Random walks on lattices with points of two colors. II. Some rigorous inequalities for symmetric random walks

We continue our investigation of a model of random walks on lattices with two kinds of points, black and white. The colors of the points are stochastic variables with a translation-invariant, but otherwise arbitrary, joint probability distribution. The steps of the random walk are independent of the colors. We are interested in the stochastic properties of the sequence of consecutive colors encountered by the walker. In this paper we first summarize and extend our earlier general results. Then, under the restriction that the random walk be symmetric, we derive a set of rigorous inequalities for the average length of the subwalk from the starting point to a first black point and of the subwalks between black points visited in succession. A remarkable difference in behavior is found between subwalks following an odd-numbered and subwalks following an evennumbered visit to a black point. The results can be applied to a trapping problem by identifying the black points with imperfect traps.     

Fusion of Infrared and Visible Images Based on Three-Scale Decomposition and ResNet Feature Transfer

Image fusion technology can process multiple single image data into more reliable and comprehensive data, which play a key role in accurate target recognition and subsequent image processing. In view of the incomplete image decomposition, redundant extraction of infrared image energy information and incomplete feature extraction of visible images by existing algorithms, a fusion algorithm for infrared and visible image based on three-scale decomposition and ResNet feature transfer is proposed. Compared with the existing image decomposition methods, the three-scale decomposition method is used to finely layer the source image through two decompositions. Then, an optimized WLS method is designed to fuse the energy layer, which fully considers the infrared energy information and visible detail information. In addition, a ResNet-feature transfer method is designed for detail layer fusion, which can extract detailed information such as deeper contour structures. Finally, the structural layers are fused by weighted average strategy. Experimental results show that the proposed algorithm performs well in both visual effects and quantitative evaluation results compared with the five methods.     

一种守恒型间断跟踪法在一维单守恒律方程上的程序实现

茅在近几年发展了一种守恒型的间断跟踪法（见[6],[7]）,该跟踪法是以解的守恒性质作为跟踪的机制而不是传统的跟踪法利用Rankine-Hugoniot条件。本文的目的是对该算法在一维单守恒律的情况进行程序实现,做成一个对任意初值问题都适应的强健的算法,可处理任意的间断相互作用。在文章的第三节给出了一个数值算例,并与用ENO格式（见[8]所算得的结果进行比较。     

SR-HARDI: Spatially Regularizing High Angular Resolution Diffusion Imaging

High angular resolution diffusion imaging (HARDI) has recently been of great interest in mapping the orientation of intravoxel crossing fibers, and such orientation information allows one to infer the connectivity patterns prevalent among different brain regions and possible changes in such connectivity over time for various neurodegenerative and neuropsychiatric diseases. The aim of this article is to propose a penalized multiscale adaptive regression model (PMARM) framework to spatially and adaptively infer the orientation distribution function (ODF) of water diffusion in regions with complex fiber configurations. In PMARM, we reformulate the HARDI imaging reconstruction as a weighted regularized least-square regression (WRLSR) problem. Similarity and distance weights are introduced to account for spatial smoothness of HARDI, while preserving the unknown discontinuities (e.g., edges between white matter and gray matter) of HARDI. The L₁ penalty function is introduced to ensure the sparse solutions of ODFs, while a scaled L₁ weighted estimator is calculated to correct the bias introduced by the L₁ penalty at each voxel. In PMARM, we integrate the multiscale adaptive regression models, the propagation-separation method, and Lasso (least absolute shrinkage and selection operator) to adaptively estimate ODFs across voxels. Experimental results indicate that PMARM can reduce the angle detection errors on fiber crossing area and provide more accurate reconstruction than standard voxel-wise methods. Supplementary materials for this article are available online.     

Averaging in SU(2) open quantum random walk

We study the average position and the symmetry of the distribution in the SU（2） open quantum random walk （OQRW）. We show that the average position in the central limit theorem （CLT） is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT.     

Potential of average force between two ions in a solvent of polarizable hard spheres

A method of obtaining the potential of average force between two ions immersed in a polarizable hard sphere fluid is described. The ions and the solvent particles may have different hard sphere diameters. For large values of the reduced polarizability of the solvent particles, ^*, the potential of average force rises near contact much more steeply than the primitive model would permit and also has maxima and minima vanishing at larger distances, in semiquantitative agreement with the similar results of Patey and Valleau. The oscillating character of the potential of average force is due above all to the oscillations of the radial distribution function between the ion and polarizable hard sphere.     

Vibrational dynamics of a light body in a liquid-filled rotating cylinder

The behavior of a light free cylindrical body in a rapidly rotating horizontal cylinder containing a liquid under vibrational action (the vibration direction is perpendicular to the rotation axis) is investigated. An intense rotation of the body relative to the cavity is detected. Depending on the vibration frequency, the body rotation velocity in the laboratory reference system may be higher or lower than the cavity rotation velocity and in the resonance region they may differ by several times. The mechanism of motion generation is theoretically described. It is shown that the motion is related with the excitation of inertial oscillations of the body: the cause of the motion is an average vibrational force generated due to nonlinear effects in the Stokes boundary layer near the oscillating body. The formation of large-scale axisymmetric vortex structures periodic along the rotation axis, which appear under conditions of inertial oscillation of the body during its motion, both leading and lagging, is detected.     

Partial-average-based equations of incompressible turbulent flow

This paper presents a detailed study of incompressible turbulent flow based on a newly developed statistical partial average scheme. As the ensemble average is taken on two groups of turbulent fluctuations separately, the partial average scheme is able to capture the first-order statistical moment of the fluctuation field, providing valuable information in addition to what have been known in the past from the conventional Reynolds average. The first-order statistical moment serves as the foundation in formulating theories of orthotropic turbulence and a momentum transfer chain in the modeling of second-order correlation terms, and eventually leads to a complete set of equations of incompressible turbulent flow. Without any empirical coefficients, the same set of the equations is used to simulate statistical mean behaviors and coherent structures of various benchmark turbulent flows. The simulated results are in good agreement with experimental data.     

铝土矿矿泥固化技术的试验研究

铝土矿选洗过程中排尾形成的高含水量矿泥,传统上采用建库堆存,泌干固结时间长,污染环境。试验研究结果表明,选用由72%水泥、20%石膏、5%石灰、3%硫酸钠组成的复合固化剂,或由72%石灰、20%石膏、5%粉煤灰、3%硫酸钠组成的复合固化剂,按固化剂与矿泥质量比1:10掺加,对矿泥进行固化处理,其固化体强度高、耐久性好,且成本低廉,具有广泛的工程应用价值。