An image analysis suite for spot detection and spot matching in two-dimensional electrophoresis gels

We propose a suite of novel algorithms for image analysis of protein expression images obtained from 2-D electrophoresis. These algorithms are a segmentation algorithm for protein spot identification, and an algorithm for matching protein spots from two corresponding images for differential expression study. The proposed segmentation algorithm employs the watershed transformation, k-means analysis, and distance transform to locate the centroids and to extract the regions of the proteins spots. The proposed spot matching algorithm is an integration of the hierarchical-based and optimization-based methods. The hierarchical method is first used to find corresponding pairs of protein spots satisfying the local cross-correlation and overlapping constraints. The matching energy function based on local structure similarity, image similarity, and spatial constraints is then formulated and optimized. Our new algorithm suite has been extensively tested on synthetic and actual 2-D gel images from various biological experiments, and in quantitative comparisons with ImageMaster2D Platinum the proposed algorithms exhibit better spot detection and spot matching.     

钛表面生物活性榍石/氧化钛复合涂层的结构和磷灰石形成机理

采用微弧氧化和热处理复合技术,在钛表面制备了具有双层结构的榍石/氧化钛复合涂层。榍石/氧化钛复合涂层的外层是由微弧氧化涂层经热处理后晶化生成;而内层是由钛基底的氧化生成,并且氧化钛表现出不同的Ti,O原子比。由于钛基底的氧化,孔径在50~500nm的微孔呈层状结构分布在涂层内层。与微弧氧化涂层相比,该复合涂层具有很好的磷灰石诱导能力,这是由于榍石沿着特定晶面和晶向与羟基磷灰石表现出良好的晶体学匹配关系,从而为磷灰石的成核和取向沉积过程提供良好的位点。     

Mathematical studies of Kekulé structures

The perfect matching vector and forcing and the Kekulé-vector of cata-benzenoids are defined. Two theorems are given which set the sufficient and necessary conditions for HKZ-vector (Harary et al. J Math Chem 6:295, 1991) and Kekulé-vector in cata-benzenoids. Additional two theorems are obtained which give sharp bounds for the modules of HKZ- and Kekulé vectors. Dedicated to Professor Tadeusz Marek Krygowski on the happy occasion of his 70th birthday.     

Films Consisting of Innumerable Tapered Nanopillars of Mesoporous Silica for Universal Antireflection Coatings

Films with a fine structure consisting of innumerable nanopillars of mesoporous silica (MPS) are formed by a reactive ion etching process with a fluorine‐containing gas. Each nanopillar has a tapered shape with a uniform height, which effectively suppresses reflection by the formation of an ideal graded refractive index structure. The nanopillars are spontaneously formed under low‐pressure conditions, wherein locally deposited Al?F compounds, originating from an alumina plate in the etching chamber, work as a fine etching mask. The high etching rate of the MPS film allows a very high aspect ratio of the nanopillars. The refractive index of the MPS nanopillars can be universally tuned by a controlled incorporation of TiO₂ into the mesopores, which results in effective reduction of reflectance on a given substrate. The outstanding antireflection performance is experimentally demonstrated for glass substrates with a wide refractive index range.     

On the Ordering of a Class of Graphs with Respect to their Matching Numbers

Based on the number of k-matching m(G,k) of a graph G, Gutman and Zhang introduced an order relation of graphs: for graphs G ₁ and G ₂, if m(G ₁,k) ≥ m(G ₂,k) for all k. The order relation has important applications in comparing Hosaya indices and energies of molecular graphs and has been widely studied. Especially, Gutman and Zhang gave complete orders of six classes of graphs with respect to the relation . In this paper, we consider a class of graphs with special structure, which is a generalization of a class of graphs studied by Gutman and Zhang. Some order relations in the class of graphs are given, and the maximum and minimum elements with respect to the order relation are determined. The new results can be applied to order some classes of graphs by their matching numbers.     

On the Randić Index of Acyclic Conjugated Molecules

The Randić index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))^−1/2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G. We give a sharp lower bound on the Randić index of conjugated trees (trees with a perfect matching) in terms of the number of vertices. A sharp lower bound on the Randić index of trees with a given size of matching is also given Mei Lu: Partially supported by NNSFC (No. 60172005) Lian-zhu Zhang: Partially supported by NNSFC (No. 10271105) Feng Tian: Partially supported by NNSFC (No. 10431020)     

Gouy phase compensation in quasi-phase matching

In any focussed nonlinear interaction the focus induced phase shift, known as the Gouy phase shift, provides an imperfection in phase matching for any linearly invariant material. However, using an appropriately designed quasi-phase matched structure it is theoretically possible to compensate for the deleterious effects of the Gouy phase shift, allowing a symmetric frequency response and tighter optimal focussing than in a uniform material.     

套链分解

Let X1,X2,...,Xk be k disjoint subsets of S with the same cardinality m.Define H(m,k) = {X (C) S: X (C) Xi for 1 ≤I ≤k} and P(m,k) = {X (C) S : X ∩ Xi ≠φ for at least two Xi's}.Suppose S = Uki=1 Xi,and let Q(m,k,2) be the collection of all subsets K of S satisfying|K ∩ Xi|≥ 2 for some 1 ≤ I ≤ k.For any two disjoint subsets Y1 and Y2 of S,we define F1,j = {X (C) S : either |X ∩ Y1|≥ 1 or |X ∩ Y2|≥ j}.It is obvious that the four posers are graded posets ordered by inclusion.In this paper we will prove that the four posets are nested chain orders.     

限位排序的若干结果

In this paper,we first consider the position restriction scheduling problems on a single machine.The problems have been solved in certain special cases,especially for those obtained by restricting the processing time pj=1.We introduce the bipartite matching algorithm to provide some polynomial-time algorithms to solve them.Then we further consider a problem on unrelated processors.     

离散几何的两个铺砌问题

利用图论和代数的方法研究离散几何中的两个铺砌问题:1)给出1×2长方形铺砌多米诺骨牌的充分必要条件;2)对高维空间盒子的情形,给出m_1×m_2×…×m_n砖能够铺砌a_1×a_2×…×a_n盒子的一些必要条件和充要条件.