Equilibrium points and central configurations for the Lennard-Jones 2-and 3-body problems

Abstract. In this paper we study the relative equilibria and their stability for a system of three point particles moving under the action of a Lennard{Jones potential. A central con guration is a special position of the particles where the position and acceleration vectors of each particle are proportional, and the constant of proportionality is the same for all particles. Since the Lennard{Jones potential depends only on the mutual distances among the particles, it is invariant under rotations. In a rotating frame the orbits coming from central con gurations become equilibrium points, the relative equilibria. Due to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum of inertia I. In this work we characterize the relative equilibria, we nd the bifurcation values of I for which the number of relative equilibria is changing, we also analyze the stability of the relative equilibria.

A Fast Gradient Approximation for Nonlinear Blind Signal Processing

When dealing with nonlinear blind processing algorithms (deconvolution or post-nonlinear source separation), complex mathematical estimations must be done giving as a result very slow algorithms. This is the case, for example, in speech processing, spike signals deconvolution or microarray data analysis. In this paper, we propose a simple method to reduce computational time for the inversion of Wiener systems or the separation of post-nonlinear mixtures, by using a linear approximation in a minimum mutual information algorithm. Simulation results demonstrate that linear spline interpolation is fast and accurate, obtaining very good results (similar to those obtained without approximation) while computational time is dramatically decreased. On the other hand, cubic spline interpolation also obtains similar good results, but due to its intrinsic complexity, the global algorithm is much more slow and hence not useful for our purpose.

Post-Nonlinear Mixtures and Beyond

Although sources in general nonlinear mixturm arc not separable iising only statistical independence, a special and realistic case of nonlinear mixtnres, the post nonlinear (PNL) mixture is separable choosing a suited separating system. Then, a natural approach is based on the estimation of tho separating Bystem parameters by minimizing an indcpendence criterion, like estimated mwce mutual information. This class of methods requires higher (than 2) order statistics, and cannot separate Gaarsian sources. However, use of [weak) prior, like source temporal correlation or nonstationarity, leads to other source separation Jgw rithms, which are able to separate Gaussian sourra, and can even, for a few of them, works with second-order statistics. Recently, modeling time correlated s011rces by Markov models, we propose vcry efficient algorithms hmed on minimization of the conditional mutual information. Currently, using the prior of temporally correlated sources, we investigate the fesihility of inverting PNL mixtures with non-bijectiw non-liacarities, like quadratic functions. In this paper, we review the main ICA and BSS results for riunlinear mixtures, present PNL models and algorithms, and finish with advanced resutts using temporally correlated snu~sm

Energy relaxation in nonlinear one-dimensional lattices

We study energy relaxation in thermalized one-dimensional nonlinear arrays of the Fermi-Pasta-Ulam type. The ends of the thermalized systems are placed in contact with a zero-temperature reservoir via damping forces. Harmonic arrays relax by sequential phonon decay into the cold reservoir, the lower-frequency modes relaxing first. The relaxation pathway for purely anharmonic arrays involves the degradation of higher-energy nonlinear modes into lower-energy ones. The lowest-energy modes are absorbed by the cold reservoir, but a small amount of energy is persistently left behind in the array in the form of almost stationary low-frequency localized modes. Arrays with interactions that contain both a harmonic and an anharmonic contribution exhibit behavior that involves the interplay of phonon modes and breather modes. At long times relaxation is extremely slow due to the spontaneous appearance and persistence of energetic high-frequency stationary breathers. Breather behavior is further ascertained by explicitly injecting a localized excitation into the thermalized arrays and observing the relaxation behavior.

Statistical mechanics of multi-edge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

A new heuristic method for solving spatially constrained forest planning problems based on mitigation of infeasibilities radiating outward from a forced choice

[Abstract]

Simulating maize phenology as a function of air temperature with a linear and a nonlinear model

The objective of this study was to adapt a nonlinear model (Wang and Engel - WE) for simulating the phenology of maize (Zea mays L.), and to evaluate this model and a linear one (thermal time), in order to predict developmental stages of a field-grown maize variety. A field experiment, during 2005/2006 and 2006/2007 was conducted in Santa Maria, RS, Brazil, in two growing seasons, with seven sowing dates each. Dates of emergence, silking, and physiological maturity of the maize variety BRS Missões were recorded in six replications in each sowing date. Data collected in 2005/2006 growing season were used to estimate the coefficients of the two models, and data collected in the 2006/2007 growing season were used as independent data set for model evaluations. The nonlinear WE model accurately predicted the date of silking and physiological maturity, and had a lower root mean square error (RMSE) than the linear (thermal time) model. The overall RMSE for silking and physiological maturity was 2.7 and 4.8 days with WE model, and 5.6 and 8.3 days with thermal time model, respectively.

