A signal adaptive diffusion filter for video coding: Mathematical framework and complexity reductions

In this paper we combine video compression and modern image processing methods. We construct novel iterative filter methods for prediction signals based on Partial Differential Equation (PDE) based methods. The mathematical framework of the employed diffusion filter class is given and some desirable properties are stated. In particular, two types of diffusion filters are constructed: a uniform diffusion filter using a fixed filter mask and a signal adaptive diffusion filter that incorporates the structures of the underlying prediction signal. The latter has the advantage of not attenuating existing edges while the uniform filter is less complex. The filters are embedded into a software based on HEVC with additional QTBT (Quadtree plus Binary Tree) and MTT (Multi-Type-Tree) block structure. In this setting, several measures to reduce the coding complexity of the tool are introduced, discussed and tested thoroughly. The coding complexity is reduced by up to 70% while maintaining over 80% of the gain. Overall, the diffusion filter method achieves average bitrate savings of 2.27% for Random Access having an average encoder runtime complexity of 119% and 117% decoder runtime complexity. For individual test sequences, results of 7.36% for Random Access are accomplished.     

层次分析中广义最小偏差法的性质

广义最小偏差法（GLDM）是层次分析中一种重要的排序方法．本文讨论了广义最小偏差法的性质和灵敏度分析问题．     

基于空间矩的灰度边缘亚像元度量精度分析

灰度图像中边缘定位受采样密度限制，亚像元精度度量方法在需要高精度的应用中受到重视，要想知识到底需要多高的分辨率才能达到定精度指标，就有必要分析特征定位方法的最坏情况的精度，文中用分析和实验的方法给出了基于空间矩的边缘定位方法，对于边缘点，边缘直线以及直边缘区域的最坏情况定位精度分析。分析和讨论的结果不但可以用来确定已知形状位置估计的最大误差，而且还可用于对准的形状几何参数，以获得较高的精度。     

Sizes of Critical Graphs with Small Maximum Degrees

In this paper, we give new lower bounds for the size of Δ-critical graphs with Δ=8,9 which improve the partial results of Luo [6] and Y. Zhao [12].     

一种改进的共同进化遗传算法及其应用

将共同进化遗传算法应用于临床营养决策优化中,虽然取得了一定成果,但算法中仍存在早熟现象、局部搜索能量弱等问题,为此提出一种改进的共同进化模型。算法使用新的子群体划分方法和交叉算子,引入精英保留策略、信息交换原则和小生境技术。通过对糖尿病营养治疗的仿真表明,改进后的算法在保证群体多样性和避免早熟现象的前提下,提高了算法的局部和全局寻优能力,且膳食配方中营养素达标率符合要求,满足专家建议的糖尿病饮食需求。     

Measurements of edge-uncolorability

Cubic bridgeless graphs with chromatic index four are called uncolorable. We introduce parameters measuring the uncolorability of those graphs and relate them to each other. For k=2,3, let c_k be the maximum size of a k-colorable subgraph of a cubic graph G=(V,E). We consider r₃=|E|−c₃ and . We show that on one side r₃ and r₂ bound each other, but on the other side that the difference between them can be arbitrarily large. We also compare them to the oddness ω of G, the smallest possible number of odd circuits in a 2-factor of G. We construct cyclically 5-edge connected cubic graphs where r₃ and ω are arbitrarily far apart, and show that for each 1c<2 there is a cubic graph such that ωcr₃. For k=2,3, let ζ_k denote the largest fraction of edges that can be k-colored. We give best possible bounds for these parameters, and relate them to each other.     

Growth of Lévy trees

We construct random locally compact real trees called Lévy trees that are the genealogical trees associated with continuous-state branching processes. More precisely, we define a growing family of discrete Galton–Watson trees with i.i.d. exponential branch lengths that is consistent under Bernoulli percolation on leaves; we define the Lévy tree as the limit of this growing family with respect to the Gromov–Hausdorff topology on metric spaces. This elementary approach notably includes supercritical trees and does not make use of the height process introduced by Le Gall and Le Jan to code the genealogy of (sub)critical continuous-state branching processes. We construct the mass measure of Lévy trees and we give a decomposition along the ancestral subtree of a Poisson sampling directed by the mass measure. T. Duquesne is supported by NSF Grants DMS-0203066 and DMS-0405779. M. Winkel is supported by Aon and the Institute of Actuaries, EPSRC Grant GR/T26368/01, le département de mathématique de l’Université d’Orsay and NSF Grant DMS-0405779.     

The analysis of thermal stresses in thermopiezoelastic semi-infinite body with an edge crack

Summary  Thermopiezoelastic materials have recently attracted considerable attention because of their potential use in intelligent or smart structural systems. The governing equations of a thermopiezoelastic medium are more complex due to the intrinsic coupling effects that take place among mechanical, electrical and thermal fields. In this analysis, we deal with the problem of a crack in a semi-infinite, transversely isotropic, thermopiezoelastic material by means of potential functions and Fourier transforms under steady heat-flux loading conditions. The problem is reduced to a singular integral equation that is solved. The thermal stress intensity factor for a crack situated in a cadmium selenide material is calculated. Received 20 March 2001; accepted for publication 18 October 2001     

Special simplices and Gorenstein toric rings

Athanasiadis [Ehrhart polynomials, simplicial polytopes, magic squares and a conjecture of Stanley, J. Reine Angew. Math., to appear.] studies an effective technique to show that Gorenstein sequences coming from compressed polytopes are unimodal. In the present paper we will use such the technique to find a rich class of Gorenstein toric rings with unimodal h-vectors arising from finite graphs.