The Problem of Distributed Consensus: a Survey Stephen Wolfram*
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Jet Development in Leading Log QCD.Pdf
17 CALT-68-740 DoE RESEARCH AND DEVELOPMENT REPORT Jet Development in Leading Log QCD * by STEPHEN WOLFRAM California Institute of Technology, Pasadena. California 91125 ABSTRACT A simple picture of jet development in QCD is described. Various appli- cations are treated, including transverse spreading of jets, hadroproduced y* pT distributions, lepton energy spectra from heavy quark decays, soft parton multiplicities and hadron cluster formation. *Work supported in part by the U.S. Department of Energy under Contract No. DE-AC-03-79ER0068 and by a Feynman Fellowship. 18 According to QCD, high-energy e+- e annihilation into hadrons is initiated by the production from the decaying virtual photon of a quark and an antiquark, ,- +- each with invariant masses up to the c.m. energy vs in the original e e collision. The q and q then travel outwards radiating gluons which serve to spread their energy and color into a jet of finite angle. After a time ~ 1/IS, the rate of gluon emissions presumably decreases roughly inversely with time, except for the logarithmic rise associated with the effective coupling con 2 stant, (a (t) ~ l/log(t/A ), where It is the invariant mass of the radiating s . quark). Finally, when emissions have degraded the energies of the partons produced until their invariant masses fall below some critical ~ (probably c a few times h), the system of quarks and gluons begins to condense into the observed hadrons. The probability for a gluon to be emitted at times of 0(--)1 is small IS and may be est~mated from the leading terms of a perturbation series in a (s). -
On the Uniqueness of Gibbs States in the Pirogov-Sinai Theory?
Commun. Math. Phys. 189, 311 – 321 (1997) Communications in Mathematical Physics c Springer-Verlag 1997 On the Uniqueness of Gibbs States in the Pirogov-Sinai Theory? J.L. Lebowitz1, A.E. Mazel2 1 Department of Mathematics and Physics, Rutgers University, New Brunswick, NJ 08903, USA 2 International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow 113556, Russia Received: 4 June 1996 / Accepted: 30 October 1996 Dedicated to the memory of Roland Dobrushin Abstract: We prove that, for low-temperature systems considered in the Pirogov-Sinai theory, uniqueness in the class of translation-periodic Gibbs states implies global unique- ness, i.e. the absence of any non-periodic Gibbs state. The approach to this infinite volume state is exponentially fast. 1. Introduction The problem of uniqueness of Gibbs states was one of R.L.Dobrushin’s favorite subjects in which he obtained many classical results. In particular when two or more translati- on-periodic states coexist, it is natural to ask whether there might also exist other, non translation-periodic, Gibbs states, which approach asymptotically, in different spatial directions, the translation periodic ones. The affirmative answer to this question was given by R.L.Dobrushin with his famous construction of such states for the Ising model, using boundary conditions, in three and higher dimensions [D]. Here we consider the opposite± situation: we will prove that in the regions of the low-temperature phase diagram where there is a unique translation-periodic Gibbs state one actually has global uniqueness of the limit Gibbs state. Moreover we show that, uniformly in boundary conditions, the finite volume probability of any local event tends to its infinite volume limit value exponentially fast in the diameter of the domain. -
A New Kind of Science; Stephen Wolfram, Wolfram Media, Inc., 2002
A New Kind of Science; Stephen Wolfram, Wolfram Media, Inc., 2002. Almost twenty years ago, I heard Stephen Wolfram speak at a Gordon Confer- ence about cellular automata (CA) and how they can be used to model seashell patterns. He had recently made a splash with a number of important papers applying CA to a variety of physical and biological systems. His early work on CA focused on a classification of the behavior of simple one-dimensional sys- tems and he published some interesting papers suggesting that CA fall into four different classes. This was original work but from a mathematical point of view, hardly rigorous. What he was essentially claiming was that even if one adds more layers of complexity to the simple rules, one does not gain anything be- yond these four simples types of behavior (which I will describe below). After a two decade hiatus from science (during which he founded Wolfram Science, the makers of Mathematica), Wolfram has self-published his magnum opus A New Kind of Science which continues along those lines of thinking. The book itself is beautiful to look at with almost a thousand pictures, 850 pages of text and over 300 pages of detailed notes. Indeed, one might suggest that the main text is for the general public while the notes (which exceed the text in total words) are aimed at a more technical audience. The book has an associated web site complete with a glowing blurb from the publisher, quotes from the media and an interview with himself to answer questions about the book. -
