Stochastic matching problem

The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the deterministic case can be solved in polynomial time, stochastic variants are worst-case intractable. We propose an efficient method to solve stochastic matching problems which combines some features of the survey propagation equations and of the cavity method. We test it on random bipartite graphs, for which we analyze the phase diagram and compare the results with exact bounds. Our approach is shown numerically to be effective on the full range of parameters, and to outperform state-of-the-art methods. Finally we discuss how the method can be generalized to other problems of optimization under uncertainty.     

Parallel filtering in global gyrokinetic simulations

In this work, a Fourier solver [B.F. McMillan, S. Jolliet, A. Bottino, P. Angelino, T.M. Tran, L. Villard, Comp. Phys. Commun. 181 (2010) 715] is implemented in the global Eulerian gyrokinetic code GT5D [Y. Idomura, H. Urano, N. Aiba, S. Tokuda, Nucl. Fusion 49 (2009) 065029] and in the global Particle-In-Cell code ORB5 [S. Jolliet, A. Bottino, P. Angelino, R. Hatzky, T.M. Tran, B.F. McMillan, O. Sauter, K. Appert, Y. Idomura, L. Villard, Comp. Phys. Commun. 177 (2007) 409] in order to reduce the memory of the matrix associated with the field equation. This scheme is verified with linear and nonlinear simulations of turbulence. It is demonstrated that the straight-field-line angle is the coordinate that optimizes the Fourier solver, that both linear and nonlinear turbulent states are unaffected by the parallel filtering, and that the k_∥ spectrum is independent of plasma size at fixed normalized poloidal wave number.     

Tunneling as a Stochastic Process

An alternative model for tunneling processes, based on the capability of the telegrapher's equation to describe stochastic processes, is able to account for delay time results of an optical experiment at the microwave scale, where superluminal behaviors have been evidenced.     

Stochastic resonance in a bistable system with global delay and two noises

The global time delay is introduced into a bistable system driven by two noises and a periodic signal. The signal power amplification factor η is employed to characterise stochastic resonance (SR) of the system. Numerical simulation results indicate the following. (1) For a periodic signal with low frequency (Ω), the typical behaviour of the SR is lowered monotonically by increasing the delay time τ; for moderate Ω, τ enhances the SR behaviour and then weakens it, with a critical value at which the SR is optimum. (2) Multiplicative noise intensity D and additive noise intensity α have different influences on the SR performance, viz D enhances the SR monotonically while α enforces the SR initially and then restrains it; (3) correlation intensity λ between the two noises always weakens the SR behaviour of the system.     

Rotation axis calibration of a turntable using constrained global optimization

For determining the rotation axis as the baseline to transform between camera and turntable coordinate frames, rotation axis calibration of a turntable using constrained global optimization is proposed. At the beginning, camera parameters are calibrated using multiple views of only one pattern positioned differently and 3D corner points are retrieved with the pattern placed onto the rotation turntable in a 360° view. Then the rotation axis direction vector is decided under the constraint of the distance between each closed circle trajectory plane and each circle with its center is determined by fitting the circle with global least squares method, respectively. Experimental results demonstrate that the proposed method is effective for estimating the parameters of rotation axis.     

Embedding as a modeling problem

Standard approaches to time-delay embedding will often fail to provide an embedding that is useful for many common applications. This happens in particular when there are multiple timescales in the dynamics. We present a modified procedure, non-uniform embedding, which overcomes such problems in many cases. For more complex nonlinear dynamics we introduce variable embedding, where, in a suitable sense, the embedding changes with the state of the system. We show how to implement these procedures by combining embedding and modeling into a single procedure with a single optimization goal.     

Efficient global geometry optimization of clusters

The method of global geometry optimization of atomic and molecular clusters by evolutionary algorithms is briefly presented and reviewed. As an exemplary application of a parallelized implementation of such an algorithm, neutral pure water clusters are globally optimized. In contrast to previous studies, the sophisticated and quantitatively reliable TTM2-F potential is employed. Significant qualitative differences to the earlier results are found, implicating a breakdown of simple water models for water clusters of non-trivial size.     

Stochastic resonance as dithering

A direct correspondence is demonstrated between the phenomenon of "stochastic resonance" in static nonlinear systems and the dithering effect well known in the theory of digital waveform coding. It is argued that many static systems displaying stochastic resonance are forms of dithered quantizers, and that the existence or absence of stochastic resonance in such systems can be predicted from the effects of "dither averaging" upon their transfer characteristics. Also, results are introduced regarding stochastic resonance in certain nonlinear systems with memory (e.g., hysteretic systems).     

Solving a class of continuous global optimization problems using quantum algorithms

We investigate the entwined roles that additional information and quantum algorithms play in reducing the complexity of a class of global optimization problems (GOP). We show that: (i) a modest amount of additional information is sufficient to map the continuous GOP into the (discrete) Grover problem; (ii) while this additional information is actually available in some GOPs, it cannot be taken advantage of within classical optimization algorithms; and (iii) quantum algorithms offer a natural framework for the efficient use of this information resulting in a speed-up of the solution of the GOP.     

Stochastic web as a generator of three-dimensional quasicrystal symmetry

It is shown that two coupled oscillators perturbed by periodic kicks generate a thin stochastic web in the four-dimensional phase space, which differs from the Arnold web. Under some resonance-type condition the web possesses a quasicrystal-type symmetry. In three-dimensional coordinate space, the web's symmetry corresponds to the icosahedral one and, due to that, the original four-dimensional map can be considered as a dynamical generator of the quasicrystal-type tiling of three-dimensional space.     

基于智能全局优化算法的理论结构预测

凝聚态物质内部的原子堆垛方式,即微观原子结构,是深入理解其各种宏观物理和化学性质的基础。近年来,随着基于群智理论的全局优化算法和第一性原理计算方法的发展,只根据物质的化学组分和外界条件,通过理论计算来确定或预测物质的微观原子结构成为可能。文章将对目前国内外主要理论结构预测方法进行简要的概述,重点介绍基于群智算法的卡里普索(CALYPSO)结构预测方法的基本原理及其在凝聚态物质结构研究中的一些典型应用。     

Bi-instability as a precursor to global mixed-mode chaos

Bi-instability, in contrast to bistability, is shown to generate unstable chaotic saddles prior to the onset of chaos. The theory and numerics are applied to a CO2 laser model with modulated losses where unstable pairs of saddles coexist, form heteroclinic connections, and allow mixing between local chaotic attractors to produce global mixed-mode chaos.