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

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

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

Fundamental properties of the Population II fiducial stars HD 122563 and Gmb 1830 from CHARA interferometric observations

We have determined the angular diameters of two metal-poor stars, HD 122563 and Gmb 1830, using CHARA and Palomar Testbed Interferometer observations. For the giant star HD 122563, we derive an angular diameter theta_3D = 0.940 +- 0.011 milliarcseconds (mas) using limb-darkening from 3D convection simulations and for the dwarf star Gmb 1830 (HD 103095) we obtain a 1D limb-darkened angular diameter theta_1D = 0.679 +- 0.007 mas. Coupling the angular diameters with photometry yields effective temperatures with precisions better than 55 K (Teff = 4598 +- 41 K and 4818 +- 54 K --- for the giant and the dwarf star, respectively). Including their distances results in very well-determined luminosities and radii (L = 230 +- 6 L_sun, R = 23.9 +- 1.9 R_sun and L = 0.213 +- 0.002 L_sun, R = 0.664 +- 0.015 R_sun, respectively). We used the CESAM2k stellar structure and evolution code in order to produce models that fit the observational data. We found values of the mixing-length parameter alpha (which describes 1D convection) that depend on the mass of the star. The masses were determined from the models with precisions of <3% and with the well-measured radii excellent constraints on the surface gravity are obtained (log g = 1.60 +- 0.04, 4.59 +- 0.02, respectively). The very small errors on both log g and Teff provide stringent constraints for spectroscopic analyses given the sensitivity of abundances to both of these values. The precise determination of Teff for the two stars brings into question the photometric scales for metal-poor stars.Comment: accepted A&A, 8 dbl-column pages, incl. 7 tables and 4 figure

Similarities between the tropical Atlantic seasonal cycle and ENSO: An energetics perspective

The tropical Pacific and Atlantic Oceans have similar mean states - easterly winds and a zonally sloping thermocline which shoals in the east - but strikingly different sea surface temperature..

Cork oak vulnerability to fire: the role of bark harvesting, tree characteristics and abiotic factors

Forest ecosystems where periodical tree bark harvesting is a major economic activity may be particularly vulnerable to disturbances such as fire, since debarking usually reduces tree vigour and protection against external agents. In this paper we asked how cork oak Quercus suber trees respond after wildfires and, in particular, how bark harvesting affects post-fire tree survival and resprouting. We gathered data from 22 wildfires (4585 trees) that occurred in three southern European countries (Portugal, Spain and France), covering a wide range of conditions characteristic of Q. suber ecosystems. Post-fire tree responses (tree mortality, stem mortality and crown resprouting) were examined in relation to management and ecological factors using generalized linear mixed-effects models. Results showed that bark thickness and bark harvesting are major factors affecting resistance of Q. suber to fire. Fire vulnerability was higher for trees with thin bark (young or recently debarked individuals) and decreased with increasing bark thickness until cork was 3–4 cm thick. This bark thickness corresponds to the moment when exploited trees are debarked again, meaning that exploited trees are vulnerable to fire during a longer period. Exploited trees were also more likely to be top-killed than unexploited trees, even for the same bark thickness. Additionally, vulnerability to fire increased with burn severity and with tree diameter, and was higher in trees burned in early summer or located in drier south-facing aspects. We provided tree response models useful to help estimating the impact of fire and to support management decisions. The results suggested that an appropriate management of surface fuels and changes in the bark harvesting regime (e.g. debarking coexisting trees in different years or increasing the harvesting cycle) would decrease vulnerability to fire and contribute to the conservation of cork oak ecosystemsinfo:eu-repo/semantics/publishedVersio

Bioavailable Trace Metals in Neurological Diseases

Medical treatment in Wilson’s disease includes chelators (d-penicillamine and trientine) or zinc salts that have to be maintain all the lifelong. This pharmacological treatment is categorised into two phases; the first being a de-coppering phase and the second a maintenance one. The best therapeutic approach remains controversial, as only a few non-controlled trials have compared these treatments. During the initial phase, progressive increase of chelators’ doses adjusted to exchangeable copper and urinary copper might help to avoid neurological deterioration. Liver transplantation is indicated in acute fulminant liver failure and decompensated cirrhosis; in cases of neurologic deterioration, it must be individually discussed. During the maintenance phase, the most important challenge is to obtain a good adherence to lifelong medical therapy. Neurodegenerative diseases that lead to a mislocalisation of iron can be caused by a culmination of localised overload (pro-oxidant siderosis) and localised deficiency (metabolic distress). A new therapeutic concept with conservative iron chelation rescues iron-overloaded neurons by scavenging labile iron and, by delivering this chelated metal to endogenous apo-transferrin, allows iron redistribution to avoid systemic loss of iron

On generalized surrogate duality in mixed-integer nonlinear programming

The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global -optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solvers can often successfully handle a moderate presence of nonconvexities, which opens the door for the use of potentially tighter nonconvex relaxations. In this work, we exploit this fact and make use of a nonconvex relaxation obtained via aggregation of constraints: a surrogate relaxation. These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since. We revisit these relaxations in an MINLP setting and show the computational benefits and challenges they can have. Additionally, we study a generalization of such relaxation that allows for multiple aggregations simultaneously and present the first algorithm that is capable of computing the best set of aggregations. We propose a multitude of computational enhancements for improving its practical performance and evaluate the algorithm’s ability to generate strong dual bounds through extensive computational experiments