Computing the Topological Entropy for Piecewise Monotonic Maps on the Interval

A new method for computing the topological entropy of a piecewise monotonic transformation on the interval is presented. It uses a transition matrix associated with the transformation. For this matrix we give a spectral theorem. This can be used for an estimation of the accuracy of the algorithm.     

A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators

Let $S$: [0, 1]→[0, 1] be a chaotic map and let $f^∗$ be a stationary density of the Frobenius-Perron operator $P_S$: $L^1$→$L^1$ associated with $S$. We develop a numerical algorithm for approximating $f^∗$, using the maximum entropy approach to an under-determined moment problem and the Chebyshev polynomials for the stability consideration. Numerical experiments show considerable improvements to both the original maximum entropy method and the discrete maximum entropy method.     

A Maximum Entropy Method for Particle Filtering

Standard ensemble or particle filtering schemes do not properly represent states of low priori probability when the number of available samples is too small, as is often the case in practical applications. We introduce here a set of parametric resampling methods to solve this problem. Motivated by a general H-theorem for relative entropy, we construct parametric models for the filter distributions as maximum-entropy/minimum-information models consistent with moments of the particle ensemble. When the prior distributions are modeled as mixtures of Gaussians, our method naturally generalizes the ensemble Kalman filter to systems with highly non-Gaussian statistics. We apply the new particle filters presented here to two simple test cases: a one-dimensional diffusion process in a double-well potential and the three-dimensional chaotic dynamical system of Lorenz.     

一种少投影光学层析新算法及其应用

研究少投影数情况下等离子体温度场重建问题。结合光学层析重建算法及等离子体光谱诊断中的谱线绝对强度法进行自由电弧等离子体温度场重建实验。理论上，详细讨论了一种基于最大熵准则及最优化原理的光学层析图像重建新算法。通过计算机数值模拟，考察了该算法对非对称温度场分布的重建效果。详细分析了投影噪声、投影方向数、场分布性质对重建精度的影响，并与代数迭代重建算法结果进行对比．结果表明，该算法以两个正交方向投影数据重建单峰余弦模拟场平均误差仅为0.3％，而代数迭代重建算法为3．81％；该算法以四个均匀角度间隔投影数据重建三峰随机高斯模拟场平均误差为1．77％，而代数迭代重建算法为2．02％。实验中，运用该算法结合谱线绝对强度法重建了自由电弧等离子体的温度分布。     

分段线性拟合方法确定光电效应遏止电压

通过对光电子工作特性的分析,得出了光电效应中的光电流是随外电压呈阶段性变化的结论。由此提出用分段线性方法拟合光电流的伏安特性曲线,并以它的变化区与反向饱和区的拟合直线的交点作为遏止电压点,有效减小了拐点区数据测量不稳定性带来的影响,提高了实验结果准确性。     

An Acceleration Method for Stationary Iterative Solution to Linear System of Equations

An acceleration scheme based on stationary iterative methods is presented for solving linear system of equations. Unlike Chebyshev semi-iterative method which requires accurate estimation of the bounds for iterative matrix eigenvalues, we use a wide range of Chebyshev-like polynomials for the accelerating process without estimating the bounds of the iterative matrix. A detailed error analysis is presented and convergence rates are obtained. Numerical experiments are carried out and comparisons with classical Jacobi and Chebyshev semi-iterative methods are provided.     

Analysis of Simulated Fluorescence Intensities Decays by a New Maximum Entropy Method Algorithm

A new algorithm for the Maximum Entropy Method (MEM) is proposed for recovering the lifetime distribution in time-resolved fluorescence decays. The procedure is based on seeking the distribution that maximizes the Skilling entropy function subjected to the chi-squared constraint χ ²?~?1 through iterative linear approximations, LU decomposition of the Hessian matrix of the lagrangian problem and the Golden Section Search for backtracking. The accuracy of this algorithm has been investigated through comparisons with simulated fluorescence decays both of narrow and broad lifetime distributions. The proposed approach is capable to analyse datasets of up to 4,096 points with a discretization ranging from 100 to 1,000 lifetimes. A good agreement with non linear fitting estimates has been observed when the method has been applied to multi-exponential decays. Remarkable results have been also obtained for the broad lifetime distributions where the position is recovered with high accuracy and the distribution width is estimated within 3 %. These results indicate that the procedure proposed generates MEM lifetime distributions that can be used to quantify the real heterogeneity of lifetimes in a sample.     

