941 resultados para Chebyshev And Binomial Distributions
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A typical implicit assumption on monopolistic competition models for trade and economic geography is that firms can produce and sell only at one place. This paper fallows endogenous determination of the number of plants in a new economic geography model and examine the stable outcomes of organization choice between single-plant and multi-plant in two regions. We explicitly consider the firms' trade-off between larger economies of scale under single plant configuration and the saving in interregional transport costs under multi-plant configuration. We show that organization change arises under decreasing transportation costs and observe several organization configurations under a generalized cost function.
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Foreign firms have clustered together in the Yangtze River Delta, and their impact on domestic firms is an important policy issue. This paper studies the spatial effect of FDI agglomeration on the regional productivity of domestic firms, using Chinese firm-level data. To identify local FDI spillovers, we estimate the causal impact of foreign firms on domestic firms in the same county and similar industries. We then estimate a spatial-autoregressive model to examine spatial spillovers from FDI clusters to other domestic firms in distant counties. Our results show that FDI agglomeration generates positive spillovers for domestic firms, which are stronger in nearby areas than in distant areas.
Pro-poor growth or poverty trap? : estimating intergenerational income mobility in rural Philippines
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Using an intergenerational database covering nearly a quarter of a century, we explored the degree of intergenerational income mobility among individuals who had grown up in rural Central Luzon, the Philippines. We found that the intergenerational income elasticity is significantly lower than unity, at roughly 0.23, indicating that the average income growth rate is higher for children born to poorer families. The detailed analysis, however, revealed that its magnitude significantly varies across percentiles in a U-shape. The results provide supporting evidence of multiple equilibria or poverty trap.
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We propose a method for the decomposition of inequality changes based on panel data regression. The method is an efficient way to quantify the contributions of variables to changes of the Theil T index while satisfying the property of uniform addition. We illustrate the method using prefectural data from Japan for the period 1955 to 1998. Japan experienced a diminishing of regional income disparity during the years of high economic growth from 1955 to 1973. After estimating production functions using panel data for prefectures in Japan, we apply the new decomposition approach to identify each production factor’s contributions to the changes of per capita income inequality among prefectures. The decomposition results show that total factor productivity (residual) growth, population change (migration), and public capital stock growth contributed to the diminishing of per capita income disparity.
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The presence of a large informal sector in developing economies poses the question of whether informal activity produces agglomeration externalities. This paper uses data on all the nonfarm establishments and enterprises in Cambodia to estimate the impact of informal agglomeration on the regional economic performance of formal and informal firms. We develop a Bayesian approach for a spatial autoregressive model with an endogenous explanatory variable to address endogeneity and spatial dependence. We find a significantly positive effect of informal agglomeration, where informal firms gain more strongly than formal firms. Calculating the spatial marginal effects of increased agglomeration, we demonstrate that more accessible regions are more likely than less accessible regions to benefit strongly from informal agglomeration.
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This paper investigates the current situation of industrial agglomeration in Costa Rica, utilizing firm-level panel data for the period 2008-2012. We calculated Location Quotient and Theil Index based on employment by industry and found that 14 cantons have the industrial agglomerations for 9 industries. The analysis is in line with the nature of specific industries, the development of areas of concentration around free zones, and the evolving participation of Costa Rica in GVCs.
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This paper proposes a general equilibrium model of a monocentric city based on Fujita and Krugman (1995). Two rates of transport costs per distance and for the same good are introduced. The model assumes that lower transport costs are available at a few points on a line. These lower costs represent new transport facilities, such as high-speed motorways and railways. Findings is that new transport facilities connecting the city and hinterlands strengthen the lock-in effects, which describes whether a city remains where it is forever after being created. Furthermore, the effect intensifies with better agricultural technologies and a larger population in the economy. The relationship between indirect utility and population size has an inverted U-shape, even if new transport facilities are used. However, the population size that maximizes indirect utility is smaller than that found in Fujita and Krugman (1995).
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The Geographical Simulation Model developed by IDE-JETRO (IDE-GSM) is a computer simulation model based on spatial economics. IDE-GSM enables us to predict the economic impacts of various trade and transport facilitation measures. Here, we mainly compare the prioritized projects of the Master Plan on ASEAN Connectivity (MPAC) and the Comprehensive Asia Development Plan (CADP). MPAC focus on specific hard or soft infrastructure projects that connect one ASEAN member state to another while the CADP emphasizes the importance of economic corridors or linkages between a large cluster and another cluster. As compared with MPAC projects, the simulation analysis shows that CADP projects have much larger positive impacts on ASEAN countries.
