2,824 research outputs found

    An asymptotical study of combinatorial optimization problems by means of statistical mechanics

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    AbstractThe analogy between combinatorial optimization and statistical mechanics has proven to be a fruitful object of study. Simulated annealing, a metaheuristic for combinatorial optimization problems, is based on this analogy. In this paper we show how a statistical mechanics formalism can be utilized to analyze the asymptotic behavior of combinatorial optimization problems with sum objective function and provide an alternative proof for the following result: Under a certain combinatorial condition and some natural probabilistic assumptions on the coefficients of the problem, the ratio between the optimal solution and an arbitrary feasible solution tends to one almost surely, as the size of the problem tends to infinity, so that the problem of optimization becomes trivial in some sense. Whereas this result can also be proven by purely probabilistic techniques, the above approach allows one to understand why the assumed combinatorial condition is essential for such a type of asymptotic behavior

    Some Insights in Superdiffusive Transport

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    In this paper we deal with high-order corrections for the Fractional Derivative approach to anomalous diffusion, in super-diffusive regime, which become relevand whenever one attempts to describe the behavior of particles close to normal diffusion.Comment: 14 pages, 7 figure

    Inference in particle tracking experiments by passing messages between images

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    Methods to extract information from the tracking of mobile objects/particles have broad interest in biological and physical sciences. Techniques based on simple criteria of proximity in time-consecutive snapshots are useful to identify the trajectories of the particles. However, they become problematic as the motility and/or the density of the particles increases due to uncertainties on the trajectories that particles followed during the images' acquisition time. Here, we report an efficient method for learning parameters of the dynamics of the particles from their positions in time-consecutive images. Our algorithm belongs to the class of message-passing algorithms, known in computer science, information theory and statistical physics as Belief Propagation (BP). The algorithm is distributed, thus allowing parallel implementation suitable for computations on multiple machines without significant inter-machine overhead. We test our method on the model example of particle tracking in turbulent flows, which is particularly challenging due to the strong transport that those flows produce. Our numerical experiments show that the BP algorithm compares in quality with exact Markov Chain Monte-Carlo algorithms, yet BP is far superior in speed. We also suggest and analyze a random-distance model that provides theoretical justification for BP accuracy. Methods developed here systematically formulate the problem of particle tracking and provide fast and reliable tools for its extensive range of applications.Comment: 18 pages, 9 figure

    "Rotterdam econometrics": publications of the econometric institute 1956-2005

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    This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005.

    Quantum walk speedup of backtracking algorithms

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    We describe a general method to obtain quantum speedups of classical algorithms which are based on the technique of backtracking, a standard approach for solving constraint satisfaction problems (CSPs). Backtracking algorithms explore a tree whose vertices are partial solutions to a CSP in an attempt to find a complete solution. Assume there is a classical backtracking algorithm which finds a solution to a CSP on n variables, or outputs that none exists, and whose corresponding tree contains T vertices, each vertex corresponding to a test of a partial solution. Then we show that there is a bounded-error quantum algorithm which completes the same task using O(sqrt(T) n^(3/2) log n) tests. In particular, this quantum algorithm can be used to speed up the DPLL algorithm, which is the basis of many of the most efficient SAT solvers used in practice. The quantum algorithm is based on the use of a quantum walk algorithm of Belovs to search in the backtracking tree. We also discuss how, for certain distributions on the inputs, the algorithm can lead to an exponential reduction in expected runtime.Comment: 23 pages; v2: minor changes to presentatio

    Seeking Affinity Structure: Strategies for Improving m-best Graph Matching

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    State-of-the-art methods for finding the m-best solutions to graph matching (QAP) rely on exclusion strategies. The k-th best solution is found by excluding all better ones from the search space. This provides diversity, a natural requirement for transforming a MAP problem into a m-best one. Since diversity enforces mode hopping, it is usually combined with a mode-approximation strategy such as marginalisation. However, these methods are generic insofar they do not incorporate the detailed structure of the problem at hand, i.e. the properties of the global affinity matrix which characterise the search space. Without this knowledge, it is thus hard to devise a practical criterion for choosing the next variable to clamp. In this paper, we propose several strategies to select the next variable to clamp, spanning the whole range between depth-first and breadth-first search, and we contribute with a unifying view for characterising the search space on the fly. Our strategies are: a) Number of factors in which the variables participate, b) centrality measures associated with the affinity matrix, and c) discrete pooling. Our experiments show that max number of factors and centrality provide a trade-off between efficiency and accuracy, whereas discrete pooling leads to an improvement of the state-of-the-art
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