Some proximity and sensitivity results in quadratic integer programming

We show that for any optimal solution for a given separable quadratic integer programming problem there exist an optimal solution for its continuous relaxation such that wheren is the number of variables and(A) is the largest absolute subdeterminant of the integer constraint matrixA. Also for any feasible solutionz, which is not optimal for the separable quadratic integer programming problem, there exists a feasible solution having greater objective function value and with . We further prove, under some additional assumptions, that the distance between a pair of optimal solutions to an integer quadratic programming problem with right hand side vectorsb andb, respectively, depends linearly on b–b₁. Finally the validity of all the results for nonseparable mixed-integer quadratic programs is established. The proximity results obtained in this paper are extensions of some of the results described in Cook et al. (1986) for linear integer programming.This research was partially supported by Natural Sciences and Engineering Research Council of Canada Grant 5-83998.     

Edge proximity and matching extension in projective planar graphs

A graph $G$ with at least $2m+2$ vertices is said to be distance $d$ $m$-extendable if, for any matching $M$ of $G$ with $m$ edges in which the edges lie at distance at least $d$ pairwise, there exists a perfect matching of $G$ containing $M$. In this paper we prove that every 5-connected triangulation on the projective plane of even order is distance 3 7-extendable and distance 4 $m$-extendable for any $m$.     

Chromophore-Assisted Proximity Labeling of DNA Reveals Chromosomal Organization in Living Cells

The spatial arrangement of chromosome within the nucleus is linked to genome function and gene expression regulation. Existing genome-wide mapping methods often rely on chemically crosslinking DNA with protein baits, which raises concerns of artifacts being introduced during cell fixation. By genetically targeting a photosensitizer protein to specific subnuclear locations, we achieved blue-light-activated labeling of local DNA with a bioorthogonal functional handle for affinity purification and sequence identification through next-generation sequencing. When applied to the nuclear lamina in human embryonic kidney 293T cells, it revealed lamina-associated domains (LADs) that cover 37.6 % of the genome. These LADs overlap with heterochromatin hallmarks and are depleted with CpG islands. This simple labeling method avoids the harsh treatment of chemical crosslinking and is generally applicable to the genome-wide high-resolution mapping of the spatial chromosome organization in living cells.     

一种邻近性的计算方法

邻近律是Gestalt定律的基本定律之一，然而迄今为止，如何在图像处理中计算元素之间的邻近性程度还没有具体方法提出．以点元素作为抽象载体提出了一种邻近性的计算方法，该方法借鉴基于最小支撑树（MST）的聚类思想，引入三角剖分和Prim算法计算元素之间的MST邻近性测度和加权MST邻近性测度用于度量元素之间的邻近性．实验结...     

包络半群与拓扑动力学中的接近关系

运用包络半群的理论，对接近关系中一个重要定理给出了一个简单证明．作为这一定理的应用，我们得到接近关系可乘性的一个结果．并且对另一种接近关系，也得到一个结果．这两个定理减弱了Ｃｌａｙ在这一领域中两个定理的条件．     

BEST PROXIMITY POINT THEOREMS FOR SINGLE- AND SET-VALUED NON-SELF MAPPINGS

We study the existence of best proximity points for single-valued non-self map-pings. Also, we prove a best proximity point theorem for set-valued non-self mappings in metric spaces with an appropriate geometric property. Examples are given to support the usability of our results.     

On a New Class of Systems of Generalized Quasi-Variational Inequalities

We introduce new types of systems of generalized quasi-variational inequalities and we prove the existence of the solutions by using results of pair equilibrium existence for free abstract economies. We consider the fuzzy models and we also introduce the random free abstract economy and the random equilibrium pair. The existence of the solutions for the systems of quasi-variational inequalities comes as consequences of the existence of equilibrium pairs for the considered free abstract economies.     

On cyclic Meir-Keeler contractions in metric spaces

Cyclic Meir-Keeler contractions are considered under the recently introduced WUC and HW properties on pairs of subsets of metric spaces. We show that, in contrast with previous results in the theory, best proximity point theorems under these properties do not directly extend from cyclic contractions to cyclic Meir-Keeler contractions. We obtain, however, a positive result for cyclic Meir-Keeler contractions under additional properties which is shown to be an extension of already existing results for cyclic contractions. Moreover, we give examples supporting the necessity of our additional conditions.     

Best Proximity Point Theorems for Some Special Proximal Contractions

This article explores some new best proximity point theorems for absolute proximal cyclic contractions and dual supreme proximal contractions which are not necessarily continuous. As a consequence of such best proximity point theorems, the famous contraction principle is elicited.