For a connected graph G = (V , E), an edge set S ⊂ E is a k-restricted edge cut if G − S is disconnected and every component of G − S contains at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is defined as the cardinality of a minimum krestricted edge cut. For U1,U2 ⊂ V (G), denote the set of edges of Gwith one end in U1 and the other in U2 by [U1,U2]. Define ξk(G...

Tree structured data such as HTML/XML files are represented by rooted trees with ordered children and edge labels. As a representation of a tree structured pattern in such tree structured data, we propose an ordered tree pattern, called a term tree, which is a rooted tree pattern consisting of ordered children and internal structured variables. A term tree is a generalization of standard tree p...

This paper addresses the problem of efficient execution of a batch of data-intensive tasks with batch-shared I/O behavior, on coupled storage and compute clusters. Two scheduling schemes are proposed: 1) a 0-1 Integer Programming (IP) based approach, which couples task scheduling and data replication, and 2) a bi-level hypergraph partitioning based heuristic approach (BiPartition), which decoup...

In this paper, we study two fast algorithms—HashRF and PGM-Hashed—for computing the Robinson-Foulds (RF) distance matrix between a collection of evolutionary trees. The RF distance matrix represents a tremendous data-mining opportunity for helping biologists understand the evolutionary relationships depicted among their trees. The novelty of our work results from using a variety of different ar...

A literature search revealed only three case reports of treatment for a symptomatic bipartite medial cuneiform [1,2,5]. Azurza and Sakellarious reported a case of a 34 year old male Soldier with a three year history of symptomatic bipartition following a soccer injury. Successful treatment consisted of arthrodesis [1]. Chiodo and Parentis reported a case of a 32 year old female Olympic marathon...

A bipartition of n is an ordered pair of partitions (λ, μ) such that the sum of all of the parts equals n. In this article, we concentrate on the function c5(n), which counts the number of bipartitions (λ, μ) of n subject to the restriction that each part of μ is divisible by 5. We explicitly establish four Ramanujan type congruences and several infinite families of congruences for c5(n) modulo 3.

Basic algorithms in real algebraic geometry and their complexity: from Sturm's theorem to the existential theory of reals. polar varieties, real equation solving, and data structures: The hypersurface case. A partial k-arboretum of graphs with bounded tree-width (tutorial). a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines....

Let G = (V, E) be a graph and let S ⊆ V . The set S is a packing in G if the vertices of S are pairwise at distance at least three apart in G. The set S is a dominating set (DS) if every vertex in V − S is adjacent to a vertex in S. Further, if every vertex in V − S is also adjacent to a vertex in V − S, then S is a restrained dominating set (RDS). The domination number of G, denoted by γ(G), i...

A set of multipartite orthogonal quantum states is strongly nonlocal if it locally irreducible for every bipartition the subsystems [S. Halder, M. Banik, S. Agrawal, and Bandyopadhyay, Phys. Rev. Lett. 122, 040403 (2019)]. Although this property has been shown in three-, four-, five-partite systems, existence sets $N$-partite systems remains unknown when $N\ensuremath{\ge}6$. In paper, we succe...

We have used a PCR assay based on the use of degenerate primers in order to characterize an internal fragment (sodA(int)) representing approximately 85% of the genes encoding the manganese-dependent superoxide dismutase in various streptococcal type strains (S. acidominimus, S. agalactiae, S. alactolyticus, S. anginosus, S. bovis, S. constellatus, S. canis, S. cricetus, S. downei, S. dysgalacti...