Techn. Universiẗat, Diss., 2003--Berlin.

No description available.

Cette thèse traite de trois modèles de géométrie aléatoire: les mosaïques de Poisson-Voronoi, les mosaïques poissoniennes d'hyperplans et le modèle de fissuration unidirectionnel de Rényi-Widom. Nous montrons tout d'abord l'équivalence entre les deux approches historiques pour l'étude statistique des mosaïques: la convergence des moyennes ergodiques et la définition au sens de Palm de la cellule typique. Nous donnons ensuite en dimension deux la loi du nombre de sommets de la cellule typique et conditionnellement à ce nombre, les lois des positions des frontières, de l'aire et du périmètre. De plus, nous explicitons la loi conjointe des rayons des disques centrés en l'origine inscrit dans (resp. circonscrit à) la cellule typique et nous en déduisons le caractère circulaire des "grandes cellules". Dans le cas Poisson-Voronoi, nous relions en toute dimension la fonction spectrale de la cellule typique au pont brownien, ce qui permet en particulier d'estimer asymptotiquement la loi de la première valeur propre en dimension deux. Dans le cas des mosaïques poissoniennes d'hyperplans, nous exploitons les techniques de Palm pour en déduire une construction explicite en toute dimension de la cellule typique à partir de sa boule inscrite et de son simplexe circonscrit. Une preuve rigoureuse d'un résultat de R. E. Miles lorsqu'on épaissit les hyperplans est également donnée. Par ailleurs, nous modélisons un phénomène de fissuration par un processus unidimensionnel stationnaire dont nous calculons la loi de la distance inter-fissures typique. Nous montrons en outre que les points successifs sont ceux d'un processus de renouvellement conditionné explicite.

In an effort to minimize the harmful effects of intracellular ice formation (IIF) during cryopreservation of confluent tissues, computer simulations based on Monte Carlo methods were performed to predict the probability of IIF in confluent monolayers during various freezing procedures. To overcome the prohibitive computational costs of such simulations for large tissues, the well-known Johnson-Mehl-Avrami (JMA) model of crystallization kinetics was implemented as a continuum approximation of IIF in tissues. This model, which describes nucleation, growth, and impingement of crystals in a supercooled melt, is analogous to the process of intracellular ice formation and propagation in biological tissues. Based on the work of Weinberg and Kapral (1989), the JMA model was modified to account for finite-size effects, and was shown to predict accurately the results of freezing simulations in 1-D tissue constructs, for various propagation rates and tissue sizes. An initial analysis of IIF kinetics in 2-D tissues is also presented. The probability of IIF in 2-D liver tissue was measured experimentally during freezing of HepG2 cells cultured in monolayers, and compared to Monte Carlo simulations and predictions of the continuum model. The Avrami coefficient and exponent for IIF in HepG2 tissue were estimated to be k = 0.19 and n = 0.45.