Pediatric drug-related problems: a multicenter study in four French-speaking countries.

BACKGROUND: Pediatric intensive care patients represent a population at high risk for drug-related problems. There are few studies that compare the activity of clinical pharmacists between countries. OBJECTIVE: To describe the drug-related problems identified and interventions by four pharmacists in a pediatric cardiac and intensive care unit. SETTING: Four pediatric centers in France, Quebec, Switzerland and Belgium. METHOD: This was a six-month multicenter, descriptive and prospective study conducted from August 1, 2009 to January 31, 2010. Drug-related problems and clinical interventions were compiled from four pediatric centers in France, Quebec, Switzerland and Belgium. Data on patients, drugs, intervention, documentation, approval and estimated impact were compiled. MAIN OUTCOME MEASURE: Number and type of drug-related problems encountered in a large pediatric inpatient population. RESULTS: A total of 996 interventions were recorded: 238 (24 %) in France, 278 (28 %) in Quebec, 351 (35 %) in Switzerland and 129 (13 %) in Belgium. These interventions targeted 270 patients (median 21 months old, 53 % male): 88 (33 %) in France, 56 (21 %) in Quebec, 57 (21 %) in Switzerland and 69 (26 %) in Belgium. The main drug-related problems were inappropriate administration technique (29 %), untreated indication (25 %) and supra-therapeutic dose (11 %). The pharmacists' interventions were mostly optimizing the mode of administration (22 %), dose adjustment (20 %) and therapeutic monitoring (16 %). The two major drug classes that led to interventions were anti-infectives for systemic use (23 %) and digestive system and metabolism drugs (22 %). Interventions mainly involved residents and all clinical staff (21 %). Among the 878 (88 %) proposed interventions requiring physician approval, 860 (98 %) were accepted. CONCLUSION: This descriptive study illustrates drug-related problems and the ability of clinical pharmacists to identify and resolve them in pediatric intensive care units in four French-speaking countries.

Machine learning for geospatial data : algorithms, software tools and case studies

