Nonparametric Message Passing Methods for Cooperative Localization and Tracking

The objective of this thesis is the development of cooperative localization and tracking algorithms using nonparametric message passing techniques. In contrast to the most well-known techniques, the goal is to estimate the posterior probability density function (PDF) of the position of each sensor. This problem can be solved using Bayesian approach, but it is intractable in general case. Nevertheless, the particle-based approximation (via nonparametric representation), and an appropriate factorization of the joint PDFs (using message passing methods), make Bayesian approach acceptable for inference in sensor networks. The well-known method for this problem, nonparametric belief propagation (NBP), can lead to inaccurate beliefs and possible non-convergence in loopy networks. Therefore, we propose four novel algorithms which alleviate these problems: nonparametric generalized belief propagation (NGBP) based on junction tree (NGBP-JT), NGBP based on pseudo-junction tree (NGBP-PJT), NBP based on spanning trees (NBP-ST), and uniformly-reweighted NBP (URW-NBP). We also extend NBP for cooperative localization in mobile networks. In contrast to the previous methods, we use an optional smoothing, provide a novel communication protocol, and increase the efficiency of the sampling techniques. Moreover, we propose novel algorithms for distributed tracking, in which the goal is to track the passive object which cannot locate itself. In particular, we develop distributed particle filtering (DPF) based on three asynchronous belief consensus (BC) algorithms: standard belief consensus (SBC), broadcast gossip (BG), and belief propagation (BP). Finally, the last part of this thesis includes the experimental analysis of some of the proposed algorithms, in which we found that the results based on real measurements are very similar with the results based on theoretical models.

Diseño y síntesis de materiales nanoestructurados basados en aluminatos de estroncio con propiedades fotoluminiscentes

