Structural analysis of a fractional matching problem

Mixed Software Programming refers to a novel software development paradigm resulting from efforts to combine two different programming approaches: Solo Programming and Pair Programming. Solo Programming refers to the traditional practice of assigning a single developer to develop a software module and Pair Programming refers to a relatively new approach where two developers work simultaneously on developing a module. In Mixed Programming, given a set of modules to be developed, a chosen subset of modules may be developed using Solo Programming and the remaining modules using Pair Programming.Motivated by applications in Mixed Software Programming, we consider the following generalization of classical fractional 1-matching problem: Given an undirected simple graph G=(V;E), and a positive number F, find values for x_e,e∈E, satisfying the following:

1.

.

2.

, where δ(i)={e∈E:e=(i,j)},i∈V.

3.

Maximize {2∑_e∈Ex_e−F|{i∈V:∑_e∈δ(i)x_e=1}|}.

We show that this problem is solvable in strongly polynomial time. Our primary focus in this paper is on obtaining the structure of the optimal solution for an arbitrary instance of the problem.     

Five-torsion in the homology of the matching complex on 14 vertices

J.L. Andersen proved that there is 5-torsion in the bottom nonvanishing homology group of the simplicial complex of graphs of degree at most two on seven vertices. We use this result to demonstrate that there is 5-torsion also in the bottom nonvanishing homology group of the matching complex on 14 vertices. Combining our observation with results due to Bouc and to Shareshian and Wachs, we conclude that the case n=14 is exceptional; for all other n, the torsion subgroup of the bottom nonvanishing homology group has exponent three or is zero. The possibility remains that there is other torsion than 3-torsion in higher-degree homology groups of when n≥13 and n≠14. Research of J. Jonsson was supported by European Graduate Program “Combinatorics, Geometry, and Computation”, DFG-GRK 588/2.     

Model reduction using the Vorobyev moment problem

Given a nonsingular complex matrix and complex vectors v and w of length N, one may wish to estimate the quadratic form w ^* A ^− 1 v, where w ^* denotes the conjugate transpose of w. This problem appears in many applications, and Gene Golub was the key figure in its investigations for decades. He focused mainly on the case A Hermitian positive definite (HPD) and emphasized the relationship of the algebraically formulated problems with classical topics in analysis - moments, orthogonal polynomials and quadrature. The essence of his view can be found in his contribution Matrix Computations and the Theory of Moments, given at the International Congress of Mathematicians in Zürich in 1994. As in many other areas, Gene Golub has inspired a long list of coauthors for work on the problem, and our contribution can also be seen as a consequence of his lasting inspiration. In this paper we will consider a general mathematical concept of matching moments model reduction, which as well as its use in many other applications, is the basis for the development of various approaches for estimation of the quadratic form above. The idea of model reduction via matching moments is well known and widely used in approximation of dynamical systems, but it goes back to Stieltjes, with some preceding work done by Chebyshev and Heine. The algebraic moment matching problem can for A HPD be formulated as a variant of the Stieltjes moment problem, and can be solved using Gauss-Christoffel quadrature. Using the operator moment problem suggested by Vorobyev, we will generalize model reduction based on matching moments to the non-Hermitian case in a straightforward way. Unlike in the model reduction literature, the presented proofs follow directly from the construction of the Vorobyev moment problem. The work was supported by the GAAS grant IAA100300802 and by the Institutional Research Plan AV0Z10300504.     

双向中继网络中基于压缩感知的稀疏信道估计

为提高双向中继网络中稀疏信道估计的精度并减少训练序列的长度, 利用双向中继信道(Two-way Relay Channel, TWRC)的潜在稀疏特性, 研究了基于压缩感知的稀疏TWRC估计问题, 提出了一种改进的正交匹配追踪(Improved Orthogonal Matching Pursuit, IOMP)算法. 新算法运用迭代重加权最小二乘估计代替了正交匹配追踪(Orthogonal Matching Pursuit, OMP)算法中的最小二乘估计过程, 通过对样本进行迭代重加权, 逐步减小了异常样本的影响, 不断地修正了估计值, 在使用相同长度的训练序列时, 提高了估计的精度. 与传统的最小二乘估计算法相比, 新算法能够在获得相同估计效果的情况下, 显著减少所需训练序列的长度. 仿真结果验证了基于新算法的稀疏TWRC估计的有效性.     

基于压缩感知及光学理论的图像信息加密

针对信息加密系统中信息安全性不理想的问题,提出一种基于压缩感知的光学图像信息加密方法.在发送端,自然图像经稀疏表示、随机投影实现图像信息加密;然后将降维后的观测值通过4F双随机相位编码光学系统进行二次加密并将其融入宿主图像,实现信息加密及隐藏.在接收端,图像信息经双随机相位编码技术解码,通过正交匹配追踪算法实现原始图像信息重构.该系统能有效降低数据传输量、减小随机相位板大小.且收发方只需按照规则生成密钥而不需传输密钥,保证了密钥的安全性.仿真结果表明:解密恢复图像质量理想,峰值信噪比为30.899 1dB,且系统能较好地抵抗裁剪、噪音污染、高通滤波、旋转等攻击,鲁棒性强,安全性高.     