Résumé Cette thèse est consacrée à l'analyse, la modélisation et la visualisation de données environnementales à référence spatiale à l'aide d'algorithmes d'apprentissage automatique (Machine Learning). L'apprentissage automatique peut être considéré au sens large comme une sous-catégorie de l'intelligence artificielle qui concerne particulièrement le développement de techniques et d'algorithmes permettant à une machine d'apprendre à partir de données. Dans cette thèse, les algorithmes d'apprentissage automatique sont adaptés pour être appliqués à des données environnementales et à la prédiction spatiale. Pourquoi l'apprentissage automatique ? Parce que la majorité des algorithmes d'apprentissage automatiques sont universels, adaptatifs, non-linéaires, robustes et efficaces pour la modélisation. Ils peuvent résoudre des problèmes de classification, de régression et de modélisation de densité de probabilités dans des espaces à haute dimension, composés de variables informatives spatialisées (« géo-features ») en plus des coordonnées géographiques. De plus, ils sont idéaux pour être implémentés en tant qu'outils d'aide à la décision pour des questions environnementales allant de la reconnaissance de pattern à la modélisation et la prédiction en passant par la cartographie automatique. Leur efficacité est comparable au modèles géostatistiques dans l'espace des coordonnées géographiques, mais ils sont indispensables pour des données à hautes dimensions incluant des géo-features. Les algorithmes d'apprentissage automatique les plus importants et les plus populaires sont présentés théoriquement et implémentés sous forme de logiciels pour les sciences environnementales. Les principaux algorithmes décrits sont le Perceptron multicouches (MultiLayer Perceptron, MLP) - l'algorithme le plus connu dans l'intelligence artificielle, le réseau de neurones de régression généralisée (General Regression Neural Networks, GRNN), le réseau de neurones probabiliste (Probabilistic Neural Networks, PNN), les cartes auto-organisées (SelfOrganized Maps, SOM), les modèles à mixture Gaussiennes (Gaussian Mixture Models, GMM), les réseaux à fonctions de base radiales (Radial Basis Functions Networks, RBF) et les réseaux à mixture de densité (Mixture Density Networks, MDN). Cette gamme d'algorithmes permet de couvrir des tâches variées telle que la classification, la régression ou l'estimation de densité de probabilité. L'analyse exploratoire des données (Exploratory Data Analysis, EDA) est le premier pas de toute analyse de données. Dans cette thèse les concepts d'analyse exploratoire de données spatiales (Exploratory Spatial Data Analysis, ESDA) sont traités selon l'approche traditionnelle de la géostatistique avec la variographie expérimentale et selon les principes de l'apprentissage automatique. La variographie expérimentale, qui étudie les relations entre pairs de points, est un outil de base pour l'analyse géostatistique de corrélations spatiales anisotropiques qui permet de détecter la présence de patterns spatiaux descriptible par une statistique. L'approche de l'apprentissage automatique pour l'ESDA est présentée à travers l'application de la méthode des k plus proches voisins qui est très simple et possède d'excellentes qualités d'interprétation et de visualisation. Une part importante de la thèse traite de sujets d'actualité comme la cartographie automatique de données spatiales. Le réseau de neurones de régression généralisée est proposé pour résoudre cette tâche efficacement. Les performances du GRNN sont démontrées par des données de Comparaison d'Interpolation Spatiale (SIC) de 2004 pour lesquelles le GRNN bat significativement toutes les autres méthodes, particulièrement lors de situations d'urgence. La thèse est composée de quatre chapitres : théorie, applications, outils logiciels et des exemples guidés. Une partie importante du travail consiste en une collection de logiciels : Machine Learning Office. Cette collection de logiciels a été développée durant les 15 dernières années et a été utilisée pour l'enseignement de nombreux cours, dont des workshops internationaux en Chine, France, Italie, Irlande et Suisse ainsi que dans des projets de recherche fondamentaux et appliqués. Les cas d'études considérés couvrent un vaste spectre de problèmes géoenvironnementaux réels à basse et haute dimensionnalité, tels que la pollution de l'air, du sol et de l'eau par des produits radioactifs et des métaux lourds, la classification de types de sols et d'unités hydrogéologiques, la cartographie des incertitudes pour l'aide à la décision et l'estimation de risques naturels (glissements de terrain, avalanches). Des outils complémentaires pour l'analyse exploratoire des données et la visualisation ont également été développés en prenant soin de créer une interface conviviale et facile à l'utilisation. Machine Learning for geospatial data: algorithms, software tools and case studies Abstract The thesis is devoted to the analysis, modeling and visualisation of spatial environmental data using machine learning algorithms. In a broad sense machine learning can be considered as a subfield of artificial intelligence. It mainly concerns with the development of techniques and algorithms that allow computers to learn from data. In this thesis machine learning algorithms are adapted to learn from spatial environmental data and to make spatial predictions. Why machine learning? In few words most of machine learning algorithms are universal, adaptive, nonlinear, robust and efficient modeling tools. They can find solutions for the classification, regression, and probability density modeling problems in high-dimensional geo-feature spaces, composed of geographical space and additional relevant spatially referenced features. They are well-suited to be implemented as predictive engines in decision support systems, for the purposes of environmental data mining including pattern recognition, modeling and predictions as well as automatic data mapping. They have competitive efficiency to the geostatistical models in low dimensional geographical spaces but are indispensable in high-dimensional geo-feature spaces. The most important and popular machine learning algorithms and models interesting for geo- and environmental sciences are presented in details: from theoretical description of the concepts to the software implementation. The main algorithms and models considered are the following: multi-layer perceptron (a workhorse of machine learning), general regression neural networks, probabilistic neural networks, self-organising (Kohonen) maps, Gaussian mixture models, radial basis functions networks, mixture density networks. This set of models covers machine learning tasks such as classification, regression, and density estimation. Exploratory data analysis (EDA) is initial and very important part of data analysis. In this thesis the concepts of exploratory spatial data analysis (ESDA) is considered using both traditional geostatistical approach such as_experimental variography and machine learning. Experimental variography is a basic tool for geostatistical analysis of anisotropic spatial correlations which helps to understand the presence of spatial patterns, at least described by two-point statistics. A machine learning approach for ESDA is presented by applying the k-nearest neighbors (k-NN) method which is simple and has very good interpretation and visualization properties. Important part of the thesis deals with a hot topic of nowadays, namely, an automatic mapping of geospatial data. General regression neural networks (GRNN) is proposed as efficient model to solve this task. Performance of the GRNN model is demonstrated on Spatial Interpolation Comparison (SIC) 2004 data where GRNN model significantly outperformed all other approaches, especially in case of emergency conditions. The thesis consists of four chapters and has the following structure: theory, applications, software tools, and how-to-do-it examples. An important part of the work is a collection of software tools - Machine Learning Office. Machine Learning Office tools were developed during last 15 years and was used both for many teaching courses, including international workshops in China, France, Italy, Ireland, Switzerland and for realizing fundamental and applied research projects. Case studies considered cover wide spectrum of the real-life low and high-dimensional geo- and environmental problems, such as air, soil and water pollution by radionuclides and heavy metals, soil types and hydro-geological units classification, decision-oriented mapping with uncertainties, natural hazards (landslides, avalanches) assessments and susceptibility mapping. Complementary tools useful for the exploratory data analysis and visualisation were developed as well. The software is user friendly and easy to use.

