Design of Large Scale Applications of Secure Multiparty Computation : Secure Linear Programming
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Three Puzzles on Mathematics, Computation, and Games
P. I. C. M. – 2018 Rio de Janeiro, Vol. 1 (551–606) THREE PUZZLES ON MATHEMATICS, COMPUTATION, AND GAMES G K Abstract In this lecture I will talk about three mathematical puzzles involving mathemat- ics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear programming. The second puzzle is about errors made when votes are counted during elections. The third puzzle is: are quantum computers possible? 1 Introduction The theory of computing and computer science as a whole are precious resources for mathematicians. They bring up new questions, profound new ideas, and new perspec- tives on classical mathematical objects, and serve as new areas for applications of math- ematics and mathematical reasoning. In my lecture I will talk about three mathematical puzzles involving mathematics and computation (and, at times, other fields) that have preoccupied me over the years. The connection between mathematics and computing is especially strong in my field of combinatorics, and I believe that being able to person- ally experience the scientific developments described here over the past three decades may give my description some added value. For all three puzzles I will try to describe in some detail both the large picture at hand, and zoom in on topics related to my own work. Puzzle 1: What can explain the success of the simplex algorithm? Linear program- ming is the problem of maximizing a linear function subject to a system of linear inequalities. The set of solutions to the linear inequalities is a convex polyhedron P . -
Integrity, Authentication and Confidentiality in Public-Key Cryptography Houda Ferradi
Integrity, authentication and confidentiality in public-key cryptography Houda Ferradi To cite this version: Houda Ferradi. Integrity, authentication and confidentiality in public-key cryptography. Cryptography and Security [cs.CR]. Université Paris sciences et lettres, 2016. English. NNT : 2016PSLEE045. tel- 01745919 HAL Id: tel-01745919 https://tel.archives-ouvertes.fr/tel-01745919 Submitted on 28 Mar 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THÈSE DE DOCTORAT de l’Université de recherche Paris Sciences et Lettres PSL Research University Préparée à l’École normale supérieure Integrity, Authentication and Confidentiality in Public-Key Cryptography École doctorale n◦386 Sciences Mathématiques de Paris Centre Spécialité Informatique COMPOSITION DU JURY M. FOUQUE Pierre-Alain Université Rennes 1 Rapporteur M. YUNG Moti Columbia University et Snapchat Rapporteur M. FERREIRA ABDALLA Michel Soutenue par Houda FERRADI CNRS, École normale supérieure le 22 septembre 2016 Membre du jury M. CORON Jean-Sébastien Université du Luxembourg Dirigée par -
Three Puzzles on Mathematics Computations, and Games
January 5, 2019 17:43 icm-961x669 main-pr page 551 P. I. C. M. – 2018 Rio de Janeiro, Vol. 1 (551–606) THREE PUZZLES ON MATHEMATICS, COMPUTATION, AND GAMES G K Abstract In this lecture I will talk about three mathematical puzzles involving mathemat- ics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear programming. The second puzzle is about errors made when votes are counted during elections. The third puzzle is: are quantum computers possible? 1 Introduction The theory of computing and computer science as a whole are precious resources for mathematicians. They bring up new questions, profound new ideas, and new perspec- tives on classical mathematical objects, and serve as new areas for applications of math- ematics and mathematical reasoning. In my lecture I will talk about three mathematical puzzles involving mathematics and computation (and, at times, other fields) that have preoccupied me over the years. The connection between mathematics and computing is especially strong in my field of combinatorics, and I believe that being able to person- ally experience the scientific developments described here over the past three decades may give my description some added value. For all three puzzles I will try to describe in some detail both the large picture at hand, and zoom in on topics related to my own work. Puzzle 1: What can explain the success of the simplex algorithm? Linear program- ming is the problem of maximizing a linear function subject to a system of linear inequalities. -
Indian Mathematicians and Their Contributions
