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46
Picking a Pooling
"... Abstract — We introduce a concept we call “mutual metainformation” as a criterion for determining the maximum statistically significant number of clusters in distributional clustering problems. In distributional clustering, one has data drawn from an ensemble of probability distributions and seeks t ..."
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to group similar distributions together. We focus on the case of multinomials, such as a set of biased coins to be organized into groups with similar bias, given count data from a finite number of tosses of each coin. If one knew in advance the number of groups and which coins belonged to which, one could
BIASED TUGOFWAR, THE BIASED INFINITY LAPLACIAN, AND COMPARISON WITH EXPONENTIAL CONES
, 811
"... Abstract. We prove that if U ⊂ R n is an open domain whose closure U is compact in the path metric, and F is a Lipschitz function on ∂U, then for each β ∈ R there exists a unique viscosity solution to the βbiased infinity Laplacian equation on U that extends F, where ∆∞u = ∇u β∇u  + ∆∞u = 0 −2 ..."
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Cited by 14 (1 self)
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i,j uxiuxixjuxj. In the proof, we extend the tugofwar ideas of Peres, Schramm, Sheffield and Wilson, and define the βbiased ǫgame as follows. The starting position is x0 ∈ U. At the k th step the two players toss a suitably biased coin (in our key example, player I wins with odds of exp(βǫ) to 1
Probability An Extreme Value Theory for Long Head Runs*
, 1986
"... Summary. For an infinite sequence of independent coin tosses with P(Heads)=pe(0,1), the longest run of consecutive heads in the first n tosses is a natural object of study. We show that the probabilistic behavior of the length of the longest pure head run is closely approximated by that of the grea ..."
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Summary. For an infinite sequence of independent coin tosses with P(Heads)=pe(0,1), the longest run of consecutive heads in the first n tosses is a natural object of study. We show that the probabilistic behavior of the length of the longest pure head run is closely approximated
September 2010 Performance Evaluation of Zero NetInvestment Strategies ∗
"... Excess returns of zero netinvestment strategies should be largely unpredictable under standard assetpricing conditions with efficient markets. But obtaining systematically positive returns only requires a successful binary directional forecast of whether to go short or long, rather than accurate f ..."
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in economics and finance. We extend these techniques to evaluate strategies from a profit or gainloss perspective and to provide methods for the threeway long/cash/short allocation problem. The formal tests that we derive allow us to determine a strategy’s merits against a “cointoss ” null as well
HISTABRUT: A Maple Package for SymbolCrunching in Probability theory
"... is presented and briefly described. It uses the polynomial ansatz to discover (often fully rigorously, but in some cases only semirigorously (yet rigorizably!)) explicit asymptotic formulas for the moments of univariate and, more impressively, bivariate, discrete probability random variables. It ..."
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Cited by 3 (2 self)
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. It would be hopefully extended, in the future, to multivariate random variables. Many sequences of discrete random variables (e.g. tossing a (fair or loaded) coin n times, and keeping track of the number of Heads minus the number of Tails) are asymptotically normal. In [Z1], I introduced and described
A Note on Independent Random Oracles
 Theoretical Computer Science
, 1992
"... It is shown that P(A) " P(B) = BPP holds for every algorithmically random oracle A \Phi B. This result extends the corresponding "probability one" characterization of AmbosSpies (1986) and Kurtz (1987). 1 Introduction Most polynomial time complexity classes are now known to admit p ..."
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Cited by 1 (1 self)
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an independent toss of a fair coin is used to decide whether each string is in B. Thus (1.1) asserts ...
On the Strategic Disclosure of Feasible Options in Bargaining
, 2011
"... Most of the economic literature on bargaining has focused on situations where the set of possible outcomes is taken as given. This paper is concerned with situations where decisionmakers first need to identify the set of feasible outcomes before they bargain over which of them is selected. Our obje ..."
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is ranked above Raiffa’s simple cointoss solution. The analysis is extended to a dynamic setting in which the bargainers can choose the timing of disclosure. 1.
Randomness and the ergodic decomposition Mathieu Hoyrup
"... Abstract. We briefly present ongoing work about MartinLöf randomness and the ergodic decomposition theorem. In [ML66], MartinLöf defined the notion of an algorithmically random infinite binary sequence. The idea was to have an individual notion of a random object, an object that is acceptable a ..."
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as an outcome of a probabilistic process (typically, the tossing of a coin). This notion has proved successful, as it turns out that random sequences in the sense of MartinLöf have all the usual properties that are proved to hold almost surely in classical probability theory. A particularly interesting
Towards a Unified Theory of Cryptographic Agents
"... In recent years there has been a fantastic boom of increasingly sophisticated “cryptographic objects ” — identitybased encryption, fullyhomomorphic encryption, functional encryption, and most recently, various forms of obfuscation. These objects often come in various flavors of security, and as t ..."
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unifies various multiparty computation tasks like commitment, cointossing and zeroknowledge proofs. Our contributions can be summarized as follows. • Our main contribution is a new model of cryptographic computation, that unifies and extends cryptographic primitives such as Obfuscation, Functional
Linear consistency testing
 In Proceedings of RANDOM
, 1999
"... We extend the notion of linearity testing to the task of checking linearconsistency of multiple functions. Informally, functions are “linear ” if their graphs form straight lines on the plane. Two such functions are “consistent ” if the lines have the same slope. We propose a variant of a test of B ..."
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Cited by 6 (1 self)
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of our results we give yet another new and tight characterization of NP, namely ∀ɛ>0, NP = MIP 1 1−ɛ, [O(log n), 3, 1]. 2 I.e., every language in NP has 3prover 1round proof systems in which the verifier tosses O(log n) coins and asks each of the three provers one question each. The provers respond
Results 11  20
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