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We study how technological progress in manufacturing and transportation to-gether with migration costs interact to shape the space-economy. Rising labor productivity in the manufacturing sector fosters the agglomeration of activities, whereas falling transport costs associated with technological and organizational in-novations fosters their dispersion. Since these two forces have been at work for a long time, the final outcome must depend on how drops in the costs of producing and trading goods interact with the various costs borne by migrants. Finally, when labor is heterogeneous, the most efficient workers of the less productive region are the first to move to the more productive region.
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We describe lpdoc, a tool which generates documentation manuals automatically from one or more logic program source files, written in Ciao, ISO-Prolog, and other (C)LP languages. It is particularly useful for documenting library modules, for which it automatically generates a rich description of the module interface. However, it can also be used quite successfully to document full applications. A fundamental advantage of using lpdoc is that it helps maintaining a true correspondence between the program and its documentation, and also identifying precisely to what versión of the program a given printed manual corresponds. The quality of the documentation generated can be greatly enhanced by including within the program text assertions (declarations with types, modes, etc. ...) for the predicates in the program, and machine-readable comments. One of the main novelties of lpdoc is that these assertions and comments are written using the Ciao system asseriion language, which is also the language of communication between the compiler and the user and between the components of the compiler. This allows a significant synergy among specification, debugging, documentation, optimization, etc. A simple compatibility library allows conventional (C)LP systems to ignore these assertions and comments and treat normally programs documented in this way. The documentation can be generated interactively from emacs or from the command line, in many formats including texinfo, dvi, ps, pdf, info, ascii, html/css, Unix nroff/man, Windows help, etc., and can include bibliographic citations and images, lpdoc can also genérate "man" pages (Unix man page format), nicely formatted plain ASCII "readme" files, installation scripts useful when the manuals are included in software distributions, brief descriptions in html/css or info formats suitable for inclusión in on-line Índices of manuals, and even complete WWW and info sites containing on-line catalogs of documents and software distributions. The lpdoc manual, all other Ciao system manuals, and parts of this paper are generated by lpdoc.
Resumo:
We describe lpdoc, a tool which generates documentation manuals automatically from one or more logic program source files, written in ISO-Prolog, Ciao, and other (C)LP languages. It is particularly useful for documenting library modules, for which it automatically generates a rich description of the module interface. However, it can also be used quite successfully to document full applications. A fundamental advantage of using lpdoc is that it helps maintaining a true correspondence between the program and its documentation, and also identifying precisely to what version of the program a given printed manual corresponds. The quality of the documentation generated can be greatly enhanced by including within the program text assertions (declarations with types, modes, etc.) for the predicates in the program, and machine-readable comments. One of the main novelties of lpdoc is that these assertions and comments are written using the Ciao system assertion language, which is also the language of communication between the compiler and the user and between the components of the compiler. This allows a significant synergy among specification, documentation, optimization, etc. A simple compatibility library allows conventional (C)LP systems to ignore these assertions and comments and treat normally programs documented in this way. The documentation can be generated in many formats including texinfo, dvi, ps, pdf, info, html/css, Unix nroff/man, Windows help, etc., and can include bibliographic citations and images. lpdoc can also generate “man” pages (Unix man page format), nicely formatted plain ascii “readme” files, installation scripts useful when the manuals are included in software distributions, brief descriptions in html/css or info formats suitable for inclusion in on-line indices of manuals, and even complete WWW and info sites containing on-line catalogs of documents and software distributions. The lpdoc manual, all other Ciao system manuals, and parts of this paper are generated by lpdoc.
Resumo:
We describe lpdoc, a tool which generates documentation manuals automatically from one or more logic program source files, written in ISO-Prolog, Ciao, and other (C)LP languages. It is particularly useful for documenting library modules, for which it automatically generates a rich description of the module interface. However, it can also be used quite successfully to document full applications. The documentation can be generated in many formats including t e x i n f o, dvi, ps, pdf, inf o, html/css, Unix nrof f/man, Windows help, etc., and can include bibliographic citations and images, lpdoc can also genérate "man" pages (Unix man page format), nicely formatted plain ascii "readme" files, installation scripts useful when the manuals are included in software distributions, brief descriptions in html/css or inf o formats suitable for inclusión in on-line Índices of manuals, and even complete WWW and inf o sites containing on-line catalogs of documents and software distributions. A fundamental advantage of using lpdoc is that it helps maintaining a true correspondence between the program and its documentation, and also identifying precisely to what versión of the program a given printed manual corresponds. The quality of the documentation generated can be greatly enhanced by including within the program text assertions (declarations with types, modes, etc. ...) for the predicates in the program, and machine-readable comments. These assertions and comments are written using the Ciao system assertion language. A simple compatibility library allows conventional (C)LP systems to ignore these assertions and comments and treat normally programs documented in this way. The lpdoc manual, all other Ciao system manuals, and most of this paper, are generated by lpdoc.