Vol-2 Issue-3 2016 IJARIIE-ISSN(O)-2395-4396 Indian Mathematicians and Their Contributions By: G. Nagamani M.sc,M.Ed Teacher, Nalgonda-Telangana State ABSTRACT Indian mathematics has its roots in Vedic literature. Between 1000 B.C. and 1800 A.D. various treatises on mathematics were authored by Indian mathematicians in which were set forth for the first time, the concept of zero, numeral system, techniques of algebra and algorithm, square root and cube root. However, despite widely available, reliable information, there is a distinct and inequitable neglect off the contributions of the sub-continent. Many of the developments of Indian mathematics remain almost completely ignored, or worse, attributed to scholars of other nationalities, often European. However a few historians (mainly European) are reluctant to acknowledge the contributions of Indian mathematicians. They believe Indians borrowed the knowledge of mathematics from Greeks. In this article author has written the significant Indian mathematicians brief history and their contributions. 1. RAMANUJAN: He was born on 22na of December 1887 in a small village of Tanjore district, Madras. He failed in English in Intermediate, so his formal studies were stopped but his self-study of mathematics continued. He sent a set of 120 theorems to Professor Hardy of Cambridge. As a result he invited Ramanujan to England. Ramanujan showed that any big number can be written as sum of not more than four prime numbers. He showed that how to divide the number into two or more squares or cubes. when Mr Litlewood came to see Ramanujan in taxi number 1729, Ramanujan said that 1729 is the smallest number which can be written in the form of sum of cubes of two numbers in two ways, i.e. -
Online Optimization: Probabilistic Analysis and Algorithm Engineering
Online Optimization: Probabilistic Analysis and Algorithm Engineering vorgelegt von Dipl.-Inf. Benjamin Hiller Von der Fakultät II – Mathematik und Naturwissenschaften der Technischen Universität Berlin zur Erlangung des akademischen Grades Doktor der Naturwissenschaften – Dr. rer. nat. – genehmigte Dissertation Berichter: Prof. Dr. Dr. h.c. mult. Martin Grötschel Dr. Tjark Vredeveld Vorsitzender: Prof. Dr. Fredi Tröltzsch Tag der wissenschaftlichen Aussprache: 15. Dezember 2009 Berlin 2010 D 83 Zusammenfassung Diese Arbeit beschäftigt sich mit Online-Optimierung, also der Steuerung von Systemen, bei denen die für die optimierte Steuerung relevanten Daten erst mit der Zeit, d. h. online, bekannt werden. Wir konzentrieren uns dabei auf kombinatorische Online-Optimierungsprobleme, bei denen die Steuerungsentscheidungen diskret sind. Im ersten, praktisch orientierten Teil der Arbeit werden Reoptimie- rungsalgorithmen für die Online-Steuerung komplexer realer Systeme vorgestellt. Ein Reoptimierungsalgorithmus trifft seine Steuerungsent- scheidung so, dass sie in einem bestimmten Sinn “günstig” für die aktuelle Situation ist. Wir benutzen Techniken der mathematischen Optimierung, insbesondere ganzzahlige Optimierung, um fortgeschrit- tene Reoptimierungsalgorithmen zu entwickeln. Unsere erste Anwen- dung ist die automatische Disposition von Pannenhilfefahrzeugen des ADAC. Hier zeigt sich, dass mathematische Optimierungsmethoden den Dispositionsprozess gegenüber der Planung mit einfachen Heuristiken verbessern und kürzere Wartezeiten für die -
News Letter Since: 11/11/2016 Dr
Editor-in-Chief Volume 1, Issue 7 News Letter Since: 11/11/2016 Dr. N.Anbazhagan Professor & Head, DM Associate Editor Mrs. B. Sundara Vadivoo We are delighted to bring to you this issue of ALU Mathematics Assistant Professor, DM News, a monthly newsletter dedicated to the emerging field of Editors Mathematics. This is the first visible ―output from the Department Dr. J. Vimala of Mathematics, Alagappa University. We are committed to make Assistant Professor, DM Dr. R. Raja ALU Mathematics News a continuing and Assistant Professor, RCHM effective vehicle to promote Dr. S. Amutha Assistant Professor, RCHM communication, education and networking, Dr. R. Jeyabalan as well as stimulate sharing of research, Assistant Professor, DM innovations and technological Dr. M. Mullai developments in the field. However, we Assistant Professor, DDE would appreciate your feedback regarding Technical & Editorial how we could improve this publication and Assistance enhance its value to the community. We are R.Suganya VS.Anushya Ilamathy keen that this publication eventually grows Dr. N. Anbazhagan D.Gandhi Mathi beyond being a mere ―news letter to J.Arockia Reeta become an invaluable information resource K.Surya prabha C.Sowmiya for the entire Mathematics community, and look forward to your L.Vijayalakshmi inputs to assist us in this endeavor. FIELDS MEDAL Fields Medal is highest honored award for Mathematics and its a prize awarded to two,three or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union(IMU), a meeting that takes place every four years. Affiliation at the ce California Year Name time of the award Wend 2006 Werner Université Paris-Sud CNRS - Institut de elin Avila Mathématiques de Institut des Hautes 2014 Artur Cordeiro Laure Jussieu-Paris Rive 2002 Lafforgue Études Scientifiques de Melo nt Gauche Manj Princeton Vladi Institute for 2014 Bhargava 2002 Voevodsky ul University, mir Advanced Study Marti University of Richa University of 2014 Hairer 1998 Borcherds n Warwick rd E. -
