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RANDERS MANIFOLDS OF POSITIVE CONSTANT Curvature
, 2003
"... We prove that any simply connected and complete Riemannian manifold, on which a Randers metric of positive constant flag curvature exists, must be diffeomorphic to an odddimensional sphere, provided a certain 1form vanishes on it. ..."
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Cited by 6 (1 self)
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We prove that any simply connected and complete Riemannian manifold, on which a Randers metric of positive constant flag curvature exists, must be diffeomorphic to an odddimensional sphere, provided a certain 1form vanishes on it.
The Capacity of LowDensity ParityCheck Codes Under MessagePassing Decoding
, 2001
"... In this paper, we present a general method for determining the capacity of lowdensity paritycheck (LDPC) codes under messagepassing decoding when used over any binaryinput memoryless channel with discrete or continuous output alphabets. Transmitting at rates below this capacity, a randomly chos ..."
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Cited by 574 (9 self)
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exponentially fast in the length of the code with arbitrarily small loss in rate.) Conversely, transmitting at rates above this capacity the probability of error is bounded away from zero by a strictly positive constant which is independent of the length of the code and of the number of iterations performed
Height estimates for surfaces with positive constant mean curvature in
 M× R. Illinois J. Math
"... Abstract. We obtain height estimates for compact embedded surfaces with positive constant mean curvature in a Riemannian product space M 2 × R and boundary on a slice. We prove that these estimates are optimal for the homogeneous spaces R 3 , S 2 × R and H 2 × R and we characterize the surfaces for ..."
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Cited by 9 (3 self)
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Abstract. We obtain height estimates for compact embedded surfaces with positive constant mean curvature in a Riemannian product space M 2 × R and boundary on a slice. We prove that these estimates are optimal for the homogeneous spaces R 3 , S 2 × R and H 2 × R and we characterize the surfaces
© Hindawi Publishing Corp. RANDERS MANIFOLDS OF POSITIVE CONSTANT
, 2001
"... We prove that any simply connected and complete Riemannian manifold, on which a Randers metric of positive constant flag curvature exists, must be diffeomorphic to an odddimensional sphere, provided a certain 1form vanishes on it. 2000 Mathematics Subject Classification: 53C60, 53C25. 1. Introduct ..."
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We prove that any simply connected and complete Riemannian manifold, on which a Randers metric of positive constant flag curvature exists, must be diffeomorphic to an odddimensional sphere, provided a certain 1form vanishes on it. 2000 Mathematics Subject Classification: 53C60, 53C25. 1
Attention and the detection of signals
 Journal of Experimental Psychology: General
, 1980
"... Detection of a visual signal requires information to reach a system capable of eliciting arbitrary responses required by the experimenter. Detection latencies are reduced when subjects receive a cue that indicates where in the visual field the signal will occur. This shift in efficiency appears to b ..."
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Cited by 565 (2 self)
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about the way in which expectancy improves performance. First, when subjects are cued on each trial, they show stronger expectancy effects than when a probable position is held constant for a block, indicating the active nature of the expectancy. Second, while information on spatial position improves
Perspectives on Program Analysis
, 1996
"... eing analysed. On the negative side, the semantic correctness of the analysis is seldom established and therefore there is often no formal justification for the program transformations for which the information is used. The semantics based approach [1; 5] is often based on domain theory in the form ..."
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Cited by 685 (35 self)
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in the form of abstract domains modelling sets of values, projections, or partial equivalence relations. The approach tends to focus more directly on discovering the extensional properties of interest: for constant propagation it might operate on sets of values with constancy corresponding to singletons
Exact Matrix Completion via Convex Optimization
, 2008
"... We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfe ..."
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Cited by 873 (26 self)
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perfectly recover most lowrank matrices from what appears to be an incomplete set of entries. We prove that if the number m of sampled entries obeys m ≥ C n 1.2 r log n for some positive numerical constant C, then with very high probability, most n × n matrices of rank r can be perfectly recovered
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 797 (39 self)
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We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts
The Dantzig selector: statistical estimation when p is much larger than n
, 2005
"... In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Ax + z, where x ∈ R p is a parameter vector of interest, A is a data matrix with possibly far fewer rows than columns, n ≪ ..."
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Cited by 879 (14 self)
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, where r is the residual vector y − A˜x and t is a positive scalar. We show that if A obeys a uniform uncertainty principle (with unitnormed columns) and if the true parameter vector x is sufficiently sparse (which here roughly guarantees that the model is identifiable), then with very large probability
Monopolistic competition and optimum product diversity. The American Economic Review,
, 1977
"... The basic issue concerning production in welfare economics is whether a market solution will yield the socially optimum kinds and quantities of commodities. It is well known that problems can arise for three broad reasons: distributive justice; external effects; and scale economies. This paper is c ..."
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Cited by 1911 (5 self)
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. Such an optimum can be realized in a market if perfectly discriminatory pricing is possible. Otherwise we face conflicting problems. A competitive market fulfilling the marginal condition would be unsustainable because total profits would be negative. An element of monopoly would allow positive profits, but would
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