Greedy splitting algorithms for approximating multiway partition problems

Given a system (V,T,f,k), where V is a finite set, is a submodular function and k2 is an integer, the general multiway partition problem (MPP) asks to find a k-partition ={V₁,V₂,...,V_k} of V that satisfiesfor all i and minimizes f(V₁)+f(V₂)+···+f(V_k), where is a k-partition of hold. MPP formulation captures a generalization in submodular systems of many NP-hard problems such as k-way cut, multiterminal cut, target split and their generalizations in hypergraphs. This paper presents a simple and unified framework for developing and analyzing approximation algorithms for various MPPs.Mathematics Subject Classification (1991): 20E28, 20G40, 20C20Acknowledgement This research is partially supported by the Scientific Grant-in-Aid from Ministry of Education, Science, Sports and Culture of Japan. The authors would like to thank the anonymous referees for their valuable comments and suggestions.     

Fluorescence Spectroscopic Studies on Phase Heterogeneity in Lipid Bilayer Membranes

There is a growing interest in functional membrane heterogeneity on the mesoscopic (several tens to hundreds of molecular dimensions) scale. However, the physical-chemical basis for this sort of heterogeneity in membranes is not entirely clear. Unambiguous methods to demonstrate that the cell plasma membrane and other cellular membranes are in fact heterogeneous on the mesoscopic level are also not generally available. Fluorescence techniques do, however, provide excellent tools for this purpose. In particular, the emerging techniques of scanning near-field optical microscopy and single-molecule fluorescence microscopy hold a great deal of promise for the near-future. All these methods require the use of fluorescent probes (lipids and/or proteins) and a clear definition of how these probes partition between domains of coexisting membrane phases. The development of the concept of membrane heterogeneity over the years since the first proposal of the fluid mosaic model is reviewed briefly. The use of lipid-binding proteins in experimental protocols for the labeling of membranes with fluorescent lipid amphiphiles as monomers in aqueous solutions at concentrations well above their critical aggregation concentrations is discussed. The methods of fluorescence spectroscopy available to the cell biologist for determining probe partition coefficients for partitioning between coexisting membrane phases are reviewed in some detail, as is the relevant theoretical and experimental work reported in the literature.     

构造非均匀剖分上局部支集样条函数的积分方法

１　引　　言 给定递增数列｛ｘｉ｝,｛ｙｉ｝,｛ｚｋ｝．对于Ｒ２,由直线｛ｘ＝ｘｉ）和｛ｙ＝ｙｊ｝形成的剖分称为非均匀矩形剖分;再连接每个矩形［ｘｉ,ｘｉ＋１］×［ｙｊ,ｙｊ＋１］的正斜率对角线形成的剖分称为非均匀Ｉ－型三角剖分,记为　１;若连接每个矩形的两条对角线,则所得剖分为非均匀Ⅱ－型三角剖分,记为　２．对于Ｒ３,由平面｛ｘ＝ｘｉ｝,｛ｙ＝ｙｊ｝,｛ｚ＝ｚｋ｝形成的剖分称为非均匀长方体剖分;若再连接每个小长方体［ｘｉ,ｘｉ＋１］×［ｙｊ,ｙｊ＋１］×［ｚｋ,ｚｋ＋１］的过点（ｘｉ,ｙｊ,ｚ…     

正整数n的m-分拆及其应用

本文引入了两个新概念,正整数n的m－分拆和正整数n的真m－分拆。通过研究我们发现,n的分拆恰是n的m－分拆的一个特例,而n的真m－分拆在二侵略产的（整）和图研究中有实际应用[8]。     

On Equivalence Relations in Ordered Sets

A relationship between equivalence relations in finite ordered sets and linear decompositions is presented.     

Applications of pseudo-monotone operators with some kind of upper semicontinuity in generalized quasi-variational inequalities on non-compact sets

Let be a topological vector space and be a non-empty subset of . Let and be two maps. Then the generalized quasi-variational inequality (GQVI) problem is to find a point and a point such that for all . We shall use Chowdhury and Tan's 1996 generalized version of Ky Fan's minimax inequality as a tool to obtain some general theorems on solutions of the GQVI on a paracompact set in a Hausdorff locally convex space where the set-valued operator is either strongly pseudo-monotone or pseudo-monotone and is upper semicontinuous from to the weak-topology on for each non-empty finite subset of .

     

Entropy for Random Partitions and Its Applications

Asymptotic properties of partitions of the unit interval are studied through the entropy for random partition

Zeros of the finite-size scaling region partition function for a model with a wetting transition

We derive a finite-size scaling representation for the partition function for an Onsager-Temperley string model with a wetting transition, and analyze the zeros of this partition function in the complex scaled coupling parameter of relevance. The system models the one-dimensional interface between two phases in a rectangular two-dimensional region (x, y) ²,–L yL,oxN. The two phases are at coexistence. The string or interface has a surface tension 2KkT per unit length and an extra Boltzmann weighta per unit length if it touches the surfaces aty=±L. There is a critical valuea _c=1/2K and fora>a _c the string is confined to one of the surfaces, while fora a _c the string moves roughly in the rectangular region. The finite-size scaling parameters are =a _c ² N/L ² and =L(a–a _c)/a _c ² . We find that for || large, the zeros of the scaled partition function lie close to the lines arg()=±/4 with re()>0. We discuss the motion of all the zeros as changes by both analytic and numerical arguments.     

Taylor expansion of polymer chain dispersion relations and spectral densities to calculate thermodynamic functions

It is shown how to calculate exactly the derivatives of the dispersion relation and the spectral density for arbitrary regular polymer chains in harmonic approximation. The theory is based on a generalization of the characteristic polynomial. In the vibrational part of the free energy and other thermodynamic functions, the integral over normal modes is done approximately by Taylor expanding the density of states.Dedicated to Professor Dr. F. H. Müller.     

用外推容量因子法测定药物的疏水性

本文利用不同体积分数的甲醇-水作流动相,用外推容量因子法测定20种不同结构类型药物的疏水性,该法操作简便、快速、测定疏水性范围宽,相关性好。