DOCSLIB.ORG

International Mathematics Research Notices

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
International Mathematics Research Notices ISSN 0002-9920 of the American Mathematical Society May 2003 Volume 50, Number 5 The Mathematics of Learning: Dealing with Data page 537 PRIMES Is in P: A Breakthrough for "Everyman" page 54 5 CQD Input: integer n > 1 ~::' 1. If n = ab for a E N and b > 1 ro q 1otli · ai output COMPOSITE. calcu 2. Find the smallest r tiarri e. such that Or ( n) > 4 log2 n. I ad n: % Or ( n) is the order of n modulo r 1ute1n · 3. If 1 < (a, n) < n for some a ::::; r illae output COMPOSITE. 4. If n ::::; r, output PRIME. tntur, 5. For a = 1 to l2..j¢(r:) lognJ do If (X+ a)n f= xn +a (mod xr - 1, n) ' l iD id ca" output COMPOSITE. ·,' )' occ % ¢(r) is Euler's totient ta Iatori 6. output PRI ME. se e n lit~Ollt res ri:uigna /emolumenta c~l>ie.,a ' ·'. qua~ t , dispendiui1i mediocre. Iargi~r .... cbmpe~ ~ ereaque sciehtia.e 'dignitas req.Uirere ''vid :rinia subsidici ad solutionern probleriichis aitis ac celehris sedulci excoiaritur. .J?ro ·dtiori.es nori dubihimus', ~ quirt , . 'd.utie ' metl ~ntes' quariim' .e fficaciari1. ac_brciuitatern . Is n prime? (see p age 553) Distance Asynchronous Online On Ct.1r11pus Education is no longer just about classrooms and labs. With the growing diversity and complexity of educational programs. you need a software system that lets you efficiently deliver effective learning tools to literally, the world. Maple· now offers yo u a choice to add ress the reality of today's mathematics education . Maple 8 - the standard Perfect for students in mathematics, sciences, and engineering. Maple 8 offers all the power, flexibility, and resources your technical students need to manage even the most complex mathematical concepts. TM ~••!"! _:"!!!"!_:!".:_~------ -. Maple T.A. - automated assessment Online math skills assessment without resorting to multiple choice •ft 4--~r ..._.,._.,.,..._,.._ ......... -.... .. _ ___ _ or true or false. Maple T.A. supports natural entry and intelligent mapkiD -- Ill, ·-------r-.--.._ ,.. ____u __ ·----r-- .,.,. .__,..... __ ~ testing of answers. A complete question-set management ---__ --r- infrastructure lets you manage even the largest class sizes. - ... - r MapleNET - online education A complete standards-based solution for authoring , • OS!!!.,..""2r _.,.._ delivering , and managing interactive learning modules • A~~ ·~ through browsers. Derived from the legendary Maple •l'loi;IIJ'I!Irr~ engine, MapleNet is the only comprehensive solution for Web based education in mathematics. Give your institution and students the cornpetitive edge. For a FREE 30-day Maple 8 Trial CD , or to register for a FREE MapleNet or Maple T.A. Online Seminar call 800.267.6583 or e-mail [email protected]. ~ Maple soft command the brIlliance www.maplesoft.com info@maplesoft .com , www.mapleapps.com , US & Canada 800.267.6583 ~f. !fJ t > ·t l rJ I' I 'I (,' v'il'Prl(,n ~.'d!J p It I 2(J•J,j M lpit; s I '"qh'f'P'fi tr ldt''l'dfk o! \'\i11t>• Ov M1ple llr Vl<lpiB:-..Oit M<ipleNPt diHJ MaJ•Ir l A Clrt:' lr1rlem;~rks ot w tlf rloo ~\lp p 111\ All Olth fr,vif'llla k::, I'< rr(Jl'\ tl, ('I 'It I fl',,1•'l J, <' d . w ' I OUTSTANDING NEW MATHEMATICS BOOKS Second Order Partial Complex Polynomials The Changing Shape of Differential Equations in Terry Shei/-Sma/1 Geometry Hilbert Spaces Srudies the geometric theory of polynomials Celebrating a Century of Geometry G. Da Prato and j. Zabczyk and rational functions in the plane. Chapters and Geometry Teaching build the foundations of complex variable Second order linear parabolic and elliptic Edited by Chris Pritchard theory, melding together ideas from algebra, equations arise frequently in mathematical Contains popular articles including sections on topology and analysis. Presents several physics, biology and finance. The authors Pythagoras, the golden ratio and recreational unsolved problems and the full solurions present a state of the art treatment of the geometry. Thirty 'Desert Island Theorems' to some well-known conjectures. subject from a new perspective, and discuss from distinguished mathematicians and 0-521 -40068-6 Hb $95.00 how the results can be applied to control educationalists give light to some surprising Cambridge Studies in Advanced Mathematics 75 theory. and beautiful results. Contributors include a 0-521-77729-1 Pb $45.00 Nobel Laureate and a Pulitzer Prizewinner. London Mathematical Society Lecture Note Series 293 Abstract Regular Polytopes 0-521-82451-6 Hb $90.00 0-521-53162-4 Pb $40.00 Peter McMullen and Egon Schulte Co-published with The Mathematical Association of A Panorama of Number