Estimadores bayesianos de la fiabilidad con muestreo censurado

El estudio de la fiabilidad de componentes y sistemas tiene gran importancia en diversos campos de la ingenieria, y muy concretamente en el de la informatica. Al analizar la duracion de los elementos de la muestra hay que tener en cuenta los elementos que no fallan en el tiempo que dure el experimento, o bien los que fallen por causas distintas a la que es objeto de estudio. Por ello surgen nuevos tipos de muestreo que contemplan estos casos. El mas general de ellos, el muestreo censurado, es el que consideramos en nuestro trabajo. En este muestreo tanto el tiempo hasta que falla el componente como el tiempo de censura son variables aleatorias. Con la hipotesis de que ambos tiempos se distribuyen exponencialmente, el profesor Hurt estudio el comportamiento asintotico del estimador de maxima verosimilitud de la funcion de fiabilidad. En principio parece interesante utilizar metodos Bayesianos en el estudio de la fiabilidad porque incorporan al analisis la informacion a priori de la que se dispone normalmente en problemas reales. Por ello hemos considerado dos estimadores Bayesianos de la fiabilidad de una distribucion exponencial que son la media y la moda de la distribucion a posteriori. Hemos calculado la expansion asint6tica de la media, varianza y error cuadratico medio de ambos estimadores cuando la distribuci6n de censura es exponencial. Hemos obtenido tambien la distribucion asintotica de los estimadores para el caso m3s general de que la distribucion de censura sea de Weibull. Dos tipos de intervalos de confianza para muestras grandes se han propuesto para cada estimador. Los resultados se han comparado con los del estimador de maxima verosimilitud, y con los de dos estimadores no parametricos: limite producto y Bayesiano, resultando un comportamiento superior por parte de uno de nuestros estimadores. Finalmente nemos comprobado mediante simulacion que nuestros estimadores son robustos frente a la supuesta distribuci6n de censura, y que uno de los intervalos de confianza propuestos es valido con muestras pequenas. Este estudio ha servido tambien para confirmar el mejor comportamiento de uno de nuestros estimadores. SETTING OUT AND SUMMARY OF THE THESIS When we study the lifetime of components it's necessary to take into account the elements that don't fail during the experiment, or those that fail by reasons which are desirable to exclude from consideration. The model of random censorship is very usefull for analysing these data. In this model the time to failure and the time censor are random variables. We obtain two Bayes estimators of the reliability function of an exponential distribution based on randomly censored data. We have calculated the asymptotic expansion of the mean, variance and mean square error of both estimators, when the censor's distribution is exponential. We have obtained also the asymptotic distribution of the estimators for the more general case of censor's Weibull distribution. Two large-sample confidence bands have been proposed for each estimator. The results have been compared with those of the maximum likelihood estimator, and with those of two non parametric estimators: Product-limit and Bayesian. One of our estimators has the best behaviour. Finally we have shown by simulation, that our estimators are robust against the assumed censor's distribution, and that one of our intervals does well in small sample situation.

Multiple attractors, long chaotic transients, and failure in small-world networks of excitable neurons.

We study the dynamical states of a small-world network of recurrently coupled excitable neurons, through both numerical and analytical methods. The dynamics of this system depend mostly on both the number of long-range connections or ?shortcuts?, and the delay associated with neuronal interactions. We find that persistent activity emerges at low density of shortcuts, and that the system undergoes a transition to failure as their density reaches a critical value. The state of persistent activity below this transition consists of multiple stable periodic attractors, whose number increases at least as fast as the number of neurons in the network. At large shortcut density and for long enough delays the network dynamics exhibit exceedingly long chaotic transients, whose failure times follow a stretched exponential distribution. We show that this functional form arises for the ensemble-averaged activity if the failure time for each individual network realization is exponen- tially distributed

Extended Triple-Junction Solar Cell 3D Distributed Model: Application to Chromatic Aberration-Related Losses

An extended 3D distributed model based on distributed circuit units for the simulation of triple‐junction solar cells under realistic conditions for the light distribution has been developed. A special emphasis has been put in the capability of the model to accurately account for current mismatch and chromatic aberration effects. This model has been validated, as shown by the good agreement between experimental and simulation results, for different light spot characteristics including spectral mismatch and irradiance non‐uniformities. This model is then used for the prediction of the performance of a triple‐junction solar cell for a light spot corresponding to a real optical architecture in order to illustrate its suitability in assisting concentrator system analysis and design process.

Study of the temperature distribution in Si nanowires under microscopic laser beam excitation

The use of laser beams as excitation sources for the characterization of semiconductor nanowires (NWs) is largely extended. Raman spectroscopy and photoluminescence (PL) are currently applied to the study of NWs. However, NWs are systems with poor thermal conductivity and poor heat dissipation, which result in unintentional heating under the excitation with a focused laser beam with microscopic size, as those usually used in microRaman and microPL experiments. On the other hand, the NWs have subwavelength diameter, which changes the optical absorption with respect to the absorption in bulk materials. Furthermore, the NW diameter is smaller than the laser beam spot, which means that the optical power absorbed by the NW depends on its position inside the laser beam spot. A detailed analysis of the interaction between a microscopic focused laser beam and semiconductor NWs is necessary for the understanding of the experiments involving laser beam excitation of NWs. We present in this work a numerical analysis of the thermal transport in Si NWs, where the heat source is the laser energy locally absorbed by the NW. This analysis takes account of the optical absorption, the thermal conductivity, the dimensions, diameter and length of the NWs, and the immersion medium. Both free standing and heat-sunk NWs are considered. Also, the temperature distribution in ensembles of NWs is discussed. This analysis intends to constitute a tool for the understanding of the thermal phenomena induced by laser beams in semiconductor NWs.