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Los estudios paleoecológicos holocenos basados en macro- y megafósiles encierran un gran valor debido a que su información tiene generalmente carácter local, su origen es conocido, pueden ser datados directamente mediante el método radiocarbónico, y pueden identificarse a un nivel taxonómicamente preciso. Sin embargo son pocas las áreas del Sur de Europa en las que sea conocida una alta densidad de yacimientos con restos leñosos de gran tamaño. En esta tesis, se presentan datos de 53 yacimientos de la sierra de Gredos y de la cordillera Cantábrica (Península Ibérica). Los restos fueron hallados en ambientes variados, como zonas higroturbosas, turberas erosionadas o lagos, y fueron identificadas mediante el estudio de la anatomía de la madera o mediante rasgos morfológicos. En la sierra de Gredos, la evidencia paleobotánica indica la existencia de un panorama relativamente estable a lo largo del Holoceno medio y principio del Holoceno final y sugiere la persistencia, a lo largo de milenios, de un piso de pinares ampliamente distribuído en cotas altas de la sierra. La información obtenida de piñas y frutos mejoran la información taxonómica disponible y revelan la existencia tanto de Pinus sylvestris como de Pinus nigra en estas sierras durante el Holoceno. La datación radiocarbónica, medición de anillos de crecimiento y sincronización preliminar de 26 secciones de troncos de subfósiles demuestran el potencial de este material de las montañas de Iberia central en la obtención de cronologías holocenas de pino. En la cordillera Cantábrica, los datos aportan información espacialmente precisa de distribuciones de ciertas especies arbóreas durante el Holoceno. En las zonas centrales de la cordillera, han sido hallados fundamentalmente restos de pino, mientras que en las zonas más occidentales los pinos estás ausentes y los restos encontrados corresponden a otras especies de caducifolios (Betula, Salix, Quercus) y arbustos (Erica, Fabaceae) Esta información paleobiogeográfica constrasta con la distribución natural actual de Pinus sylvestris y Pinus nigra en el área de estudio. En la sierra de Gredos, la naturalidad de las escasos rodales de pinos que aún persisten ha sido discutida, mientras que en la cordillera Cantábrica, la única especie del grupo que persiste es P. sylvestris y está localizada en unos pocos relictos. El clima pudo haber jugado un papel importante en una primera fase de declive de los pinares durante el Holoceno inicial, mostrado en numerosos registros polínicos de manera casi sincrónica y asociada a una expansión de frondosas. Sin embargo la información histórica disponible y la comparación entre las áreas de distribución de los pinares en el presente, modelizada y en momentos anteriores a la la generalización de la presión antrópica sugiere que durante los últimos dos milenios, la actividad humana ha sido responsable de la desaparición de estas especies como árboles naturales en áreas extensas. ABSTRACTMacro- and megafossil studies provide information of great value in palaeoecology because such evidence is spatially precise, directly radiocarbon dated and usually taxon-specific. However, few areas of southern Europe have a high density of sites with Holocene woody remains. Here, local data from 53 sites in the Gredos Mountains and the Cantabrian Range (Iberian Peninsula) is presented. Woody remains were recovered from mires, eroded peat bogs and lakes and were identified by their wood anatomy or morphological traits. In the Gredos Mountains, palaeobotanical evidence portrays a relatively stable picture of tree distribution over the mid- and beggining of the late-Holocene, and suggests the persistence of a widespread belt of pinewoods. Cones and fruits enlarge the taxonomic information available and reveal that both Pinus sylvestris and Pinus nigra were present locally during the Holocene. Radiocarbon dating, tree ring measurement and preliminary cross-dating of 26 pine sub-fossil logs demonstrate the potential of obtaining a long pine chronology from subfossil wood from the mountains of Central Iberia. In the Cantabrian Range the data provide spatially precise evidence of tree distribution in the region during the Holocene. Pines were mostly identified in the central areas, whereas at the western edge no pine evidence was detected and deciduous trees (Betula, Salix, Quercus) and shrubs (Erica, Fabaceae) were identified. This palaeoecological information contrasts with the current natural distribution ranges of P. sylvestris and P. nigra in the study area. In the Gredos Mountains, the naturality of the few pine stands currently growing has been heavily debated. In the Cantabrian Range P. sylvestris is the only pine species that is today present, and its natural presence is now limited to a few enclaves. Climate may have played a key role in the early-Holocene, as pollen archives document a pine demise that is synchronous with the spread of broadleaved taxa. However, available historical data and the comparison of the reconstructed distribution of pinewoods before extensive human forest disturbance with both present and modelled distributions suggests that during the last two millennia, anthropogenic activity may have removed these species as native trees from a large territory.
