Analysis of the capillary forces between two small solid spheres binded by a convex liquid bridge

This work deals with a theoretical study of convex liquid bridges, where solid particles are partially wetted by an amount of liquid whose profile is convex. In our analysis, we adopt a two particle model assuming that the solids are spherical and with the same size and properties, and that the liquid meniscus features an arc-of-circumference contour. We analyze different parameters which govern the liquid bridge: inter-particle separation, wetting angle and liquid volume. The results are compiled in liquid volume-wetting angle diagrams in which the regions of existence of the bridge are delimited in terms of maximum and minimal inter-particle distances. The capillary force is found to present both attractive and repulsive characters for wetting angles smaller and higher than 90°. A map delimiting this force character is also presented.     

Time optimal cyclic crystallization

A time optimal cyclic control scheme for shape manipulation of multivariate crystal populations involving sequences of subsequent growth and dissolution phases is proposed in this note. Such strategies employ the unequal growth and dissolution rates for attaining morphologies that do not result directly from a pure growth or dissolution phase only. We prove that minimum time trajectories can be constructed by means of convex programs resulting in globally optimal bimodal control policies with piecewise constant supersaturation.     

基于低秩张量补全的多声道音频信号恢复方法

多声道音频信号在采集、压缩、传输过程中可能造成音频数据丢失,为了确保给听众带来更真实的听觉感受,该文提出一种基于低秩张量补全的音频丢失数据恢复方法。首先,把多声道音频信号表示为一个张量;其次,把张量补全作为一个凸优化问题建模,利用松弛技术和变量分离技术得到闭合的增强拉格朗日函数;最后,通过交替迭代方法求解得到恢复的音频张量。在不同数据丢失率的实验中,通过与线性预测、加权优化的CANDECOMP /PARAFAC分解方法进行对比分析,表明利用张量补全方法具有更高的音频信号恢复精度,隐藏参考和基准的多激励测试结果也显示低秩张量补全方法能够有效地恢复多声道音频的丢失数据,从而获得更好的听觉效果。     

Semidefinite spectral clustering

Multi-way partitioning of an undirected weighted graph where pairwise similarities are assigned as edge weights, provides an important tool for data clustering, but is an NP-hard problem. Spectral relaxation is a popular way of relaxation, leading to spectral clustering where the clustering is performed by the eigen-decomposition of the (normalized) graph Laplacian. On the other hand, semidefinite relaxation, is an alternative way of relaxing a combinatorial optimization, leading to a convex optimization. In this paper we employ a semidefinite programming (SDP) approach to the graph equipartitioning for clustering, where sufficient conditions for strong duality hold. The method is referred to as semidefinite spectral clustering, where the clustering is based on the eigen-decomposition of the optimal feasible matrix computed by SDP. Numerical experiments with several data sets, demonstrate the useful behavior of our semidefinite spectral clustering, compared to existing spectral clustering methods.     

基于凸包求解的简单多边形方向判断新算法

Graham ScanA求解简单多边形凸包算法简洁高效,但是对于未确定方向的简单多边形,该算法需设定一个方向求解其凸包。提出一种新的算法,该算法通过利用凸包求解的Graham ScanA算法来判断简单多边形的方向。算法取得了较好的实用效果。     

基于迭代二阶锥的唯相位波束形成

唯相位自适应波束形成技术对普通相控阵雷达自适应干扰抑制是非常重要的,在数字阵列雷达中,唯相位技术则可以充分利用各阵元发射模块微波功率从而提高雷达的威力。该文提出了一种新的唯相位波束形成方法,假定初始唯相位权重矢量有个较小的相位扰动,将唯相位模型的目标函数和约束函数在该相位扰动区域内分别用泰勒一阶展开式来近似,则可以将原来的非凸问题转化为凸优化问题,通过二阶锥规划方法(SOCP)求得使当前目标函数最小的扰动矢量,然后更新得到新的权重矢量并代替原来的权重矢量,重复上述迭代过程直到满足停止条件,可以得到满足要求的唯相位权重。计算机仿真结果验证了该方法的正确性和有效性。     

A Multi-criteria Convex Quadratic Programming model for credit data analysis

Speed and scalability are two essential issues in data mining and knowledge discovery. This paper proposed a mathematical programming model that addresses these two issues and applied the model to Credit Classification Problems. The proposed Multi-criteria Convex Quadric Programming (MCQP) model is highly efficient (computing time complexity O(n^1.5–2)) and scalable to massive problems (size of O(10⁹)) because it only needs to solve linear equations to find the global optimal solution. Kernel functions were introduced to the model to solve nonlinear problems. In addition, the theoretical relationship between the proposed MCQP model and SVM was discussed.     

Pore bifurcation, growth and pore termination in nanoporous alumina with concave and convex surfaces

The growth of nanoporous alumina on concave or convex aluminium surfaces has been investigated. The number of pores during anodic oxidation increases or decreases almost linearly with the thickness of the oxide which is due to bifurcation or termination of single pores during alumina growth. The anodic oxidation has been constantly conducted in oxalic acid at 40 V. Therefore the average interpore distance has not changed during alumina growth. In earlier papers it has been shown that a bifurcation of pores is the result of the change of voltage and the electrolyte. In this work we have demonstrated that a termination or a bifurcation of pores is also possible by structuring the aluminium to a curved surface with concave or convex properties before oxidation. Those results do not depend on the substrate characteristics or on the alumina preparation techniques.     

Non-smooth SOR for L 1-Fitting: Convergence Study and Discussion of Related Issues

In this article, the denoising of smooth (H ¹-regular) images is considered. To reach this objective, we introduce a simple and highly efficient over-relaxation technique for solving the convex, non-smooth optimization problems resulting from the denoising formulation. We describe the algorithm, discuss its convergence and present the results of numerical experiments, which validate the methods under consideration with respect to both efficiency and denoising capability. Several issues concerning the convergence of an Uzawa algorithm for the solution of the same problem are also discussed.     

The importance of generalizability for anomaly detection

In security-related areas there is concern over novel “zero-day” attacks that penetrate system defenses and wreak havoc. The best methods for countering these threats are recognizing “nonself” as in an Artificial Immune System or recognizing “self” through clustering. For either case, the concern remains that something that appears similar to self could be missed. Given this situation, one could incorrectly assume that a preference for a tighter fit to self over generalizability is important for false positive reduction in this type of learning problem. This article confirms that in anomaly detection as in other forms of classification a tight fit, although important, does not supersede model generality. This is shown using three systems each with a different geometric bias in the decision space. The first two use spherical and ellipsoid clusters with a k-means algorithm modified to work on the one-class/blind classification problem. The third is based on wrapping the self points with a multidimensional convex hull (polytope) algorithm capable of learning disjunctive concepts via a thresholding constant. All three of these algorithms are tested using the Voting dataset from the UCI Machine Learning Repository, the MIT Lincoln Labs intrusion detection dataset, and the lossy-compressed steganalysis domain. Gilbert “Bert” Peterson is an Assistant Professor of Computer Engineering at the Air Force Institute of Technology. Dr. Peterson received a BS degree in Architecture, and an M.S. and Ph.D. in Computer Science at the University of Texas at Arlington. He teaches and conducts research in digital forensics and artificial intelligence. Brent McBride is a Communications and Information Systems officer in the United States Air Force. He received a B.S. in Computer Science from Brigham Young University and an M.S. in Computer Science from the Air Force Institute of Technology. He currently serves as Senior Software Engineer at the Air Force Wargaming Institute.