To any triangulated category with tensor product (K,⊗), we associate a topological space Spc(K,⊗), by means of thick subcategories of K, à la Hopkins-Neeman-Thomason. Moreover, to each open subset U of this space Spc(K,⊗), we associate a triangulated category K(U), producing what could be thought of as a presheaf of triangulated categories. Applying this to the derived category (K,⊗) := (D(X),⊗...

In a graph G, k disjoint paths joining a single source and k distinct sinks that cover all the vertices in the graph are called a one-tomany k-disjoint path cover of G. We consider a k-disjoint path cover in a graph with faulty vertices and/or edges obtained by merging two graphs H0 and H1, |V (H0)| = |V (H1)| = n, with n pairwise nonadjacent edges joining vertices in H0 and vertices in H1. We ...

Brain tumor segmentation aims to separate the different tumor tissues such as active cells, necrotic core, and edema from normal brain tissues of White Matter (WM), Gray Matter (GM), and Cerebrospinal Fluid (CSF). MRI based brain tumor segmentation studies are attracting more and more attention in recent years due to non-invasive imaging and good soft tissue contrast of Magnetic Resonance Imagi...

The original LR(k) parser generation algorithm of Knuth in 1965 is very expensive in time and space. Different approaches have been proposed to achieve LR(k) with better practical performance. This work designed a new LR(k) algorithm called the edge-pushing algorithm, which is based on recursively applying the lane-tracing process. The algorithm has been implemented into the parser generator Hy...