Theory This book is the first comprehensive, America or The View from Baker•s up-to-date account of this subject and its Garden ramifications. Over the past rwenry years, a rich new theory featuring an attractive Graph Directed Edited by Gisbert Wiistholz interplay of mathematical areas, including Markov Systems The papers presented here cover a broad geometry, combinatorics, group theory and Geometry and Dynamics of Limit Sets spectrum of number theory including topology has arisen. Dan Mauldin and Mariusz Urbanski geometric, algebrao-geometric and analytic 0-521-81496-0 Hb $110.00 This far-reaching generalization of the theory aspects, appealing to number theorists, Encyclopedia of Mathematics and its Applications 92 algebraic geometers, and geometers with of conformal iterated systems can be applied a number theoretic background. in many situations, including the theory of 0-521-80799-9 Hb $80.00 Hodge Theory and Complex dynamical systems. Includes much of the Algebraic Geometry necessary background material and an extensive list of references suggesting further reading. Volume I A Second Course in 0-521-82538-5 Hb $55.00* Mathematical Analysis Claire Voisin Cambridge Tracts in Mathematics 1.48 Second Edition Translated by Leila Schneps }.C. Burkill and H. Burki/1 A modern introduction to Kaehlerian Quasi-Frobenius Rings geometry and Hodge structure, this book This straightforward course, based on the starts with basic material on complex WK. Nicholson and M.F.Yousif idea of a limit, is intended for students of variables, complex manifolds, holomorphic This book provides an elementary, complete mathematics and physics who have acquired vector bundles, sheaves and cohomology account of quasi-Frobenius rings at a level a working knowledge of calculus and are theory, and culminates with the Hodge allowing researchers and graduate students ready for a more systematic treatment. decomposition theorem. Includes exercises. to gain entry to the field. 0-521-52343-5 Pb $45.00 0-521-80260-1 Hb $80.00 0-521-81593-2 Hb $70.00* Cambridge Mathematical Library Cambridge Studies in Advanced Mathematics 76 Cambridge TractS in Mathematics !54 *Prices subject to change. A Panorama ofNumber Theory or The Vieo.v from taker's Garden CAMBRIDGE 800-872-7423 Available in bookstores or from UNIVERSITY PRESS us.cambridge.org/mathematics NEW f6 NOTEWORTHY from Birkhiiuser The Topos of Music Mathematical Finance Partially Observable Geometric Logic of Concepts, and Probability Linear Systems Under Theory, and Performance Discrete Introduction Dependent Noises G. MAZZOLA, University of Zurich, Switzerland P. KOCH MEDINA, Swiss Re; and S. MERINO, UBS, both, In Collaboration with S. GOLLER and S. MULLER A. E. BASHIROV, Eastern Mediterranean University, Zurich, Switzerland Famagusta, Cypras The Tapas of Music is an updated, in-depth English This work gives a self-contained presentation of the This book provides a mathematical view of specific extension of the German Geometrie der TOne. It reflects theory underlying the valuation of derivative financial the dramatic progress of mathematical music theory engineering problems with known and new methods of instruments, a standard part of the toolbox of finance control and estimation in noisy media. The main feature and its use of information technology. The conceptual professionals. The material will be accessible to basis has been generalized to tapas-theoretic founda­ is the examination of stochastic optimal control and students and practitioners who have a worki ng know­ estimation problems with the noise processes acting tions, including geometric musical logic. The theoretical ledge of linear algebra and calculus. The book also models and results include topologies for rhythm, dependently on the state (or signal) and observation off ers an introduction to modern probability theory, systems. melody, and harmony, as well as a classification theory primarily within the context of finite sample spaces. of musical objects that comprises the framework of the 2003/3 64 PP./HARDCOVER/$99 .00 2002/ 336 PP./SOFTCOVER/$49. 