The Sampling-and-Learning Framework: A Statistical View of Evolutionary Algorithms

Evolutionary algorithms (EAs), a large class of general purpose optimization algorithms inspired from the natural phenomena, are widely used in various industrial optimizations and often show excellent performance. This paper presents an attempt towards revealing their general power from a statistical view of EAs. By summarizing a large range of EAs into the sampling-and-learning framework, we show that the framework directly admits a general analysis on the probable-absolute-approximate (PAA) query complexity. We particularly focus on the framework with the learning subroutine being restricted as a binary classification, which results in the sampling-and-classification (SAC) algorithms. With the help of the learning theory, we obtain a general upper bound on the PAA query complexity of SAC algorithms. We further compare SAC algorithms with the uniform search in different situations. Under the error-target independence condition, we show that SAC algorithms can achieve polynomial speedup to the uniform search, but not super-polynomial speedup. Under the one-side-error condition, we show that super-polynomial speedup can be achieved. This work only touches the surface of the framework. Its power under other conditions is still open

Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications

We derive the field correction to the Berry curvature of Bloch electrons, which can be traced back to a positional shift due to the interband mixing induced by external electromagnetic fields. The resulting semiclassical dynamics is accurate to second order in the fields, in the same form as before, provided that the wave packet energy is derived up to the same order. As applications, we discuss the orbital magnetoelectric polarizability and predict nonlinear anomalous Hall effects

High Fill-Out, Extreme Mass Ratio Overcontact Binary Systems. X. The new discovered binary XY Leonis Minoris

The new discovered short-period close binary star, XY LMi, was monitored photometrically since 2006. It is shown that the light curves are typical EW-type and show complete eclipses with an eclipse duration of about 80 minutes. By analyzing the complete B, V, R, and I light curves with the 2003 version of the W-D code, photometric solutions were determined. It is discovered that XY LMi is a high fill-out, extreme mass ratio overcontact binary system with a mass ratio of q=0.148 and a fill-out factor of f=74.1%, suggesting that it is on the late evolutionary stage of late-type tidal-locked binary stars. As observed in other overcontact binary stars, evidence for the presence of two dark spots on both components are given. Based on our 19 epoches of eclipse times, it is found that the orbital period of the overcontact binary is decreasing continuously at a rate of dP/dt=-1.67\times10^{-7}\,days/year, which may be caused by the mass transfer from the primary to the secondary or/and angular momentum loss via magnetic stellar wind. The decrease of the orbital period may result in the increase of the fill-out, and finally, it will evolve into a single rapid-rotation star when the fluid surface reaching the outer critical Roche Lobe.Comment: 19 pages, 4 figures, 9 table