The Distance Matching Extension in K_(1,k)-free Graphs with High Local Connectedness

A matching is extendable in a graph G if G has a perfect matching containing it.A distance q matching is a matching such that the distance between any two distinct matching edges is at least q.In this paper,we prove that any distance 2k-3 matching is extendable in a connected and locally(k-1)-connected K1,k-free graph of even order.Furthermore,we also prove that any distance q matching M in an r-connected and locally(k-1)-connected K1,k-free graph of even order is extendable provided that|M|is bounded by a function on r,k and q.Our results improve some results in[J.Graph Theory 93(2020),5–20].

2D registration based on contour matching for partial matching images

The mean Hausdorff distance, though highly applicable in image registration, does not work well on partial matching images. An improvement upon traditional Hausdorff-distance-based image registration method is proposed, which consists of the following two aspects. One is to estimate transformation parameters between two images from the distributions of geometric property differences instead of establishing explicit feature correspondences. This procedure is treated as the pre-registration. The other aspect is that mean Hausdorff distance computation is replaced with the analysis of the second difference of generalized Hausdorff distance so as to eliminate the redundant points. Experimental results show that our registration method outperforms the method based on mean Hausdorff distance. The registration errors are noticeably reduced in the partial matching images.

Phenotypic and molecular diversity-based prediction of heterosis in pearl millet(Pennisetum glaucum L.(R.)Br.)

Genetic distances between hybrid parents based on phenotypic traits and molecular markers were investigated to assess their relationship with heterosis for grain and stover yield and other traits in pearl millet(Pennisetum glaucum [L.] R. Br.). Fifty-one hybrids developed using 101 hybrid parents(B and R lines) and showing a wide range of genetic distance between their parents based on eight phenotypic traits and 28–38 SSRs were evaluated in two sets for two seasons. The correlation between Euclidean distance(phenotypic distance, ED) and simple matching distance(molecular distance, SM) for parents of both sets was low but positive and significant(r = 0.2, P < 0.001).The correlation of ED in parents with better-parent heterosis for grain yield was similar in both sets(r =0.38, P < 0.05). SM was not correlated with heterosis for grain yield in either set of hybrids.The results showed that phenotypic distance could be a better predictor of heterosis than molecular distance. The correlation between phenotypic distance and heterosis was not strong enough to permit the use of phenotypic diversity among parents as a major selection criterion for selection of parental lines displaying high levels of heterosis for grain and stover yield in pearl millet.

A NEW APPROXIMATION ALGORITHM FOR THE MATCHING DISTANCE IN MULTIDIMENSIONAL PERSISTENCE

Topological Persistence has proven to be a promising framework for dealing with problems concerning shape analysis and comparison.In this contexts,it was originally introduced by taking into account 1-dimensional properties of shapes,modeled by real-valued functions.More recently,Topological Persistence has been generalized to consider multidimensional proper ties of shapes,coded by vect or-valued functions.This extension has led to int roduce suitable shape descrip tors,named the multidimensional persis tence Betti numbers functions,and a distance to compare them,the so-called multidimensional matching distance.In this paper we propose a new computational framework to deal with the multidimensional matching distance.We start by proving some new theoretical results,and then we use them to formulate an algorithm for computing such a distance up to an arbitrary threshold error.