As a common generalization of matchings and matroid intersection, W.H. Cunningham and J.F. Geelen introduced the notion of path-matchings, then they introduced the more general notion of even factor in weakly symmetric digraphs. Here we give a min-max formula for the maximum cardinality of an even factor. Our proof is purely combinatorial. We also provide a Gallai-Edmonds-type structure theorem...

Last lecture we covered matroid intersection, and defined matroid union. In this lecture we review the definitions of matroid intersection, and then show that the matroid intersection polytope is TDI. This is Chapter 41 in Schrijver’s book. Next we review matroid union, and show that unlike matroid intersection, the union of two matroids is again a matroid. This material is largely contained in...

In this contribution, we are concerned with the detection and re ned localization of 3D point landmarks. We propose multi-step di erential procedures which are generalizations of an existing two-step procedure for subpixel localization of 2D point landmarks. This two-step procedure combines landmark detection by applying a di erential operator with re ned localization through a di erential edge...

We present an (1+ε)-approximation algorithm with quasi-polynomial running time for computing the maximum weight independent set of polygons out of a given set of polygons in the plane (specifically, the running time is nO(poly(logn,1/ε))). Contrasting this, the best known polynomial time algorithm for the problem has an approximation ratio of nε. Surprisingly, we can extend the algorithm to the...

the class of ads modules with the sip (briefly‎, ‎$sa$-modules) is studied‎. ‎various conditions for a module to be $sa$-module are given‎. ‎it is proved that for a quasi-continuous module $m$‎, ‎$m$ is a uc-module if and only if $m$ is an $sa$-module‎. ‎also‎, ‎it is proved that the direct sum of two $sa$-modules as $r$-modules is an $sa$-module when $r$ is the sum of the annihilators of these...

in this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. following this, we establish the minkowski and brunn-minkowski inequalities for volumes difference function of the projection and intersection bodies.

Some of these curves are considered in a rather incidental way in the writings of Poincare.** However, the full concept of pseudo closed trajectories does not seem to have been discussed explicitly heretofore. We assume that all of the variables in the equations (1) are real, that the functions X and Y are continuous in an open connected region R in the xy-plane, that these functions satisfy Li...

The intersection between an illumination and a reflectance edge is characterised by the 'ratio-invariant' property, that is the luminance ratio of the regions under different illumination remains the same. In a CRT experiment, we shaped two areas, one surrounding the other, and simulated an illumination edge dividing them in two frames of illumination. The portion of the illumination edge stand...

For a set S of n lines labeled from 1 to n, we say that S supports an n-vertex planar graph G if for every labeling from 1 to n of its vertices, G has a straight-line crossing-free drawing with each vertex drawn as a point on its associated line. It is known from previous work [4] that no set of n parallel lines supports all n-vertex planar graphs. We show that intersecting lines, even if they ...