95 ISBN 3-7643-6999-X tapas-theoretic concept. The book's formal language ISBN 3-7643-6921-3 and models are currently being used by leading SYSTEMS AND CONTROL: FOUNDATIONS AND APPLICATIONS researchers in Europe and Northern America and have become a foundation of music software design. Adaptive Finite Element Operator Theory: 2002/ 1,3 68 PP./HARDCOVER WITH CD-ROM/$ 139.00 Methods for Differential Advances and Applications ISBN 3-7643-5731-2 Equations Series Ed iter: l. GOHBERG, Tel Aviv University, W. BAN GERTH, The University of Texas at Austin, TX; and RamatAviv, Isreal Cryptographic Applications R. RANNACHER, University of Heidelberg, Germany This series is devoted to the publication of current of Analytical Number This work discusses the concept of "self-adaptivity" in research in operator theory, with particular emphasis Theory the numerical solution of differential equations, with on applications to classical analysis and the theory of emphasis on Galerkin finite element methods. The key integral equations, as well as to numerical analysis, Complexity Lower Bounds and mathematical physics and mathematical methods in Pseudorandomness issues are a posteriori error estimation and automatic mesh adaptation. Besides the traditional approach of electrical engineering. I. SHPARLINSKI, Macquarie University, Sydney, Australia energy-norm error control, a new duality-based tech­ This book introduces new applications for analytic nique, the Dual Weighted Residual method for goal­ Hilbert Space, Boundary Value number theory in cryptography and related areas, such oriented error estimation, is discussed in detail.
Load more

Recommended publications
  • Poincaré Prize 2015 Alexei Borodin I Am Very Pleased and Honored To
    Poincar´ePrize 2015 Alexei Borodin I am very pleased and honored to give the laudatio for Alexei Borodin on his winning the Poincar´ePrize for 2015. Alexei was born and went to school in Donetsk in the Ukraine. In 1992 he was accepted into the famous \mech-mat" Department at Moscow State University, graduating in 1997. At Moscow State he began working with Grigori Olshanski in a marvelous collaboration that continues to this day. He received his PhD under Alexander Kirillov from the University of Pennsylvania in 2001. He was a professor at Caltech from 2003 to 2010, and since then he has been at MIT. I met Borodin about 15 years ago when he was a student at UPenn, and I have been following his career closely since then. His mathematical interests lie in the circle of ideas which connect the representation theory of \big" groups, combinatorics, integrable interacting particle systems and random matrix theory. When I met Borodin I was struck immediately by the freshness of his approach, combined with a professional maturity well beyond his years. He seemed to know and understand everything and I had to keep reminding myself that I was speaking to a young PhD student and not a seasoned colleague of many years standing. Borodin's mathematical and professional maturity was recognized with his very first academic appointment as a full Professor at Caltech in 2003. Following on earlier work of Kerov, Olshanski and Vershik, the key observation of Borodin and Olshanski in the representation theory of \big" groups, such as the infinite symmetric group and the infinite unitary group, is that the characters for the group are naturally associated with stochastic point processes.
    [Show full text]
  • TWAS an Rep IMP
    annual re2p0or1t 0 TWAS, the academy of sciences for the developing world, is an autonomous international organization that promotes scientific capacity and excellence in the South. Founded in 1983 by a group of eminent scientists under the leadership of the late Nobel laureate Abdus Salam of Pakistan, TWAS was officially launched in Trieste, Italy, in 1985, by the secretary-general of the United Nations. TWAS has nearly 1,000 members from over 90 countries. More than 80% of its members are from developing countries. A 13-member council directs the Academy activities. A secretariat, headed by an executive director, coordinates the programmes. The Academy’s secretariat is located on the premises of the Abdus Salam International Centre for Theoretical Physics (ICTP) in Trieste, Italy. TWAS’s administration and finances are overseen by the United Nations Educational, Scientific and Cultural Organization (UNESCO) in accordance with an agreement signed by the two organizations. The Italian government provides a major portion of the Academy’s funding. The main objectives of TWAS are to: • Recognize, support and promote excellence in scientific research in the developing world; • Respond to the needs of young researchers in science and technology- lagging developing countries; • Promote South-South and South-North cooperation in science, technology and innovation; • Encourage scientific research and sharing of experiences in solving major problems facing developing countries. To help achieve these objectives, TWAS collaborates with a number of organizations, most notably UNESCO, ICTP and the International Centre for Biotechnology and Genetic Engineering (ICGEB). academy of sciences for the developing world TWAS COUNCIL President Jacob Palis (Brazil) Immediate Past President C.N.R.
