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44
HamiltonJacobi Skeletons
, 1999
"... The eikonal equation and variants of it are of significant interest for problems in computer vision and image processing. It is the basis for continuous versions of mathematical morphology, stereo, shapefromshading and for recent dynamic theories of shape. Its numerical simulation can be delicate, ..."
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Cited by 119 (12 self)
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The eikonal equation and variants of it are of significant interest for problems in computer vision and image processing. It is the basis for continuous versions of mathematical morphology, stereo, shapefromshading and for recent dynamic theories of shape. Its numerical simulation can be delicate, owing to the formation of singularities in the evolving front and is typically based on level set methods. However, there are more classical approaches rooted in Hamiltonian physics which have yet to be widely used by the computer vision community. In this paper we review the Hamiltonian formulation, which offers specific advantages when it comes to the detection of singularities or shocks. We specialize to the case of Blum's grass fire flow and measure the average outward ux of the vector field that underlies the Hamiltonian system. This measure has very different limiting behaviors depending upon whether the region over which it is computed shrinks to a singular point or a nonsingular one. Hence, it is an effective way to distinguish between these two cases. We combine the ux measurement with a homotopy preserving thinning process applied in a discrete lattice. This leads to a robust and accurate algorithm for computing skeletons in 2D as well as 3D, which has low computational complexity. We illustrate the approach with several computational examples.
Onedimensional quantum walks with absorbing boundaries. arXiv.org ePrint quantph/0207008
, 2002
"... In this paper we analyze the behavior of quantum random walks. In particular we present several new results for the absorption probabilities in systems with both one and two absorbing walls for the onedimensional case. We compute these probabilities both by employing generating functions and by use ..."
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Cited by 22 (2 self)
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In this paper we analyze the behavior of quantum random walks. In particular we present several new results for the absorption probabilities in systems with both one and two absorbing walls for the onedimensional case. We compute these probabilities both by employing generating functions and by use of an eigenfunction approach. The generating function method is used to determine some simple properties of the walks we consider, but appears to have limitations. The eigenfunction approach works by relating the problem of absorption to a unitary problem that has identical dynamics inside a certain domain, and can be used to compute several additional interesting properties, such as the time dependence of absorption. The eigenfunction method has the distinct advantage that it can be extended to arbitrary dimensionality. We outline the solution of the absorption probability problem of a (D − 1)dimensional wall in a Ddimensional space. 1
Quantum dynamics of human decisionmaking
, 2006
"... A quantum dynamic model of decisionmaking is presented, and it is compared with a previously established Markov model. Both the quantum and the Markov models are formulated as random walk decision processes, but the probabilistic principles differ between the two approaches. Quantum dynamics descri ..."
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Cited by 14 (4 self)
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A quantum dynamic model of decisionmaking is presented, and it is compared with a previously established Markov model. Both the quantum and the Markov models are formulated as random walk decision processes, but the probabilistic principles differ between the two approaches. Quantum dynamics describe the evolution of complex valued probability amplitudes over time, whereas Markov models describe the evolution of real valued probabilities over time. Quantum dynamics generate interference effects, which are not possible with Markov models. An interference effect occurs when the probability of the union of two possible paths is smaller than each individual path alone. The choice probabilities and distribution of choice response time for the quantum model are derived, and the predictions are contrasted with the Markov model.
Population Markov Chain Monte Carlo
 Machine Learning
, 2003
"... Stochastic search algorithms inspired by physical and biological systems are applied to the problem of learning directed graphical probability models in the presence of missing observations and hidden variables. For this class of problems, deterministic search algorithms tend to halt at local optima ..."
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Cited by 12 (2 self)
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Stochastic search algorithms inspired by physical and biological systems are applied to the problem of learning directed graphical probability models in the presence of missing observations and hidden variables. For this class of problems, deterministic search algorithms tend to halt at local optima, requiring random restarts to obtain solutions of acceptable quality. We compare three stochastic search algorithms: a MetropolisHastings Sampler (MHS), an Evolutionary Algorithm (EA), and a new hybrid algorithm called Population Markov Chain Monte Carlo, or popMCMC. PopMCMC uses statistical information from a population of MHSs to inform the proposal distributions for individual samplers in the population. Experimental results show that popMCMC and EAs learn more efficiently than the MHS with no information exchange. Populations of MCMC samplers exhibit more diversity than populations evolving according to EAs not satisfying physicsinspired local reversibility conditions. KEY WORDS: Markov Chain Monte Carlo, MetropolisHastings Algorithm, Graphical Probabilistic Models, Bayesian Networks, Bayesian Learning, Evolutionary Algorithms Machine Learning MCMC Issue 1 5/16/01 1.
Quantum neural networks
 In Journal of Computer and System Sciences
, 2001
"... This paper initiates the study of quantum computing within the constraints of using a polylogarithmic (O(log k n),k ≥ 1) number of qubits and a polylogarithmic number of computation steps. The current research in the literature has focussed on using a polynomial number of qubits. A new mathematical ..."