Durante la última década, se han llevado acabo numeroso estudios sobre la síntesis de materiales fotoluminiscentes sub-micrónicos, en gran medida, al amplio número de aplicaciones que demandan este tipo de materiales. En concreto dentro de los materiales fosforescentes o también denominados materiales con una prolongada persistencia de la luminiscencia, los estudios se han enfocado en la matriz de SrAl2O4 dopada con Europio (Eu2+) y Disprosio (Dy3+) dado que tiene mayor estabilidad y persistencia de la fosforescencia con respecto a otras matrices. Estos materiales se emplean mayoritariamente en pinturas luminiscentes, tintas, señalización de seguridad pública, cerámicas, relojes, textiles y juguetes fosforescentes. Dado al amplio campo de aplicación de los SrAl2O4:Eu, Dy, se han investigado múltiples rutas de síntesis como la ruta sol-gel, la síntesis hidrotermal, la síntesis por combustión, la síntesis láser y la síntesis en estado sólido con el fin de desarrollar un método eficiente y que sea fácilmente escalable. Sin embargo, en la actualidad el método que se emplea para el procesamiento a nivel industrial de los materiales basados en aluminato de estroncio es la síntesis por estado sólido, que requiere de temperaturas de entre 1300 a 1900oC y largos tiempos de procesamiento. Además el material obtenido tiene un tamaño de partícula de 20 a 100 μm; siendo este tamaño restrictivo para el empleo de este tipo de material en determinadas aplicaciones. Por tanto, el objetivo de este trabajo es el desarrollo de nuevas estrategias que solventen las actuales limitaciones. Dentro de este marco se plantean una serie de objetivos específicos: Estudio de los parámetros que gobiernan los procesos de reducción del tamaño de partícula mediante molienda y su relación en la respuesta fotoluminiscente. Estudio de la síntesis por combustión de SrAl2O4:Eu, Dy, evaluando el efecto de la temperatura y la cantidad de combustible (urea) en el proceso para la obtención de partículas cristalinas minimizando la presencia de fases secundarias. Desarrollo de nuevas rutas de síntesis de SrAl2O4:Eu, Dy empleando el método de sales fundidas. Determinación de los mecanismos de reacción en presencia de la sal fundida en función de los parámetros de proceso que comprende la relación de sales y reactivos, la naturaleza de la alúmina y su tamaño, la temperatura y atmósfera de tratamiento. Mejora de la eficiencia de los procesos de síntesis para obtener productos con propiedades finales óptimas en procesos factibles industrialmente para su transferencia tecnológica. Es este trabajo han sido evaluados los efectos de diferentes procesos de molienda para la reducción del tamaño de partícula del material de SrAl2O4:Eu, Dy comercial. En el proceso de molienda en medio húmedo por atrición se observa la alteración de la estructura cristalina del material debido a la reacción de hidrólisis generada incluso empleando como medio líquido etanol absoluto. Con el fin de solventar las desventajas de la molienda en medio húmedo se llevo a cabo un estudio de la molturación en seco del material. La molturación en seco de alta energía reduce significativamente el tamaño medio de partícula. Sin embargo, procesos de molienda superiores a una duración de 10 minutos ocasionan un aumento del estado de aglomeración de las partículas y disminuyen drásticamente la respuesta fotoluminiscente del material. Por tanto, se lleva a cabo un proceso de molienda en seco de baja energía. Mediante este método se consigue reducir el tamaño medio de partícula, d50=2.8 μm, y se mejora la homogeneidad de la distribución del tamaño de partícula evitando la amorfización del material. A partir de los resultados obtenidos mediante difracción de rayos X y microscopia electrónica de barrido se infiere que la disminución de la intensidad de la fotoluminiscencia después de la molienda en seco de alta energía con respecto al material inicial se debe principalmente a la reducción del tamaño de cristalito. Se observan menores variaciones en la intensidad de la fotoluminiscencia cuando se emplea un método de molienda de baja de energía ya que en estos procesos se preserva el dominio cristalino y se reduce la amorfización significativamente. Estos resultados corroboran que la intensidad de la fotoluminiscencia y la persistencia de la luminiscencia de los materiales de SrAl2O4:Eu2+, Dy3+ dependen extrínsecamente de la morfología de las partículas, del tamaño de partícula, el tamaño de grano, los defectos superficiales e intrínsecamente del tamaño de cristalito. Siendo las características intrínsecas las que dominan con respecto a las extrínsecas y por tanto tienen mayor relevancia en la respuesta fotoluminiscente. Mediante síntesis por combustión se obtuvieron láminas nanoestructuradas de SrAl2O4:Eu, Dy de ≤1 μm de espesor. La cantidad de combustible, urea, en la reacción influye significativamente en la formación de determinadas fases cristalinas. Para la síntesis del material de SrAl2O4:Eu, Dy es necesario incluir un contenido de urea mayor que el estequiométrico (siendo m=1 la relación estequiométrica). La incorporación de un exceso de urea (m>1) requiere de la presencia de un agente oxidante interno, HNO3, para que la reacción tenga lugar. El empleo de un mayor contenido de urea como combustible permite una quelación efectiva de los cationes en el sistema y la creación de las condiciones reductoras para obtener un material de mayor cristalinidad y con mejores propiedades fotoluminiscentes. El material de SrAl2O4:Eu, Dy sintetizado a una temperatura de ignición de 600oC tiene un tamaño medio 5-25 μm con un espesor de ≤1 μm. Mediante procesos de molturación en seco de baja energía es posible disminuir el tamaño medio de partícula ≈2 μm y homogenizar la distribución del tamaño de partícula pero hay un deterioro asociado de la respuesta luminiscente. Sin embargo, se puede mejorar la respuesta fotoluminiscente empleando un tratamiento térmico posterior a 900oC N2-H2 durante 1 hora que no supone un aumento del tamaño de partícula pero si permite aumentar el tamaño de cristalito y la reducción del Eu3+ a Eu2+. Con respecto a la respuesta fotoluminiscente, se obtiene valores de la intensidad de la fotoluminiscencia entre un 35%-21% con respecto a la intensidad de un material comercial de referencia. Además la intensidad inicial del decaimiento de la fosforescencia es un 20% de la intensidad del material de referencia. Por tanto, teniendo en cuenta estos resultados, es necesario explorar otros métodos de síntesis para la obtención