First-passage and escape problems in the Feller process

The Feller process is an one-dimensional diffusion process with linear drift and state-dependent diffusion coefficient vanishing at the origin. The process is positive definite and it is this property along with its linear character that have made Feller process a convenient candidate for the modeling of a number of phenomena ranging from single-neuron firing to volatility of financial assets. While general properties of the process have long been well known, less known are properties related to level crossing such as the first-passage and the escape problems. In this work we thoroughly address these questions.

Diffusion in stationary flow from mesoscopic nonequilibrium thermodynamics

We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of nonequilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation that is compared with others derived from the kinetic theory and projector operator techniques. This equation exhibits violation of the fluctuation-dissipation theorem. By implementing the hydrodynamic regime described by the first moments of the nonequilibrium distribution, we find relaxation equations for the diffusion current and pressure tensor, allowing us to arrive at a complete description of the system in the inertial and diffusion regimes. The simplicity and generality of the method we propose makes it applicable to more complex situations, often encountered in problems of soft-condensed matter, in which not only one but more degrees of freedom are coupled to a nonequilibrium bath.

Robust Nonlinear Mapping of Soil Contamination Using Support Regression

Spatial data analysis mapping and visualization is of great importance in various fields: environment, pollution, natural hazards and risks, epidemiology, spatial econometrics, etc. A basic task of spatial mapping is to make predictions based on some empirical data (measurements). A number of state-of-the-art methods can be used for the task: deterministic interpolations, methods of geostatistics: the family of kriging estimators (Deutsch and Journel, 1997), machine learning algorithms such as artificial neural networks (ANN) of different architectures, hybrid ANN-geostatistics models (Kanevski and Maignan, 2004; Kanevski et al., 1996), etc. All the methods mentioned above can be used for solving the problem of spatial data mapping. Environmental empirical data are always contaminated/corrupted by noise, and often with noise of unknown nature. That's one of the reasons why deterministic models can be inconsistent, since they treat the measurements as values of some unknown function that should be interpolated. Kriging estimators treat the measurements as the realization of some spatial randomn process. To obtain the estimation with kriging one has to model the spatial structure of the data: spatial correlation function or (semi-)variogram. This task can be complicated if there is not sufficient number of measurements and variogram is sensitive to outliers and extremes. ANN is a powerful tool, but it also suffers from the number of reasons. of a special type ? multiplayer perceptrons ? are often used as a detrending tool in hybrid (ANN+geostatistics) models (Kanevski and Maignank, 2004). Therefore, development and adaptation of the method that would be nonlinear and robust to noise in measurements, would deal with the small empirical datasets and which has solid mathematical background is of great importance. The present paper deals with such model, based on Statistical Learning Theory (SLT) - Support Vector Regression. SLT is a general mathematical framework devoted to the problem of estimation of the dependencies from empirical data (Hastie et al, 2004; Vapnik, 1998). SLT models for classification - Support Vector Machines - have shown good results on different machine learning tasks. The results of SVM classification of spatial data are also promising (Kanevski et al, 2002). The properties of SVM for regression - Support Vector Regression (SVR) are less studied. First results of the application of SVR for spatial mapping of physical quantities were obtained by the authorsin for mapping of medium porosity (Kanevski et al, 1999), and for mapping of radioactively contaminated territories (Kanevski and Canu, 2000). The present paper is devoted to further understanding of the properties of SVR model for spatial data analysis and mapping. Detailed description of the SVR theory can be found in (Cristianini and Shawe-Taylor, 2000; Smola, 1996) and basic equations for the nonlinear modeling are given in section 2. Section 3 discusses the application of SVR for spatial data mapping on the real case study - soil pollution by Cs137 radionuclide. Section 4 discusses the properties of the modelapplied to noised data or data with outliers.

Odorant binding proteins of the red imported fire ant, Solenopsis invicta: an example of the problems facing the analysis of widely divergent proteins.

We describe the odorant binding proteins (OBPs) of the red imported fire ant, Solenopsis invicta, obtained from analyses of an EST library and separate 454 sequencing runs of two normalized cDNA libraries. We identified a total of 18 putative functional OBPs in this ant. A third of the fire ant OBPs are orthologs to honey bee OBPs. Another third of the OBPs belong to a lineage-specific expansion, which is a common feature of insect OBP evolution. Like other OBPs, the different fire ant OBPs share little sequence similarity (∼ 20%), rendering evolutionary analyses difficult. We discuss the resulting problems with sequence alignment, phylogenetic analysis, and tests of selection. As previously suggested, our results underscore the importance for careful exploration of the sensitivity to the effects of alignment methods for data comprising widely divergent sequences.