PARTON and HADRON PRODUCTION in E+E- ANNIHILATION Stephen Wolfram California Institute of Technology, Pasadena, California 91125
549 * PARTON AND HADRON PRODUCTION IN e+e- ANNIHILATION Stephen Wolfram California Institute of Technology, Pasadena, California 91125 Ab stract: The production of showers of partons in e+e- annihilation final states is described according to QCD , and the formation of hadrons is dis cussed. Resume : On y decrit la production d'averses d� partons dans la theorie QCD qui forment l'etat final de !'annihilation e+ e , ainsi que leur transform ation en hadrons. *Work supported in part by the U.S. Department of Energy under contract no. DE-AC-03-79ER0068. SSt1 Introduction In these notes , I discuss some attemp ts e ri the cl!evellope1!1t of - to d s c be hadron final states in e e annihilation events ll>Sing. QCD. few featm11res A (barely visible at available+ energies} of this deve l"'P"1'ent amenab lle· are lt<J a precise and formal analysis in QCD by means of pe·rturbatirnc• the<J ry. lfor the mos t part, however, existing are quite inadle<!i""' lte! theoretical mett:l�ods one must therefore simply try to identify dl-iimam;t physical p.l:ten<0melilla tt:he to be expected from QCD, and make estll!att:es of dne:i.r effects , vi.th the hop·e that results so obtained will provide a good appro�::illliatimn to eventllLal'c ex act calculations . In so far as such estllma�es r necessa�y� pre�ise �r..uan- a e titative tests of QCD are precluded . On the ott:her handl , if QC!Ji is ass11l!med correct, then existing experimental data to inve•stigate its be may \JJ:SE•«f havior in regions not yet explored by theoreticalbe llJleaums . -
Purchase a Nicer, Printable PDF of This Issue. Or Nicest of All, Subscribe To
Mel says, “This is swell! But it’s not ideal—it’s a free, grainy PDF.” Attain your ideals! Purchase a nicer, printable PDF of this issue. Or nicest of all, subscribe to the paper version of the Annals of Improbable Research (six issues per year, delivered to your doorstep!). To purchase pretty PDFs, or to subscribe to splendid paper, go to http://www.improbable.com/magazine/ ANNALS OF Special Issue THE 2009 IG® NOBEL PRIZES Panda poo spinoff, Tequila-based diamonds, 11> Chernobyl-inspired bra/mask… NOVEMBER|DECEMBER 2009 (volume 15, number 6) $6.50 US|$9.50 CAN 027447088921 The journal of record for inflated research and personalities Annals of © 2009 Annals of Improbable Research Improbable Research ISSN 1079-5146 print / 1935-6862 online AIR, P.O. Box 380853, Cambridge, MA 02238, USA “Improbable Research” and “Ig” and the tumbled thinker logo are all reg. U.S. Pat. & Tm. Off. 617-491-4437 FAX: 617-661-0927 www.improbable.com [email protected] EDITORIAL: [email protected] The journal of record for inflated research and personalities Co-founders Commutative Editor VP, Human Resources Circulation (Counter-clockwise) Marc Abrahams Stanley Eigen Robin Abrahams James Mahoney Alexander Kohn Northeastern U. Research Researchers Webmaster Editor Associative Editor Kristine Danowski, Julia Lunetta Marc Abrahams Mark Dionne Martin Gardiner, Tom Gill, [email protected] Mary Kroner, Wendy Mattson, General Factotum (web) [email protected] Dissociative Editor Katherine Meusey, Srinivasan Jesse Eppers Rose Fox Rajagopalan, Tom Roberts, Admin Tom Ulrich Technical Eminence Grise Lisa Birk Psychology Editor Dave Feldman Robin Abrahams Design and Art European Bureau Geri Sullivan Art Director emerita Kees Moeliker, Bureau Chief Contributing Editors PROmote Communications Peaco Todd Rotterdam Otto Didact, Stephen Drew, Ernest Lois Malone Webmaster emerita [email protected] Ersatz, Emil Filterbag, Karen Rich & Famous Graphics Steve Farrar, Edinburgh Desk Chief Hopkin, Alice Kaswell, Nick Kim, Amy Gorin Erwin J.O. -
Obituary Roland Lvovich Dobrushin, 1929 – 1995
Obituary Roland Lvovich Dobrushin, 1929 ± 1995 Roland Lvovich Dobrushin, an outstanding scientist in the domain of probability theory, information theory and mathematical physics, died of cancer in Moscow, on November 12, 1995, at the age of 66. Dobrushin's premature decease is a tremendous loss to Russian and world science. Dobrushin was born on July 20, 1929 in Leningrad (St.