The 2-5A-dependent RNase (RNase L) is a tightly regulated endoribonuclease of higher vertebrates that is catalytically active only after engaging unusual effector molecules consisting of the 2',5'-linked oligoadenylates, p1-3A(2'p5'A)>/=2 (2-5A). Progressive truncations from either terminus have provided insight into the structure, function, and regulation of RNase L. We determined that deletio...

In this paper we prove the knight move theorem for the chromatic graph cohomologies with rational coefficients introduced by L. HelmeGuizon and Y. Rong. Namely, for a connected graph Γ with n vertices the only non-trivial cohomology groups H(Γ), H(Γ) come in isomorphic pairs: H(Γ) = H(Γ) for i > 0 if Γ is non-bipartite, and for i > 0 if Γ is bipartite. As a corollary, the ranks of the cohomolog...

ontology is a requirement engineering product and the key to knowledge discovery. it includes the terminology to describe a set of facts, assumptions, and relations with which the detailed meanings of vocabularies among communities can be determined. this is a qualitative content analysis research. this study has made use of ontology for the first time to discover the knowledge of vaccine in ir...

Motivated by the research in reconfigurable memory array structures, this paper studies the complexity and algorithms for the constrained minimum vertex cover problem on bipartite graphs (min-cvcb) defined as follows: given a bipartite graph G 1⁄4 ðV ;EÞ with vertex bipartition V 1⁄4 U,L and two integers ku and kl ; decide whether there is a minimum vertex cover in G with at most ku vertices in...

Let q be a prime power, Fq be the field of q elements, and k, m be positive integers. A bipartite graph G = Gq(g, h, k,m) is defined as follows. The vertex set of G is a union of two copies P and L of two-dimensional vector spaces over Fq, with two vertices (p1, p2) ∈ P and [ l1, l2 ] ∈ L being adjacent if and only if p2 + l2 = p1l 1 . We prove that graphs Gq(k, m) and Gq′(k,m) are isomorphic i...

for 1 <; i < k. L. Carlitz [2] first derived the generating function for restricted bipartite partitions. Subsequently Carlitz and Roselle [3] enumerated certain special families of these partitions e.g., restricted bipartite partitions where the m< and % are all odd. Finally both Roselle [4] and Andrews [1] have obtained different generalizations for multipartite partitions. All these results ...

The intersection dimension of a bipartite graph with respect to a type L is the smallest number t for which it is possible to assign sets Ax ⊆ {1, . . . , t} of labels to vertices x so that any two vertices x and y from different parts are adjacent if and only if |Ax ∩Ay| ∈ L. The weight of such a representation is the sum ∑x |Ax| over all vertices x. We exhibit explicit bipartite n×n graphs wh...

A labeled graph is said to be weakly bipartite if the clutter of its odd cycles is ideal. Seymour conjectured that a labeled graph is weakly bipartite if and only if it does not contain a minor called an oddK5. A proof of this conjecture is given in this paper. Let G = (V;E) be a graph and E. We call edges in odd and edges in E even. The pair (G; ) is called a labeled graph. A subset L E(G) is ...

A hica is a highest weight, homogeneous, indecomposable, Calabi-Yau category of dimension 0. A hica has length l if its objects have Loewy length l and smaller. We classify hicas of length ≤ 4, up to equivalence, and study their properties. Over a fixed field F , we prove that hicas of length 4 are in one-one correspondence with bipartite graphs. We prove that an algebra AΓ controlling the hica...

In this paper we provide a new method to generate hard k-SAT instances. We incrementally construct a high girth bipartite incidence graph of the k-SAT instance. Having high girth assures high expansion for the graph, and high expansion implies high resolution width. We have extended this approach to generate hard n-ary CSP instances and we have also adapted this idea to increase the expansion o...