Subspace arrangements as generalized star configurations

In this note, we show that any projective subspace arrangement can be realized as a generalized star configuration variety. This type of interpolation result may be useful in designing linear codes with prescribed codewords of minimum weight, as well as in answering a couple of questions about the number of equations needed to define a generalized star configuration variety.     

基于集成最小二乘支持向量机方法的近红外光谱分析

针对近红外（Near Infrared,NIR）光谱测量中的小样本问题。本文提出了一种集成最小二乘支持向量机（Ensemble Least Squares Support Vector Machine,ELS-SVM）新算法。首先使用随机子空间算法（Random Subspace Method,RSM）原始高维变量空间划分为若干个低维度的子空间,然后分别在各个子空间建立最小二乘支持向量机（LS-SVM）模型,最后构造一个集成结果来进行预测。针对一批柴油样本的实验结果表明,本法对柴油十六烷值的预测精度优于传统的LS-SVM方法。     

New inequalities for subspace arrangements

For each positive integer n?4, we give an inequality satisfied by rank functions of arrangements of n subspaces. When n=4 we recover Ingleton's inequality; for higher n the inequalities are all new. These inequalities can be thought of as a hierarchy of necessary conditions for a (poly)matroid to be realizable. Some related open questions about the “cone of realizable polymatroids” are also presented.     

带约束条件和多余参数的线性模型的比较

对于带约束条件和多余参数的两个线性模型ｅ１＝Ｌ（Ｘ１β＋Ｚ１γ，Ｖ１，Ｌ１）和ｄ２＝Ｌ（Ｘ２β＋Ｚ２δ，Ｖ２，Ｌ２），其中Ｖ１和Ｖ２是已知对称的正定矩阵，γ和δ是多余参数，Ｌ１和Ｌ２是已知的约束矩阵，文中给出了一种新的比较准则，并得到了几个充要条件。     

交连续dcpo的遗传性和不变性

讨论了交连续dcpo的遗传性和不变性,证明了如下结论:(1)交连续dcpo对于开子空间和闭子空间都是可遗传的;(2)交连续dcpo在加最大元和去最小元运算下保持交连续性;(3)交连续dcpo的收缩核为交连续dcpo.另外,给出了交连续的主理想刻画的一个直接证明;构造了反例说明交连续dcpo对于主滤子是不可遗传的;也构造了反例说明所有主滤子都交连续的一个dcpo,自身不必是交连续的.     

Integral points, divisibility between values of polynomials and entire curves on surfaces

We prove some new degeneracy results for integral points and entire curves on surfaces; in particular, we provide the first examples, to our knowledge, of a simply connected smooth variety whose sets of integral points are never Zariski-dense. Some of our results are connected with divisibility problems, i.e. the problem of describing the integral points in the plane where the values of some given polynomials in two variables divide the values of other given polynomials.     

Wavelet subspace decomposition of thermal infrared images for defect detection in artworks

Health of ancient artworks must be routinely monitored for their adequate preservation. Faults in these artworks may develop over time and must be identified as precisely as possible. The classical acoustic testing techniques, being invasive, risk causing permanent damage during periodic inspections. Infrared thermometry offers a promising solution to map faults in artworks. It involves heating the artwork and recording its thermal response using infrared camera. A novel strategy based on pseudo-random binary excitation principle is used in this work to suppress the risks associated with prolonged heating. The objective of this work is to develop an automatic scheme for detecting faults in the captured images. An efficient scheme based on wavelet based subspace decomposition is developed which favors identification of, the otherwise invisible, weaker faults. Two major problems addressed in this work are the selection of the optimal wavelet basis and the subspace level selection. A novel criterion based on regional mutual information is proposed for the latter. The approach is successfully tested on a laboratory based sample as well as real artworks. A new contrast enhancement metric is developed to demonstrate the quantitative efficiency of the algorithm. The algorithm is successfully deployed for both laboratory based and real artworks.     

Optimal expansion of subspaces for eigenvector approximations

We consider the problem of how to expand a given subspace for approximating an eigenvalue and eigenvector of a matrix A. Specifically, we consider which vector in the subspace, after multiplied by A, provides optimal expansion of the existing subspace for the eigenvalue problem. We determine the optimal vector, when the quality of subspace for approximation is measured by the angle between the subspace and the eigenvector. We have also derived some characterization of the angle that might lead to more practically useful choice of the expansion vector.