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Neuronal morphology is a key feature in the study of brain circuits, as it is highly related to information processing and functional identification. Neuronal morphology affects the process of integration of inputs from other neurons and determines the neurons which receive the output of the neurons. Different parts of the neurons can operate semi-independently according to the spatial location of the synaptic connections. As a result, there is considerable interest in the analysis of the microanatomy of nervous cells since it constitutes an excellent tool for better understanding cortical function. However, the morphologies, molecular features and electrophysiological properties of neuronal cells are extremely variable. Except for some special cases, this variability makes it hard to find a set of features that unambiguously define a neuronal type. In addition, there are distinct types of neurons in particular regions of the brain. This morphological variability makes the analysis and modeling of neuronal morphology a challenge. Uncertainty is a key feature in many complex real-world problems. Probability theory provides a framework for modeling and reasoning with uncertainty. Probabilistic graphical models combine statistical theory and graph theory to provide a tool for managing domains with uncertainty. In particular, we focus on Bayesian networks, the most commonly used probabilistic graphical model. In this dissertation, we design new methods for learning Bayesian networks and apply them to the problem of modeling and analyzing morphological data from neurons. The morphology of a neuron can be quantified using a number of measurements, e.g., the length of the dendrites and the axon, the number of bifurcations, the direction of the dendrites and the axon, etc. These measurements can be modeled as discrete or continuous data. The continuous data can be linear (e.g., the length or the width of a dendrite) or directional (e.g., the direction of the axon). These data may follow complex probability distributions and may not fit any known parametric distribution. Modeling this kind of problems using hybrid Bayesian networks with discrete, linear and directional variables poses a number of challenges regarding learning from data, inference, etc. In this dissertation, we propose a method for modeling and simulating basal dendritic trees from pyramidal neurons using Bayesian networks to capture the interactions between the variables in the problem domain. A complete set of variables is measured from the dendrites, and a learning algorithm is applied to find the structure and estimate the parameters of the probability distributions included in the Bayesian networks. Then, a simulation algorithm is used to build the virtual dendrites by sampling values from the Bayesian networks, and a thorough evaluation is performed to show the model’s ability to generate realistic dendrites. In this first approach, the variables are discretized so that discrete Bayesian networks can be learned and simulated. Then, we address the problem of learning hybrid Bayesian networks with different kinds of variables. Mixtures of polynomials have been proposed as a way of representing probability densities in hybrid Bayesian networks. We present a method for learning mixtures of polynomials approximations of one-dimensional, multidimensional and conditional probability densities from data. The method is based on basis spline interpolation, where a density is approximated as a linear combination of basis splines. The proposed algorithms are evaluated using artificial datasets. We also use the proposed methods as a non-parametric density estimation technique in Bayesian network classifiers. Next, we address the problem of including directional data in Bayesian networks. These data have some special properties that rule out the use of classical statistics. Therefore, different distributions and statistics, such as the univariate von Mises and the multivariate von Mises–Fisher distributions, should be used to deal with this kind of information. In particular, we extend the naive Bayes classifier to the case where the conditional probability distributions of the predictive variables given the class follow either of these distributions. We consider the simple scenario, where only directional predictive variables are used, and the hybrid case, where discrete, Gaussian and directional distributions are mixed. The classifier decision functions and their decision surfaces are studied at length. Artificial examples are used to illustrate the behavior of the classifiers. The proposed classifiers are empirically evaluated over real datasets. We also study the problem of interneuron classification. An extensive group of experts is asked to classify a set of neurons according to their most prominent anatomical features. A web application is developed to retrieve the experts’ classifications. We compute agreement measures to analyze the consensus between the experts when classifying the neurons. Using Bayesian networks and clustering algorithms on the resulting data, we investigate the suitability of the anatomical terms and neuron types commonly used in the literature. Additionally, we apply supervised learning approaches to automatically classify interneurons using the values of their morphological measurements. Then, a methodology for building a model which captures the opinions of all the experts is presented. First, one Bayesian network is learned for each expert, and we propose an algorithm for clustering Bayesian networks corresponding to experts with