de los materiales bajo estudio. Por esta razón, en este trabajo se desarrollo una ruta de síntesis novedosa para sintetizar SrAl2O4:Eu, Dy mediante el método de sales fundidas para la obtención de materiales de gran cristalinidad con tamaños de cristalito del orden nanométrico. Se empleo como sal fundente la mezcla eutéctica de NaCl y KCl, denominada (NaCl-KCl)e. La principal ventaja de la incorporación de la mezcla es el incremento la reactividad del sistema, reduciendo la temperatura de formación del SrAl2O4 y la duración del tratamiento térmico en comparación con la síntesis en estado sólido. La formación del SrAl2O4 es favorecida ya que se aumenta la difusión de los cationes de Sr2+ en el medio líquido. Se emplearon diferentes tipos de Al2O3 para evaluar el papel del tamaño de partícula y su naturaleza en la reacción asistida por sales fundidas y por tanto en la morfología y propiedades del producto final. Se obtuvieron partículas de morfología pseudo-esférica de tamaño ≤0.5 μm al emplear como alúmina precursora partículas sub-micrónicas ( 0.5 μm Al2O3, 0.1 μm Al2 O3 y γ-Al2O3). El mecanismo de reacción que tiene lugar se asocia a procesos de disolución-precipitación que dominan al emplear partículas de alúmina pequeñas y reactivas. Mientras al emplear una alúmina de 6 μm Al2O3 prevalecen los procesos de crecimiento cristalino siguiendo un patrón o plantilla debido a la menor reactividad del sistema. La nucleación y crecimiento de nanocristales de SrAl2O4:Eu, Dy se genera sobre la superficie de la alúmina que actúa como soporte. De esta forma se desarrolla una estructura del tipo coraza-núcleo («core-shell» en inglés) donde la superficie externa está formada por los cristales fosforescentes de SrAl2O4 y el núcleo está formado por alúmina. Las partículas obtenidas tienen una respuesta fotoluminiscente diferente en función de la morfología final obtenida. La optimización de la relación Al2O3/SrO del material de SrAl2O4:Eu, Dy sintetizado a partir de la alúmina de 6 μm permite reducir las fases secundarias y la concentración de dopantes manteniendo la respuesta fotoluminiscente. Comparativamente con un material comercial de SrAl2O4:Eu, Dy de referencia, se han alcanzado valores de la intensidad de la emisión de hasta el 90% y de la intensidad inicial de las curvas de decaimiento de la luminiscencia de un 60% para el material sintetizado por sales fundidas que tiene un tamaño medio ≤ 10μm. Por otra parte, es necesario tener en cuenta que el SrAl2O4 tiene dos polimorfos, la fase monoclínica que es estable a temperaturas inferiores a 650oC y la fase hexagonal, fase de alta temperatura, estable a temperaturas superiores de 650oC. Se ha determinado que fase monoclínica presenta propiedades luminiscentes, sin embargo existen discordancias a cerca de las propiedades luminiscentes de la fase hexagonal. Mediante la síntesis por sales fundidas es posible estabilizar la fase hexagonal empleando como alúmina precursora γ-Al2O3 y un exceso de Al2O3 (Al2O3/SrO:2). La estabilización de la fase hexagonal a temperatura ambiente se produce cuando el tamaño de los cristales de SrAl2O4 es ≤20 nm. Además se observó que la fase hexagonal presenta respuesta fotoluminiscente. El diseño de materiales de SrAl2O4:Eu,Dy nanoestructurados permite modular la morfología del material y por tanto la intensidad de la de la fotoluminiscencia y la persistencia de la luminiscencia. La disminución de los materiales precursores, la temperatura y el tiempo de tratamiento significa la reducción de los costes económicos del material. De ahí la viabilidad de los materiales de SrAl2O4:Eu,Dy obtenidos mediante los procesos de síntesis propuestos en esta memoria de tesis para su posterior escalado industrial. ABSTRACT The synthesis of sub-micron photoluminescent particles has been widely studied during the past decade because of the promising industrial applications of these materials. A large number of matrices has been developed, being SrAl2O4 host doped with europium (Eu2+) and dysprosium (Dy3+) the most extensively studied, because of its better stability and long-lasting luminescence. These functional inorganic materials have a wide field of application in persistent luminous paints, inks and ceramics. Large attention has been paid to the development of an efficient method of preparation of SrAl2O4 powders, including solgel method, hydrothermal synthesis, laser synthesis, combustion synthesis and solid state reaction. Many of these techniques are not compatible with large-scale production and with the principles of sustainability. Moreover, industrial processing of highly crystalline powders usually requires high synthesis temperatures, typically between 1300 a 1900oC, with long processing times, especially for solid state reaction. As a result, the average particle size is typically within the 20-100 μm range. This large particle size is limiting for current applications that demand sub-micron particles. Therefore, the objective of this work is to develop new approaches to overcome these limitations. Within this frame, it is necessary to undertake the following purposes: To study the parameters that govern the particle size reduction by milling and their relation with the photoluminescence properties. To obtain SrAl2O4:Eu, Dy by combustion synthesis, assessing the effect of the temperature and the amount of fuel (urea) to synthesize highly crystalline particles minimizing the presence of secondary phases. To develop new synthesis methods to obtain SrAl2O4:Eu, Dy powders. The molten salt synthesis has been proposed. As the method is a novel route, the reaction mechanism should be determine as a function of the salt mixture, the ratio of the salt, the kind of Al2O3 and their particle size and the temperature and the atmosphere of the thermal treatment. To improve the efficiency of the synthesis process to obtain SrAl2O4:Eu, Dy powders with optimal final properties and easily scalable. On the basis of decreasing the particle size by using commercial product SrAl2O4:Eu2+, Dy3+ as raw material, the effects of different milling methods have been evaluated. Wet milling can significantly alter the structure of the material through hydrolysis reaction even in ethanol media. For overcoming the drawbacks of wet milling, a dry milling-based processes are studied. High energy dry milling process allows a great reduction of the particle size, however milling times above 10 min produce agglomeration and accelerates the decrease of the photoluminescence feature. To solve these issues the