Association Schemes and Fusion Algebras (An Introduction)

We introduce the concept of fusion algebras at algebraic level, as a purely algebraic concept for the fusion algebras which appear in conformal field theory in mathematical physics. We first discuss the connection between fusion algebras at algebraic level and character algebras, a purely algebraic concept for Bose-Mesner algebras of association schemes. Through this correspondence, we establish the condition when the matrix S of a fusion algebra at algebraic level is unitary or symmetric. We construct integral fusion algebras at algebraic level, from association schemes, in particular from group association schemes, whose matrix S is unitary and symmetric. Finally, we consider whether the modular invariance property is satisfied or not, namely whether there exists a diagonal matrix T satisfying the condition (ST)³ = S ². We prove that this property does not hold for some integral fusion algebras at algebraic level coming from the group association scheme of certain groups of order 64, and we also prove that the (nonintegral) fusion algebra at algebraic level obtained from the Hamming association scheme H(d, q) has the modular invariance property.     

基于主成分分析下候选基因关联检验的数学模型

对候选基因的关联检验,都是针对性状在候选基因内使用多个SNP标记,并通过检验SNP单倍型来完成的,众所周知,多标记单倍型方法往往要比单标记方法表达出更多的信息,但是,单倍型的数量往往会随着所标记的SNP的数目增多而急剧的增加,这又会大大增加检验统计量的自由度,使用统计学中的主成分分析法来降低单倍型空间的维数,并构造关联检验来检验一个数量性状与多个单倍型的关联情况,模拟结果显示,此检验方法是较合理的.     

基于粗糙集理论的超稠油油藏水平井吞吐效果评价及其影响因素分析

影响超稠油油藏水平井蒸汽吞吐开发效果的因素包括地质参数、流体参数、开发参数、水平井设计参数等众多因素,寻找主要因素对于超稠油油藏水平井吞吐效果评价及开发调整设计具有重要意义.基于粗糙集理论对影响超稠油油藏水平井吞吐效果的10个因素进行数据属性约简,同时利用灰色关联分析,对这些因素进行敏感性分析;应用Elman神经网络比较上述两种结果,证明了粗糙集理论进行数据属性约简的方法更准确.最终得到注汽干度、注汽强度、注汽速度、水平段长度和注汽压力对水平井的开发效果影响最大.实例计算表明,方法实用有效,精度较高,可用于超稠油油藏水平井吞吐效果评价及开发、调整设计.     

Association Phenomena of Poly(arylene ether sulfone)s in Dimethylformamide

Three poly(arylene ether sulfone)s (two polymers and one copolymer) containing diphenylfluorene, phenolphthalein and 2,4-bis[(4-chlorophenyl)sulfonyl]-1-(phenyltio) benzene)] units were synthesized by the classical Williamson polyetherification reaction. The association phenomenon in N,N-dimethylformamide (DMF) was investigated by different methods: gel permeation chromatography (GPC), viscosity, atomic force microscopy (AFM), fluorescence spectroscopy and dynamic light scattering (DLS). Both AFM and DLS measurements evidenced the formation of aggregates with spherical or ellipsoidal shape at a concentration around 0.05 wt.%. This behavior could be explained by dipole-dipole interactions between macromolecular chains, probably with the participation of solvent molecules, and by H-bonds involving hydroxyl end groups.     

Weighted enumeration of spanning subgraphs in locally tree‐like graphs

Using the theory of negative association for measures and the notion of unimodularity for random weak limits of sparse graphs, we establish the validity of the cavity method for counting spanning subgraphs subject to local constraints in asymptotically tree‐like graphs. Specifically, the normalized logarithm of the associated partition function (free energy) is shown to converge along any sequence of graphs whose random weak limit is a tree, and the limit is directly expressed in terms of the unique solution to a limiting cavity equation. On a Galton–Watson tree, the latter simplifies into a recursive distributional equation which can be solved explicitly. As an illustration, we provide a new asymptotic formula for the maximum size of a b‐matching in the Erd?s–Rényi random graph with fixed average degree and diverging size, for any $b\in\mathbb{N}Using the theory of negative association for measures and the notion of unimodularity for random weak limits of sparse graphs, we establish the validity of the cavity method for counting spanning subgraphs subject to local constraints in asymptotically tree‐like graphs. Specifically, the normalized logarithm of the associated partition function (free energy) is shown to converge along any sequence of graphs whose random weak limit is a tree, and the limit is directly expressed in terms of the unique solution to a limiting cavity equation. On a Galton–Watson tree, the latter simplifies into a recursive distributional equation which can be solved explicitly. As an illustration, we provide a new asymptotic formula for the maximum size of a b‐matching in the Erd?s–Rényi random graph with fixed average degree and diverging size, for any $b\in\mathbb{N}$. To the best of our knowledge, this is the first time that correlation inequalities and unimodularity are combined together to yield a general proof of uniqueness of Gibbs measures on infinite trees. We believe that a similar argument is applicable to other Gibbs measures than those over spanning subgraphs considered here. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013     