similar behaviors. Then, a Bayesian network which represents the opinions of each group of experts is induced. Finally, a consensus Bayesian multinet which models the opinions of the whole group of experts is built. A thorough analysis of the consensus model identifies different behaviors between the experts when classifying the interneurons in the experiment. A set of characterizing morphological traits for the neuronal types can be defined by performing inference in the Bayesian multinet. These findings are used to validate the model and to gain some insights into neuron morphology. Finally, we study a classification problem where the true class label of the training instances is not known. Instead, a set of class labels is available for each instance. This is inspired by the neuron classification problem, where a group of experts is asked to individually provide a class label for each instance. We propose a novel approach for learning Bayesian networks using count vectors which represent the number of experts who selected each class label for each instance. These Bayesian networks are evaluated using artificial datasets from supervised learning problems. Resumen La morfología neuronal es una característica clave en el estudio de los circuitos cerebrales, ya que está altamente relacionada con el procesado de información y con los roles funcionales. La morfología neuronal afecta al proceso de integración de las señales de entrada y determina las neuronas que reciben las salidas de otras neuronas. Las diferentes partes de la neurona pueden operar de forma semi-independiente de acuerdo a la localización espacial de las conexiones sinápticas. Por tanto, existe un interés considerable en el análisis de la microanatomía de las células nerviosas, ya que constituye una excelente herramienta para comprender mejor el funcionamiento de la corteza cerebral. Sin embargo, las propiedades morfológicas, moleculares y electrofisiológicas de las células neuronales son extremadamente variables. Excepto en algunos casos especiales, esta variabilidad morfológica dificulta la definición de un conjunto de características que distingan claramente un tipo neuronal. Además, existen diferentes tipos de neuronas en regiones particulares del cerebro. La variabilidad neuronal hace que el análisis y el modelado de la morfología neuronal sean un importante reto científico. La incertidumbre es una propiedad clave en muchos problemas reales. La teoría de la probabilidad proporciona un marco para modelar y razonar bajo incertidumbre. Los modelos gráficos probabilísticos combinan la teoría estadística y la teoría de grafos con el objetivo de proporcionar una herramienta con la que trabajar bajo incertidumbre. En particular, nos centraremos en las redes bayesianas, el modelo más utilizado dentro de los modelos gráficos probabilísticos. En esta tesis hemos diseñado nuevos métodos para aprender redes bayesianas, inspirados por y aplicados al problema del modelado y análisis de datos morfológicos de neuronas. La morfología de una neurona puede ser cuantificada usando una serie de medidas, por ejemplo, la longitud de las dendritas y el axón, el número de bifurcaciones, la dirección de las dendritas y el axón, etc. Estas medidas pueden ser modeladas como datos continuos o discretos. A su vez, los datos continuos pueden ser lineales (por ejemplo, la longitud o la anchura de una dendrita) o direccionales (por ejemplo, la dirección del axón). Estos datos pueden llegar a seguir distribuciones de probabilidad muy complejas y pueden no ajustarse a ninguna distribución paramétrica conocida. El modelado de este tipo de problemas con redes bayesianas híbridas incluyendo variables discretas, lineales y direccionales presenta una serie de retos en relación al aprendizaje a partir de datos, la inferencia, etc. En esta tesis se propone un método para modelar y simular árboles dendríticos basales de neuronas piramidales usando redes bayesianas para capturar las interacciones entre las variables del problema. Para ello, se mide un amplio conjunto de variables de las dendritas y se aplica un algoritmo de aprendizaje con el que se aprende la estructura y se estiman los parámetros de las distribuciones de probabilidad que constituyen las redes bayesianas. Después, se usa un algoritmo de simulación para construir dendritas virtuales mediante el muestreo de valores de las redes bayesianas. Finalmente, se lleva a cabo una profunda evaluaci ón para verificar la capacidad del modelo a la hora de generar dendritas realistas. En esta primera aproximación, las variables fueron discretizadas para poder aprender y muestrear las redes bayesianas. A continuación, se aborda el problema del aprendizaje de redes bayesianas con diferentes tipos de variables. Las mixturas de polinomios constituyen un método para representar densidades de probabilidad en redes bayesianas híbridas. Presentamos un método para aprender aproximaciones de densidades unidimensionales, multidimensionales y condicionales a partir de datos utilizando mixturas de polinomios. El método se basa en interpolación con splines, que aproxima una densidad como una combinación lineal de splines. Los algoritmos propuestos se evalúan utilizando bases de datos artificiales. Además, las mixturas de polinomios son utilizadas como un método no paramétrico de estimación de densidades para clasificadores basados en redes bayesianas. Después, se estudia el problema de incluir información direccional en redes bayesianas. Este tipo de datos presenta una serie de características especiales que impiden el uso de las técnicas estadísticas clásicas. Por ello, para manejar este tipo de información