low energy dry milling process proposed effectively reduces the particle size to d50=2.8 μm, and improves the homogeneity avoiding the amorphization in comparison with previous methods. The X-ray diffraction and scanning electron microscope characterization allow to infer that the large variations in PL (Photoluminescence) values by high energy milling process are a consequence mainly of the crystallite size reduction. The lesser variation in PL values by low energy milling proces is related to the coherent crystalline domain preservation and the unnoticeable amorphization. These results corroborate that the photoluminescence intensity and the persistent luminescence of the SrAl2O4:Eu2+, Dy3+ powders depend extrinsically on the morphology of the particles such as particle size, grain size, surface damage and intrinsically on the crystallinity (crystallite size); being the intrinsically effects the ones that have a significant influence on the photoluminescent response. By combustion method, nanostructured SrAl2O4:Eu2+, Dy3+ sheets with a thickness ≤1 μm have been obtained. The amount of fuel (urea) in the reaction has an important influence on the phase composition; urea contents larger than the stoichiometric one require the presence of an oxidant agent such as HNO3 to complete the reaction. A higher amount of urea (excess of urea: denoted m>1, being m=1 the stoichiometric composition) including an oxidizing agent produces SrAl2O4:Eu2+,Dy3+ particles with persistent luminescence due to the effective chelation of the cations and the creation of suitable atmospheric conditions to reduce the Eu3+ to Eu2+. Therefore, optimizing the synthesis parameters in combustion synthesis by using a higher amount of urea and an internal oxidizing agent allows to complete the reaction. The amount of secondary phases can be significantly reduced and the photoluminescence response can be enhanced. This situation is attributed to a higher energy that improves the crystallinity of the powders. The powders obtained have a particle size c.a. 5-25 μm with a thickness ≤1 μm and require relatively low ignition temperatures (600oC). It is possible to reduce the particle size by a low energy dry milling but this process implies the decrease of the photoluminescent response. However, a post-thermal treatment in a reducing atmosphere allows the improvement of the properties due to the increment of crystallinity and the reduction of Eu3+ to Eu2+. Compared with the powder resulted from solid state method (commercial reference: average particle size, 20 μm and heterogeneous particle size distribution) the emission intensity of the powder prepared by combustion method achieve the values between 35% to 21% of the reference powder intensity. Moreover, the initial intensity of the decay curve is 20% of the intensity of the reference powder. Taking in account these results, it is necessary to explore other methods to synthesize the powders For that reason, an original synthetic route has been developed in this study: the molten salt assisted process to obtain highly crystalline SrAl2O4 powders with nanometric sized crystallites. The molten salt was composed of a mixture of NaCl and KCl using a 0.5:0.5 molar ratio (eutectic mixture hereafter abbreviated as (NaCl-KCl)e). The main advantages of salt addition is the increase of the reaction rate, the significant reduction of the synthesis temperature and the duration of the thermal treatment in comparison with classic solid state method. The SrAl2O4 formation is promoted due to the high mobility of the Sr2+ cations in the liquid medium. Different kinds of Al2O3 have been employed to evaluate the role of the size and the nature of this precursor on the kinetics of reaction, on the morphology and the final properties of the product. The SrAl2O4:Eu2+, Dy3+ powders have pseudo-spherical morphology and particle size ≤0.5 μm when a sub-micron Al2O3 ( 0.5 μm Al2O3, 0.1 μm Al2O3 and γ-Al2O3) has been used. This can be attributed to a higher reactivity in the system and the dominance of dissolution-precipitation mechanism. However, the use of larger alumina (6 μm Al2O3) modifies the reaction pathway leading to a different reaction evolution. More specifically, the growth of SrAl2O4 sub-micron particles on the surface of hexagonal platelets of 6μm Al2O3 is promoted. The particles retain the shape of the original Al2O3 and this formation process can be attributed to a «core-shell» mechanism. The particles obtained exhibit different photoluminescent response as a function of the final morphology of the powder. Therefore, through this study, it has been elucidated the reaction mechanisms of SrAl2O4 formation assisted by (NaCl-KCl)e that are governed by the diffusion of SrCO3 and the reactivity of the alumina particles. Optimizing the Al2O3/SrO ratio of the SrAl2O4:Eu, Dy powders synthesized with 6 μm Al2O3 as a precursor, the secondary phases and the concentration of dopant needed can be reduced keeping the photoluminescent response of the synthesized powder. Compared with the commercial reference powder, up to 90% of the emission intensity of the reference powder has been achieved for the powder prepared by molten salt method using 6μm Al2O3 as alumina precursor. Concerning the initial intensity of the decay curve, 60% of the initial intensity of the reference powder has been obtained. Additionally, it is necessary to take into account that SrAl2O4 has two polymorphs: monoclinic symmetry that is stable at temperatures below 650oC and hexagonal symmetry that is stable above this temperature. Monoclinic phase shows luminescent properties. However, there is no clear agreement on the emission of the hexagonal structure. By molten salt, it is possible to stabilize the hexagonal phase of SrAl2O4 employing an excess of Al2O3 (Al2O3/SrO: 2) and γ-Al2O3 as a precursor. The existence of nanometric crystalline domains with lower size (≤20 nm) allows the stabilization of the hexagonal phase. Moreover, it has been evidenced that the hexagonal polymorph exhibits photoluminescent response. To sum up, the design of nanostructured SrAl2O4:Eu2+, Dy3+ materials allows to obtain different morphologies and as consequence different photoluminescent responses. The reduction of temperature, duration of the thermal treatment and the precursors materials needed imply the decrease of the economic cost of the material. Therefore, the viability, suitability and scalability of the synthesis strategy developed in this work to process SrAl2O4:Eu2+, Dy3+ are demonstrated.