Algorithms and Hardness for Linear Algebra on Geometric Graphs
Algorithms and Hardness for Linear Algebra on Geometric Graphs∗ Josh Alman† Timothy Chu‡ Aaron Schild§ Zhao Song¶ Abstract d d d For a function K : R R R≥ , and a set P = x ,...,xn R of n points, the K × → 0 { 1 } ⊂ graph GP of P is the complete graph on n nodes where the weight between nodes i and j is given by K(xi, xj ). In this paper, we initiate the study of when efficient spectral graph theory is possible on these graphs. We investigate whether or not it is possible to solve the following 1+o(1) o(1) problems in n time for a K-graph GP when d<n : • Multiply a given vector by the adjacency matrix or Laplacian matrix of GP • Find a spectral sparsifier of GP • Solve a Laplacian system in GP ’s Laplacian matrix 2 For each of these problems, we consider all functions of the form K(u, v) = f( u v 2) for a function f : R R. We provide algorithms and comparable hardness resultsk for−manyk such K, including the→ Gaussian kernel, Neural tangent kernels, and more. For example, in dimension d = Ω(log n), we show that there is a parameter associated with the function f for which low parameter values imply n1+o(1) time algorithms for all three of these problems and high parameter values imply the nonexistence of subquadratic time algorithms assuming Strong Exponential Time Hypothesis (SETH), given natural assumptions on f. As part of our results, we also show that the exponential dependence on the dimension d in the celebrated fast multipole method of Greengard and Rokhlin cannot be improved, assuming SETH, for a broad class of functions f. -
Algorithms and Hardness for Linear Algebra on Geometric Graphs
2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS) Algorithms and Hardness for Linear Algebra on Geometric Graphs Josh Alman Timothy Chu Aaron Schild Zhao Song [email protected] [email protected] [email protected] [email protected] Harvard U. Carnegie Mellon U. U. of Washington Columbia, Princeton, IAS d d Abstract—For a function K : R × R → R≥0, and a set learning. The first task is a celebrated application of the P {x ,...,x }⊂Rd n K G P = 1 n of points, the graph P of fast multipole method of Greengard and Rokhlin [GR87], n is the complete graph on nodes where the weight between [GR88], [GR89], voted one of the top ten algorithms of the nodes i and j is given by K(xi,xj ). In this paper, we initiate the study of when efficient spectral graph theory is possible twentieth century by the editors of Computing in Science and on these graphs. We investigate whether or not it is possible Engineering [DS00]. The second task is spectral clustering to solve the following problems in n1+o(1) time for a K-graph [NJW02], [LWDH13], a popular algorithm for clustering o(1) GP when d<n : data. The third task is to label a full set of data given only • Multiply a given vector by the adjacency matrix or a small set of partial labels [Zhu05b], [CSZ09], [ZL05], Laplacian matrix of GP which has seen increasing use in machine learning. One • G Find a spectral sparsifier of P notable method for performing semi-supervised learning is • Solve a Laplacian system in GP ’s Laplacian matrix the graph-based Laplacian regularizer method [LSZ+19b], For each of these problems, we consider all functions of the K u, v f u − v2 f R → R [ZL05], [BNS06], [Zhu05a]. -
CECS 328 Lectures
CECS 328 Lectures Darin Goldstein 1 Review of Asymptotics 1. The Force: Certain functions are always eventually larger than others. This list goes from smallest to largest. (a) constants, sin, cos, tan−1 constant (b) (log n) (c) nconstant (d) constantn (e) n! (f) nn Be very careful with the final two levels. YOU MAY ONLY USE THE FORCE ADDITIVELY, NOT MULTIPLICATIVELY! Examples below. 2. Growth of functions: All functions we consider in this class will be even- tually positive. (a) O: f = O(g) ) There exists constants c > 0 and Nc such that for 2 3 every n ≥ Nc, f(x) ≤ cg(x). Example: 5x + 20 = O(x ) (b) Ω: f = Ω(g) ) There exists constants c > 0 and Nc such that for x3 2 every n ≥ Nc, f(x) ≥ cg(x). Example: 3 − 9x = Ω(x ) (c) Θ: f = Θ(g) ) f = O(g) and f = Ω(g). Example: 3x2 − 8x + 2 = Θ(x2) f(x) 2 3 (d) o: f = o(g) ) limx!1 g(x) = 0. Example: x = o(x ) g(x) p (e) !: f = !(g) ) limx!1 f(x) = 0. Example: x = !(log x) The following are exercises based on what you've learned so far: 1. Find the smallest n so that f = O(xn) if such an exists. Find the largest n so that f = Ω(xn) if such an n exists. Find a function g so that f = Θ(g). (a) f(x) = (x3 + x2 log x)(log x + 1) + (17 log x + 19)(x3 + 2) 6 x −3x+12p (b) f(x) = x2 log x+πx x 1 2 3 p 5x log x+x (c) f(x) = x(log x)2+x3 log x (d) f(x) = (2x + x2)(x3 + 3x) x 2 (e) f(x) = x2 + xx 2. -
Contents U U U
