Closed form analysis of Poisson cellular networks: a stochastic geometry approach

Ultra dense networks (UDNs) allow for efficient spatial reuse of the spectrum, giving rise to substantial capacity and power gains. In order to exploit those gains, tractable mathematical models need to be derived, allowing for the analysis and optimization of the network operation. In this course, stochastic geometry has emerged as a powerful tool for large-scale analysis and modeling of wireless cellular networks. In particular, the employment of stochastic geometry has been proven instrumental for the characterization of the network performance and for providing significant insights into network densification. Fundamental issues, however, remain open in order to use stochastic geometry tools for the optimization of wireless networks, with the biggest challenge being the lack of tractable closed form expressions for the derived figures of merit. To this end, the present thesis revisits stochastic geometry and provides a novel stochastic geometry framework with a twofold contribution. The first part of the thesis focuses on the derivation of simple, albeit accurate closed form approximations for the ergodic rate of Poisson cellular networks under a noise limited, an interference limited and a general case scenario. The ergodic rate constitutes the most sensible figure of merit for characterizing the system performance, but due to the inherent intractability of the available stochastic geometry frameworks, had not been formulated in closed form hitherto. To demonstrate the potential of the aforementioned tractable expressions with respect to network optimization, the present thesis proposes a flexible connectivity paradigm and employs part of the developed expressions to optimize the network connectivity. The proposed flexible connectivity paradigm exploits the downlink uplink decoupling (DUDe) configuration, which is a promising framework providing substantial capacity and outage gains in UDNs and introduces the DUDe connectivity gains into the 5G era and beyond. Subsequently, the last part of the thesis provides an analytical formulation of the probability density function (PDF) of the aggregate inter-cell interference in Poisson cellular networks. The introduced PDF is an accurate approximation of the exact PDF that could not be analytically formulated hitherto, even though it constituted a crucial tool for the analysis and optimization of cellular networks. The lack of an analytical expression for the PDF of the interference in Poisson cellular networks had imposed the use of intricate formulas, in order to derive sensible figures of merit by employing only the moment generating function (MGF). Hence, the present thesis introduces an innovative framework able to simplify the analysis of Poisson cellular networks to a great extent, while addressing fundamental issues related to network optimization and design.Las redes ultra densas (UDNs) permiten una reutilización espacial del espectro, proporcionando ventajas en términos de mejora de capacidad y ahorro de potencia. Para explotar estas ventajas se necesitan modelos matemáticos simples que permitan el análisis y la optimización de la operación de la red. Por esta razón, la geometría estocástica se ha convertido en una potente herramienta para el análisis de redes celulares. En particular, el empleo de la geometría estocástica ha sido fundamental para la caracterización del rendimiento de la red y para proporcionar información importante sobre la densificación de la misma. Sin embargo, hay problemas fundamentales que deben resolverse para utilizar estas herramientas de geometría estocástica, siendo el mayor desafío la falta de expresiones simples de forma cerrada para las funciones objetivo de interés. Por este motivo, la presente tesis examina la geometría estocástica y proporciona un marco novedoso con una doble contribución. La primera parte de la tesis se centra en la derivación de aproximaciones cerradas simples pero ajustadas para la capacidad ergódica de las redes de Poisson en escenarios limitados por ruido, por interferencia y por ambos. La capacidad ergódica constituye la figura de mérito más apropiada para caracterizar el rendimiento del sistema, pero no se ha formulado en forma cerrada debido a la complejidad inherente de las expresiones de geometría estocástica disponibles. Para demostrar el potencial de las expresiones simples propuestas, la presente tesis propone un paradigma de conectividad flexible y utiliza parte de las expresiones desarrolladas para optimizar la conectividad de la red. El paradigma de conectividad flexible propuesto explota la configuración de "Downlink Uplink Decoupling" (DUDe), que es un marco que proporciona ventajas sustanciales en términos de incremento de capacidad y reducción de la probabilidad de bloqueo en UDNs e introduce mejoras de conectividad DUDe en la era de 5G. Más adelante, la última parte de la tesis proporciona una formulación analítica de la función de densidad de probabilidad (PDF) de la interferencia agregada en las redes celulares de Poisson. La PDF desarrollada es una aproximación precisa de la PDF exacta que hasta ahora no se ha podido formular analíticamente, a pesar de que se trata de una herramienta crucial para el análisis y la optimización de las redes celulares. La falta de una expresión analítica para la PDF de la interferencia en las redes celulares de Poisson había impuesto el uso de fórmulas complejas, a fin de derivar funciones objetivas apropiadas empleando solo la función generadora de momentos (MGF). Por lo tanto, la presente tesis presenta un marco innovador capaz de simplificar el análisis de las redes celulares de Poisson y así resolver problemas fundamentales relacionados con la optimización y el diseño de la red

