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Synthesis, isolation, and structural characterization of unique metal rich diamagnetic cobaltaborane clusters are reported. They were obtained from reactions monoborane as well modified borohydride reagents with cobalt sources. For example, the reaction [Cp*CoCl]2 [LiBH4·THF] subsequent photolysis excess [BH3·THF] (THF = tetrahydrofuran) at room temperature afforded 11-vertex tricobaltaborane n...

We here consider the problem of modeling network evolution with joint edge and vertex dynamics. It is natural to expect that the accuracy of vertex prediction strongly affect the ability to predict dynamic network evolution accurately. A latent graphical model is here employed to model vertex evolution. This model family can incorporate dependence in vertex co-presence, of the form found in man...

We prove a number of results around kernelization of problems parameterized by the size of a given vertex cover of the input graph. We provide three sets of simple general conditions characterizing problems admitting kernels of polynomial size. Our characterizations not only give generic explanations for the existence of many known polynomial kernels for problems like q-Coloring, Odd Cycle Tran...

A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. A graph is well-covered if all its maximal stable sets are of the same size, co-well-covered if its complement is well-covered, and vertex-transitive if, for every pair of vertices, there exists an automorphism of the graph mapping one to the other. We show that a vertex-transitive graph is CIS if and o...

We show that any simple n-vertex polygon can be made convex, without losing internal visibilities between vertices, using n moves. Each move translates a vertex of the current polygon along an edge to a neighbouring vertex. In general, a vertex of the current polygon represents a set of vertices of the original polygon that have become co-incident. We also show how to modify the method so that ...

let g be a graph with p vertices and q edges and a = {0, 1, 2, . . . , [q/2]}. a vertex labeling f : v (g) → a induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv. for a ∈ a, let vf (a) be the number of vertices v with f(v) = a. a graph g is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in a, |vf (a) − vf (b)| ≤ 1 and the in...

Using the pure spinor formalism for the superstring, the vertex operator for the first massive states of the open superstring is constructed in a manifestly super-Poincaré co-variant manner. This vertex operator describes a massive spin-two multiplet in terms of ten-dimensional superfields.

Using the pure spinor formalism for the superstring, the vertex operator for the first massive states of the open superstring is constructed in a manifestly super-Poincaré co-variant manner. This vertex operator describes a massive spin-two multiplet in terms of ten-dimensional superfields.

Word Sense Induction (WSI) is the task of identifying the different senses (uses) of a target word in a given text. Traditional graph-based approaches create and then cluster a graph, in which each vertex corresponds to a word that co-occurs with the target word, and edges between vertices are weighted based on the co-occurrence frequency of their associated words. In contrast, in our approach ...