基于分形脊波神经网络的遥感图像分类研究

在分形理论和脊波神经网络的基础上，综合利用彩色遥感图像的光谱、纹理和形状特征，提出了一种彩色遥感图像的分类新方法．该方法把彩色图像的蓝、绿、红波段作为3个光谱特征，由分形理论计算的DBC维和多重分形维数作为2个纹理特征，平均不变矩作为1个形状特征，并利用对曲线具有极强方向识别能力的脊波神经网络作为分类器．实验结果表明，提出的彩色遥感图像分类方法具有较高的分类准确率和较强的抗噪音能力．     

Polarization synchronization in quasi-isotropic CO2 lasers

We present experimental evidence of the in-phase and out-phase synchronization of the polarization in two coupled quasi-isotropic CO₂ lasers. We also show, by means of numerical simulations, how it is possible to retrieve message encoded in the polarization of the master laser from the observation of the slave laser alone, due to the synchronization.     

Information entropy of a dynamical system driven by quasimonochromatic noise

This paper shows the Fokker-Planck equation of a dynamical system driven by quasimonochromatic noise. Based on the Fokker-Planck equation and the definition of Shannon's information entropy, the exact time dependence of entropy flux and entropy production for the system is calculated. The relationship between the properties of quasimonochromatic noise and dissipative parameter and their effects on entropy flux and entropy production are discussed.     

The Tsallis entropy of natural information

Estimating the information contained in natural data, such as electroencephalography data, is unusually difficult because the relationship between the physical data and the information that it encodes is unknown. This unknown relationship is often called the encoding problem. The present work provides a solution to this problem by deriving a method to estimate the Tsallis entropy in natural data. The method is based on two findings. The first finding is that the physical instantiation of any information event, that is, the physical occurrence of a symbol of information, must begin and end at a discontinuity or critical point (maximum, minimum, or saddle point) in the data. The second finding is that, in certain data types such as the encephalogram (EEG), the variance within of an EEG waveform event is directly proportional to its probability of occurrence.These two outcomes yield two results. The first is the easy binning of data into separate information events. The second is the ability to estimate probabilities in two ways: frequency counting and computing the variance within of an EEG waveform. These results are used to derive a linear estimator of the Tsallis entropy functional, allowing it to be estimated without deducing the encoding.This method for estimating the Tsallis entropy is first used to estimate the information in simple signals. The amount of information estimated is highly accurate. The method is then applied to two problems in electroencephalography. The first is distinguishing normal aging from very early Alzheimer's disease (mild cognitive impairment), and the second is medication monitoring of Alzheimer's disease treatment. The former is done with an accuracy of 92% and the latter with an accuracy of 91%. This detection accuracy is the highest published accuracy in the literature, which suggests that this method for Tsallis entropy estimation is both accurate and useful.     

Z-DNA-induced super-transport of energy within genomes

Spontaneous transitions of genomic DNA segments from right-handed B-DNA into the left-handed, high-energy Z conformation are unstable within topologically relaxed DNA molecules, such as mammalian chromosomes. Here we show, from direct application of the principles of statistical physics with a promoter region in the mouse genome as a representative example, that the life span for this alternate DNA conformation may be much smaller than the characteristic time of thermal fluctuations that cause the B-to-Z transition. Surprisingly, such a short existence of Z-DNA is important because it can be responsible for super-transport of energy within a genome. This type of energy transport can be utilized by a cell to communicate information about the state of particular chromatin domains within chromosomes or as a buffer against genome instability.     

纳米AT13陶瓷喷涂层结合强度的分形维数表征

应用分形维数对微弧等离子喷涂纳米AT13涂层的界面进行研究，结果表明：随喷涂电流的增加，纳米AT13涂层的界面分维不断增大，其结合强度也不断提高；随着氩气压力的增加，纳米AT13涂层的界面分维和结合强度都先增大后减小；界面分维D可用于表征涂层结合强度σ，σ随D的增大而增大，且ln(σ)与D之间呈近似线性关系：ln(σ)=17.6D-26.2.     

非均匀Ⅱ型三角剖分上的双周期三次样条函数空间

本文确立了非均匀Ⅱ型三角剖分上双周期三次样条函数空间的维数,并给出了一组具有局部支集的基底.     

一类四阶非线性抛物型发展方程的吸引子[英文]

本文讨论实轴上的与Cahn-Hilliard方程有联系的一类四阶非线性抛物型方程Эu/Эt σЭ^4u/Эx^4 αu uЭu/Эx g(u)=f(x,t)的长时间行为。在外力f(x,t)是时间t的拟周期函数，非线性项g(u)满足一定的条件下，通过引入过程的概念，证明系统存在一致吸引子，并给出吸引子维数的上界估计。     

Density Modulo 1 of Sublacunary Sequences

We prove the existence of real numbers badly approximated by rational fractions whose denominators form a sublacunar sequence. For example, for the ascending sequence s _n , n = 1, 2, 3, ..., generated by the ordered numbers of the form 2ⁱ3^j, i, j = 1, 2, 3, ..., we prove that the set of real numbers α such that inf _n∈ℕ n‖s _n α‖ > 0 is a set of Hausdorff dimension 1. The divergence of the series implies that the Lebesgue measure of those numbers is zero.__________Translated from Matematicheskie Zametki, vol. 77, no. 6, 2005, pp. 803–813.Original Russian Text Copyright ©2005 by R. K. Akhunzhanov, N. G. Moshchevitin.