A secret sharing scheme based on exponentiation in Galois fields

To provide more efficient and flexible alternatives for the applications of secret sharing schemes, this paper describes a threshold sharing scheme based on exponentiation of matrices in Galois fields. A significant characteristic of the proposed scheme is that each participant has to keep only one master secret share which can be used to reconstruct different group secrets according to the number of threshold values.

Operators Factoring through Banach Lattices and Ideal Norms

A new, unified presentation of the ideal norms of factorization of operators through Banach lattices and related ideal norms is given.

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

Cumulon: Simplified Matrix-Based Data Analytics in the Cloud

Cumulon is a system aimed at simplifying the development and deployment of statistical analysis of big data in public clouds. Cumulon allows users to program in their familiar language of matrices and linear algebra, without worrying about how to map data and computation to specific hardware and cloud software platforms. Given user-specified requirements in terms of time, monetary cost, and risk tolerance, Cumulon automatically makes intelligent decisions on implementation alternatives, execution parameters, as well as hardware provisioning and configuration settings -- such as what type of machines and how many of them to acquire. Cumulon also supports clouds with auction-based markets: it effectively utilizes computing resources whose availability varies according to market conditions, and suggests best bidding strategies for them. Cumulon explores two alternative approaches toward supporting such markets, with different trade-offs between system and optimization complexity. Experimental study is conducted to show the efficiency of Cumulon's execution engine, as well as the optimizer's effectiveness in finding the optimal plan in the vast plan space.

