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Quantum complexity theory
 in Proc. 25th Annual ACM Symposium on Theory of Computing, ACM
, 1993
"... Abstract. In this paper we study quantum computation from a complexity theoretic viewpoint. Our first result is the existence of an efficient universal quantum Turing machine in Deutsch’s model of a quantum Turing machine (QTM) [Proc. Roy. Soc. London Ser. A, 400 (1985), pp. 97–117]. This constructi ..."
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Cited by 574 (5 self)
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the modern (complexity theoretic) formulation of the Church–Turing thesis. We show the existence of a problem, relative to an oracle, that can be solved in polynomial time on a quantum Turing machine, but requires superpolynomial time on a boundederror probabilistic Turing machine, and thus not in the class
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 907 (36 self)
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. In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating
A probabilistic theory of occupancy and emptiness
 In Proceedings of European Conference on Computer Vision (ECCV
, 2002
"... Abstract. This paper studies the inference of 3D shape from a set of Ò noisy photos. We derive a probabilistic framework to specify what one can infer about 3D shape for arbitrarilyshaped, Lambertian scenes and arbitrary viewpoint configurations. Based on formal definitions of visibility, occupancy ..."
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Cited by 30 (3 self)
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Abstract. This paper studies the inference of 3D shape from a set of Ò noisy photos. We derive a probabilistic framework to specify what one can infer about 3D shape for arbitrarilyshaped, Lambertian scenes and arbitrary viewpoint configurations. Based on formal definitions of visibility
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 819 (28 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical
Probabilistic Theory of Transport Processes with Polarization
 SIAM APPL. MATH
, 2000
"... We derive a probabilistic representation for solutions of matrixvalued transport equations that account for polarization eects. Such equations arise in radiative transport for the Stokes parameters that model the propagation of light through turbulent atmospheres. They also arise in radiative tran ..."
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Cited by 4 (3 self)
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We derive a probabilistic representation for solutions of matrixvalued transport equations that account for polarization eects. Such equations arise in radiative transport for the Stokes parameters that model the propagation of light through turbulent atmospheres. They also arise in radiative
PROBABILISTIC THEORIES: WHAT IS SPECIAL ABOUT QUANTUM MECHANICS?
, 2009
"... Quantum Mechanics (QM) is a very special probabilistic theory, yet we don’t know which operational principles make it so. All axiomatization attempts suffer at least one postulate of a mathematical nature. Here I will analyze the possibility of deriving QM as the mathematical representation of a fa ..."
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Cited by 24 (5 self)
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Quantum Mechanics (QM) is a very special probabilistic theory, yet we don’t know which operational principles make it so. All axiomatization attempts suffer at least one postulate of a mathematical nature. Here I will analyze the possibility of deriving QM as the mathematical representation of a
A Probabilistic Theory for Intertemporal Indifference
, 2014
"... This paper provides a closed form distribution for the probability of intertemporal indifference between a certain quantity of a commodity now, ()Q q00 = , and some future quantity ()Q T q = at time t = T assuming a discount weight, ( ) ()w T 0,1 ∈. ..."
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This paper provides a closed form distribution for the probability of intertemporal indifference between a certain quantity of a commodity now, ()Q q00 = , and some future quantity ()Q T q = at time t = T assuming a discount weight, ( ) ()w T 0,1 ∈.
Fusion, Propagation, and Structuring in Belief Networks
 ARTIFICIAL INTELLIGENCE
, 1986
"... Belief networks are directed acyclic graphs in which the nodes represent propositions (or variables), the arcs signify direct dependencies between the linked propositions, and the strengths of these dependencies are quantified by conditional probabilities. A network of this sort can be used to repre ..."
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Cited by 484 (8 self)
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with the task of fusing and propagating the impacts of new information through the networks in such a way that, when equilibrium is reached, each proposition will be assigned a measure of belief consistent with the axioms of probability theory. It is shown that if the network is singly connected (e.g. tree
Combining symbolic and neural learning to revise probabilistic theories
 IN PROCEEDINGS OF THE 1992 MACHINE LEARNING WORKSHOP ON INTEGRATED LEARNING IN REAL DOMAINS
, 1992
"... This paper describes Rapture  a system for revising probabilistic theories that combines symbolic and neuralnetwork learning methods. Rapture uses a modified version of backpropagation to refine the certainty factors of a Mycinstyle rulebase and it uses ID3's information gain heuristic to ..."
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Cited by 9 (1 self)
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This paper describes Rapture  a system for revising probabilistic theories that combines symbolic and neuralnetwork learning methods. Rapture uses a modified version of backpropagation to refine the certainty factors of a Mycinstyle rulebase and it uses ID3's information gain heuristic
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 475 (67 self)
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the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae
Results 11  20
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4,307