122 research outputs found
Compact relaxations for polynomial programming problems
Reduced RLT constraints are a special class of Reformulation- Linearization Technique (RLT) constraints. They apply to nonconvex (both continuous and mixed-integer) quadratic programming problems subject to systems of linear equality constraints. We present an extension to the general case of polynomial programming problems and discuss the derived convex relaxation. We then show how to perform rRLT constraint generation so as to reduce the number of inequality constraints in the relaxation, thereby making it more compact and faster to solve. We present some computational results validating our approach
On the composition of convex envelopes for quadrilinear terms
International audienceWithin the framework of the spatial Branch-and-Bound algorithm for solving Mixed-Integer Nonlinear Programs, different convex relaxations can be obtained for multilinear terms by applying associativity in different ways. The two groupings ((x1x2)x3)x4 and (x1x2x3)x4 of a quadrilinear term, for example, give rise to two different convex relaxations. In [6] we prove that having fewer groupings of longer terms yields tighter convex relaxations. In this paper we give an alternative proof of the same fact and perform a computational study to assess the impact of the tightened convex relaxation in a spatial Branch-and-Bound setting
Finding and testing network communities by lumped Markov chains
Identifying communities (or clusters), namely groups of nodes with
comparatively strong internal connectivity, is a fundamental task for deeply
understanding the structure and function of a network. Yet, there is a lack of
formal criteria for defining communities and for testing their significance. We
propose a sharp definition which is based on a significance threshold. By means
of a lumped Markov chain model of a random walker, a quality measure called
"persistence probability" is associated to a cluster. Then the cluster is
defined as an "-community" if such a probability is not smaller than
. Consistently, a partition composed of -communities is an
"-partition". These definitions turn out to be very effective for
finding and testing communities. If a set of candidate partitions is available,
setting the desired -level allows one to immediately select the
-partition with the finest decomposition. Simultaneously, the
persistence probabilities quantify the significance of each single community.
Given its ability in individually assessing the quality of each cluster, this
approach can also disclose single well-defined communities even in networks
which overall do not possess a definite clusterized structure
Struttura chimica ed attivitĂ farmacologica degli alcaloidi isolati da poriferi appartenenti alla famiglia delle Agelsidae
Comunicazione poste
Nuove Saponine Triterpeniche dalla spugna Caraibica Ectyoplasia ferox
Comunicazione poste
Ectyoplasides A-B, Unique Triterpene Oligoglycosides from the Caribbean Sponge Ectyoplasia ferox.
Two novel norlanostane triglycosides, ectyoplasides A (1) and B (2), have been isolated from the methanolic extracts of the Caribbean sponge Ectyoplasia ferox (Raspaliidae, Axinellida). Their structures have been established by extensive application of high-resolution FABMS and two- dimensional NMR techniques, supported by chemical and enzymatic degradation methods. Ectyoplasides A and B have been shown to possess identical sugar chains (composed of two β-galactose units and one α-arabinose unit), but to differ in their aglycone moieties, which possess nortriterpene skeletons with an unprecedented substitution pattern on ring A. Ectyoplasides A and B show moderate cytotoxic activity when tested in vitro towards various cell lines
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