Vermiculitas tratadas quimicamente na obtenção de sólidos microporosos como precursores para híbridos inorgânico-orgânicos com aplicações adsortivas

ALVES, Ana paula Melo. Vermiculitas tratadas quimicamente na obtenção de sólidos microporosos como precursores para híbridos inorgânico-orgânicos com aplicações adsortivas. 2009. 124 f. Tese (Doutorado em Quimica) - Centro de Ciências Exatas e da Natureza, Universidade Federal da Paraíba, João Pessoa, PB, 2009.

Problems in Algebraic Vision

Thesis (Ph.D.)--University of Washington, 2016-08

Vermiculitas tratadas quimicamente na obtenção de sólidos microporosos como precursores para híbridos inorgânico-orgânicos com aplicações adsortivas

ALVES, Ana paula Melo. Vermiculitas tratadas quimicamente na obtenção de sólidos microporosos como precursores para híbridos inorgânico-orgânicos com aplicações adsortivas. 2009. 124 f. Tese (Doutorado em Quimica) - Centro de Ciências Exatas e da Natureza, Universidade Federal da Paraíba, João Pessoa, PB, 2009.

Unpolarized transverse momentum dependent parton distribution and fragmentation functions at next-to-next-to-leading order

The transverse momentum dependent parton distribution/fragmentation functions (TMDs) are essential in the factorization of a number of processes like Drell-Yan scattering, vector boson production, semi-inclusive deep inelastic scattering, etc. We provide a comprehensive study of unpolarized TMDs at next-to-next-to-leading order, which includes an explicit calculation of these TMDs and an extraction of their matching coefficients onto their integrated analogues, for all flavor combinations. The obtained matching coefficients are important for any kind of phenomenology involving TMDs. In the present study each individual TMD is calculated without any reference to a specific process. We recover the known results for parton distribution functions and provide new results for the fragmentation functions. The results for the gluon transverse momentum dependent fragmentation functions are presented for the first time at one and two loops. We also discuss the structure of singularities of TMD operators and TMD matrix elements, crossing relations between TMD parton distribution functions and TMD fragmentation functions, and renormalization group equations. In addition, we consider the behavior of the matching coefficients at threshold and make a conjecture on their structure to all orders in perturbation theory.

Viver no campo ou na cidade? resposta dos morcegos (Mammalia, Chiroptera) à antropização da paisagem

Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Biológicas, Departamento de Ecologia, Programa de Pós-Graduação em Ecologia, 2015.

Approximate factorization constraint preconditioners for saddle-point matrices

We consider the application of the conjugate gradient method to the solution of large, symmetric indefinite linear systems. Special emphasis is put on the use of constraint preconditioners and a new factorization that can reduce the number of flops required by the preconditioning step. Results concerning the eigenvalues of the preconditioned matrix and its minimum polynomial are given. Numerical experiments validate these conclusions.

The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

Porcine skin as a source of biodegradable matrices: alkaline treatment and glutaraldehyde crosslinking

In this work, the modifications promoted by alkaline hydrolysis and glutaraldehyde (GA) crosslinking on type I collagen found in porcine skin have been studied. Collagen matrices were obtained from the alkaline hydrolysis of porcine skin, with subsequent GA crosslinking in different concentrations and reaction times. The elastin content determination showed that independent of the treatment, elastin was present in the matrices. Results obtained from in vitro trypsin degradation indicated that with the increase of GA concentration and reaction time, the degradation rate decreased. From thermogravimetry and differential scanning calorimetry analysis it can be observed that the collagen in the matrices becomes more resistant to thermal degradation as a consequence of the increasing crosslink degree. Scanning electron microscopy analysis indicated that after the GA crosslinking, collagen fibers become more organized and well-defined. Therefore, the preparations of porcine skin matrices with different degradation rates, which can be used in soft tissue reconstruction, are viable.