    [Show full text]
  • Patent Filed, Commercialized & Granted Data
    Granted IPR Legends Applied IPR Total IPR filed till date 1995 S.No. Inventors Title IPA Date Grant Date 1 Prof. P K Bhattacharya (ChE) Process for the Recovery of 814/DEL/1995 03.05.1995 189310 05.05.2005 Inorganic Sodium Compounds from Kraft Black Liquor 1996 S.No. Inventors Title IPA Date Grant Date 1 Dr. Sudipta Mukherjee (ME), A Novel Attachment for Affixing to 1321/DEL/1996 12.08.1996 192495 28.10.2005 Anupam Nagory (Student, ME) Luggage Articles 2 Prof. Kunal Ghosh (AE) A Device for Extracting Power from 2673/DEL/1996 02.12.1996 212643 10.12.2007 to-and-fro Wind 1997 S.No. Inventors Title IPA Date Grant Date 1 Dr. D Manjunath, Jayesh V Shah Split-table Atm Multicast Switch 983/DEL/1997 17.04.1997 233357 29.03.2009 1998 S.No. Inventors Title IPA Date Grant Date 1999 1 Prof. K. A. Padmanabhan, Dr. Rajat Portable Computer Prinet 1521/DEL/1999 06.12.1999 212999 20.12.2007 Moona, Mr. Rohit Toshniwal, Mr. Bipul Parua 2000 S.No. Inventors Title IPA Date Grant Date 1 Prof. S. SundarManoharan (Chem), A Magnetic Polymer Composition 858/DEL/2000 22.09.2000 216744 24.03.2008 Manju Lata Rao and Process for the Preparation of the Same 2 Prof. S. Sundar Manoharan (Chem) Magnetic Cro2 &#8211; Polymer 933/DEL/2000 22.09.2000 217159 27.03.2008 Composite Blends 3 Prof. S. Sundar Manoharan (Chem) A Magneto Conductive Polymer 859/DEL/2000 22.09.2000 216743 19.03.2008 Compositon for Read and Write Head and a Process for Preparation Thereof 4 Prof.
    [Show full text]
  • Design Programme Indian Institute of Technology Kanpur
    Design Programme Indian Institute of Technology Kanpur Contents Overview 01- 38 Academic 39-44 Profile Achievements 45-78 Design Infrastructure 79-92 Proposal for Ph.D program 93-98 Vision 99-104 01 ew The design-phase of a product is like a womb of a mother where the most important attributes of a life are concieved. The designer is required to consider all stages of a product-life like manufacturing, marketing, maintenance, and the disposal after completion of product life-cycle. The design-phase, which is based on creativity, is often exciting and satisfying. But the designer has to work hard worrying about a large number of parameters of man. In Indian context, the design of products is still at an embryonic stage. The design- phase of a product is often neglected in lieu of manufacturing. A rapid growth of design activities in India is a must to bring the edge difference in the world of mass manufacturing and mass accessibility. The start of Design Programme at IIT Kanpur in the year 2001, is a step in this direction. overvi The Design Program at IIT-Kanpur was established with the objective of advancing our intellectual and scientific understanding of the theory and practice of design, along with the system of design process management and product semantics. The programme, since its inception in 2002, aimed at training post-graduate students in the technical, aesthetic and ergonomic practices of the field and to help them to comprehend the broader cultural issues associated with contemporary design. True to its interdisciplinary approach, the faculty members are from varied fields of engineering like mechanical, computer science, bio sciences, electrical and chemical engineering and humanities.