An Efficient Computational Algorithm for Implementing the Maximum Entropy Method in Deconvolution Inversion Problems

We discuss a theoretical informational approach to solving ill-posed problems of function recovery based on the use of the maximum entropy principle. On this basis, we propose an efficient computational algorithm for implementing the procedure of solving the function-recovery problem and the method of regularization of the problem of function recovery from the convolution. In many cases, the proposed regularization method ensures high recovery quality. If the recovery accuracy is insufficient, then the Largange multipliers obtained by this method can be the best initial approximation (in the sense of the least squares) for their iterative refinement.     

Quarkonia at Finite T: An Approach Based On QCD Sum Rules and the Maximum Entropy Method

Quarkonium spectral functions at finite temperature are studied, making use of a recently developed method of analyzing QCD sum rules by the maximum entropy method. This approach enables us to directly obtain the spectral function from the sum rules, without having to introduce any specific assumption about its functional form. QCD sum rules for heavy quarkonia incorporate finite temperature effects in form of changing values of the various gluonic condensates that appear in the operator product expansion. These changes depend on the energy density and pressure at finite temperature, which we extract from quenched lattice QCD calculations. As a result, it is found that the charmonium ground states of both S-wave and P-wave channels dissolve into the continuum already at temperatures around or slightly above the critical temperature T _c , while the bottomonium states are less influenced by temperature effects, surviving up to about 2.5 T _c or higher for S-wave and about 2.0 T _c for P-wave states.     

On the Convergence of Entropy for Stationary Exclusion Processes with Open Boundaries

We prove that, for a wide class of stochastic lattice gases in contact with reservoirs, despite long-range correlations, the leading-order term of the Gibbs–Shannon entropy in the nonequilibrium stationary state is given by the local equilibrium entropy.     

基于双线性插值最值滤波的Mura改善方法

为改善液晶面板的Mura缺陷,提出了一种灰度补偿校正Mura缺陷的方法.针对典型灰度级的亮度分布矩阵,采用双线性插值最值滤波法进行图像滤波,计算全屏目标亮度,根据各像素点拟合出的亮度-灰度关系曲线,得到各灰度级的补偿数据.实验结果表明,经过Mura补偿,55英寸的液晶模组上显示灰度图像的Mura条纹消失,Mura指数降低,且补偿并未对屏幕总体亮度和对比度等造成明显改变.     

Topographic Distribution of Photon Measurement Density Functions on the Brain Surface by Hybrid Radiosity-Diffusion Method

An accurate modelling of light propagation in the head is required to develop an algorithm to reconstruct the image of brain activity. Most previous studies have calculated the light propagation in two dimensional models because of their advantage in computation time and memory requirement over three dimensional models. However, in topographic imaging, the sensitivity distribution in the cross sections parallel to the brain surface which cannot be obtained from a two dimensional model is most important to reconstruct the image. In this study, the light propagation in three dimensional adult head models is calculated by finite element method and hybrid radiosity-diffusion method. The light propagation in the adult head is strongly affected by the non-scattering cerebrospinal fluid (CSF) layer surrounding the brain. The sensitive area is shifted toward the deeper region, and is spread around the CSF layer. The intensely sensitive region on the brain surface is broadly distributed between the source and detector. However, the sensitive region does not penetrate into the deeper part of the brain.     

Harmonic Averages and New Explicit Constants for Invariant Densities of Piecewise Expanding Maps of the Interval

The statistical behavior of families of maps is important in studying the stability properties of chaotic maps. For a piecewise expanding map τ whose slope >2 in magnitude, much is known about the stability of the associated invariant density. However, when the map has slope magnitude ≤2 many different behaviors can occur as shown in (Keller in Monatsh. Math. 94(4): 313–333, 1982) for W maps. The main results of this note use a harmonic average of slopes condition to obtain new explicit constants for the upper and lower bounds of the invariant probability density function associated with the map, as well as a bound for the speed of convergence to the density. Since these constants are determined explicitly the results can be extended to families of approximating maps.     