Architectures for Video-on-Demand content distribution in managed networks

La demanda de contenidos de vídeo ha aumentado rápidamente en los últimos años como resultado del gran despliegue de la TV sobre IP (IPTV) y la variedad de servicios ofrecidos por los operadores de red. Uno de los servicios que se ha vuelto especialmente atractivo para los clientes es el vídeo bajo demanda (VoD) en tiempo real, ya que ofrece una transmisión (streaming) inmediata de gran variedad de contenidos de vídeo. El precio que los operadores tienen que pagar por este servicio es el aumento del tráfico en las redes, que están cada vez más congestionadas debido a la mayor demanda de contenidos de VoD y al aumento de la calidad de los propios contenidos de vídeo. Así, uno de los principales objetivos de esta tesis es encontrar soluciones que reduzcan el tráfico en el núcleo de la red, manteniendo la calidad del servicio en el nivel adecuado y reduciendo el coste del tráfico. La tesis propone un sistema jerárquico de servidores de streaming en el que se ejecuta un algoritmo para la ubicación óptima de los contenidos de acuerdo con el comportamiento de los usuarios y el estado de la red. Debido a que cualquier algoritmo óptimo de distribución de contenidos alcanza un límite en el que no se puede llegar a nuevas mejoras, la inclusión de los propios clientes del servicio (los peers) en el proceso de streaming puede reducir aún más el tráfico de red. Este proceso se logra aprovechando el control que el operador tiene en las redes de gestión privada sobre los equipos receptores (Set-Top Box) ubicados en las instalaciones de los clientes. El operador se reserva cierta capacidad de almacenamiento y streaming de los peers para almacenar los contenidos de vídeo y para transmitirlos a otros clientes con el fin de aliviar a los servidores de streaming. Debido a la incapacidad de los peers para sustituir completamente a los servidores de streaming, la tesis propone un sistema de streaming asistido por peers. Algunas de las cuestiones importantes que se abordan en la tesis son saber cómo los parámetros del sistema y las distintas distribuciones de los contenidos de vídeo en los peers afectan al rendimiento general del sistema. Para dar respuesta a estas preguntas, la tesis propone un modelo estocástico preciso y flexible que tiene en cuenta parámetros como las capacidades de enlace de subida y de almacenamiento de los peers, el número de peers, el tamaño de la biblioteca de contenidos de vídeo, el tamaño de los contenidos y el esquema de distribución de contenidos para estimar los beneficios del streaming asistido por los peers. El trabajo también propone una versión extendida del modelo matemático mediante la inclusión de la probabilidad de fallo de los peers y su tiempo de recuperación en el conjunto de parámetros del modelo. Estos modelos se utilizan como una herramienta para la realización de exhaustivos análisis del sistema de streaming de VoD asistido por los peers para la amplia gama de parámetros definidos en los modelos. Abstract The demand of video contents has rapidly increased in the past years as a result of the wide deployment of IPTV and the variety of services offered by the network operators. One of the services that has especially become attractive to the customers is real-time Video on Demand (VoD) because it offers an immediate streaming of a large variety of video contents. The price that the operators have to pay for this convenience is the increased traffic in the networks, which are becoming more congested due to the higher demand for VoD contents and the increased quality of the videos. Therefore, one of the main objectives of this thesis is finding solutions that would reduce the traffic in the core of the network, keeping the quality of service on satisfactory level and reducing the traffic cost. The thesis proposes a system of hierarchical structure of streaming servers that runs an algorithm for optimal placement of the contents according to the users’ behavior and the state of the network. Since any algorithm for optimal content distribution reaches a limit upon which no further improvements can be made, including service customers themselves (the peers) in the streaming process can further reduce the network traffic. This process is achieved by taking advantage of the control that the operator has in the privately managed networks over the Set-Top Boxes placed at the clients’ premises. The operator reserves certain storage and streaming capacity on the peers to store the video contents and to stream them to the other clients in order to alleviate the streaming servers. Because of the inability of the peers to completely substitute the streaming servers, the thesis proposes a system for peer-assisted streaming. Some of the important questions addressed in the thesis are how the system parameters and the various distributions of the video contents on the peers would impact the overall system performance. In order to give answers to these questions, the thesis proposes a precise and flexible stochastic model that takes into consideration parameters like uplink and storage capacity of the peers, number of peers, size of the video content library, size of contents and content distribution scheme to estimate the benefits of the peer-assisted streaming. The work also proposes an extended version of the mathematical model by including the failure probability of the peers and their recovery time in the set of parameters. These models are used as tools for conducting thorough analyses of the peer-assisted system for VoD streaming for the wide range of defined parameters.

An extension of Mohring’s model for land rent distribution

In an early paper Herbert Mohring (J. Poi Et on , 49 (1961)) presented a model for land rent distribution yielding the well-known result that the price of land must fall with the distance from the city center to offset transportation costs. Our paper is an extension of Mohring's model in which we relax some of his drastic simplifying assumptions. This extended model has been incorporated in a method for economic evaluation of city master plans which has been applied to a Swedish city. In this method the interdependence among housing, heating, and transportation, the dura-bility of urban structures, and the uncertainty of future demand are explicitly considered within a cost-benefit approach. Some empirical results from this pilot study concerning land rent distributions are also presented here.