Locating fuel breaks to minimise the risk of impact of wild fire

In order to respond the question “Where to locate fuel breaks?”, a peculiar location model is presented involving stochastic mixed integer nonlinear optimization, Bayesian networks and directional statistic inference. From a first simple approximation to the large model, will be shown what motivates follow models and its complexity incorporated. Also, a case study with real data about Corsica region is presented

Dendritic-branching angles of pyramidal neurons of the human cerebral cortex

In this article, we analyze branching angles of the basal dendrites of pyramidal neurons of layers III and V of the human temporal cortex. For this, we use a novel probability directional statistical distribution called truncated von Mises distribution that is able to describe more accurately the dendritic-branching angles than the previous proposals. Then, we perform comparative studies using this statistical method to determine similarities and/or differences between branches and branching angles that belong to different cortical layers and regions. Using this methodology, we found that common design principles exist and govern the patterns found in the different branches that compose the basal dendrites of human pyramidal cells of the temporal cortex. However, particular differences were found between supra and infragranular cells. Furthermore, we compared the branching angles of human layer III pyramidal neurons with data obtained in the previous studies in layer III of both the rat somatosensory cortex and of several cortical areas of the mouse. Finally, we study the branching angle differences between the humans that compose our data

Laminar differences in dendritic structure of pyramidal neurons in the juvenile rat somatosensory cortex

Pyramidal cell structure varies between different cortical areas and species, indicating that the cortical circuits that these cells participate in are likely to be characterized by different functional capabilities. Structural differences between cortical layers have been traditionally reported using either the Golgi method or intracellular labeling, but the structure of pyramidal cells has not previously been systematically analyzed across all cortical layers at a particular age. In the present study, we investigated the dendritic architecture of complete basal arbors of pyramidal neurons in layers II, III, IV, Va, Vb, and VI of the hindlimb somatosensory cortical region of postnatal day 14 rats. We found that the characteristics of basal dendritic morphologies are statistically different in each cortical layer. The variations in size and branching pattern that exist between pyramidal cells of different cortical layers probably re flect the particular functional propertiesthat are characteristic of the cortical circuit in which they participate. This new set of complete basal dendritic arbors of 3D-reconstructed pyramidal cell morphologies across each cortical layer will provide new insights into interlaminar information processing in the cerebral cortex