On the Validity of Entropy Production Principles for Linear Electrical Circuits

We explain the (non-)validity of close-to-equilibrium entropy production principles in the context of linear electrical circuits. Both the minimum and the maximum entropy production principles are understood within dynamical fluctuation theory. The starting point are Langevin equations obtained by combining Kirchoff’s laws with a Johnson-Nyquist noise at each dissipative element in the circuit. The main observation is that the fluctuation functional for time averages, that can be read off from the path-space action, is in first order around equilibrium given by an entropy production rate. That allows to understand beyond the schemes of irreversible thermodynamics (1) the validity of the least dissipation, the minimum entropy production, and the maximum entropy production principles close to equilibrium; (2) the role of the observables’ parity under time-reversal and, in particular, the origin of Landauer’s counterexample (1975) from the fact that the fluctuating observable there is odd under time-reversal; (3) the critical remark of Jaynes (1980) concerning the apparent inappropriateness of entropy production principles in temperature-inhomogeneous circuits.     

基于多模态平稳序列建模的雷达高分辨距离像有限样本目标识别方法

为了解决雷达高分辨距离像识别系统对训练样本需求量过大的问题,提出了一种有限样本条件下的目标识别新方法。分析了距离像频谱幅度的统计特性,从其广义平稳性和多模态分布特性出发,定义一种线性混合高斯状态空间模型对其统计建模,利用期望最大化算法进行了模型参数估计。实验结果表明:即使在很少的训练样本条件下,该方法仍能获得较高的正确识别率和良好的拒判性能。     

A Hybrid Method for Dynamic Mesh Generation Based on Radial Basis Functions and Delaunay Graph Mapping

Aiming at complex configuration and large deformation, an efficient hybrid method for dynamic mesh generation is presented in this paper, which is based on Radial Basis Functions (RBFs) and Delaunay graph mapping. Based on the computational mesh, a set of very coarse grid named as background grid is generated firstly, and then the computational mesh can be located at the background grid by Delaunay graph mapping technique. After that, the RBFs method is applied to deform the background grid by choosing partial mesh points on the boundary as the control points. Finally, Delaunay graph mapping method is used to relocate the computational mesh by employing area or volume weight coefficients. By applying different dynamic mesh methods to a moving NACA0012 airfoil, it can be found that the RBFs-Delaunay graph mapping hybrid method is as accurate as RBFs and is as efficient as Delaunay graph mapping technique. Numerical results show that the dynamic meshes for all test cases including one two-dimensional (2D) and two three-dimensional (3D) problems with different complexities, can be generated in an accurate and efficient manner by using the present hybrid method.     

Towards a Kneading Theory for Lozi Mappings. II: Monotonicity of the Topological Entropy and Hausdorff Dimension of Attractors

We construct a kneading theory à la Milnor–Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in terms of the pruning pair only. As an application of this result, in the current paper we show the partial monotonicity of the topological entropy and of bifurcations for the Lozi family near horseshoes. Upper and lower bounds for the Hausdorff dimension of the Lozi attractor are also given in terms of parameters. Dédié au Professeur A. Douady pour son 60ème anniversaire Received: 1 September 1996 / Accepted: 16 April 1997     

A Modal Interpretation of Quantum Mechanics Based on a Principle of Entropy Minimization

Within many approaches to the interpretation of quantum mechanics, especially modal interpretations, one singles out a particular decomposition of the state vector in order to fix the properties that are well-defined for the system. We present a novel proposal for this preferred decomposition. Given a distinguished factorization of the Hilbert space, it is the decomposition that minimizes the Ingarden–Urbanik entropy from among all product decompositions with respect to the distinguished factorization. We incorporate this choice of preferred decomposition into a framework for modal interpretations and investigate in detail the extent to which it provides a solution to the measurement problem and the extent to which it ensures that measurements whose outcomes are predictable with probability 1 reveal pre-existing properties of the system under investigation.