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Good News and Bad News: Representation Theorems and Applications
 Bell Journal of Economics
"... prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtai ..."
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Cited by 684 (3 self)
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prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
Hypergraph Extension of the Alonâ€“Tarsi List Coloring Theorem
, 2002
"... An Eulerian subgraph in a digraph is a subgraph in which indegree equals outdegree at each vertex. Alon and Tarsi [2] proved that a graph is dchoosable when it has an orientation that has no vertex of outdegree at least d and has the property that the numbers of Eulerian subgraphs with evensized a ..."
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Cited by 5 (0 self)
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An Eulerian subgraph in a digraph is a subgraph in which indegree equals outdegree at each vertex. Alon and Tarsi [2] proved that a graph is dchoosable when it has an orientation that has no vertex of outdegree at least d and has the property that the numbers of Eulerian subgraphs with even
Compression of Individual Sequences via VariableRate Coding
, 1978
"... this paper contains two parts: descrip five part (Section II) where all the results are stated 532 XEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 1T24, NO. 5, SEPTEMF..R 1978 and discussed and a formal part (Section III) where all proofs except that of Theorem 2 are given. The proof of Theorem 2, w ..."
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Cited by 937 (9 self)
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this paper contains two parts: descrip five part (Section II) where all the results are stated 532 XEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 1T24, NO. 5, SEPTEMF..R 1978 and discussed and a formal part (Section III) where all proofs except that of Theorem 2 are given. The proof of Theorem 2
Theorems for free!
 FUNCTIONAL PROGRAMMING LANGUAGES AND COMPUTER ARCHITECTURE
, 1989
"... From the type of a polymorphic function we can derive a theorem that it satisfies. Every function of the same type satisfies the same theorem. This provides a free source of useful theorems, courtesy of Reynolds' abstraction theorem for the polymorphic lambda calculus. ..."
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Cited by 380 (8 self)
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From the type of a polymorphic function we can derive a theorem that it satisfies. Every function of the same type satisfies the same theorem. This provides a free source of useful theorems, courtesy of Reynolds' abstraction theorem for the polymorphic lambda calculus.
Symmetry and Related Properties via the Maximum Principle
, 1979
"... We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting plan ..."
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Cited by 539 (4 self)
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We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting plane. We treat solutions in bounded domains and in the entire space.
Parametric Shape Analysis via 3Valued Logic
, 2001
"... Shape Analysis concerns the problem of determining "shape invariants"... ..."
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Cited by 660 (79 self)
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Shape Analysis concerns the problem of determining "shape invariants"...
Teleporting an Unknown Quantum State via Dual Classical and EPR Channels
, 1993
"... An unknown quantum state jOEi can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical EPR correlations. To do so the sender, "Alice," and the receiver, "Bob," must prearrange the sharing of an EPRcorrelated pair of particles. ..."
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Cited by 648 (22 self)
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An unknown quantum state jOEi can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical EPR correlations. To do so the sender, "Alice," and the receiver, "Bob," must prearrange the sharing of an EPRcorrelated pair of particles. Alice makes a joint measurement on her EPR particle and the unknown quantum system, and sends Bob the classical result of this measurement. Knowing this, Bob can convert the state of his EPR particle into an exact replica of the unknown state jOEi which Alice destroyed. Expanded version of manuscript submitted to Phys. Rev. Lett. December 1992 PACS numbers: 03.65.Bz, 42.50.Dv, 89.70.+c (a) Permanent address. The existence of long range correlations between EinsteinPodolskyRosen (EPR) [1] pairs of particles raises the question of their use for information transfer. Einstein himself used the word "telepathically" in this context [2]. It is known that instantaneous information transfer is definitely impossib...
Estimating the number of clusters in a dataset via the Gap statistic
, 2000
"... We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. kmeans or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference ..."
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Cited by 492 (1 self)
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We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. kmeans or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference null distribution. Some theory is developed for the proposal and a simulation study that shows that the Gap statistic usually outperforms other methods that have been proposed in the literature. We also briey explore application of the same technique to the problem for estimating the number of linear principal components. 1 Introduction Cluster analysis is an important tool for \unsupervised" learning the problem of nding groups in data without the help of a response variable. A major challenge in cluster analysis is estimation of the optimal number of \clusters". Figure 1 (top right) shows a typical plot of an error measure W k (the within cluster dispersion dened below) for a clustering pr...
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