh Sankaran Research Scholar, IIT Bombay It was my first trip to the US. It had not yet sunk in that I had been chosen by ACM India as one of two Ph.D. students from India to attend the big ACM Turing Centenary Celebration in San Francisco until I saw the familiar face of Stephen Cook enter a room in the hotel a short distance from mine; later, Moshe Vardi recognized me from his trip to IITB during FSTTCS, 2011. I recognized Nitin Saurabh from IMSc Chennai, the other student chosen by ACM-India; 11 ACM SIG©s had sponsored students and there were about 75 from all over the world. Registration started at 8am on 15th June, along with breakfast. Collecting my ©Student Scholar© badge and stuffing in some food, I entered a large hall with several hundred seats, a brightly lit podium with a large screen in the middle flanked by two others. The program began with a video giving a brief biography of Alan Turing from his boyhood to the dynamic young man who was to change the world forever. There were inaugural speeches by John White, CEO of ACM, and Vint Cerf, the 2004 Turing Award winner and incoming ACM President. The MC for the event, Paul Saffo, took over and the panel discussions and speeches commenced. A live Twitter feed made it possible for people in the audience and elsewhere to post questions/comments which were actually taken up in the discussions. Of the many sessions that took place in the next two days, I will describe three that I found most interesting. -
October 2008
THE LONDON MATHEMATICAL SOCIETY NEWSLETTER No. 374 October 2008 Society THE PROPOSAL FOR A NEW SOCIETY Meetings In all likelihood you will now have present form fulfil many of the and Events received a copy of the proposal hopes and expectations of their for a new society, combining the members, times are changing and 2008 present London Mathematical the need for mathematics as a uni- Friday 21 November Society and Institute of Mathe- fied activity to hold and defend AGM, London matics and its Applications. For its position in the public sphere [page 3] a new society to be formed, the grows constantly greater. IMA and the LMS must both vote As the Presidents’ letter which 12–13 December separately in favour of the accompanies the report makes Joint Meeting with proposal. clear, there is a pressing need to the Edinburgh There has been debate about engage effectively with govern- Mathematical Society this for several years but mem- ment, with external bodies, with Edinburgh [page 7] bers could be forgiven for think- the media and with the public. ing that, despite progress reports A society that represents the 2009 appearing in Mathematics Today broad spectrum of the mathemat- Friday 27 February and the Newsletter, things had ical community and has a larger Mary Cartwright ‘gone quiet’. The process leading membership must inevitably carry Lecture, London up to the present proposal has greater weight. been protracted not because the Your view is important and you 31 March – 4 April two societies disagree with one will soon have an opportunity to LMS Invited Lectures another, which they do not, but take part in this important deci- Edinburgh because those developing the new sion. -
Alan Mathison Turing and the Turing Award Winners
Alan Turing and the Turing Award Winners A Short Journey Through the History of Computer TítuloScience do capítulo Luis Lamb, 22 June 2012 Slides by Luis C. Lamb Alan Mathison Turing A.M. Turing, 1951 Turing by Stephen Kettle, 2007 by Slides by Luis C. Lamb Assumptions • I assume knowlege of Computing as a Science. • I shall not talk about computing before Turing: Leibniz, Babbage, Boole, Gödel... • I shall not detail theorems or algorithms. • I shall apologize for omissions at the end of this presentation. • Comprehensive information about Turing can be found at http://www.mathcomp.leeds.ac.uk/turing2012/ • The full version of this talk is available upon request. Slides by Luis C. Lamb Alan Mathison Turing § Born 23 June 1912: 2 Warrington Crescent, Maida Vale, London W9 Google maps Slides by Luis C. Lamb Alan Mathison Turing: short biography • 1922: Attends Hazlehurst Preparatory School • ’26: Sherborne School Dorset • ’31: King’s College Cambridge, Maths (graduates in ‘34). • ’35: Elected to Fellowship of King’s College Cambridge • ’36: Publishes “On Computable Numbers, with an Application to the Entscheindungsproblem”, Journal of the London Math. Soc. • ’38: PhD Princeton (viva on 21 June) : “Systems of Logic Based on Ordinals”, supervised by Alonzo Church. • Letter to Philipp Hall: “I hope Hitler will not have invaded England before I come back.” • ’39 Joins Bletchley Park: designs the “Bombe”. • ’40: First Bombes are fully operational • ’41: Breaks the German Naval Enigma. • ’42-44: Several contibutions to war effort on codebreaking; secure speech devices; computing. • ’45: Automatic Computing Engine (ACE) Computer. Slides by Luis C. -
School of Computer Science
MANCHESTER 1824 School of Computer Science Weekly Newsletter 20 February 2012 Contents News from Head of School News from HoS Royal Visit This Week Prince Andrew visited the School on Tuesday 14th February. Prince Andrew was School Events given a tour of the graphene laboratories by Andre Geim, and made a sample of graphene himself, which he viewed under the microscope. External Events Members of the graphene research team told the Prince about future Funding Opps applications of graphene, which is the world’s thinnest, strongest and most conductive material. Prize & Award Opps http://www.manchester.ac.uk/aboutus/news/display/?id=7977 Research Awards The visit in connection with the announcement of the new £45M graphene building: Staff News http://www.manchester.ac.uk/aboutus/news/display/?id=7930 Vacancies Turing Centenary Conference Andrei Voronkov has announced the Turing Centenary Conference, to be held in Links Manchester, June 22-25, 2012: http://www.turing100.manchester.ac.uk/ News Submissions Andrei has secured Ten Turing Award winners, a Templeton Award winner and Newsletter Archive Garry Kasparov as invited speakers: School Strategy Confirmed invited speakers: School Intranet - Fred Brooks (University of North Carolina) - Rodney Brooks (MIT) School Seminars - Vint Cerf (Google) ESNW Seminars - Ed Clarke (Carnegie Mellon University) NaCTeM Seminars - Jack Copeland (University of Canterbury, New Zealand) - George Francis Rayner Ellis (University of Cape Town) - David Ferrucci (IBM) - Tony Hoare (Microsoft Research) - Garry Kasparov (Kasparov Chess Foundation) - Don Knuth (Stanford University) - Yuri Matiyasevich (Institute of Mathematics, St. Petersburg) - Roger Penrose (Oxford) - Adi Shamir (Weizmann Institute of Science) - Michael Rabin (Harvard) - Leslie Valiant (Harvard) - Manuela M. -
Kronecker Products, Low-Depth Circuits, and Matrix Rigidity
Kronecker Products, Low-Depth Circuits, and Matrix Rigidity Josh Alman∗ February 25, 2021 Abstract For a matrix M and a positive integer r, the rank r rigidity of M is the smallest number of entries of M which one must change to make its rank at most r. There are many known applications of rigidity lower bounds to a variety of areas in complexity theory, but fewer known applications of rigidity upper bounds. In this paper, we use rigidity upper bounds to prove new upper bounds in a few different models of computation. Our results include: • For any d> 1, and over any field F, the N N Walsh-Hadamard transform has a depth-d linear circuit of size O(d N 1+0.96/d). This× circumvents a known lower bound of Ω(d N 1+1/d) for circuits with· bounded coefficients over C [Pud00], by using coefficients of· magnitude polynomial in N. Our construction also generalizes to linear transformations given by a Kronecker power of any fixed 2 2 matrix. × • The N N Walsh-Hadamard transform has a linear circuit of size (1.81+o(1))N log N, × ≤ 2 improving on the bound of 1.88N log2 N which one obtains from the standard fast Walsh-Hadamard transform. ≈ • A new rigidity upper bound, showing that the following classes of matrices are not rigid enough to prove circuit lower bounds using Valiant’s approach: n n n 2 ×2 – for any field F and any function f : 0, 1 F, the matrix Vf F given by, n { } → ∈ for any x, y 0, 1 , Vf [x, y]= f(x y), and ∈{ } ∧ q×q – for any field F and any fixed-size matrices M1,...,M F , the Kronecker product n ∈ M1 M2 M .