    [Show full text]
  • Mathematics in African History and Cultures
    Paulus Gerdes & Ahmed Djebbar MATHEMATICS IN AFRICAN HISTORY AND CULTURES: AN ANNOTATED BIBLIOGRAPHY African Mathematical Union Commission on the History of Mathematics in Africa (AMUCHMA) Mathematics in African History and Cultures Second edition, 2007 First edition: African Mathematical Union, Cape Town, South Africa, 2004 ISBN: 978-1-4303-1537-7 Published by Lulu. Copyright © 2007 by Paulus Gerdes & Ahmed Djebbar Authors Paulus Gerdes Research Centre for Mathematics, Culture and Education, C.P. 915, Maputo, Mozambique E-mail: [email protected] Ahmed Djebbar Département de mathématiques, Bt. M 2, Université de Lille 1, 59655 Villeneuve D’Asq Cedex, France E-mail: [email protected], [email protected] Cover design inspired by a pattern on a mat woven in the 19th century by a Yombe woman from the Lower Congo area (Cf. GER-04b, p. 96). 2 Table of contents page Preface by the President of the African 7 Mathematical Union (Prof. Jan Persens) Introduction 9 Introduction to the new edition 14 Bibliography A 15 B 43 C 65 D 77 E 105 F 115 G 121 H 162 I 173 J 179 K 182 L 194 M 207 N 223 O 228 P 234 R 241 S 252 T 274 U 281 V 283 3 Mathematics in African History and Cultures page W 290 Y 296 Z 298 Appendices 1 On mathematicians of African descent / 307 Diaspora 2 Publications by Africans on the History of 313 Mathematics outside Africa (including reviews of these publications) 3 On Time-reckoning and Astronomy in 317 African History and Cultures 4 String figures in Africa 338 5 Examples of other Mathematical Books and 343
    [Show full text]
  • 2010 Integral
    Autumn 2010 Volume 5 Massachusetts Institute of Technology 1ntegral n e w s f r o m t h e mathematics d e p a r t m e n t a t m i t The retirement of seven of our illustrious col- leagues this year—Mike Artin, David Ben- Inside ney, Dan Kleitman, Arthur Mattuck, Is Sing- er, Dan Stroock, and Alar Toomre—marks • Faculty news 2–3 a shift to a new generation of faculty, from • Women in math 3 those who entered the field in the Sputnik era to those who never knew life without email • A minority perspective 4 and the Internet. The older generation built • Student news 4–5 the department into the academic power- house it is today—indeed they were the core • Funds for RSI and SPUR 5 of the department, its leadership and most • Retiring faculty and staff 6–7 distinguished members, during my early years at MIT. Now, as they are in the process • Alumni corner 8 of retiring, I look around and see that my con- temporaries are becoming the department’s Dear Friends, older group. Yikes! another year gone by and what a year it Other big changes are in the works. Two of Marina Chen have taken the lead in raising an was. We’re getting older, and younger, cele- our dedicated long-term administrators— endowment for them. Together with those of brating prizes and long careers, remembering Joanne Jonsson and Linda Okun—have Tim Lu ’79 and Peiti Tung ’79, their commit- our past and looking to the future.
