Let G = (N, E) be an edge-weightedundirected graph. The graph partitioning problem is the problem of partitioning the node set N into k disjoint subsets of specified sizes so as to minimize the total weight of the edges connecting nodes in distinct subsets of the partition. We present a numerical study on the use of eigenvalue-based techniques to find upper and lower bounds for this problem. Re...

We show that a well-known linearization technique initially proposed for quadratic assignment problems can be generalized to a broader class of quadratic 0-1 mixed-integer problems subject to assignment constraints. The resulting linearized formulation is more compact and tighter than that obtained with a more usual linearization technique. We discuss the application of the compact linearizatio...

Artocarpus communis is an agricultural plant that is also used in folk medicine to prevent skin diseases, including acne and dermatitis. Extracts of A. communis have been used to effectively inhibit melanogenesis; however, the antimelanogenesis mechanism of these extracts has not yet been investigated. The present study utilized a cell-free tyrosinase assay as well as α-melanocyte stimulating h...

The partition ratios of radioactive fatty acids between n-heptane and a physiological buffer at 37 degrees C were measured. The fatty acids included the saturated acids with an even number of carbons from 10 to 18 and the unsaturated acids oleic, linoleic, and linolenic. In addition, the partition ratios of decanoate, myristate, and palmitate were determined over a wide pH range. Any single plo...

This paper explores integrable structures of a generalized melting crystal model that has two q-parameters q1, q2. This model, like the ordinary one with a single q-parameter, is formulated as a model of random plane partitions (or, equivalently, random 3D Young diagrams). The Boltzmann weight contains an infinite number of external potentials that depend on the shape of the diagonal slice of p...

In phylogenomic analysis the collection of trees with identical score (maximum likelihood or parsimony score) may hamper tree search algorithms. Such collections are coined phylogenetic terraces. For sparse supermatrices with a lot of missing data, the number of terraces and the number of trees on the terraces can be very large. If terraces are not taken into account, a lot of computation time ...

Three-dimensional torus is a common topology of network interconnects of multicomputers due to its simplicity and high scalability. A parallel job submitted to a three-dimensional toroidal machine typically requires an isolated, contiguous, rectangular partition connected as a mesh or a torus. Such partitioning leads to fragmentation and thus reduces resource utilization of the machines. In par...

Let S be a set of n points in Rd. A Steiner convex partition is a tiling of conv(S) with empty convex bodies. For every integer d, we show that S admits a Steiner convex partition with at most ⌈(n − 1)/d⌉ tiles. This bound is the best possible for points in general position in the plane, and it is best possible apart from constant factors in every fixed dimension d ≥ 3. We also give the first c...

Since the hardware-software partitioning problem is a key aspect of the codesign of digital electronic systems, extensive researches have been performed with diverse definitions of partitioning problems. However, existent partitioning solutions are not applicable to many real applications partly because of restricted input specification or insufficient constraints. In this paper, we aim to iden...

Local optimality conditions are given for a quadratic programming formulation of the multiset graph partitioning problem. These conditions are related to the structure of the graph and properties of the weights.