-Petersburg). In early childhood he lost his father; his mother died when he was still a schoolboy. In 1936, after his father's death, the family moved to Moscow. In 1947, on leaving school, Dobrushin entered the Mechanico-Mathematical Department of Moscow Univer- sity and after graduating from it did postgraduate studies. Then, from 1955 to 1965, he worked at the Proba- bility Theory Section of the Mechanico-Mathematical Department of Moscow University, and since 1967 until his demise was Head of the Multicomponent Random Systems Laboratory, within the Institute for Information Transmission Problems of the Russian Academy of Sciences (the Academy of Sciences of the USSR). Since 1967 Dobrushin was a Professor in the Electromagnetic Waves Section of the Moscow Physics Technologies Institute and since 1991 he was a Professor in the Probability Theory Section at Moscow University as well. In 1955 Dobrushin presented his candidate's thesis, and in 1962 he took his Doctor's degree. Even as a schoolboy Dobrushin conceived an interest in mathematics and participated in school mathemat- ical contests where he won a number of prizes. While at the University Dobrushin was an active member of E.B. Dynkin's seminar 1 . On A.N. -
A. Toom. Cellular Automata with Errors: Problems for Students Of
Chapter 4 CELLULAR AUTOMATA WITH ERRORS: PROBLEMS for STUDENTS of PROBABILITY Andrei Toom Incarnate Word College San Antonio, Texas Abstract ABSTRACT. This is a survey of some problems and methods in the theory of probabilistic cellular automata. It is addressed to those students who love to learn a theory by solving problems. The only prerequisite is a standard course in probability. General methods are illustrated by examples, some of which have played important roles in the development of these methods. More than a hundred exercises and problems and more than a dozen of unsolved problems are discussed. Special attention is paid to the computational aspect; several pseudo-codes are given to show how to program processes in question. We consider probabilistic systems with local interactions, which may be thought of as special kinds of Markov processes. Informally speaking, they describe the functioning of a finite or infinite system of automata, all of which update their states at every moment of discrete time, according to some deterministic or stochastic rule depending on their neighbors’ states. From statistical physics came the question of uniqueness of the limit as t → ∞ behavior of the infinite system. Existence of at least one limit follows from the famous fixed-point theorem and is proved here as Theorem 1. Systems which have a unique limit behavior and converge to it from any initial condition may be said to forget everything when time tends to infinity, while the others remember something forever. The former systems are called ergodic, the latter non-ergodic. In statistical physics the non-ergodic systems help us understand conservation of non-symmetry in macro-objects. -
SOMMAIRE DU No 110
SOMMAIRE DU No 110 SMF Mot de la Pr´esidente ................................................................ 3 MATHEMATIQUES´ Le probl`eme des nombres congruents, Pierre Colmez ................................ 9 MATHEMATIQUES´ ET PHYSIQUE Hommage `a Feliks A. Berezin, C. Roger ............................................ 23 Br`eve biographie scientifique de F.A. Berezin, R.A. Minlos .......................... 30 Souvenirs, A.M. Vershik ............................................................ 45 Lettre au Recteur de l’Universit´ed’Etat´ de Moscou, F.A. Berezin .................... 47 ENSEIGNEMENT Suite du d´ebat au Conseil de la SMF du 7-01-2006 Pour lancer le d´ebat, M. Andler .................................................... 57 Vers une r´e´evaluation de l’enseignement des math´ematiques et des sciences, J.-P. Demailly . .................................................................... 61 Les « sp´ecialit´es » au Bac S : une approche historique, D. Duverney ................ 65 Quelques ´el´ements de r´eflexion, C. Schwartz ........................................ 79 Conclusion, Le Bureau de la SMF .................................................. 81 PRIX ET DISTINCTIONS La vulgarisation des math´ematiques, P. Boulanger .................................. 83 Le prix Anatole Decerf 2006 d´ecern´e`a Centre-Sciences, P. Maheux .................. 89 INFORMATIONS Quel bagage math´ematique pour l’ing´enieur europ´een ? Lˆe Thanh-Tˆam .............. 93 Irish Mathematical Society, M. OReilly ............................................. -
A New Kind of Science: a 15-Year View
A New Kind of Science: A 15-Year View Stephen Wolfram Founder and CEO Wolfram Research, Inc. [email protected] Starting now, in celebration of its 15th anniversary, A New Kind of Science will be freely available in its entirety, with high-resolution images, on the web or for download. It’s now 15 years since I published my book A New Kind of Science — more than 25 since I started writing it, and more than 35 since I started working towards it. But with every passing year I feel I under- stand more about what the book is really about—and why it’s impor- tant. I wrote the book, as its title suggests, to contribute to the progress of science. But as the years have gone by, I’ve realized that the core of what’s in the book actually goes far beyond science—into many areas that will be increasingly important in defining our whole future. So, viewed from a distance of 15 years, what is the book really about? At its core, it’s about something profoundly abstract: the the- ory of all possible theories, or the universe of all possible universes. But for me one of the achievements of the book is the realization that one can explore such fundamental things concretely—by doing actual experiments in the computational universe of possible programs. And https://doi.org/10.25088/ComplexSystems.26.3.197 198 S. Wolfram in the end the book is full of what might at first seem like quite alien pictures made just by running very simple such programs. -