    [Show full text]
  • Research Notices
    AMERICAN MATHEMATICAL SOCIETY Research in Collegiate Mathematics Education. V Annie Selden, Tennessee Technological University, Cookeville, Ed Dubinsky, Kent State University, OH, Guershon Hare I, University of California San Diego, La jolla, and Fernando Hitt, C/NVESTAV, Mexico, Editors This volume presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level. The articles are peer-reviewed for two major features: (I) advancing our understanding of collegiate mathematics education, and (2) readability by a wide audience of practicing mathematicians interested in issues affecting their students. This is not a collection of scholarly arcana, but a compilation of useful and informative research regarding how students think about and learn mathematics. This series is published in cooperation with the Mathematical Association of America. CBMS Issues in Mathematics Education, Volume 12; 2003; 206 pages; Softcover; ISBN 0-8218-3302-2; List $49;AII individuals $39; Order code CBMATH/12N044 MATHEMATICS EDUCATION Also of interest .. RESEARCH: AGul<lelbrthe Mathematics Education Research: Hothomatldan- A Guide for the Research Mathematician --lllll'tj.M...,.a.,-- Curtis McKnight, Andy Magid, and -- Teri J. Murphy, University of Oklahoma, Norman, and Michelynn McKnight, Norman, OK 2000; I 06 pages; Softcover; ISBN 0-8218-20 16-8; List $20;AII AMS members $16; Order code MERN044 Teaching Mathematics in Colleges and Universities: Case Studies for Today's Classroom Graduate Student Edition Faculty
    [Show full text]
  • Thesis Title
    Exp(n+d)-time Algorithms for Computing Division, GCD and Identity Testing of Polynomials A Thesis Submitted in Partial Fulfilment of the Requirements for the Degree of Master of Technology by Kartik Kale Roll No. : 15111019 under the guidance of Prof. Nitin Saxena Department of Computer Science and Engineering Indian Institute of Technology Kanpur June, 2017 Abstract Agrawal and Vinay showed that a poly(s) hitting set for ΣΠaΣΠb(n) circuits of size s, where a is !(1) and b is O(log s) , gives us a quasipolynomial hitting set for general VP circuits [AV08]. Recently, improving the work of Agrawal and Vinay, it was showed that a poly(s) hitting set for Σ ^a ΣΠb(n) circuits of size s, where a is !(1) and n, b are O(log s), gives us a quasipolynomial hitting set for general VP circuits [AFGS17]. The inputs to the ^ gates are polynomials whose arity and total degree is O(log s). (These polynomials are sometimes called `tiny' polynomials). In this thesis, we will give a new 2O(n+d)-time algorithm to divide an n-variate polynomial of total degree d by its factor. Note that this is not an algorithm to compute division with remainder, but it finds the quotient under the promise that the divisor completely divides the dividend. The intuition behind allowing exponential time complexity here is that we will later apply these algorithms on `tiny' polynomials, and 2O(n+d) is just poly(s) in case of tiny polynomials. We will also describe an 2O(n+d)-time algorithm to find the GCD of two n-variate polynomials of total degree d.
    [Show full text]
  • Downloaded 2021-09-25T22:20:55Z
    Provided by the author(s) and University College Dublin Library in accordance with publisher policies. Please cite the published version when available. Title Realistic Computer Models Authors(s) Ajwani, Deepak; Meyerhenke, Henning Publication date 2010-01-01 Publication information Muller-Hannemann, M., Schirra, S. (eds.). Algorithm Engineering: Bridging the Gap between Algorithm Theory and Practice Series Lecture Notes in Computer Science (LNCS, volume 5971) Publisher Springer Item record/more information http://hdl.handle.net/10197/9901 Publisher's statement The final publication is available at www.springerlink.com. Publisher's version (DOI) 10.1007/978-3-642-14866-8_5 Downloaded 2021-09-25T22:20:55Z The UCD community has made this article openly available. Please share how this access benefits you. Your story matters! (@ucd_oa) © Some rights reserved. For more information, please see the item record link above. Chapter 5. Realistic Computer Models Deepak Ajwani ⋆ and Henning Meyerhenke ⋆⋆ 5.1 Introduction Many real-world applications involve storing and processing large amounts of data. These data sets need to be either stored over the memory hierarchy of one computer or distributed and processed over many parallel computing devices or both. In fact, in many such applications, choosing a realistic computation model proves to be a critical factor in obtaining practically acceptable solutions. In this chapter, we focus on realistic computation models that capture the running time of algorithms involving large data sets on modern computers better than the traditional RAM (and its parallel counterpart PRAM) model. 5.1.1 Large Data Sets Large data sets arise naturally in many applications. We consider a few examples here.
