Top-down partitioning has focused on minimum cut or ratio cut objectives, while bottom-up clustering has focused on density-based objectives. In seeking a more uni ed perspective, we propose a new sum of densities measure for multi-way circuit decomposition, where the density of a subhypergraph is the ratio of the number of edges to the number of nodes in the subhypergraph. Finding a k-way part...

A (1, k)-composition of a positive integer n consists of an ordered sequence of the integers 1 and k whose sum is n. A palindromic (1, k)-composition is one for which the sequence is the same from left to right as from right to left. We give recursive equations and generating functions for the total number of such compositions and palindromes, and for the number of 1’s, k’s, “+”signs and summan...

Blood flow phenomena occurring when flow is within the magnetic resonance (MR) imaging plane were analyzed. In this situation, the signal intensity of vascular lumina is predominantly determined by spin-phase change phenomena, and section transition effects of moving spins can be neglected. In this paper, we develop the concepts of in-plane flow, with emphasis on the notion that the spatial var...

cancellations in the perturbation series of certain completely integrable Hamiltonian systems. and existence of heteroclinic chains in Hamiltonian three time scales systems, Preprint, 1997. Ge1] Gentile, G: A proof of existence of whiskered tori with quasi at homoclinic intersections in a class of almost integrable Hamiltonians systems, Forum Mathematicum 17 Draft #1 DB k?1 (k ? 1)!? 0 C(;) ?1 ...