Cellular Automation
John von Neumann Cellular automation A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays.[2] A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. An initial state (time t = 0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the stochastic cellular automaton and asynchronous cellular automaton. The concept was originally discovered in the 1940s by Stanislaw Ulam and John von Neumann while they were contemporaries at Los Alamos National Laboratory. While studied by some throughout the 1950s and 1960s, it was not until the 1970s and Conway's Game of Life, a two-dimensional cellular automaton, that interest in the subject expanded beyond academia. -
A New Kind of Science
Wolfram|Alpha, A New Kind of Science A New Kind of Science Wolfram|Alpha, A New Kind of Science by Bruce Walters April 18, 2011 Research Paper for Spring 2012 INFSY 556 Data Warehousing Professor Rhoda Joseph, Ph.D. Penn State University at Harrisburg Wolfram|Alpha, A New Kind of Science Page 2 of 8 Abstract The core mission of Wolfram|Alpha is “to take expert-level knowledge, and create a system that can apply it automatically whenever and wherever it’s needed” says Stephen Wolfram, the technologies inventor (Wolfram, 2009-02). This paper examines Wolfram|Alpha in its present form. Introduction As the internet became available to the world mass population, British computer scientist Tim Berners-Lee provided “hypertext” as a means for its general consumption, and coined the phrase World Wide Web. The World Wide Web is often referred to simply as the Web, and Web 1.0 transformed how we communicate. Now, with Web 2.0 firmly entrenched in our being and going with us wherever we go, can 3.0 be far behind? Web 3.0, the semantic web, is a web that endeavors to understand meaning rather than syntactically precise commands (Andersen, 2010). Enter Wolfram|Alpha. Wolfram Alpha, officially launched in May 2009, is a rapidly evolving "computational search engine,” but rather than searching pre‐existing documents, it actually computes the answer, every time (Andersen, 2010). Wolfram|Alpha relies on a knowledgebase of data in order to perform these computations, which despite efforts to date, is still only a fraction of world’s knowledge. Scientist, author, and inventor Stephen Wolfram refers to the world’s knowledge this way: “It’s a sad but true fact that most data that’s generated or collected, even with considerable effort, never gets any kind of serious analysis” (Wolfram, 2009-02). -
Downloadable PDF of the 77500-Word Manuscript
From left: W. Daniel Hillis, Neil Gershenfeld, Frank Wilczek, David Chalmers, Robert Axelrod, Tom Griffiths, Caroline Jones, Peter Galison, Alison Gopnik, John Brockman, George Dyson, Freeman Dyson, Seth Lloyd, Rod Brooks, Stephen Wolfram, Ian McEwan. In absentia: Andy Clark, George Church, Daniel Kahneman, Alex "Sandy" Pentland (Click to expand photo) INTRODUCTION by Venki Ramakrishnan The field of machine learning and AI is changing at such a rapid pace that we cannot foresee what new technical breakthroughs lie ahead, where the technology will lead us or the ways in which it will completely transform society. So it is appropriate to take a regular look at the landscape to see where we are, what lies ahead, where we should be going and, just as importantly, what we should be avoiding as a society. We want to bring a mix of people with deep expertise in the technology as well as broad 1 thinkers from a variety of disciplines to make regular critical assessments of the state and future of AI. —Venki Ramakrishnan, President of the Royal Society and Nobel Laureate in Chemistry, 2009, is Group Leader & Former Deputy Director, MRC Laboratory of Molecular Biology; Author, Gene Machine: The Race to Decipher the Secrets of the Ribosome. [ED. NOTE: In recent months, Edge has published the fifteen individual talks and discussions from its two-and-a-half-day Possible Minds Conference held in Morris, CT, an update from the field following on from the publication of the group-authored book Possible Minds: Twenty-Five Ways of Looking at AI. As a special event for the long Thanksgiving weekend, we are pleased to publish the complete conference—10 hours plus of audio and video, as well as this downloadable PDF of the 77,500-word manuscript.