Directional-linear Bayesian networks and applications in neuroscience

Debido a la naturaleza direccional de ciertos datos presentes en múltiples areas para los que la estadística tradicional es ineficaz, la estadística direccional ha ido ganando relevancia en las últimas décadas, cobrando especial importancia en campos como meteorología, geología, biología o neurociencia. Esta importancia viene ligada al desarrollo de nuevas tecnologías que permiten la obtención y proceso de una elevada cantidad de datos. Uno de los problemas más recurrentes cuando se trabaja con todo tipo de datos es la incertidumbre. Para trabajar bajo condiciones de incertidumbre, los modelos gráficos probabilísticos son un recurso muy útil. En concreto, las redes Bayesianas combinan teoría de la probabilidad con teoría de gratos para proporcionar una potente herramienta en minería de datos. En esta tesis, aplicamos técnicas de estadística direccional en redes Bayesianas. Desarrollamos modelos de redes Bayesianas capaces de trabajar con datos de naturaleza direccional, que posteriormente adaptamos para aplicar a problemas de clasificación supervisada donde las variables predictoras son todas de dicha naturaleza. Generalmente, estos datos de naturaleza direccional se encuentran junto a datos de naturaleza lineal. Ya se han desarrollados métodos para trabajar conjuntamente con datos direccionales y lineales, pero nunca en redes Bayesianas. Por lo tanto, también se aborda este problema en esta tesis, donde proponemos un modelo de red Bayesiana que permite tratar variables tanto de naturaleza direccional como lineal. Para ello, proponemos una medida de dependencia entre las variables de diferente naturaleza contenidas en el modelo, basada en la similitud entre su función de densidad conjunta y sus funciones de densidad marginales. De este modo, utilizamos esta medida para capturar la dependencia entre las variables direccionales y lineales para desarrollar un modelo de red Bayesiana con estructura de árbol. La neurociencia es otro de los campos que ha experimentado un fuerte progreso en los últimos tiempos. El desarrollo de nuevas técnicas de estudio y avances en microscopía están impulsando significativamente el avance de esta ciencia. Estos avances demandan la incorporación de nuevas técnicas estadísticas y computacionales que permitan el manejo y análisis de los datos y resultados obtenidos por los experimentos neurocientíficos. En esta tesis se trabaja en la morfología neuronal, ya que pese a los numerosos avances y la inversión científica que se está realizando en este área, la estructura de las neuronas no se conoce aún con precisión. Además, la morfología neuronal desempeña un importante papel dentro de las características funcionales y computacionales del cerebro, de forma que los avances en este campo de estudio pueden aportar valiosa información sobre el cerebro y el sistema nervioso. Dentro de la morfología de la neurona, las dendritas son las que se encargan de la recepción sináptica y la propagación de la neurona por el cerebro. En el estudio de las dendritas se encuentran medidas de tipo discreto, continuo y direccional. El ajuste de distribuciones de probabilidad a estas medidas puede ser complejo e incluso inexistente, por lo que este tipo de problemas representa un reto en su modelización. Esta tesis aborda el estudio de la estructura dendrítica basal en neuronas piramidales. Se propone un método para estudiar y modelizar árboles dendríticos básales a partir de los ángulos de bifurcación producidos por la división de las dendritas partiendo desde el soma. Para ello, se usan técnicas de estadística direccional que permiten el manejo de los datos direccionales (es decir, de los ángulos de bifurcación) adecuadamente. Posteriormente, se estudia el comportamiento de dichos ángulos en función del tipo de dendrita del que provienen y la capa cerebral en la que esta localizada su neurona (su soma). Ahondando en el estudio de la morfología neuronal, también se estudia el problema de la clasificación de las neuronas piramidales entre las capas de la corteza cerebral con respecto a los ángulos de bifurcación de sus dendritas básales. Para ello, se usan los modelos de redes Bayesianas desarrollados para clasificación supervisada con variables predictoras direccionales desarrollados en esta tesis. Posteriormente, se compara la precisión de clasificación entre estos modelos de clasificación direccional para evaluar su eficiencia. También se compara con la clasificación aleatoria. ----------ABSTRACT---------- Since the directional nature of certain data present in multiple areas makes traditional statistics ineffective, directional statistics has gained relevancy in the last decades, having special importance in fields such as meteorology, geology, biology or neuroscience. This importance is connected to the development of new technologies that allow obtaining and processing huge amounts of data. One of the most frequent problems when dealing with any data is uncertainty. In order to work under uncertainty conditions, probabilistic graphical models are a very useful resource. In particular, Bayesian networks combine probability theory with graph theory to provide a powerful data mining tool. In this dissertation, we apply directional statistics techniques in Bayesian networks. We develop Bayesian network models able to deal with data of a directional nature, which we later adapt to address supervised classification problems where the predictor variables are all directional. Usually, this directional nature data is jointly observed with linear nature data. Several methods have already been used to deal with data from directional and linear nature together. Nevertheless, never in Bayesian networks. Therefore, this problem is also addressed in this dissertation, where we propose a Bayesian network model that allows the use of variables from either directional or linear nature. To do this, we introduce a dependence measure between variables from different nature. This dependence measure is based on the similarity between the joint density function and the product of its marginal density functions. Thus, we use this measure to capture the dependence between directional and linear variables to develop a Bayesian network model with tree-structure. Neuroscience is another research field that has experimented a great impulse in recent times. The development of new study techniques and advances in microscopy are driving significant advances in this science. These advances require the use of new statistical and computational techniques that allow the data management and data analysis of the results obtained by neuroscientific experiments. In this dissertation we work on the study of neuronal morphology. Despite the numerous advances and scientific investment being made in this area, the structure of the neurons is not known with precision yet. Furthermore, neuronal morphology plays an important role within the functional and computational characteristics of the brain. Hence, making further advances in this field of study can provide relevant information about the brain and the nervous system. Within the morphology of the neuron, dendrites are responsible for the synaptic reception and the spread of the neuron through the brain. In the study of the dendrites there are measures of discrete, continuous and directional type. Fitting probability distributions to these measures can be complex or even non-existent, so this type of problem represents a modelling challenge. This dissertation addresses the study of basal dendritic structure in pyramidal neurons. We propose a method to study and model basal dendritic arbors from the branching angles produced by the dendritic split starting from the soma. To do this, we use directional statistics techniques that allow the proper management of directional data (i.e., the bifurcation angles). Afterwards, we study the behaviour of these angles depending on the type of dendrite from which it originates and the brain layer in which its neuron (its soma) is located. Going further on neuronal morphology, we also study the pyramidal neuron classification problem into cerebral cortex layers based on their basal dendrites bifurcation angles. To do this, we use the supervised classification Bayesian network models for directional variables developed in this dissertation. Later, we compare the classification accuracy among these directional classification models to evaluate their efficiency. We also compare with random classification

