LP formulations of the shortest path tree problem

Based on a pair of primal-dual LP formulations of the shortest path tree problem, the first algorithmic approach to reoptimizing the shortest paths subject to changes in the edge weights was proposed by S. Pallottino and M.G. Scutellá in 2003. We shall here focus solely on their introductory sections, propose some simplifications of the models considered, and finally relate the resulting models to the presentation of single-source shortest path problems in textbooks treating this subject with but limited or no reference to LP.Received: April 2004, Revised: August 2004, MSC classification: 90C05, 90C35, 90B10 Dedicated to the memory of Stefano Pallottino     

Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping

We present a framework aimed to reveal directed interactions of activated brain areas using time-resolved fMRI and vector autoregressive (VAR) modeling in the context of Granger causality. After describing the underlying mathematical concepts, we present simulations helping to characterize the conditions under which VAR modeling and Granger causality can reveal directed interactions from fluctuations in BOLD-like signal time courses. We apply the proposed approach to a dynamic sensorimotor mapping paradigm. In an event-related fMRI experiment, subjects performed a visuomotor mapping task for which the mapping of two stimuli (“faces” vs “houses”) to two responses (“left” or “right”) alternated periodically between the two possible mappings. Besides expected activity in sensory and motor areas, a fronto-parietal network was found to be active during presentation of a cue indicating a change in the stimulus-response (S-R) mapping. The observed network includes the superior parietal lobule and premotor areas. These areas might be involved in setting up and maintaining stimulus-response associations. The Granger causality analysis revealed a directed influence exerted by the left lateral prefrontal cortex and premotor areas on the left posterior parietal cortex.     

The Riemann Surface of the Chiral Potts Model Free Energy Function

In a recent paper we derived the free energy or partition function of the N-state chiral Potts model by using the infinite lattice inversion relation method, together with a non-obvious extra symmetry. This gave us three recursion relations for the partition function per site T _pq of the infinite lattice. Here we use these recursion relations to obtain the full Riemann surface of T _pq . In terms of the t _p ,t _q variables, it consists of an infinite number of Riemann sheets, each sheet corresponding to a point on a (2N–1)-dimensional lattice (for N>2). The function T _pq is meromorphic on this surface: we obtain the orders of all the zeros and poles. For N odd, we show that these orders are determined by the usual inversion and rotation relations (without the extra symmetry), together with a simple linearity ansatz. For N even, this method does not give the orders uniquely, but leaves only [(N+4)/4] parameters to be determined.     

用于细胞及组织培养的中等强度LED生物光源

研制出可用于细胞及组织培养的中等强度发光二极管光源,介绍了光源的光路原理和简要结构,测试了该光源的辐射照度及其强度分布,使用统计分析软件SPSS拟合得到该光源的辐射照度经验公式。     

线阵CCD拼接技术的应用

介绍采用性能先进的线阵CCD器件拼接技术实现光学系统的技术要求,给出了使用结果。     

Sparse matrix multiplications for linear scaling electronic structure calculations in an atom-centered basis set using multiatom blocks

A sparse matrix multiplication scheme with multiatom blocks is reported, a tool that can be very useful for developing linear-scaling methods with atom-centered basis functions. Compared to conventional element-by-element sparse matrix multiplication schemes, efficiency is gained by the use of the highly optimized basic linear algebra subroutines (BLAS). However, some sparsity is lost in the multiatom blocking scheme because these matrix blocks will in general contain negligible elements. As a result, an optimal block size that minimizes the CPU time by balancing these two effects is recovered. In calculations on linear alkanes, polyglycines, estane polymers, and water clusters the optimal block size is found to be between 40 and 100 basis functions, where about 55-75% of the machine peak performance was achieved on an IBM RS6000 workstation. In these calculations, the blocked sparse matrix multiplications can be 10 times faster than a standard element-by-element sparse matrix package.     

准周期链状聚合物电子谱及特征

研究了链状聚合物的长短键结构呈准周期排列的电子谱。利用紧束缚近似和转移矩阵方法通过理论证明和计算表明：这种准周期排列聚合物的电子谱,当长短键长度相差很小时,具有类似于金属晶体的能带结构;相差很大时,具有无序系统一维能级结构;而对于一般情形,其电子谱与上两者均异,形成所谓的类Cantor集。这3类不同的谱结构反映在链状聚合物的宏观物理性质上也将有所不同,它无疑会影响聚合物的稳定性及相关(超)导电性能,深入研究这方面问题将有助于对有机超导的认识。     

Orders on Braid Groups

It is shown that the braid group defies lattice ordering.