Observations on darwiche and Pearl's approach for iterated belief revision

© 2019 International Joint Conferences on Artificial Intelligence. All rights reserved. Notwithstanding the extensive work on iterated belief revision, there is, still, no fully satisfactory solution within the classical AGM paradigm. The seminal work of Darwiche and Pearl (DP approach, for short) remains the most dominant, despite its well-documented shortcomings. In this article, we make further observations on the DP approach. Firstly, we prove that the DP postulates are, in a strong sense, inconsistent with Parikh's relevance-sensitive axiom (P), extending previous initial conflicts. Immediate consequences of this result are that an entire class of intuitive revision operators, which includes Dalal's operator, violates the DP postulates, as well as that the Independence postulate and Spohn's conditionalization are inconsistent with (P). Lastly, we show that the DP postulates allow for more revision polices than the ones that can be captured by identifying belief states with total preorders over possible worlds, a fact implying that a preference ordering (over possible worlds) is an insufficient representation for a belief state

An Epistemological Study of Theory Change

Belief Revision is a well-established field of research that deals with how agents rationally change their minds in the face of new information. The milestone of Belief Revision is a general and versatile formal framework introduced by Alchourrón, Gärdenfors and Makinson, known as the AGM paradigm, which has been, to this date, the dominant model within the field. A main shortcoming of the AGM paradigm, as originally proposed, is its lack of any guidelines for relevant change. To remedy this weakness, Parikh proposed a relevance-sensitive axiom, which applies on splittable theories; i.e., theories that can be divided into syntax-disjoint compartments. The aim of this article is to provide an epistemological interpretation of the dynamics (revision) of splittable theories, from the perspective of Kuhn's inuential work on the evolution of scientific knowledge, through the consideration of principal belief-change scenarios. The whole study establishes a conceptual bridge between rational belief revision and traditional philosophy of science, which sheds light on the application of formal epistemological tools on the dynamics of knowledge

Closed-form capacity bounds for downlink and uplink decoupling

©2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Downlink (DL) and uplink (UL) decoupling (DUDe) is a new architectural paradigm where DL and UL are not constrained to be associated to the same base station (BS). Thus, a user having access to multiple BSs within a dense cellular network can receive the DL traffic from one BS and send its UL traffic through another. Building upon this architectural paradigm, the present paper provides tight analytical bounds in closed form for the UL ergodic capacity that depend solely on the density of the infrastructure. The devised bounds account for the backbone network congestion and the synchronization of the acknowledgments of the decoupled channels. The proposed bounds are compared against extensive numerical simulations demonstrating the tractability and accuracy of the expressions.Peer ReviewedPostprint (author's final draft

