8,782 research outputs found
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 on the number of agents
and the memory length 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
Lipschitz equivalence of a class of self-similar sets
We consider a class of homogeneous self-similar sets with complete overlaps
and give a sufficient condition for the Lipschitz equivalence between members
in this class.Comment: A remark was added. To appear in Ann. Acad. Sci. Fenn. Mat
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
- …