Circular Bayesian classifiers using wrapped Cauchy distributions

Capturing the dependences among circular variables within supervised classification models is a challenging task. In this paper, we propose four different supervised Bayesian classification algorithms where the predictor variables follow all circular wrapped Cauchy distributions. For this purpose, we introduce four wrapped Cauchy classifiers. The bivariate wrapped Cauchy distribution is the only bivariate circular distribution whose marginals and conditionals are also wrapped Cauchy distributions, a property that makes it possible to define these models easily. Furthermore, the wrapped Cauchy tree-augmented naive Bayes classifier requires the definition of a conditional circular mutual information measure between variables that follow wrapped Cauchy distributions. Synthetic data is used to illustrate, compare and evaluate the classification algorithms (including a comparison with the Gaussian TAN classifier, decision tree, random forest, multinomial logistic regression, support vector machine and simple neural network), leading to satisfactory predictive results. We also use a real neuromorphological dataset obtained from juvenile rat somatosensory cortex cells, where we measure the bifurcation angles of the dendritic basal arbors

Tree-structured Bayesian networks for wrapped Cauchy directional distributions

Modelling the relationship between directional variables is a nearly unexplored field. The bivariate wrapped Cauchy distribution has recently emerged as the first closed family of bivariate directional distri- butions (marginals and conditionals belong to the same family). In this paper, we introduce a tree-structured Bayesian network suitable for mod- elling directional data with bivariate wrapped Cauchy distributions. We describe the structure learning algorithm used to learn the Bayesian net- work. We also report some simulation studies to illustrate the algorithms including a comparison with the Gaussian structure learning algorithm and an empirical experiment on real morphological data from juvenile rat somatosensory cortex cells

Hybrid mutual information between directional and linear variables

Measuring the mutual dependence between two linear variables has been studied at length in Rényi (1959a,b) and Lloyd (1962), among many others. Mutual in- formation (Shannon 1949, Cover and Thomas 2012) between two linear variables is a general measure that determines the similarity between the joint distribu- tion and the product of their marginal distributions. For directional statistics, the circular mutual information was recently proposed in Leguey et al. (2016). This is suitable when the underlying paired distributions follow bivariate wrapped Cauchy distributions (Kato and Pewsey 2015), whose marginals and conditionals belong to the univariate wrapped Cauchy family. Here we go one step further by presenting the hybrid mutual information, which allows to express in a closed form the mutual information measure between a circular-linear or a linear-circular pair of variables regardless of the marginal distribution of each variable

A Bayesian network model for linear circular data

In numerous academic fields, it is common that data include circular observations expressed as angles [−π, π). Because of the periodic nature of circular observations, a direct application of ordinary Bayesian network techniques could lead to an erroneous result in analysis. In this talk, we propose a tree-structured Bayesian network model for ‘linear–circular’ data, namely, data comprising of multiple linear and circular observations. The proposed model is an extension of the Bayesian network model of Leguey et al. (2016) for multivariate circular dat

Hybrid mutual information between directional and linear variables

Measuring the mutual dependence between two linear variables has been studied at length in Rényi (1959a,b) and Lloyd (1962), among many others. Mutual in- formation (Shannon 1949, Cover and Thomas 2012) between two linear variables is a general measure that determines the similarity between the joint distribu- tion and the product of their marginal distributions. For directional statistics, the circular mutual information was recently proposed in Leguey et al. (2016). This is suitable when the underlying paired distributions follow bivariate wrapped Cauchy distributions (Kato and Pewsey 2015), whose marginals and conditionals belong to the univariate wrapped Cauchy family. Here we go one step further by presenting the hybrid mutual information, which allows to express in a closed form the mutual information measure between a circular-linear or a linear-circular pair of variables regardless of the marginal distribution of each variable

Dendritic-branching angles of pyramidal neurons of the human cerebral cortex

© The Author(s) 2016In this article, we analyze branching angles of the basal dendrites of pyramidal neurons of layers III and V of the human temporal cortex. For this, we use a novel probability directional statistical distribution called truncated von Mises distribution that is able to describe more accurately the dendritic-branching angles than the previous proposals. Then, we perform comparative studies using this statistical method to determine similarities and/or differences between branches and branching angles that belong to different cortical layers and regions. Using this methodology, we found that common design principles exist and govern the patterns found in the different branches that compose the basal dendrites of human pyramidal cells of the temporal cortex. However, particular differences were found between supra and infragranular cells. Furthermore, we compared the branching angles of human layer III pyramidal neurons with data obtained in the previous studies in layer III of both the rat somatosensory cortex and of several cortical areas of the mouse. Finally, we study the branching angle differences between the humans that compose our data.This work has been partially supported by the Spanish Ministry of Economy and Competitiveness through the Cajal Blue Brain (C080020-09; the Spanish partner of the Blue Brain initiative from EPFL) and TIN2013-41592-P projects, by the Regional Government of Madrid through the S2013/ICE-2845-CASI-CAM-CM project, by the European Union’s Seventh Framework Programme (FP7/2007-2013) under Grant agreement no. 604102 (Human Brain Project), and by the Spanish Ministry of Education, Culture, and Sport Fellowship (FPU13/01941)