Contents u u u ACM Awards Reception and Banquet, June 2018 .................................................. 2 Introduction ......................................................................................................................... 3 A.M. Turing Award .............................................................................................................. 4 ACM Prize in Computing ................................................................................................. 5 ACM Charles P. “Chuck” Thacker Breakthrough in Computing Award ............. 6 ACM – AAAI Allen Newell Award .................................................................................. 7 Software System Award ................................................................................................... 8 Grace Murray Hopper Award ......................................................................................... 9 Paris Kanellakis Theory and Practice Award ...........................................................10 Karl V. Karlstrom Outstanding Educator Award .....................................................11 Eugene L. Lawler Award for Humanitarian Contributions within Computer Science and Informatics ..........................................................12 Distinguished Service Award .......................................................................................13 ACM Athena Lecturer Award ........................................................................................14 Outstanding Contribution -
2010 Nevanlinna Prize Awarded
image processing. A version of such an algorithm teaching assistantship at Université de Strasbourg. has been installed in the space mission Herschel He received his Ph.D. from Strasbourg in 1966. of the European Space Agency, which is aimed at He has been a professor at École Polytechnique providing images of the oldest and coldest stars and Université Paris-Dauphine and has also held in the universe. a full research position at Centre National de la “To my knowledge,” says Wolfgang Dahmen, Recherche Scientifique. He was professor at École “Meyer has never worked directly on a concrete Normale Supérieure de Cachan, France, from 1999 application problem.” Thus Meyer’s mathematics to 2009 and is currently professor emeritus. He provide good examples of how the investigations is a foreign honorary member of the American of fundamental mathematical questions often yield Academy of Arts and Sciences. He has also been surprising results that benefit humanity. awarded a doctorate (Honoris causa) by Universi- Yves Meyer was born in 1939. After graduating dad Autonoma de Madrid. from Ecole Normale Supérieure, Paris, in 1960, he —from an IMU news release taught high school for three years, then took a 2010 Nevanlinna Prize Awarded On August 19, 2010, the 2010 Rolf Nevanlinna geometric terms, the constraints Prize was awarded at the opening ceremonies define a convex polyhedron in a of the International Congress of Mathematicians high-dimensional space, and the (ICM) in Hyderabad, India. The prizewinner is simplex algorithm reaches the Daniel Spielman of Yale University. optimum by moving from one In 1982 the University of Helsinki granted funds vertex to a neighboring vertex to award the Nevanlinna Prize, which honors the of the polyhedron. -
Return of Organization Exempt from Income
r OMB NO 1545-004 Return of Organization Exempt From Income Tax Form Under section 501(c), 527, or 4947(a)(1) of the Internal Revenue Code (except black lung 2004 990 benefit trust or private foundation) Department of the Treasury Open to Public Internal Revenue Service " The organization may have to use a copy of this return to satisfy state reporting requirements. Inspection A For the 2004 calendar year, or tax year beginning JAN 1 2004 and B Check .r C Name of organization D Employer identification number applicable please, use IRS ssociation for Computing Address label or change print or Machinery, Inc . 1J -171+1J Name type =change Number and street (or P.O. box if mail is not delivered to street address) Room/suite E Telephone number Initial See return Specific 1515 Broadway 17th Floor Final Instruc- ~return lions City or town, state or country, and ZIP + 4 F Accounting method U IC-171 $ Accrual aAmended return New York NY 10036 - 5701 Application pending 0 Section 501(c)(3) organizations and 4947(a)(1) nonexempt charitable trusts H and I are not applicable to section 527 organizations. must attach pleted Schedule A (Foror 990-EZ) . H(a) Is this a group return for affiliates? Yes No H(b) If "Yes ;" enter number of affdiates " J Organization type (cneckonly one)10- LXJ 501(c) ( 3 ) 1 cnsert no) L_j 4947(a)(1)orU 52 H(c) Are all affiliates included? N/A D Yes 0 No (If "No ;' attach a list.) K Check here 1[:j if the organization's gross receipts are normally not more than $25,000 .