Owing to its ability to improve both spectral and energy efficiency of wireless networks, massive multiple-input multiple-output (mMIMO) has become one of the key enablers of the fifth-generation (5G) and beyond communication systems. For successful integration of this promising physical layer technique in the upcoming cellular standards, it is essential to have a comprehensive understanding of its network-level performance. Over the last decade, stochastic geometry has been instrumental in obtaining useful system design insights of wireless networks through accurate and tractable theoretical analysis. Hence, it is only natural to consider modeling and analyzing the mMIMO systems using appropriate statistical constructs from the stochastic geometry literature and gain insights for its future implementation. With this broader objective in mind, we first focus on modeling a cellular mMIMO network that uses fractional pilot reuse to mitigate the sole performance-limiting factor of mMIMO networks, namely, pilot contamination. Leveraging constructs from the stochastic geometry literature, such as Johnson-Mehl cells, we derive analytical expressions for the uplink (UL) signal-to-interference-and-noise ratio (SINR) coverage probability and average spectral efficiency for a random user. From our system analysis, we present a partitioning rule for the number of pilot sequences to be reserved for the cell-center and cell-edge users that improves the average cell-edge user spectral efficiency while achieving similar cell-center user spectral efficiency with respect to unity pilot reuse. In addition, using the analytical approach developed for the cell-center user performance evaluation, we study the performance of a small cell system where user and base station (BS) locations are coupled. The impact of distance-dependent UL power control on the performance of an mMIMO network with unity pilot reuse is analyzed and subsequent system design guidelines are also presented. Next, we focus on the performance analysis of the cell-free mMIMO network, which is a distributed implementation of the mMIMO system that leads to the second and third contributions of this dissertation. Similar to the cellular counterpart, the cell-free systems also suffer from pilot contamination due to the reuse of pilot sequences throughout the network. Inspired by a hardcore point process known as the random sequential adsorption (RSA) process, we develop a new distributed pilot assignment algorithm that mitigates the effect of pilot contamination by ensuring a minimum distance among the co-pilot users. This pilot assignment scheme leads to the construction of a new point process, namely the multilayer RSA process. We study the statistical properties of this point process both in one and two-dimensional spaces by deriving approximate but accurate expressions for the density and pair correlation functions. Leveraging these new results, for a cell-free network with the proposed RSA-based pilot assignment scheme, we present an analytical approach that determines the minimum number of pilots required to schedule a user with probabilistic guarantees. In addition, to benchmark the performance of the RSA-based scheme, we propose two optimization-based centralized pilot allocation schemes using linear programming principles. Through extensive numerical simulations, we validate the efficacy of the distributed and scalable RSA-based pilot assignment scheme compared to the proposed centralized algorithms. Apart from pilot contamination, another impediment to the performance of a cell-free mMIMO is limited fronthaul capacity between the baseband unit and the access points (APs). In our fourth contribution, using appropriate stochastic geometry-based tools, we model and analyze the downlink of such a network for two different implementation scenarios. In the first scenario, we consider a finite network where each AP serves all the users in the network. In the second scenario, we consider an infinite network where each user is served by a few nearby APs in order to limit the load on fronthaul links. From our analyses, we observe that for the finite network, the achievable average system sum-rate is a strictly quasi-concave function of the number of users in the network, which serves as a key guideline for scheduler design for such systems. Further, for the user-centric architecture, we observe that there exists an optimal number of serving APs that maximizes the average user rate. The fifth and final contribution of this dissertation focuses on the potential improvement that is possible by the use of mMIMO in citizen broadband radio service (CBRS) spectrum sharing systems. As a first concrete step, we present comprehensive modeling and analysis of this system with omni-directional transmissions. Our model takes into account the key guidelines by the Federal Communications Commission for co-existence between licensed and unlicensed networks in the 3.5 GHz CBRS frequency band. Leveraging the properties of the Poisson hole process and Matern hardcore point process of type II, a.k.a. ghost RSA process, we analytically characterize the impact of different system parameters on various performance metrics such as medium access probability, coverage probability, and area spectral efficiency. Further, we provide useful system design guidelines for successful co-existence between these networks. Building upon this omni-directional model, we also characterize the performance benefits of using mMIMO in such a spectrum sharing network. / Doctor of Philosophy / The emergence of cloud-based video and audio streaming services, online gaming platforms, instantaneous sharing of multimedia contents (e.g., photos, videos) through social networking platforms, and virtual collaborative workspace/meetings require the cellular communication networks to provide high data-rate as well as reliable and ubiquitous connectivity. These constantly evolving requirements can be met by designing a wireless network that harmoniously exploits the symbiotic co-existence among different types of cutting-edge wireless technologies. One such technology is massive multiple-input multiple-output (mMIMO), whose core idea is to equip the cellular base stations (BSs) with a large number of antennas that can be leveraged through appropriate signal processing algorithms to simultaneously accommodate multiple users with reduced network interference. For successful deployment of mMIMO in the upcoming cellular standards, i.e., fifth-generation (5G) and beyond systems, it is necessary to characterize its performance in a large-scale wireless network taking into account the inherent spatial randomness in the BS and user locations. To achieve this goal, in this dissertation, we propose different statistical methods for the performance analysis of mMIMO networks using tools from stochastic geometry, which is a field of mathematics related to the study of random patterns of points. One of the major deployment issues of mMIMO systems is pilot contamination, which is a form of coherent network interference that degrades user performance. The main reason behind pilot contamination is the reuse of pilot sequences, which are a finite number of known signal waveforms used for channel estimation between a user and its serving BS. Further, the effect of pilot contamination is more severe for the cell-edge users, which are farther from their own BSs. An efficient scheme to mitigate the effect of pilot contamination is fractional pilot reuse (FPR). However, the efficiency of this scheme depends on the pilot partitioning rule that decides the fraction of total pilot sequences that should be used by the cell-edge users. Using appropriate statistical constructs from the stochastic geometry literature, such as Johnson-Mehl cells, we present a partitioning rule for efficient implementation of the FPR scheme in a cellular mMIMO network. Next, we focus on the performance analysis of the cell-free mMIMO network. In contrast to the cellular network, where each user is served by a single BS, in a cell-free network each user can be served by multiple access points (APs), which have less complex hardware compared to a BS. Owing to this cooperative and distributed implementation, there are no cell-edge users. Similar to the cellular counterpart, the cell-free systems also suffer from pilot contamination due to the reuse of pilot sequences throughout the network. Inspired by a hardcore point process known as the random sequential adsorption (RSA) process, we develop a new distributed pilot assignment algorithm that mitigates the effect of pilot contamination by ensuring a minimum distance among the co-pilot users. Further, we show that the performance of this distributed pilot assignment scheme is appreciable compared to different centralized pilot assignment schemes, which are algorithmically more complex and difficult to implement in a network. Moreover, this pilot assignment scheme leads to the construction of a new point process, namely the multilayer RSA process. We derive the statistical properties of this point process both in one and two-dimensional spaces. Further, in a cell-free mMIMO network, the APs are connected to a centralized baseband unit (BBU) that performs the bulk of the signal processing operations through finite capacity links, such as fiber optic cables. Apart from pilot contamination, another implementational issue associated with the cell-free mMIMO systems is the finite capacity of fronthaul links that results in user performance degradation. Using appropriate stochastic geometry-based tools, we model and analyze this network for two different implementation scenarios. In the first scenario, we consider a finite network where each AP serves all the users in the network. In the second scenario, we consider an infinite network where each user is served by a few nearby APs. As a consequence of this user-centric implementation, for each user, the BBU only needs to communicate with fewer APs thereby reducing information load on fronthaul links. From our analyses, we propose key guidelines for the deployment of both types of scenarios. The type of mMIMO systems that are discussed in this work will be operated in the sub-6 GHz frequency range of the electromagnetic spectrum. Owing to the limited availability of spectrum resources, usually, spectrum sharing is encouraged among different cellular operators in such bands. One such example is the citizen broadband radio service (CBRS) spectrum sharing systems proposed by the Federal Communications Commission (FCC). The final contribution of this dissertation focuses on the potential improvement that is possible by the use of mMIMO in the CBRS systems. As our first step, using tools from stochastic geometry, we model and analyze this system with a single antenna at the BSs. In our model, we take into account the key guidelines by the FCC for co-existence between licensed and unlicensed operators. Leveraging properties of the Poisson hole process and hardcore process, we provide useful theoretical expressions for different performance metrics such as medium access probability, coverage probability, and area spectral efficiency. These results are used to obtain system design guidelines for successful co-existence between these networks. We further highlight the potential improvement in the user performance with multiple antennas at the unlicensed BS.

