Proof. The first equality follows directly from (1). To see the second equality, first let M be a matching of size ν(G). For each of the |V | − 2|M | vertices v missed by M , add to M an edge covering v. We obtain an edge cover of size |M |+ (|V | − 2|M |) = |V | − |M |. Hence ρ(G) ≤ |V | − ν(G). Second, let F be an edge cover of size ρ(G). For each v ∈ V delete from F , dF (v) − 1 edges incide...

Feature detection and pattern matching play an important role in visualization. Originally developed for images and scalar fields, pattern matching methods become increasingly interesting for other applications, e.g., vector fields. To apply pattern matching to vector fields the basic concepts of convolution and fast Fourier transform (FFT) have to be generalized to vector fields. A formalism s...

background: the present work aims to study the out-of-field photon calculation accuracy of a commercial treatment planning system (tps), oncentra, for three-dimensional conformal radiotherapy (3d-crt) and intensity modulated radiation therapy (imrt) treatment techniques from elekta synergy medical linear accelerator. materials and methods: accuracy of individual out-of-field dose components was...

background: to reduce uncertainties of patient positioning, the computerized tomography (ct) images acquired at the treatment planning time can be compared with those images obtained during radiation dose delivery. this can be followed during dose delivery procedure as image guided radiotherapy (igrt) to verify the prescribed radiation dose delivery to the target as well as to monitor radiation...

We present a single, connected tile which can the plane but only non-periodically. The is hexagonal with edge markings, impose simple rules as to how adjacent tiles are allowed meet across edges. first of these standard matching rule, that certain decorations match second condition new type allows when in particular orientation given opposite charge. This forces form hierarchy triangles, follow...

Typographical data entry errors and incomplete documents, produce imperfect records in real world databases. These errors generate distinct records which belong to the same entity. The aim of Approximate Record Matching is to find multiple records which belong to an entity. In this paper, an algorithm for Approximate Record Matching is proposed that can be adapted automatically with input error...

Background: The present work aims to study the out-of-field photon calculation accuracy of a commercial treatment planning system (TPS), Oncentra, for three-dimensional conformal radiotherapy (3D-CRT) and intensity modulated radiation therapy (IMRT) treatment techniques from Elekta Synergy medical linear accelerator. Materials and Methods: Accuracy of individual out-of-field dose components was...

Uncertain graphs are employed to describe graph models with indeterministicinformation that produced by human beings. This paper aims to study themaximum matching problem in uncertain graphs.The number of edges of a maximum matching in a graph is called matching numberof the graph. Due to the existence of uncertain edges, the matching number of an uncertain graph is essentially an uncertain var...

Given a bipartite graph G = (A∪B,E) with strict preference lists and e∗ ∈ E, we ask if there exists a popular matching in G that contains the edge e∗. We call this the popular edge problem. A matching M is popular if there is no matching M′ such that the vertices that prefer M′ to M outnumber those that prefer M to M′. It is known that every stable matching is popular; however G may have no sta...