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 "$\alpha$-community" if such a probability is not smaller than $\alpha$. Consistently, a partition composed of $\alpha$-communities is an "$\alpha$-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 $\alpha$-level allows one to immediately select the $\alpha$-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 attività farmacologica degli alcaloidi isolati da poriferi appartenenti alla famiglia delle Agelsidae

Comunicazione poste

Nuove Saponine Triterpeniche dalla spugna Caraibica Ectyoplasia ferox

Comunicazione poste

Alcaloidi bromopirrolici bioattivi da quattro spugne Caraibiche del genere Agelas

Comunicazione Oral

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