se deben usar estadísticos y distribuciones de probabilidad específicos, como la distribución univariante von Mises y la distribución multivariante von Mises–Fisher. En concreto, en esta tesis extendemos el clasificador naive Bayes al caso en el que las distribuciones de probabilidad condicionada de las variables predictoras dada la clase siguen alguna de estas distribuciones. Se estudia el caso base, en el que sólo se utilizan variables direccionales, y el caso híbrido, en el que variables discretas, lineales y direccionales aparecen mezcladas. También se estudian los clasificadores desde un punto de vista teórico, derivando sus funciones de decisión y las superficies de decisión asociadas. El comportamiento de los clasificadores se ilustra utilizando bases de datos artificiales. Además, los clasificadores son evaluados empíricamente utilizando bases de datos reales. También se estudia el problema de la clasificación de interneuronas. Desarrollamos una aplicación web que permite a un grupo de expertos clasificar un conjunto de neuronas de acuerdo a sus características morfológicas más destacadas. Se utilizan medidas de concordancia para analizar el consenso entre los expertos a la hora de clasificar las neuronas. Se investiga la idoneidad de los términos anatómicos y de los tipos neuronales utilizados frecuentemente en la literatura a través del análisis de redes bayesianas y la aplicación de algoritmos de clustering. Además, se aplican técnicas de aprendizaje supervisado con el objetivo de clasificar de forma automática las interneuronas a partir de sus valores morfológicos. A continuación, se presenta una metodología para construir un modelo que captura las opiniones de todos los expertos. Primero, se genera una red bayesiana para cada experto y se propone un algoritmo para agrupar las redes bayesianas que se corresponden con expertos con comportamientos similares. Después, se induce una red bayesiana que modela la opinión de cada grupo de expertos. Por último, se construye una multired bayesiana que modela las opiniones del conjunto completo de expertos. El análisis del modelo consensuado permite identificar diferentes comportamientos entre los expertos a la hora de clasificar las neuronas. Además, permite extraer un conjunto de características morfológicas relevantes para cada uno de los tipos neuronales mediante inferencia con la multired bayesiana. Estos descubrimientos se utilizan para validar el modelo y constituyen información relevante acerca de la morfología neuronal. Por último, se estudia un problema de clasificación en el que la etiqueta de clase de los datos de entrenamiento es incierta. En cambio, disponemos de un conjunto de etiquetas para cada instancia. Este problema está inspirado en el problema de la clasificación de neuronas, en el que un grupo de expertos proporciona una etiqueta de clase para cada instancia de manera individual. Se propone un método para aprender redes bayesianas utilizando vectores de cuentas, que representan el número de expertos que seleccionan cada etiqueta de clase para cada instancia. Estas redes bayesianas se evalúan utilizando bases de datos artificiales de problemas de aprendizaje supervisado.
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“Por lo tanto, la cristalización de polímeros se supone, y en las teorías se describe a menudo, como un proceso de múltiples pasos con muchos aspectos físico-químicos y estructurales influyendo en él. Debido a la propia estructura de la cadena, es fácil entender que un proceso que es termodinámicamente forzado a aumentar su ordenamiento local, se vea obstaculizado geométricamente y, por tanto, no puede conducirse a un estado de equilibrio final. Como resultado, se forman habitualmente estructuras de no equilibrio con diferentes características dependiendo de la temperatura, presión, cizallamiento y otros parámetros físico-químicos del sistema”. Estas palabras, pronunciadas recientemente por el profesor Bernhard Wunderlich, uno de los mas relevantes fisico-quimicos que han abordado en las ultimas décadas el estudio del estado físico de las macromoléculas, adelantan lo que de alguna manera se explicita en esta memoria y constituyen el “leitmotiv” de este trabajo de tesis. El mecanismo de la cristalización de polímeros esta aun bajo debate en la comunidad de la física de polímeros y la mayoría de los abordajes experimentales se explican a través de la teoría LH. Esta teoría clásica debida a Lauritzen y Hoffman (LH), y que es una generalización de la teoría de cristalización de una molécula pequeña desde la fase de vapor, describe satisfactoriamente muchas observaciones experimentales aunque esta lejos de explicar el complejo fenómeno de la cristalización de polímeros. De hecho, la formulación original de esta teoría en el National Bureau of Standards, a comienzos de la década de los 70, sufrió varias reformulaciones importantes a lo largo de la década de los 80, buscando su adaptación a los hallazgos experimentales. Así nació el régimen III de cristalización que posibilita la creacion de nichos moleculares en la superficie y que dio pie al paradigma ofrecido por Sadler y col., para justificar los experimentos que se obtenian por “scattering” de neutrones y otras técnicas como la técnica de “droplets” o enfriamiento rapido. Por encima de todo, el gran éxito de la teoría radica en que explica la dependencia inversa entre el tamaño del plegado molecular y el subenfriamiento, definido este ultimo como el intervalo de temperatura que media entre la temperatura de equilibrio y la temperatura de cristalización. El problema concreto que aborda esta tesis es el estudio de los procesos de