Caracterización y simulación de arborizaciones dentríticas con redes bayesianas incluyendo variables angulares

El funcionamiento interno del cerebro es todavía hoy en día un misterio, siendo su comprensión uno de los principales desafíos a los que se enfrenta la ciencia moderna. El córtex cerebral es el área del cerebro donde tienen lugar los procesos cerebrales de más alto nivel, cómo la imaginación, el juicio o el pensamiento abstracto. Las neuronas piramidales, un tipo específico de neurona, suponen cerca del 80% de los cerca de los 10.000 millones de que componen el córtex cerebral, haciendo de ellas un objetivo principal en el estudio del funcionamiento del cerebro. La morfología neuronal, y más específicamente la morfología dendrítica, determina cómo estas procesan la información y los patrones de conexión entre neuronas, siendo los modelos computacionales herramientas imprescindibles para el estudio de su rol en el funcionamiento del cerebro. En este trabajo hemos creado un modelo computacional, con más de 50 variables relativas a la morfología dendrítica, capaz de simular el crecimiento de arborizaciones dendríticas basales completas a partir de reconstrucciones de neuronas piramidales reales, abarcando desde el número de dendritas hasta el crecimiento los los árboles dendríticos. A diferencia de los trabajos anteriores, nuestro modelo basado en redes Bayesianas contempla la arborización dendrítica en su conjunto, teniendo en cuenta las interacciones entre dendritas y detectando de forma automática las relaciones entre las variables morfológicas que caracterizan la arborización. Además, el análisis de las redes Bayesianas puede ayudar a identificar relaciones hasta ahora desconocidas entre variables morfológicas. Motivado por el estudio de la orientación de las dendritas basales, en este trabajo se introduce una regularización L1 generalizada, aplicada al aprendizaje de la distribución von Mises multivariante, una de las principales distribuciones de probabilidad direccional multivariante. También se propone una distancia circular multivariante que puede utilizarse para estimar la divergencia de Kullback-Leibler entre dos muestras de datos circulares. Comparamos los modelos con y sin regularizaci ón en el estudio de la orientación de la dendritas basales en neuronas humanas, comprobando que, en general, el modelo regularizado obtiene mejores resultados. El muestreo, ajuste y representación de la distribución von Mises multivariante se implementa en un nuevo paquete de R denominado mvCircular.---ABSTRACT---The inner workings of the brain are, as of today, a mystery. To understand the brain is one of the main challenges faced by current science. The cerebral cortex is the region of the brain where all superior brain processes, like imagination, judge and abstract reasoning take place. Pyramidal neurons, a specific type of neurons, constitute approximately the 80% of the more than 10.000 million neurons that compound the cerebral cortex. It makes the study of the pyramidal neurons crucial in order to understand how the brain works. Neuron morphology, and specifically the dendritic morphology, determines how the information is processed in the neurons, as well as the connection patterns among neurons. Computational models are one of the main tools for studying dendritic morphology and its role in the brain function. We have built a computational model that contains more than 50 morphological variables of the dendritic arborizations. This model is able to simulate the growth of complete dendritic arborizations from real neuron reconstructions, starting with the number of basal dendrites, and ending modeling the growth of dendritic trees. One of the main diferences between our approach, mainly based on the use of Bayesian networks, and other models in the state of the art is that we model the whole dendritic arborization instead of focusing on individual trees, which makes us able to take into account the interactions between dendrites and to automatically detect relationships between the morphologic variables that characterize the arborization. Moreover, the posterior analysis of the relationships in the model can help to identify new relations between morphological variables. Motivated by the study of the basal dendrites orientation, a generalized L1 regularization applied to the multivariate von Mises distribution, one of the most used distributions in multivariate directional statistics, is also introduced in this work. We also propose a circular multivariate distance that can be used to estimate the Kullback-Leibler divergence between two circular data samples. We compare the regularized and unregularized models on basal dendrites orientation of human neurons and prove that regularized model achieves better results than non regularized von Mises model. Sampling, fitting and plotting functions for the multivariate von Mises are implemented in a new R packaged called mvCircular.

Change of extreme rainfall indexes at Ebro River Basin

The purpose of this work is to provide a description of the heavy rainfall phenomenon on statistical tools from a Spanish region. We want to quantify the effect of the climate change to verify the rapidity of its evolution across the variation of the probability distributions. Our conclusions have special interest for the agrarian insurances, which may make estimates of costs more realistically. In this work, the analysis mainly focuses on: The distribution of consecutive days without rain for each gauge stations and season. We estimate density Kernel functions and Generalized Pareto Distribution (GPD) for a network of station from the Ebro River basin until a threshold value u. We can establish a relation between distributional parameters and regional characteristics. Moreover we analyze especially the tail of the probability distribution. These tails are governed by law of power means that the number of events n can be expressed as the power of another quantity x : n(x) = x? . ? can be estimated as the slope of log-log plot the number of events and the size. The most convenient way to analyze n(x) is using the empirical probability distribution. Pr(X mayor que x) ? x-?. The distribution of rainfall over percentile of order 0.95 from wet days at the seasonal scale and in a yearly scale with the same treatment of tails than in the previous section.

Distributed Estimation of Distribution Algorithms for continuous optimization: how does the exchanged information influence their behavior?

One of the most promising areas in which probabilistic graphical models have shown an incipient activity is the field of heuristic optimization and, in particular, in Estimation of Distribution Algorithms. Due to their inherent parallelism, different research lines have been studied trying to improve Estimation of Distribution Algorithms from the point of view of execution time and/or accuracy. Among these proposals, we focus on the so-called distributed or island-based models. This approach defines several islands (algorithms instances) running independently and exchanging information with a given frequency. The information sent by the islands can be either a set of individuals or a probabilistic model. This paper presents a comparative study for a distributed univariate Estimation of Distribution Algorithm and a multivariate version, paying special attention to the comparison of two alternative methods for exchanging information, over a wide set of parameters and problems ? the standard benchmark developed for the IEEE Workshop on Evolutionary Algorithms and other Metaheuristics for Continuous Optimization Problems of the ISDA 2009 Conference. Several analyses from different points of view have been conducted to analyze both the influence of the parameters and the relationships between them including a characterization of the configurations according to their behavior on the proposed benchmark.