Let G be a connected bipartite graph. An involution α of G that preserves the bipartition of G is called bipartite. Let Gα be the graph obtained from G by adding to G the natural perfect matching induced by α. We show that the k-cube Qk is isomorphic to the direct product G×H if and only if G is isomorphic to Qk−1 for some bipartite involution α of Qk−1 and H = K2.

We consider processing an n× d matrix A in a stream with row-wise updates according to a recent algorithm called Frequent Directions (Liberty, KDD 2013). This algorithm maintains an l× d matrix Q deterministically, processing each row in O(dl) time; the processing time can be decreased to O(dl) with a slight modification in the algorithm and a constant increase in space. Then for any unit vecto...

Alternative splicing of the qkI transcript generates multiple isoforms of the selective RNA-binding protein QKI, which play key roles in controlling the homeostasis of their mRNA targets. QKI deficiency in oligodendrocytes of homozygous quakingviable (qk /qk ) mutant mice results in severe hypomyelination, indicating the essential function of QKI in myelinogenesis. However, the molecular mechan...

More general form of the notion of quasi-coincidence of a fuzzy point with a fuzzy subset is considered, and generalization of fuzzy fated of R0-algebras is discussed. The notion of an (∈,∈∨ qk)-fuzzy fated filter in a R0-algebra is introduced, and several properties are investigated. Characterizations of an (∈,∈∨ qk)-fuzzy fated filter in an R0-algebra are discussed. Using a collection of fate...

Hamiltonian system LetA ⊆ R be an open set andH :A×R×R → R be a smooth function (A×R is called the phase space). Consider the system of ordinary differential equations q̇k = ∂H(q, p, t)/∂pk, ṗk = −∂H(q, p, t)/∂qk, for k = 1, . . . , d. The equations are called Hamilton equations, and H is called a Hamiltonian function. A dynamical system described by Hamilton equations is called a Hamiltonian sy...

The transition probability of a two-photon absorption (TPA) process in atomic Cesium, excited by phase-controlled temporally focused ultrashort pulses is shown to be spatially modulated in a controlled manner. In particular, we demonstrate the generation of a dark nonlinear focus. By controlling the excitation pulse shape along the propagation coordinate we create a region in space where the TP...

High spatial resolution QuickBird satellite data have provided new opportunities for remote sensing applications in agriculture. In this study, image-based algorithms for atmospheric correction were evaluated on QuickBird imagery for retrieving surface reflectance (qk) of corn and potato canopies in Minnesota. The algorithms included the dark object subtraction technique (DOS), the cosine appro...

We study the matrices Qk of in-forests of a weighted digraph Γ and their connections with the Laplacian matrix L of Γ. The (i, j) entry of Qk is the total weight of spanning converging forests (in-forests) with k arcs such that i belongs to a tree rooted at j. The forest matrices, Qk, can be calculated recursively and expressed by polynomials in the Laplacian matrix; they provide representation...