Already regarded as one of the top teams in Negro League baseball, the Kansas City Monarchs became known as a powerhouse unit in the 1930s and 40s. They rolled into towns with lights, amazing athletes, and competitive play. They won championship after championship during these years as Kansas City baseball fans strongly supported them. As they became an integral part of the city, the Monarchs' success, open-seating policy, and jazzy home openers fostered a large following of mixed-race fans. The local black newspaper, the Kansas City Call, held them up on a pedestal, while sportswriters for the mainstream Kansas City Star/Times downplayed the Monarchs' accomplishments and influence in the community. This thesis focuses on the relationship the Call had with the best team in black baseball through the context of its treatment of games, players, league officials, and team owners, as well as other patterns and tactics. Analysis of the Star/Times coverage is also considered to show variances in coverage between one city's race-divided newspapers. Negro League baseball and the African American newspapers that covered the teams grew out of and illustrated the segregation laws and prejudices feelings that existed in the United States during most of the twentieth century. Over time, especially when the sports world moved into the post-integration period, the Call's bolstering of the Monarchs deteriorated as the paper's promotion of democracy steered its sportswriters away from a baseball organization that symbolized segregation. The different types of coverage by the Call throughout the twenty-year study can be described as all-out promotion, balance, and abandonment. In the 1950s nostalgia and conflict existed, as the Call's sportswriters became torn on how to cover a team that was once the pride of the black community, but now represented inequality. In an attempt to remedy this torment, the Call tried to convince black baseball officials to remove the “Negro League” stigma by signing players of all races in order to mirror the more democratic Major Leagues. The white press, meanwhile, ignored the bigger issues of black baseball as one Negro League team after another died in the 1950s. The Star/Times peripheral coverage of the Monarchs provides context to the social issues and discriminatory practices at play in Missouri. As this thesis outlines the coverage of the Monarchs through the Black and White newspapers of Kansas City, previous research is substantiated and challenged to provide a fuller account of Jim Crow's effects.