    [Show full text]
  • Poly-Time Blackbox Identity Testing for Sum of Log-Variate Constant-Width Roabps
    Poly-time blackbox identity testing for sum of log-variate constant-width ROABPs Pranav Bisht ∗ Nitin Saxena † Abstract Blackbox polynomial identity testing (PIT) affords ‘extreme variable-bootstrapping’ (Agrawal et al, STOC’18; PNAS’19; Guo et al, FOCS’19). This motivates us to study log-variate read-once oblivious algebraic branching programs (ROABP). We restrict width of ROABP to a constant and study the more general sum-of-ROABPs model. We give the first poly(s)-time blackbox PIT for sum of constant-many, size-s, O(log s)-variate constant-width ROABPs. The previous best for this model was quasi-polynomial time (Gurjar et al, CCC’15; CC’16) which is comparable to brute-force in the log-variate setting. Also, we handle unbounded-many such ROABPs if each ROABP computes a homogeneous polynomial. Our new techniques comprise– (1) an ROABP computing a homogeneous polynomial can be made syntactically homogeneous in the same width; and (2) overcome the hurdle of unknown variable order in sum-of-ROABPs in the log-variate setting (over any field). 2012 ACM CCS concept: Theory of computation– Algebraic complexity theory, Fixed parameter tractability, Pseudorandomness and derandomization; Computing methodologies– Algebraic algorithms; Mathematics of computing– Combinatoric problems. Keywords: identity test, hitting-set, ROABP, blackbox, log variate, width, diagonal, derandom- ization, homogeneous, sparsity. 1 Introduction Polynomial Identity Testing (PIT) is the problem of testing whether a given multivariate polynomial is identically zero or not. The input polynomial to be tested is usually given in a compact representation– like an algebraic circuit or an algebraic branching program (ABP).
    [Show full text]
  • Indian Roots of Cryptography
    Algologic Technical Report # 2/2013 The Indian roots of cryptography S. Parthasarathy [email protected] Ref.: newcryptoroots.tex Ver. code: 20190123a Keywords : Alice, Bob, Sita, Rama, Vatsyayana, Kamasutra, Hemachan- dra, Fibonacci, Hindu, Arab, Numeral, Ramanujan, Agarwal, AKS, IITK Abstract This note is a sequel to my article [2] about the dramatis personae of cryptography. The article, provoked a world-wide reaction. In fact, a related Google search resulted in over 6 million hits, making me a kind of celebrity ! For those who care to be more reasonable and logical, here is some more evidence to strengthen the proposal I made earlier in my article about Sita and Rama. 1 The Indian roots of cryptography The article [2] about Alice and Bob, talks about the dramatis personae of cryptography, and proposes a much more meaningful alternative. The au- thor came across many situations when contributions by India are unfairly understated or ignored completely by the cryptography community. We take a quick look at some of them. One remarkable exception is the book by Kim Plofker [15], a well-documented book which is free of bias and exaggeration. Most books on cryptography invariably include the Caesar’s cipher as an example of substitution cipher. It is strange that they all ignore, or are unaware of another substitution cipher which was in use a few centuries before Caesar’s cipher. According to [1] Cryptography is recommended in the Kama Sutra (ca 400 BCE) as a way for lovers to communicate without inconvenient discovery. 1 The Signal Corps Association [3], gives an interesting explanation of the kama sutra cipher.
    [Show full text]
  • The-St-Petersburg-Times-2014-12.Pdf
    NO. 12 (1804) САНКТ-ПЕТЕРБУРГ-ТАЙМС WEDNESDAY, APRIL 2, 2014 WWW.SPTIMES.RU ALEXANDER BELENKY / SPT Due to unseasonably warm weather, despite Monday’s brief snowstorm, the Neva River opened for navigation on Apr. 1, a month earlier than usual. Early- OPENING NIGHT morning openings of the drawbridges along the river are to be rolled out over the next few days. For the latest schedule of opening times, visit www.sptimes.ru. BUSINESS FEATURE Irina Prokhorova Russian Dogs TRAVEL Led to Greener Myshkin: Pastures Where The Mouse Is King International humane societies make it their The fairy-tale origin of a sleepy On publishing, education mission to find homes town along the Volga. Page 18. and social change. Page 9. for Russian dogs. Page 6. LocalNews www.sptimes.ru | Wednesday, April 2, 2014 ❖ 2 Ombudsman Releases Report on Human Rights By Sergey Chernov which led to the effective cancellation of THE ST. PETERSBURG TIMES screenings, while anti-gay groups gath- Xenophobia in the city rose to alarming ered outside festival venues and at- heights in 2013, sometimes resulting in tempted to force their way in. violent crime, St. Petersburg ombuds- The most serious offence took place man Alexander Shishlov pointed out in on Nov. 3, 2013, when two masked men the presentation for his annual report at entered the LGBT community center the Legislative Assembly on Mar. 26. LaSky and began shooting a pneumatic The year was marked by the right- firearm at those present. The attack left wing initiative called “Russian clean- LGBT activist Dmitry Chizhevsky blind ups,” directed against migrant vendors in one eye.
    [Show full text]