Generic optimality conditions for semi-algebraic convex programs

We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique \active" manifold, around which F is \partly smooth", and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F, and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.

Hard instances of algorithms and proof systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

Qualité des données fournies par la statistique médicale VESKA: le cas de la fracture du fémur proximal. [Quality of data provided by VESKA medical statistics: the case of the fractured proximal femur].

Within the framework of a retrospective study of the incidence of hip fractures in the canton of Vaud (Switzerland), all cases of hip fracture occurring among the resident population in 1986 and treated in the hospitals of the canton were identified from among five different information sources. Relevant data were then extracted from the medical records. At least two sources of information were used to identify cases in each hospital, among them the statistics of the Swiss Hospital Association (VESKA). These statistics were available for 9 of the 18 hospitals in the canton that participated in the study. The number of cases identified from the VESKA statistics was compared to the total number of cases for each hospital. For the 9 hospitals the number of cases in the VESKA statistics was 407, whereas, after having excluded diagnoses that were actually "status after fracture" and double entries, the total for these hospitals was 392, that is 4% less than the VESKA statistics indicate. It is concluded that the VESKA statistics provide a good approximation of the actual number of cases treated in these hospitals, with a tendency to overestimate this number. In order to use these statistics for calculating incidence figures, however, it is imperative that a greater proportion of all hospitals (50% presently in the canton, 35% nationwide) participate in these statistics.

Resultats a llarg termini del tractament quirúrgic de les fractures d’húmer proximal intervingudes mitjançant sutures aïllades o associades a claus d’Ender modificats

Valorem els resultats funcionals i de qualitat de vida a mig i a llarg termini de 38 fractures de l’húmer proximal, tractades en 17 casos amb fixació amb sutures transòssies i en 21 associant claus d’Ender modificats. Els pacients intervinguts amb sutures transòssies obtingueren millors resultats funcionals amb diferències significatives. Les fractures en 3 parts en valg obtingueren millors resultats funcionals que les desplaçades en var No s’observaren diferències de qualitat de vida segons tècnica quirúrgica i tipus de fractura. La fixació amb sutures associades o no a claus d’Ender modificats és una tècnica, útil, segura i amb baix índex de complicacions.

Morbi-mortalidad en fracturas de húmero proximal tratadas quirúrgicamente

L’objectiu es valorar si els pacients afectats de fractura d’húmer proximal tractats quirúrgicament tenen menys morbi-mortalitat a mig termini que els que presenten una fractura de fèmur proximal tractada quirúrgicament. Observem una menor mortalitat en les fractures d’húmer proximal amb un 14.43% respecte al 36% de les fractures de maluc als 8 anys de seguiment. El 79.5% dels pacients amb fractures d’húmer continuen essent independents per a les activitats de la vida diària. Un 26% han tingut fractures posteriors a la fractura d’húmer i un 11.3% ja estaven diagnosticats d’osteoporosis amb anterioritat.

RACE (Rapid Arterial oCclusion Evaluation): Diseño y validación prehospitalaria de una escala neurológica para la predicción de una oclusión arterial proximal en los pacientes con un ictus isquémico agudo de la circulación cerebral anterior

La Rapid Arterial oCclusion Evaluation és una escala neurològica prehospitalària que prediu la presència d’una oclusió arterial proximal (OAP) en els pacients amb un ictus isquèmic agut de la circulació cerebral anterior (IIACCA). Fou dissenyada valorant retrospectivament a 654 pacients amb un IIACCA, seleccionant la combinació dels ítems de la National Institutes of Health Stroke Scale que mostraven una major associació amb la presència d’una OAP: parèsia facial, parèsia braquial, parèsia crural, desviació oculocefàlica y agnòsia/afàsia. Fou validada valorant prospectivament a 93 activacions del Codi Ictus, mostrant una sensibilitat del 88% y una especificitat del 65% per una puntuació ≥ 4.

