Given a probabilistic graphical model, its density of states is a distribution that, for any likelihood value, gives the number of configurations with that probability. We introduce a novel message-passing algorithm called Density Propagation (DP) for estimating this distribution. We show that DP is exact for tree-structured graphical models and is, in general, a strict generalization of both s...

We develop and experiment with new upper bounds for the constrained maximum-entropy sampling problem. Our partition bounds are based on Fischer's inequality. Further new upper bounds combine the use of Fischer's inequality with previously developed bounds. We demonstrate this in detail by using the partitioning idea to strengthen the spectral bounds of Ko, Lee and Queyranne and of Lee. Computat...

An employee transporting problem is described and a set partitioning model is developed. An investigation of the model leads to a knapsack problem as a surrogate problem. Finding a partition corresponding to the knapsack problem provides a solution to the problem. An exact algorithm is proposed to obtain a partition (subset-vehicle combination) corresponding to the knapsack solution. It require...

We develop and experiment with new upper bounds for the constrained maximum-entropy sampling problem. Our partition bounds are based on Fischer's inequality. Further new upper bounds combine the use of Fischer's inequality with previously developed bounds. We demonstrate this in detail by using the partitioning idea to strengthen the spectral bounds of Ko, Lee and Queyranne and of Lee. Computat...

We develop and experiment with new upper bounds for the constrained maximum-entropy sampling problem. Our partition bounds are based on Fischer’s inequality. Further new upper bounds combine the use of Fischer’s inequality with previously developed bounds. We demonstrate this in detail by using the partitioning idea to strengthen the spectral bounds of Ko, Lee and Queyranne and of Lee. Computat...

Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower and upper approximations. It seems somewhat unreasonable since the basic idea of rough set theory aims at describing vague concepts by the lower and upper app...

State-of-the-art branch-and-bound algorithms for the maximum clique problem (Maxclique) frequently use an upper bound based on a partition P of a graph into independent sets for a maximum clique of the graph, which cannot be very tight for imperfect graphs. In this paper we propose a new encoding from Maxclique into MaxSAT and use MaxSAT technology to improve the upper bound based on the partit...

A theorem of Lovv asz asserts that (H)== (H) r=2 for every r-partite hy-pergraph H (where and denote the covering number and fractional covering number respectively). Here it is shown that the same upper bound is valid for a more general class of hypergraphs: those which admit a partition (V 1 ; : : : ; V k) of the vertex set and a partition p 1 + +p k of r such that je\V i j p i r=2 for every ...

Regarding the Specht modules associated to two-row partition (n, n), we provide a combinatorial path model study transitioning matrix from tableau basis A1-web (i.e. cup diagrams), and prove that entries in this are positive upper-triangular portion with respect certain partial order.