PPT-Some Limits on Non-Local Randomness Expansion

Matt Coudron and Henry Yuen 6845 121212 God does not play dice Albert Einstein Einstein stop telling God what to do Niels Bohr The Motivating Question Is it possible to test randomness. The original motivation for extractors was to simulate randomized algorithms with weak random sources as might arise in nature This motivation is still compelling but extractors have taken on a much wider signi64257cance in the years since they were . device. independent . randomness. . amplification. with . few. devices. F.G.S.L Brandao. 1. , R. . . Ramanathan. 2. . A. Grudka. 3. , K.. 4. , M.. 5. ,P.. 6. Horodeccy. 1. Department . of Computer Science, University College London. How can we draw the line?. Taner Edis. Department . of Physics,. . Truman . State . University. Supernatural fiction. Stories of ghosts, gods, spirits, magic, the occult.. Personality and agency (“spirit”) somehow fundamental to how the world works.. Dr. X. Topics. What Does Randomness Mean?. Randomness in . games. Generating Random Values. Random events in real life: measuring . randomness. What is Randomness?. Unpredictability?. Does it characterize a single event or a sequence of events?. Presented by . Lin McMullin. National Math and Science Initiative . Continuity. What happens at . x. = 2? . What is . f. (2)?. What happens . near. . x . = 2? . f. (. x. ) is . near . -. Greg Kelly, Hanford High School, Richland, Washington. Photo by Vickie Kelly, 2007. Grand Teton National Park, Wyoming. Suppose you drive 200 miles, and it takes you 4 hours.. Then your average speed is:. minimal. assumptions. needed for. infinite. randomness . expansion?. Henry Yuen . (MIT). Stellenbosch, South Africa. 27 October 2015. 0. 1. 1. 0. 1. 1. 0. 1. 0. 1. 0. 0. 1. 1. 1. 0. 1. 0. 1. 1. 1. 0. Vertical Asymptotes (VA). If . then . x=a is a VA of f(x. ). To find VA algebraically – set denominator = 0. Example 1 – Find VA. Finding limits on either side of a VA. Randomness. ？. 隨機是指缺乏模式及可預測性的. 事件. e.g.. . 擲骰、六合彩、粒子運動等. 甚麼是機率. Probability. ？. 機率是用以描述隨機事件結果的數學. Objective: Evaluate a limit using properties of limits . Miss . Battaglia. AB/BC Calculus. Properties of Limits. Remember that the limit of f(x) as x approaches c does not depend on the value of f at x=c… But it might happen!. With gratitude to the John Templeton Foundation who supported this project but is not responsible for its content. . “… if purpose is part of this universe, then randomness, by definition, is not possible. This is also one of the rationales for religious opposition to evolution, where, according to theory, (non-random) selection is applied to the results of random genetic variation.” . 'I li :: 52 P. SUPPES pp. 229-2301. 522 P. SUPPES PROOF: Suppose not. Without loss of generality let BIA � Axiom 5 we have AIX - AnBlB and AnBlA � BIX, whence A nB/X An B/X, which is Lovett (IAS). Coding, Complexity and . Sparsity. workshop. August 2011. Overview. Pseudo-randomness – what? why?. Concrete examples. Local independence. Expander graphs. Small space computations. Lynn A. Knight, CEcD. Key Facts About Business Retention And Expansion. 80%+ of growth comes from expansion of . existing. firms. BRE is essential intelligence gathering. BRE can help speed up local investment.