Miklavič and Milanič (2011) introduced the connections among the classes of equistable, general partition and triangle graphs. We present results concerning the three classes aforementioned. In particular, we show that the general partition and triangle classes are both closed under the operations of substitution, induction and contraction of modules. Moreover, we show that the triangle conditi...

Accurate DNA partition at cell division is vital to all living organisms. In bacteria, this process can involve partition loci, which are found on both chromosomes and plasmids. The initial step in Escherichia coli plasmid R1 partition involves the formation of a partition complex between the DNA-binding protein ParR and its cognate centromere site parC on the DNA. The partition complex is reco...

By means of the Drinfeld twists, we derive the determinant representations of the partition functions for the gl(1|1) and gl(2|1) supersymmetric vertex models with domain wall boundary conditions. In the homogenous limit, these determinants degenerate to simple functions.

For each rational number q ≥ 1, we describe two partitions of the vertex set of a graph G, called the q-brick partition and the q-superbrick partition. The special cases when q = 1 are the partitions given by the connected components and the 2-edge-connected components of G, respectively. We obtain structural results on these partitions and describe their relationship to the principal partition...

We investigate the problem of computing the partition function of a probabilistic context-free grammar, and consider a number of applicable methods. Particular attention is devoted to PCFGs that result from the intersection of another PCFG and a finite automaton. We report experiments involving the Wall Street Journal corpus.

The simulation of three dimensional structural dynamics on massively parallel platforms places stringent requirements on the existing software infrastructure. A constrained and nonlinear graph partitioning problem that arises in scalable iterative substructuring methods, such as FETI methods, is identified. New sufficient criteria on a partition are presented that ensure the applicability of FE...