Modelling of a novel high-impedance matching layer for high frequency (>30 MHz) ultrasonic transducers

This work describes a new approach to impedance matching for ultrasonic transducers. A single matching layer with high acoustic impedance of 16 MRayls is demonstrated to show a bandwidth of around 70%, compared with conventional single matching layer designs of around 50%. Although as a consequence of this improvement in bandwidth, there is a loss in sensitivity, this is found to be similar to an equivalent double matching layer design. Designs are calculated by using the KLM model and are then verified by FEA simulation, with very good agreement Considering the fabrication difficulties encountered in creating a high-frequency double matched design due to the requirement for materials with specific acoustic impedances, the need to accurately control the thickness of layers, and the relatively narrow bandwidths available for conventional single matched designs, the new approach shows advantages in that alternative (and perhaps more practical) materials become available, and offers a bandwidth close to that of a double layer design with the simplicity of a single layer design. The disadvantage is a trade-off in sensitivity. A typical example of a piezoceramic transducer matched to water can give a 70% fractional bandwidth (comparable to an ideal double matched design of 72%) with a 3 dB penalty in insertion loss.     

Microfabrication of stacks of acoustic matching layers for 15 MHz ultrasonic transducers

This paper presents a novel method used to manufacture stacks of multiple matching layers for 15 MHz piezoelectric ultrasonic transducers, using fabrication technology derived from the MEMS industry. The acoustic matching layers were made on a silicon wafer substrate using micromachining techniques, i.e., lithography and etch, to design silicon and polymer layers with the desired acoustic properties. Two matching layer configurations were tested: a double layer structure consisting of a silicon–polymer composite and polymer and a triple layer structure consisting of silicon, composite, and polymer. The composite is a biphase material of silicon and polymer in 2-2 connectivity. The matching layers were manufactured by anisotropic wet etch of a (1 1 0)-oriented Silicon-on-Insulator wafer. The wafer was etched by KOH 40 wt%, to form 83 μm deep and 4.5 mm long trenches that were subsequently filled with Spurr’s epoxy, which has acoustic impedance 2.4 MRayl. This resulted in a stack of three layers: The silicon substrate, a silicon–polymer composite intermediate layer, and a polymer layer on the top. The stacks were bonded to PZT disks to form acoustic transducers and the acoustic performance of the fabricated transducers was tested in a pulse-echo setup, where center frequency, −6 dB relative bandwidth and insertion loss were measured. The transducer with two matching layers was measured to have a relative bandwidth of 70%, two-way insertion loss 18.4 dB and pulse length 196 ns. The transducers with three matching layers had fractional bandwidths from 90% to 93%, two-way insertion loss ranging from 18.3 to 25.4 dB, and pulse lengths 326 and 446 ns. The long pulse lengths of the transducers with three matching layers were attributed to ripple in the passband.     

一种快速稀疏分解图像去噪新方法*

提出了一种基于分层树型结构正交匹配追踪算法的快速图像去噪方法.通过选择高斯函数和墨西哥草帽小波母函数构建混合冗余字典,采用分层树状结构表示字典,结合构正交匹配追踪算法,实现图像稀疏表示,提高了图像表示的稀疏性,降低了算法的复杂度.依据噪音能量阈值,通过多次迭代达到图像去噪的目的.实验结果表明,在相同的噪音水平下,该迭代去噪算法取得了较高的较好的PSNR,获得更好的视觉效果.     

未知方向密度估计的收敛率

设Ｘ为ｐ维随机向量,对于未知的投影方向θｏ（‖θｏ‖＝１）,本文利用θｏ的估计与核密度估计相结合的方法给出了θ＾Ｔ０Ｘ的密度（方向密度）的核型密度估计,获得了此估计的逐点渐近正态性,逐点精确强收敛率,一致精确强收敛率以及均方误差收敛率,所得结果与最优性与已知方向上的核密度估计完全一致。作为例子,对θｏ为Ｘ协方差阵的最大特征值所对应的特征方向,我们给出了θｏ的满足条件的估计极其方向密度估计。     

用投影寻踪方法研究环烷烃保留指数与拓扑指数的定量构性关系

对化合物色谱保留行为与结构关系的研究是色谱领域的一个热点[1～ 8] .当定量构性模型的相关系数较高 (如 R2 =0 .99)时 ,往往认为模型很理想 .但仍可能具有不可接受的较大残差 ,从而导致较差的预测能力 [1] .如本文涉及的 1 77个环烷烃的保留指数用多达 1 8个拓扑指数构建的线性回归模型 ,虽然相关系数 R达到 0 .996,但残差很大 ,标准误差为 1 3 .7指数单位 (i.u.) ,最大残差达 48.6i.u..这可能是由于所选结构描述符未能很好表征保留值所致 .我们[2 ,3] 曾用投影寻踪技术研究了烷烃和烯烃的保留指数与拓扑指数的内在结构关系 .本文用此技…