An interior point algorithm for minimum sum-of-squares clustering

Copyright @ 2000 SIAM PublicationsAn exact algorithm is proposed for minimum sum-of-squares nonhierarchical clustering, i.e., for partitioning a given set of points from a Euclidean m-space into a given number of clusters in order to minimize the sum of squared distances from all points to the centroid of the cluster to which they belong. This problem is expressed as a constrained hyperbolic program in 0-1 variables. The resolution method combines an interior point algorithm, i.e., a weighted analytic center column generation method, with branch-and-bound. The auxiliary problem of determining the entering column (i.e., the oracle) is an unconstrained hyperbolic program in 0-1 variables with a quadratic numerator and linear denominator. It is solved through a sequence of unconstrained quadratic programs in 0-1 variables. To accelerate resolution, variable neighborhood search heuristics are used both to get a good initial solution and to solve quickly the auxiliary problem as long as global optimality is not reached. Estimated bounds for the dual variables are deduced from the heuristic solution and used in the resolution process as a trust region. Proved minimum sum-of-squares partitions are determined for the rst time for several fairly large data sets from the literature, including Fisher's 150 iris.This research was supported by the Fonds National de la Recherche Scientifique Suisse, NSERC-Canada, and FCAR-Quebec

Avant-propos

From several points of view (geographical, biological and hu man), the Mont Ventoux exemplifies many of the problems cur rently facing the limestone areas of Provence. For this reason, a wide range of studies was carried out there between 1972 & 1976, to investigate the climate, vegetation, fauna and certain sociolo gical problems ; these are described in the following articles (except the climatological work, which is not yet complete)

Objective analysis of simulated Equatorial Atlantic ocean data on seasonal time scales

In this study we objectively analyze simulated Equatorial Atlantic ocean data on seasonal time scales using a technique based on optimal interpolation. The purpose is twofold : (1) to estimate the accuracy of the FOCAL/SEQUAL (Programme Français Océan-Climat en Atlantique Equatorial/Seasonal Equatorial Atlantic Response Program) array for mapping large-scale seasonal variations in the depth of the 20° isotherm, and (2) to examine the potential of 20 FOCAL drifting buoys drogued with thermistor chains for enhancing that mapping accuracy. This latter point leads to the development of heuristic model for drifter motion in order to identify the most favorable time and location for buoy deployments. Results are discussed for a number of assumptions about oceanic variability required by both the optimal interpolation procedure and the drifting buoy model. (D'après résumé d'auteur

Les peuplements de fourmis et les peuplements d’acridiens du mont Ventoux III. — Les peuplements d’Acridiens

The composition of the grasshopper communities was studied and an estimate made of the maximum density of each species during the year : in addition, their ecological and altitudinal amplitudes were described. The adults of some species were found to migrate to areas where they were unable to reproduce, so that the breeding sites are only a part of the total area of distribu tion. The richness and/or composition of these communities differ between vegetation zones. All the communities have a hierar chical structure and are very varied, but three species are predo minant : Chorthippus biguttulus, and (to a lesser extent) Stauro- derus scalaris and Myrmeleotettix maculatus. Altitudinal and seasonal changes in the communities are discussed, as is the pullulation of certain species. Temperature is the most important of the environmental features, producing an altitudinal zonation of species and commu nities (less marked, however, than among the ants). Aridity leads to vertical discontinuities in the ranges of certain species on the southern slope of the mountain

An in silico model for identification of small RNAs in whole bacterial genomes: characterization of antisense RNAs in pathogenic Escherichia coli and Streptococcus agalactiae strains

Characterization of small non-coding ribonucleic acids (sRNA) among the large volume of data generated by high-throughput RNA-seq or tiling microarray analyses remains a challenge. Thus, there is still a need for accurate in silico prediction methods to identify sRNAs within a given bacterial species. After years of effort, dedicated software were developed based on comparative genomic analyses or mathematical/statistical models. Although these genomic analyses enabled sRNAs in intergenic regions to be efficiently identified, they all failed to predict antisense sRNA genes (asRNA), i.e. RNA genes located on the DNA strand complementary to that which encodes the protein. The statistical models enabled any genomic region to be analyzed theorically but not efficiently. We present a new model for in silico identification of sRNA and asRNA candidates within an entire bacterial genome. This model was successfully used to analyze the Gram-negative Escherichia coli and Gram-positive Streptococcus agalactiae. In both bacteria, numerous asRNAs are transcribed from the complementary strand of genes located in pathogenicity islands, strongly suggesting that these asRNAs are regulators of the virulence expression. In particular, we characterized an asRNA that acted as an enhancer-like regulator of the type 1 fimbriae production involved in the virulence of extra-intestinal pathogenic E. coli

les peupleuments de Fourmis et les peuplements d'Acridiens du Mont Ventoux. II. Les peuplements de Fourmis

The composition of the ant communities and the relative frequency of each species are described, as well as their ecological and altitudinal amplitudes. The richness and/or the composition of the communities differs from one vegetation zone to another. All the communities show a very hierarchical structure. The Shannon' eaver index of evenness is roughly equal in all communities. The communities are very varied, but three species are predominant over the mountain : Lasiw; niger, Tetramorium caespitum and Formica lemani. Of the environmental features, temperature is the most important, producing a marked altitudinal zonation of species and communities. The effects of aridity are important among certain species, leading to vertical discontinuities in their ranges. The vegetation caver affects species dependant on particular plants ; these species have been considerably affected by reafforestation, especially on the lower parts of the southern slopes, leading to a notable increase in L. niger. At the summit, the main limiting factor is temperature on the northern slope ; and the dessicating effects of the winds on the southern slopes

Repression of invasion genes and decreased invasion in high-level fluoroquinolone-resistant Salmonella Typhimurium mutant

Nalidixic acid resistance among Salmonella Typhimurium clinical isolates has steadily increased, whereas the level of ciprofloxacin resistance remains low. The main objective of this study was to characterize the fluoroquinolone resistance mechanisms acquired in a S. Typhimurium mutant selected with ciprofloxacin from a susceptible isolate and to investigate its invasion ability

Le point sur certains ravageurs du cèdre de l'Atlas en Afrique du nord, en France et en Europe.

Cette synthèse fait le point sur les connaissances acquises depuis une vingtaine d'années sur certains ravageurs du cèdre de l'Atlas dans son aire naturelle en Afrique du nord (Algérie, Maroc) et dans son aire d'extension en France et en Europe

La végétation du mont Ventoux

The vegetation map (see Appendix) is based on the concept of the vegetation series, within which different stages (mature forest, pre-climax forest, scrub, grassland and reafforested areas) are recognised. The most important native trees are Quercus ilex, Q. pubescens, Fagus sglvatica, Pinus halepensis, P. sglvestris, P. uncinata and Abies alba. The vegetation contains elements of both the Mediterranean and the Central European phyto-geogra- phical regions. The former is more typical of the southern slope and the lower part of the northern slope ; the latter occurs on the upper part of the northern slope (extending over to the summit of the southern slope) and part of the eastern ridge. Each of the vegetation series is restricted to one subgroup of these two broad divisions. The Mont Ventoux contains most of the vege tation series known from the limestone regions of southern France ; and the combination of a Mediterranean vegetation on the southern slopes with a Central European type on the northern slopes make it a typical example of the southern prealpine mountains