Extreme Precipitation Modelling Using Geostatistics and Machine Learning Algorithms

The paper presents an approach for mapping of precipitation data. The main goal is to perform spatial predictions and simulations of precipitation fields using geostatistical methods (ordinary kriging, kriging with external drift) as well as machine learning algorithms (neural networks). More practically, the objective is to reproduce simultaneously both the spatial patterns and the extreme values. This objective is best reached by models integrating geostatistics and machine learning algorithms. To demonstrate how such models work, two case studies have been considered: first, a 2-day accumulation of heavy precipitation and second, a 6-day accumulation of extreme orographic precipitation. The first example is used to compare the performance of two optimization algorithms (conjugate gradients and Levenberg-Marquardt) of a neural network for the reproduction of extreme values. Hybrid models, which combine geostatistical and machine learning algorithms, are also treated in this context. The second dataset is used to analyze the contribution of radar Doppler imagery when used as external drift or as input in the models (kriging with external drift and neural networks). Model assessment is carried out by comparing independent validation errors as well as analyzing data patterns.

Incidence des fractures du fémur proximal dans le canton de Vaud. [Incidence of proximal femoral fractures in the Canton of Vaud].

Hip fractures place a major and increasing burden on health services in Western countries. Reported incidence rates vary considerably from one geographic area to another. No published data are available for Switzerland or surrounding countries, but such descriptive indicators are indispensable in orienting national or regional policies. To fill this gap and to assess the similarity of hip fracture incidence in Switzerland and other countries, we collected data from several sources in 26 public and private hospitals, in the Canton of Vaud (total population: 538,000) for 1986, which allowed us to calculate the incidence (for people over twenty years old) and assess related parameters. 577 hip fractures were identified among the resident population, indicating a crude average annual incidence rate of 140 per 100,000 (95% confidence interval: 128, 152). Corresponding rates for males and females were 58 (47, 68) and 213 (193, 232). Standardized rates and international comparisons show that Swiss rates are slightly lower than those of most industrial countries. More detailed results of relative risks for various study variables are presented and the pathogenesis of hip fractures is discussed.

Proximale Humerusmehrfragmentfrakturen--Misserfolge nach T-Platten-Osteosynthesen [Proximal humeral multiple fragment fractures--failures after T-plate osteosynthesis].

Dislocated compound fractures of the proximal humerus are often difficult to treat. The choice of treatment influences the final functional result. From 1984-1991 108 patients with dislocated compound fractures of the proximal humerus were operated with a T-plate osteosynthesis, retrospectively examined and classified according to the Neer-Classification. At an average follow up time of 5 years 72 patients had a clinical and radiological examination. 68% of these patients with 3-fragment fractures and 80% with 4-fragment fractures showed a modest to unsatisfactory result caused by fracture biology, imprecise fracture reduction or poor surgical procedure. Incorrect position of T-plates and inadequate material were distinguishable. The T-plate which was widely used in the late eighties for internal fixation has to be considered a failure for these particular types of fractures and should be limited for Collum chirurgicum fractures.

Machine learning algorithms for spatial data. Case studies: Environmental pollution, natural hazards, renewable resources

This paper presents general problems and approaches for the spatial data analysis using machine learning algorithms. Machine learning is a very powerful approach to adaptive data analysis, modelling and visualisation. The key feature of the machine learning algorithms is that they learn from empirical data and can be used in cases when the modelled environmental phenomena are hidden, nonlinear, noisy and highly variable in space and in time. Most of the machines learning algorithms are universal and adaptive modelling tools developed to solve basic problems of learning from data: classification/pattern recognition, regression/mapping and probability density modelling. In the present report some of the widely used machine learning algorithms, namely artificial neural networks (ANN) of different architectures and Support Vector Machines (SVM), are adapted to the problems of the analysis and modelling of geo-spatial data. Machine learning algorithms have an important advantage over traditional models of spatial statistics when problems are considered in a high dimensional geo-feature spaces, when the dimension of space exceeds 5. Such features are usually generated, for example, from digital elevation models, remote sensing images, etc. An important extension of models concerns considering of real space constrains like geomorphology, networks, and other natural structures. Recent developments in semi-supervised learning can improve modelling of environmental phenomena taking into account on geo-manifolds. An important part of the study deals with the analysis of relevant variables and models' inputs. This problem is approached by using different feature selection/feature extraction nonlinear tools. To demonstrate the application of machine learning algorithms several interesting case studies are considered: digital soil mapping using SVM, automatic mapping of soil and water system pollution using ANN; natural hazards risk analysis (avalanches, landslides), assessments of renewable resources (wind fields) with SVM and ANN models, etc. The dimensionality of spaces considered varies from 2 to more than 30. Figures 1, 2, 3 demonstrate some results of the studies and their outputs. Finally, the results of environmental mapping are discussed and compared with traditional models of geostatistics.