1,664 research outputs found
Accelerated Stochastic Sampling of Discrete Statistical Systems
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
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
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
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 --
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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