ordenamiento de poliolefinas con distinto grado de ramificacion mediante simulaciones numéricas. Los copolimeros estudiados en esta tesis se consideran materiales modelo de gran homogeneidad molecular desde el punto de vista de la distribución de tamaños y de ramificaciones en la cadena polimérica. Se eligieron estas poliolefinas debido al gran interes experimental en conocer el cambio en las propiedades fisicas de los materiales dependiendo del tipo y cantidad de comonomero utilizado. Además, son modelos sobre los que existen una ingente cantidad de información experimental, que es algo que preocupa siempre al crear una realidad virtual como es la simulación. La experiencia en el grupo Biophym es que los resultados de simulación deben de tener siempre un correlato mas o menos próximo experimental y ese argumento se maneja a lo largo de esta memoria. Empíricamente, se conoce muy bien que las propiedades físicas de las poliolefinas, en suma dependen del tipo y de la cantidad de ramificaciones que presenta el material polimérico. Sin embargo, tal como se ha explicado no existen modelos teóricos adecuados que expliquen los mecanismos subyacentes de los efectos de las ramas. La memoria de este trabajo es amplia por la complejidad del tema. Se inicia con una extensa introducción sobre los conceptos básicos de una macromolecula que son relevantes para entender el contenido del resto de la memoria. Se definen los conceptos de macromolecula flexible, distribuciones y momentos, y su comportamiento en disolución y fundido con los correspondientes parametros caracteristicos. Se pone especial énfasis en el concepto de “entanglement” o enmaranamiento por considerarse clave a la hora de tratar macromoléculas con una longitud superior a la longitud critica de enmaranamiento. Finaliza esta introducción con una reseña sobre el estado del arte en la simulación de los procesos de cristalización. En un segundo capitulo del trabajo se expone detalladamente la metodología usada en cada grupo de casos. En el primer capitulo de resultados, se discuten los estudios de simulación en disolución diluida para sistemas lineales y ramificados de cadena única. Este caso mas simple depende claramente del potencial de torsión elegido tal como se discute a lo largo del texto. La formación de los núcleos “babys” propuestos por Muthukumar parece que son consecuencia del potencial de torsión, ya que este facilita los estados de torsión mas estables. Así que se propone el análisis de otros potenciales que son igualmente utilizados y los resultados obtenidos sobre la cristalización, discutidos en consecuencia. Seguidamente, en un segundo capitulo de resultados se estudian moleculas de alcanos de cadena larga lineales y ramificados en un fundido por simulaciones atomisticas como un modelo de polietileno. Los resultados atomisticos pese a ser de gran detalle no logran captar en su totalidad los efectos experimentales que se observan en los fundidos subenfriados en su etapa previa al estado ordenado. Por esta razon se discuten en los capítulos 3 y 4 de resultados sistemas de cadenas cortas y largas utilizando dos modelos de grano grueso (CG-PVA y CG-PE). El modelo CG-PE se desarrollo durante la tesis. El uso de modelos de grano grueso garantiza una mayor eficiencia computacional con respecto a los modelos atomísticos y son suficientes para mostrar los fenómenos a la escala relevante para la cristalización. En todos estos estudios mencionados se sigue la evolución de los procesos de ordenamiento y de fusión en simulaciones de relajación isoterma y no isoterma. Como resultado de los modelos de simulación, se han evaluado distintas propiedades fisicas como la longitud de segmento ordenado, la cristalinidad, temperaturas de fusion/cristalizacion, etc., lo que permite una comparación con los resultados experimentales. Se demuestra claramente que los sistemas ramificados retrasan y dificultan el orden de la cadena polimérica y por tanto, las regiones cristalinas ordenadas decrecen al crecer las ramas. Como una conclusión general parece mostrarse una tendencia a la formación de estructuras localmente ordenadas que crecen como bloques para completar el espacio de cristalización que puede alcanzarse a una temperatura y a una escala de tiempo determinada. Finalmente hay que señalar que los efectos observados, estan en concordancia con otros resultados tanto teoricos/simulacion como experimentales discutidos a lo largo de esta memoria. Su resumen se muestra en un capitulo de conclusiones y líneas futuras de investigación que se abren como consecuencia de esta memoria. Hay que mencionar que el ritmo de investigación se ha acentuado notablemente en el ultimo ano de trabajo, en parte debido a las ventajas notables obtenidas por el uso de la metodología de grano grueso que pese a ser muy importante para esta memoria no repercute fácilmente en trabajos publicables. Todo ello justifica que gran parte de los resultados esten en fase de publicación. Abstract “Polymer crystallization is therefore assumed, and in theories often described, to be a multi step process with many influencing aspects. Because of the chain structure, it is easy to understand that a process which is thermodynamically forced to increase local ordering but is geometrically hindered cannot proceed into a final equilibrium state. As a result, nonequilibrium structures with different characteristics are usually formed, which depend on temperature, pressure, shearing and other parameters”. These words, recently written by Professor Bernhard Wunderlich, one of the most prominent researchers in polymer physics, put somehow in value the "leitmotiv "of this thesis. The