An iterative algorithm for homology computation on simplicial shapes

We propose a new iterative algorithm for computing the homology of arbitrary shapes discretized through simplicial complexes. We demonstrate how the simplicial homology of a shape can be effectively expressed in terms of the homology of its sub-components. The proposed algorithm retrieves the complete homological information of an input shape including the Betti numbers, the torsion coefficients and the representative homology generators.To the best of our knowledge, this is the first algorithm based on the constructive Mayer–Vietoris sequence, which relates the homology of a topological space to the homologies of its sub-spaces, i.e. the sub-components of the input shape and their intersections. We demonstrate the validity of our approach through a specific shape decomposition, based only on topological properties, which minimizes the size of the intersections between the sub-components and increases the efficiency of the algorithm.     

Unified approach to coefficient-based regularized regression

In this paper, we consider the coefficient-based regularized least-squares regression problem with the l^q-regularizer (1≤q≤2) and data dependent hypothesis spaces. Algorithms in data dependent hypothesis spaces perform well with the property of flexibility. We conduct a unified error analysis by a stepping stone technique. An empirical covering number technique is also employed in our study to improve sample error. Comparing with existing results, we make a few improvements: First, we obtain a significantly sharper learning rate that can be arbitrarily close to O(m⁻¹) under reasonable conditions, which is regarded as the best learning rate in learning theory. Second, our results cover the case q=1, which is novel. Finally, our results hold under very general conditions.     

小剪跨比钢筋混凝土实腹支托的受力性能及非线性全过程分析

本文用非线性全过程分析和足尺试件的破损试验的方法对工业建筑结构中常用的小剪跨比钢筋混凝土支托进行力学性能的讨论。文章提出了小剪跨比支托不同于一般支托的力学特性和破坏机理,认为“剪摩理论”对于小剪跨比支托的适用性是存在的。     

AZ81镁合金挤压组织和性能研究

对AZ81镁舍金铸锭进行(390±10)℃×15h的固溶处理后,在400℃进行挤压,挤压比为32∶1,研究其组织和力学性能.结果表明,挤压AZ81镁合金具有较细的晶粒组织,第二相Mg17Al12被破碎,其分布变得弥散,个别呈流线分布;挤压AZ81镁合金比铸造AZ81镁合金的力学性能有较大提高,其屈服强度为221.6MPa,抗拉强度为311.5MPa,伸长率为14.2%.其挤压态断口表现出明显的塑性断裂特征.     

Analysis of essential carboxylic amino acid residues for catalytic activity of fungal chitosanases by site-directed mutagenesis

A comparison of amino acid sequences of fungal chitosanases, belonging to family 75 of glycosyl hydrolases, revealed three carboxylic amino acid residues completely conserved among all of the chitosanases. To study the role of these residues in catalysis, they were replaced with other residues by site-directed mutagenesis in the chitosanase gene of Fusarium solani. The mutated genes were expressed in the yeast Saccharomyces cerevisiae and the resulting recombinant chitosanases were used in kinetic analysis. Chitosanases with Asp-175-->Asn and Glu-188-->Gln mutations were essentially inactive, whereas those with Asp-175-->Glu and Glu-188-->Asp mutations retained 25-50% specific activity as compared with the wild-type enzyme. The mutation of Asp-212-->Asn did not decrease specific activity to a large extent. Circular dichroism analysis confirmed that the mutant chitosanases had similar secondary structures to that of the wild-type enzyme. These results indicate that Asp-175 and Glu-188 are essential residues for the catalytic activity of chitosanase. Time-dependent (1)H-NMR analysis for the hydrolysis of D-glucosamine hexamer revealed that a fungal chitosanase is an inverting enzyme producing only the alpha anomeric form of reaction products.     

Optimal dynamic hedging via copula-threshold-GARCH models

The contribution of this paper is twofold. First, we exploit copula methodology, with two threshold GARCH models as marginals, to construct a bivariate copula-threshold-GARCH model, simultaneously capturing asymmetric nonlinear behaviour in univariate stock returns of spot and futures markets and bivariate dependency, in a flexible manner. Two elliptical copulas (Gaussian and Student's-t) and three Archimedean copulas (Clayton, Gumbel and the Mixture of Clayton and Gumbel) are utilized. Second, we employ the presenting models to investigate the hedging performance for five East Asian spot and futures stock markets: Hong Kong, Japan, Korea, Singapore and Taiwan. Compared with conventional hedging strategies, including Engle's dynamic conditional correlation GARCH model, the results show that hedge ratios constructed by a Gaussian or Mixture copula are the best-performed in variance reduction for all markets except Japan and Singapore, and provide close to the best returns on a hedging portfolio over the sample period.     

The Efficient Computation of Certain Determinants Arising in the Treatment of Schrödinger's Equations

The solution of Schrödinger's equation leads to a high number N of independent variables. Furthermore, the restriction to (anti)symmetric functions implies some complications. We propose a sparse-grid approximation which leads to a set of non-orthogonal basis. Due to the antisymmetry, scalar products are expressed by sums of N×N-determinants. Because of the sparsity of the sparse-grid approximation, these determinants can be reduced from N×N to a much smaller size K×K. The sums over all permutations reduce to the quantities det _K (α₁,…,α _K ):=∑≤i ₁,i ₂,…,i _K ≤Ndet(a _iα ,i _β ^(αβ))_{α,β=1,…, K} to be determined, where a _i , _j ^(αβ) are certain one-dimensional scalar products involving (sparse-grid) basis functions ?α_β. We propose a method to evaluate this expression such that the asymptotics of the computational cost with respect to N is O(N ³) for fixed K, while the storage requirements increase only with the factor N ². Furthermore, we describe a parallel version (N processors) with full speed up.     

New applications of clique separator decomposition for the Maximum Weight Stable Set problem

Graph decompositions such as decomposition by clique separators and modular decomposition are of crucial importance for designing efficient graph algorithms. Clique separators in graphs were used by Tarjan as a divide-and-conquer approach for solving various problems such as the Maximum Weight Stable Set (MWS) problem, Colouring and Minimum Fill-in. The basic tool is a decomposition tree of the graph whose leaves have no clique separator (so-called atoms), and the problem can be solved efficiently on the graph if it is efficiently solvable on its atoms. We give new examples where the clique separator decomposition works well for the MWS problem; our results improve and extend various recently published results. In particular, we describe the atom structure for some new classes of graphs whose atoms are P₅-free (the P₅ is the induced path with five vertices) and obtain new polynomial time results for the MWS problem. The complexity of this problem on the class of P₅-free graphs is still unknown.     

稀土元素Y、Nd对AZ81镁合金组织和高温性能的影响

研究了稀土元素Y、Nd对AZ81镁合金组织和高温力学性能的影响。结果表明，稀土元素Y、Nd的加入明显细化了AZ81镁合金的显微组织，减少了β（Mg17Al12）相的析出。分析认为，稀土元素Y和Nd主要是通过固溶强化、析出强化和细晶强化提高了合金的室温和高温强度，改善了合金的塑性。复合加入2％的Y和Nd，合金的室温强度最高，达282．5MPa，与未加稀土的AZ81相比，约提高了39％。含1％Y的AZ81合金在150℃下的高温强度高达220MPa，与不含稀土的AZ81相比高温强度约提高40％。