Phase-field study of free growth in a channel: from thermal to chemical solidification

The thermal and the chemical phase-field models for free growth in a two-dimensional channel are both studied in their one-sided version for which diffusion only occurs in the liquid. We compare the steady state fingers obtained in our phase-field simulations with the results of boundary integral techniques available in the literature. The excellent agreement found between both methods provides a valuable benchmark of the one-sided thin-interface phase model which makes use of an antitrapping current. Coexistence of several steady states predicted by the Green’s function calculations is also recovered. The dynamical stability of two competing modes (symmetric and asymmetric finger) is studied and the extension of their respective basins of attraction is evaluated. General implications of our results for a large class of isotropic systems are discussed.     

Analyzing and modeling real-world phenomena with complex networks: a survey of applications

The success of new scientific areas can be assessed by their potential in contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely well in both of these aspects, with their sound theoretical basis being developed over the years and with a variety of applications. In this survey, we analyze the applications of complex networks to real-world problems and data, with emphasis in representation, analysis and modeling. A diversity of phenomena are surveyed, which may be classified into no less than 11 areas, providing a clear indication of the impact of the field of complex networks.     

Spatio-temporal patterns in a square-lattice Hodgkin-Huxley neural network

The collective behaviour of a square-lattice Hodgkin-Huxley neural network model with white noise is investigated by numerical methods. It is found that for an intermediate value of noise the Hodgkin-Huxley neurons in the square lattice exhibit an ordered circular structure. However, as the noise level increases, the ordered circular structures are distorted, and eventually totally destroyed. Thereby, the constructive role of appropriately pronounced random perturbations in the studied network is revealed. Furthermore, it is shown that as the diffusive coefficient increases, the typical width of the spatial waves also increases accordingly, which results in a decrease of the number of cycles by a given size of the spatial grid. More interestingly, it is observed that the spatio-temporal coherence resonance is enhanced as the diffusive coefficient is increased. Finally, the dependence of the typical width and the average period of the firing rate function on the diffusive coefficient is studied. Results presented in this paper should prove valuable for the understanding of information processing of neural systems in the presence of noise.     

The limit of a Stanley–Wilf sequence is not always rational, and layered patterns beat monotone patterns

We show the first known example for a pattern q for which is not an integer, where S_n(q) denotes the number of permutations of length n avoiding the pattern q. We find the exact value of the limit and show that it is irrational, but algebraic. Then we generalize our results to an infinite sequence of patterns. We provide further generalizations that start explaining why certain patterns are easier to avoid than others. Finally, we show that if q is a layered pattern of length k, then L(q)(k-1)² holds.     

A Variational Theory for Point Defects in Patterns

We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross–Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen in experimental studies of the corresponding physical systems and in numerical simulations of the microscopic equations that describe these systems.      

人脸图像光照预处理的一种新方法

人脸识别是图像分析和理解领域中最成功的应用之一,近年来得到了迅速的发展,但是阻碍人脸识别技术应用到实际中的瓶颈之一——光照问题,一直没能得到很好的解决。局部二值模式是最近发展起来的一种理论简单但功能强大的纹理分析算法,在计算机视觉等领域表现出良好的性能。将该纹理提取算法应用到图像预处理中并并利用大规模中国人脸图像数据库CAS-PEAL-R1来检验这种方法的有效性。实验结果表明:加入LBP纹理后,该方法能较好解决光照变化问题,提高识别性能。     

Fixed points avoiding Abelian k-powers

We show that the problem of whether the fixed point of a morphism avoids Abelian k-powers is decidable under rather general conditions, the most important being that the frequency matrix M of the morphism be invertible and that |M−1|<1, where |⋅| denotes a certain matrix norm.