1,664 research outputs found

    Accelerated Stochastic Sampling of Discrete Statistical Systems

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    We propose a method to reduce the relaxation time towards equilibrium in stochastic sampling of complex energy landscapes in statistical systems with discrete degrees of freedom by generalizing the platform previously developed for continuous systems. The method starts from a master equation, in contrast to the Fokker-Planck equation for the continuous case. The master equation is transformed into an imaginary-time Schr\"odinger equation. The Hamiltonian of the Schr\"odinger equation is modified by adding a projector to its known ground state. We show how this transformation decreases the relaxation time and propose a way to use it to accelerate simulated annealing for optimization problems. We implement our method in a simplified kinetic Monte Carlo scheme and show an acceleration by an order of magnitude in simulated annealing of the symmetric traveling salesman problem. Comparisons of simulated annealing are made with the exchange Monte Carlo algorithm for the three-dimensional Ising spin glass. Our implementation can be seen as a step toward accelerating the stochastic sampling of generic systems with complex landscapes and long equilibration times.Comment: 18 pages, 6 figures, to appear in Phys. Rev.

    The Traveling Salesman Problem in the Natural Environment

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    Is it possible for humans to navigate in the natural environment wherein the path taken between various destinations is 'optimal' in some way? In the domain of optimization this challenge is traditionally framed as the "Traveling Salesman Problem" (TSP). What strategies and ecological considerations are plausible for human navigation? When given a two-dimensional map-like presentation of the destinations, participants solve this optimization exceptionally well (only 2-3% longer than optimum)^1, 2^. In the following experiments we investigate the effect of effort and its environmental affordance on navigation decisions when humans solve the TSP in the natural environment. Fifteen locations were marked on two outdoor landscapes with flat and varied terrains respectively. Performance in the flat-field condition was excellent (∼6% error) and was worse but still quite good in the variable-terrain condition (∼20% error), suggesting participants do not globally pre-plan routes but rather develop them on the fly. We suggest that perceived effort guides participant solutions due to the dynamic constraints of effortful locomotion and obstacle avoidance

    Comparing Mean Field and Euclidean Matching Problems

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    Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional systems. Our focus here is on minimum matching problems, because they are computationally tractable while both frustrated and disordered. We first study a mean field model taking the link lengths between points to be independent random variables. For this model we find perfect agreement with the results of a replica calculation. Then we study the case where the points to be matched are placed at random in a d-dimensional Euclidean space. Using the mean field model as an approximation to the Euclidean case, we show numerically that the mean field predictions are very accurate even at low dimension, and that the error due to the approximation is O(1/d^2). Furthermore, it is possible to improve upon this approximation by including the effects of Euclidean correlations among k link lengths. Using k=3 (3-link correlations such as the triangle inequality), the resulting errors in the energy density are already less than 0.5% at d>=2. However, we argue that the Euclidean model's 1/d series expansion is beyond all orders in k of the expansion in k-link correlations.Comment: 11 pages, 1 figur

    3D environment mapping using the Kinect V2 and path planning based on RRT algorithms

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    This paper describes a 3D path planning system that is able to provide a solution trajectory for the automatic control of a robot. The proposed system uses a point cloud obtained from the robot workspace, with a Kinect V2 sensor to identify the interest regions and the obstacles of the environment. Our proposal includes a collision-free path planner based on the Rapidly-exploring Random Trees variant (RRT*), for a safe and optimal navigation of robots in 3D spaces. Results on RGB-D segmentation and recognition, point cloud processing, and comparisons between different RRT* algorithms, are presented.Peer ReviewedPostprint (published version

    A Method to Change Phase Transition Nature -- Toward Annealing Method --

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    In this paper, we review a way to change nature of phase transition with annealing methods in mind. Annealing methods are regarded as a general technique to solve optimization problems efficiently. In annealing methods, we introduce a controllable parameter which represents a kind of fluctuation and decrease the parameter gradually. Annealing methods face with a difficulty when a phase transition point exists during the protocol. Then, it is important to develop a method to avoid the phase transition by introducing a new type of fluctuation. By taking the Potts model for instance, we review a way to change the phase transition nature. Although the method described in this paper does not succeed to avoid the phase transition, we believe that the concept of the method will be useful for optimization problems.Comment: 27 pages, 3 figures, revised version will appear in proceedings of Kinki University Quantum Computing Series Vo.
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