Hopf algebras, Hopf monads and derived categories of sheaves

The aim of this thesis is to explain how the theory of Hopf monads on monoidal categories can be used to investigate the Hopf algebra object in a category of which objects are complexes of sheaves on a smooth complex projective variety. In particular, we associate to a smooth complex projective variety X the category of orbits of the bounded derived category of coherent sheaves of the variety under the double shift functor and discuss its structure. We explain why the derived functors on the level of bounded derived categories of coherent sheaves induce functors on the level of categories of orbits. We prove that if the variety is of even dimension and has trivial canonical bundle, then the Serre functor on the orbit category is trivialised. As a direct application of this, we obtain functors on the level of orbit categories which have the same left and right adjoint functor. Next, we work in a general categorical level considering monoidal categories with duals and a pair of adjoint functors defined between them. Moreover, we assume that the right adjoint is a strong symmetric monoidal functor and has a right quasi-inverse which is also a strong monoidal functor. We prove that every such pair of adjoint functors defines an augmented Hopf monad. From the theory of augmented Hopf monads of Brugières, Lack and Virelizier we obtain that these Hopf monads are equivalent to central Hopf algebras. We explain why the orbit category of an even dimensional smooth complex projective variety X with trivial canonical bundle is a symmetric monoidal category with duals. In addition we explain why the diagonal embedding map of the variety gives rise to a pair of adjoint functors on the level orbit categories such that the right adjoint is strong symmetric monoidal and has a right quasi-inverse. As a result, we obtain a Hopf monad on the orbit category and pin down the Hopf algebra with explicit morphisms

Closed form analysis of Poisson cellular networks: a stochastic geometry approach

Ultra dense networks (UDNs) allow for efficient spatial reuse of the spectrum, giving rise to substantial capacity and power gains. In order to exploit those gains, tractable mathematical models need to be derived, allowing for the analysis and optimization of the network operation. In this course, stochastic geometry has emerged as a powerful tool for large-scale analysis and modeling of wireless cellular networks. In particular, the employment of stochastic geometry has been proven instrumental for the characterization of the network performance and for providing significant insights into network densification. Fundamental issues, however, remain open in order to use stochastic geometry tools for the optimization of wireless networks, with the biggest challenge being the lack of tractable closed form expressions for the derived figures of merit. To this end, the present thesis revisits stochastic geometry and provides a novel stochastic geometry framework with a twofold contribution. The first part of the thesis focuses on the derivation of simple, albeit accurate closed form approximations for the ergodic rate of Poisson cellular networks under a noise limited, an interference limited and a general case scenario. The ergodic rate constitutes the most sensible figure of merit for characterizing the system performance, but due to the inherent intractability of the available stochastic geometry frameworks, had not been formulated in closed form hitherto. To demonstrate the potential of the aforementioned tractable expressions with respect to network optimization, the present thesis proposes a flexible connectivity paradigm and employs part of the developed expressions to optimize the network connectivity. The proposed flexible connectivity paradigm exploits the downlink uplink decoupling (DUDe) configuration, which is a promising framework providing substantial capacity and outage gains in UDNs and introduces the DUDe connectivity gains into the 5G era and beyond. Subsequently, the last part of the thesis provides an analytical formulation of the probability density function (PDF) of the aggregate inter-cell interference in Poisson cellular networks. The introduced PDF is an accurate approximation of the exact PDF that could not be analytically formulated hitherto, even though it constituted a crucial tool for the analysis and optimization of cellular networks. The lack of an analytical expression for the PDF of the interference in Poisson cellular networks had imposed the use of intricate formulas, in order to derive sensible figures of merit by employing only the moment generating function (MGF). Hence, the present thesis introduces an innovative framework able to simplify the analysis of Poisson cellular networks to a great extent, while addressing fundamental issues related to network optimization and design.Las redes ultra densas (UDNs) permiten una reutilización espacial del espectro, proporcionando ventajas en términos de mejora de capacidad y ahorro de potencia. Para explotar estas ventajas se necesitan modelos matemáticos simples que permitan el análisis y la optimización de la operación de la red. Por esta razón, la geometría estocástica se ha convertido en una potente herramienta para el análisis de redes celulares. En particular, el empleo de la geometría estocástica ha sido fundamental para la caracterización del rendimiento de la red y para proporcionar información importante sobre la densificación de la misma. Sin embargo, hay problemas fundamentales que deben resolverse para utilizar estas herramientas de geometría estocástica, siendo el mayor desafío la falta de expresiones simples de forma cerrada para las funciones objetivo de interés. Por este motivo, la presente tesis examina la geometría estocástica y proporciona un marco novedoso con una doble contribución. La primera parte de la tesis se centra en la derivación de aproximaciones cerradas simples pero ajustadas para la capacidad ergódica de las redes de Poisson en escenarios limitados por ruido, por interferencia y por ambos. La capacidad ergódica constituye la figura de mérito más apropiada para caracterizar el rendimiento del sistema, pero no se ha formulado en forma cerrada debido a la complejidad inherente de las expresiones de geometría estocástica disponibles. Para demostrar el potencial de las expresiones simples propuestas, la presente tesis propone un paradigma de conectividad flexible y utiliza parte de las expresiones desarrolladas para optimizar la conectividad de la red. El paradigma de conectividad flexible propuesto explota la configuración de "Downlink Uplink Decoupling" (DUDe), que es un marco que proporciona ventajas sustanciales en términos de incremento de capacidad y reducción de la probabilidad de bloqueo en UDNs e introduce mejoras de conectividad DUDe en la era de 5G. Más adelante, la última parte de la tesis proporciona una formulación analítica de la función de densidad de probabilidad (PDF) de la interferencia agregada en las redes celulares de Poisson. La PDF desarrollada es una aproximación precisa de la PDF exacta que hasta ahora no se ha podido formular analíticamente, a pesar de que se trata de una herramienta crucial para el análisis y la optimización de las redes celulares. La falta de una expresión analítica para la PDF de la interferencia en las redes celulares de Poisson había impuesto el uso de fórmulas complejas, a fin de derivar funciones objetivas apropiadas empleando solo la función generadora de momentos (MGF). Por lo tanto, la presente tesis presenta un marco innovador capaz de simplificar el análisis de las redes celulares de Poisson y así resolver problemas fundamentales relacionados con la optimización y el diseño de la red.Postprint (published version