血液化验二次分组模型的简捷算法

运用概率和微分学基本理论推导血液二次分组化验最佳分组方案,给出确定二次分组化验最佳分组组数和最佳分组人数的方法,并将血液二次分组化验最佳分组方式与一次分组化验进行比较.     

On Conditional Independence,Mixing, and Association

Abstract

This is a follow-up to a recent article by Prakasa Rao [15 Prakasa Rao , B.L.S. 2008 . Conditional independence, conditional mixing and association . Annals of the Institute of Statistical Mathematics AISM , doi: 10.1007/S10463-007-0152-2 . [Google Scholar]] on conditional independence, conditional mixing and conditional association. The purpose of this article is to derive rigorously some results following from conditioning. To this end, a brief review is presented of the concepts of conditional independence of events, classes of events, and random variables, followed by a conditional version of a factorization theorem, as well as a first installment of some basic results. Next, the concepts of conditional covariance and variance are introduced, and a second installment of basic results follows. Furthermore, a certain representation of the covariance is established in detail, followed by a conditional version of it, as well as a generalization. The concept of the conditional characteristic function is also recalled, and a certain inequality is established. Finally, the concept of conditional positive (negative) quadrant dependence, as well as that of conditional positive (negative) association are introduced. The article concludes with the derivation of the conditional versions of some known results, regarding positive (negative) association. This is done anticipating that conditional association (and also conditional mixing) will prove to be of significant applicability.     

Molecular Dynamics Simulations of Water-Mediated Cholesterol Capture within an Open-Ended Single-Walled Carbon Nanotube

The excess concentration of cholesterol in the bloodstream can be brought down to a safer level by utilizing a potential cholesterol-binding agent such as a carbon nanotube (CNT). Here, we have probed solvent-mediated interactions between cholesterol and CNT by performing molecular dynamics simulations and potential-of-mean force (PMF) calculations. Simulations predict favorable interactions between water-mediated cholesterol and CNT owing to strong mutual interactions between them, whereas water plays an opposing role in the association. The breakdown of PMF into its enthalpic and entropic contributions indicates that contrary to traditional entropy-driven hydrophobic association, the cholesterol encapsulation within a CNT is primarily driven by enthalpy.     

Structure of molecular associates of fluorescent probes in solutions of human serum albumin

Spectral-luminescent characteristics and molecular association processes in solutions of human serum albumin are analyzed at different pH values for three fluorescent probes (eosin, erythrosin, and fluorescein). Common features for all three probes in protein solutions are quenching of the fluorescence, a red shift of the fluorescence maximum, a decrease in the degree of association, and an increase in the angle between dipole moments of dye molecules in dimers. This being so, differences between fluorescein and its halogen derivatives (eosin and erythrosin) are observed in the pH dependences of fluorescence, degree of association, and the angle between dipole moments of probe molecules in dimers. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 6, pp. 782–787, November–December, 2008.     

强背景下模糊闪烁成像目标探测与跟踪

 强背景下空中运动目标主要表现为边缘残缺、模糊,甚至出现闪烁、间断等复杂成像特性,这成为制约目标探测和成像跟踪的瓶颈问题。结合跟踪过程反馈信息来确定目标点扩展函数,利用一种新的Ben-Ezra图像复原模型,解决了目标运动模糊的图像复原问题;采用基于特征伴随值的相似性判断方法,构造联结机制的联想网络模型,来解决目标闪烁和残缺特征的联想问题。对提出的方法进行了图像序列的仿真,取得了较好的实验结果。