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Cited by 9 (0 self)
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This paper initiates the study of quantum computing within the constraints of using a polylogarithmic (O(log k n),k ≥ 1) number of qubits and a polylogarithmic number of computation steps. The current research in the literature has focussed on using a polynomial number of qubits. A new mathematical model of computation called Quantum Neural Networks (QNNs) is defined, building on Deutsch’s model of quantum computational network. The model introduces a nonlinear and irreversible gate, similar to the speculative operator defined by Abrams and Lloyd. The precise dynamics of this operator are defined and while giving examples in which nonlinear Schrödinger’s equations are applied, we speculate on its possible implementation. The many practical problems associated with the current model of quantum computing are alleviated in the new model. It is shown that QNNs of logarithmic size and constant depth have the same computational power as threshold circuits, which are used for modeling neural networks. QNNs of polylogarithmic size and polylogarithmic depth can solve the problems in NC, the class of problems with theoretically fast parallel solutions. Thus, the new model may indeed provide an approach for building scalable parallel computers.
On the explanation for quantum statistics
"... Abstract The concept of classical indistinguishability is analyzed and defended against a number of wellknown criticisms, with particular attention to the Gibbs ’ paradox. Granted that it is as much at home in classical as in quantum statistical mechanics, the question arises as to why indistinguis ..."
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Cited by 8 (3 self)
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Abstract The concept of classical indistinguishability is analyzed and defended against a number of wellknown criticisms, with particular attention to the Gibbs ’ paradox. Granted that it is as much at home in classical as in quantum statistical mechanics, the question arises as to why indistinguishability, in quantum mechanics but not in classical mechanics, forces a change in statistics. The answer, illustrated with simple examples, is that the equilibrium measure on classical phase space is continuous, whilst on Hilbert space it is discrete. The relevance of names, or equivalently, properties stable in time that can be used as names, is also discussed.
Magnetoreception through cryptochrome may involve superoxide
 Biophys. J
, 2009
"... ABSTRACT In the last decades, it has been demonstrated that many animal species orient in the Earth magnetic field. One of the beststudied examples is the use of the geomagnetic field by migratory birds for orientation and navigation. However, the biophysical mechanism underlying animal magnetorece ..."
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Cited by 5 (0 self)
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ABSTRACT In the last decades, it has been demonstrated that many animal species orient in the Earth magnetic field. One of the beststudied examples is the use of the geomagnetic field by migratory birds for orientation and navigation. However, the biophysical mechanism underlying animal magnetoreception is still not understood. One theory for magnetoreception in birds invokes the socalled radicalpair model. This mechanism involves a pair of reactive radicals, whose chemical fate can be influenced by the orientation with respect to the magnetic field of the Earth through Zeeman and hyperfine interactions. The fact that the geomagnetic field is weak, i.e., ~0.5 G, puts a severe constraint on the radical pair that can establish the magnetic compass sense. For a noticeable change of the reaction yield in a redirected geomagnetic field, the hyperfine interaction has to be as weak as the Earth field Zeeman interaction, i.e., unusually weak for an organic compound. Such weak hyperfine interaction can be achieved if one of the radicals is completely devoid of this interaction as realized in a radical pair containing an oxygen molecule as one of the radicals. Accordingly, we investigate here a possible radical pairbased reaction in the photoreceptor cryptochrome that reduces the protein’s flavin group from its signaling state FADH to the inactive state FADH – (which reacts to the likewise inactive FAD) by means of the superoxide radical, O2 –. We argue that the spin dynamics in the suggested reaction can act as a geomagnetic compass and that the very low physiological concentration (nMmM) of otherwise toxic O2 is sufficient, even favorable, for the biological function.
Reasoning Formally about Quantum Systems: An Overview
, 2005
"... This article is intended as an introduction to the subject of quantum logic, and as a brief survey of the relevant literature. Also discussed here are logics for speci cation and analysis of quantum information systems, in particular, recent work by P. Mateus and A. Sernadas, and also by R. van der ..."
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Cited by 2 (0 self)
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This article is intended as an introduction to the subject of quantum logic, and as a brief survey of the relevant literature. Also discussed here are logics for speci cation and analysis of quantum information systems, in particular, recent work by P. Mateus and A. Sernadas, and also by R. van der Meyden and M. Patra. Overall, our objective is to provide a highlevel presentation of the logical aspects of quantum theory. Mateus ' and Sernadas ' EQPL logic is illustrated with a small example, namely the state of an entangled pair of qubits. The "KT" logic of van der Meyden and Patra is demonstrated brie y in the context of the B92 protocol for quantum key distribution. 1
Quantum Information Theory
"... Quantum information theory provides a foundation for such topics as quantum cryptography, quantum errorcorrection and quantum teleportation. This paper seeks to provide an introduction to quantum information theory for nonphysicists at an undergraduate level. It covers basic concepts in quantum me ..."
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Cited by 1 (0 self)
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Quantum information theory provides a foundation for such topics as quantum cryptography, quantum errorcorrection and quantum teleportation. This paper seeks to provide an introduction to quantum information theory for nonphysicists at an undergraduate level. It covers basic concepts in quantum mechanics as well as in information theory, and proceeds to explore some results such as Von Neumann entropy, Schumacher coding and quantum errorcorrection. 1