A general learning algorithm for solving optimization problems and its application to the spin glass problem

We propose a general learning algorithm for solving optimization problems, based on a simple strategy of trial and adaptation. The algorithm maintains a probability distribution of possible solutions (configurations), which is updated continuously in the learning process. As the probability distribution evolves, better and better solutions are shown to emerge. The performance of the algorithm is illustrated by the application to the problem of finding the ground state of the Ising spin glass. A simple theoretical understanding of the algorithm is also presented.Comment: 9 pages, 3 figure

Evolutionary Dynamics and the Phase Structure of the Minority Game

We show that a simple evolutionary scheme, when applied to the minority game (MG), changes the phase structure of the game. In this scheme each agent evolves individually whenever his wealth reaches the specified bankruptcy level, in contrast to the evolutionary schemes used in the previous works. We show that evolution greatly suppresses herding behavior, and it leads to better overall performance of the agents. Similar to the standard non-evolutionary MG, the dependence of the standard deviation $\sigma$ on the number of agents $N$ and the memory length $m$ can be characterized by a universal curve. We suggest a Crowd-Anticrowd theory for understanding the effect of evolution in the MG.Comment: 4 pages and 3 figure

Dynamics of Dry Friction: A Numerical Investigation

We perform extended numerical simulation of the dynamics of dry friction, based on a model derived from the phenomenological description proposed by T. Baumberger et al.. In the case of small deviation from the steady sliding motion, the model is shown to be equivalent to the state- and rate-dependent friction law which was first introduced by Rice and Ruina on the basis of experiments on rocks. We obtain the dynamical phase diagram that agrees well with the experimental results on the paper-on-paper systems. In particular, the bifurcation between stick-slip and steady sliding are shown to change from a direct (supercritical) Hopf type to an inverted (subcritical) one as the driving velocity increases, in agreement with the experiments.Comment: 7 pages, 5 figures, using RevTe

Generalized laws of reflection and refraction from transformation optics

Based on transformation optics, we introduce another set of generalized laws of reflection and refraction (differs from that of [Science 334, 333 (2011)]), through which a transformation media slab is derived as a meta-surface, producing anomalous reflection and refraction for all polarizations of incident light.Comment: 7 pages, 3 figure