crystallization mechanism of polymers is still under debate in the physics community and most of the experimental findings are still explained by invoking the LH theory. This classical theory, which was initially formulated by Lauritzen and Hoffman (LH), is indeed a generalization of the crystallization theory for small molecules from the vapor phase. Even though it describes satisfactorily many experimental observations, it is far from explaining the complex phenomenon of polymer crystallization. This theory was firstly devised in the early 70s at the National Bureau of Standards. It was successively reformulated along the 80s to fit the experimental findings. Thus, the crystallization regime III was introduced into the theory in order to explain the results found in neutron scattering, droplet or quenching experiments. This concept defines the roughness of the crystallization surface leading to the paradigm proposed by Sadler et al. The great success of this theory is the ability to explain the inverse dependence of the molecular folding size on the supercooling, the latter defined as the temperature interval between the equilibrium temperature and the crystallization temperature. The main scope of this thesis is the study of ordering processes in polyolefins with different degree of branching by using computer simulations. The copolymers studied along this work are considered materials of high molecular homogeneity, from the point of view of both size and branching distributions of the polymer chain. These polyolefins were selected due to the great interest to understand their structure– property relationships. It is important to note that there is a vast amount of experimental data concerning these materials, which is essential to create a virtual reality as is the simulation. The Biophym research group has a wide experience in the correlation between simulation data and experimental results, being this idea highly alive along this work. Empirically, it is well-known that the physical properties of the polyolefins depend on the type and amount of branches presented in the polymeric material. However, there are not suitable models to explain the underlying mechanisms associated to branching. This report is extensive due to the complexity of the topic under study. It begins with a general introduction to the basics concepts of macromolecular physics. This chapter is relevant to understand the content of the present document. Some concepts are defined along this section, among others the flexibility of macromolecules, size distributions and moments, and the behavior in solution and melt along with their corresponding characteristic parameters. Special emphasis is placed on the concept of "entanglement" which is a key item when dealing with macromolecules having a molecular size greater than the critical entanglement length. The introduction finishes with a review of the state of art on the simulation of crystallization processes. The second chapter of the thesis describes, in detail, the computational methodology used in each study. In the first results section, we discuss the simulation studies in dilute solution for linear and short chain branched single chain models. The simplest case is clearly dependent on the selected torsion potential as it is discussed throughout the text. For example, the formation of baby nuclei proposed by Mutukhumar seems to result from the effects of the torsion potential. Thus, we propose the analysis of other torsion potentials that are also used by other research groups. The results obtained on crystallization processes are accordingly discussed. Then, in a second results section, we study linear and branched long-chain alkane molecules in a melt by atomistic simulations as a polyethylene-like model. In spite of the great detail given by atomistic simulations, they are not able to fully capture the experimental facts observed in supercooled melts, in particular the pre-ordered states. For this reason, we discuss short and long chains systems using two coarse-grained models (CG-PVA and CG-PE) in section 3 and 4 of chapter 2. The CG-PE model was developed during the thesis. The use of coarse-grained models ensures greater computational efficiency with respect to atomistic models and is enough to show the relevant scale phenomena for crystallization. In all the analysis we follow the evolution of the ordering and melting processes by both isothermal and non isothermal simulations. During this thesis we have obtained different physical properties such as stem length, crystallinity, melting/crystallization temperatures, and so on. We show that branches in the chains cause a delay in the crystallization and hinder the ordering of the polymer chain. Therefore, crystalline regions decrease in size as branching increases. As a general conclusion, it seems that there is a tendency in the macromolecular systems to form ordered structures, which can grown locally as blocks, occupying the crystallization space at a given temperature and time scale. Finally it should be noted that the observed effects are consistent with both, other theoretical/simulation and experimental results. The summary is provided in the conclusions chapter along with future research lines that open as result of this report. It should be mentioned that the research work has speeded up markedly in the last year, in part because of the remarkable benefits obtained by the use of coarse-grained methodology that despite being very important for this thesis work, is not easily publishable by itself. All this justify that most of the results are still in the publication phase.