Evaluation of the efficiency of conductor coverings for electrostatical shielding and dissipation of static charge in an insulating polymer

Neste trabalho foram processadas tintas base epóxi pigmentadas com polianilina (PAni), que é um polímero intrinsecamente condutor, em diferentes composições. O objetivo foi avaliar a eficiência dos revestimentos condutores em um substrato isolante como o copolímero Acrinonitrila-Butadieno-Estireno (ABS) para blindagem e dissipação da carga estática. Foi realizada uma investigação por análise de infravermelho no revestimento da mistura entre PAni e epóxi, para verificar se houve reações que resultassem em novas ligações químicas. Foi avaliada a distribuição das fibras da PAni e a rugosidade dos revestimentos através de um microscópio eletrônico de varredura e um rugosímetro para analisar a influência dessas características dos filmes na condutividade final das amostras. As medições da condutividade foram feitas por um ensaio em quatro pontas e desse modo foi avaliada a influência da degradação na condutância desses revestimentos. Comparando com indicadores estabelecidos em outros trabalhos se constatou a possibilidade do uso dos revestimentos pigmentados com PAni para blindagem e dissipação da carga estática do material não condutor, que é o copolímero ABS.In this work, epoxy base paints pigmented with polyaniline (PAni), which is an intrinsically conductive polymer, were accomplished in different compositions. The objective was to evaluate an efficient conductive coating on an insulating substrate, such as the Acrylonitrile-Butadiene-Styrene (ABS), for shielding and dissipation of the static charge. An investigation was performed by infrared analysis on the coating of the mixture between PAni and epoxy, to verify if there were reactions that resulted in new chemical bonds. The distribution of the PAni fibers and the roughness of the coatings were evaluated by scanning electron microscopy and rugosimetry to analyze the characteristics of the conductive inks in the samples. Conductivity measurements were carried out at four points and the influence of the degradation on the conductance of these coatings was evaluated. Comparing with the indicators established in other studies, it was possible to use conductive coatings pigmented with PAni for shielding and dissipation of the static load of nonconductive materials

Um Olhar Sobre os Processos de Acidentes de Trabalho no Rio Grande do Sul (1934-1950)

O trabalho pretende expor uma pesquisa recentemente iniciada que faz uso de uma fonte documental inédita na história operária do Rio Grande do Sul: os processos de acidentes de trabalho, no estado, no período de 1934 a 1950. Busca-se historicizar estes processos no contexto das leis trabalhistas da era Vargas, caracterizar o discurso jurídico do período a respeito destes acidentes, bem como trazer informações sobre as condições de vida e de saúde dos operários que reivindicam este seu direito de indenização