O presente trabalho é uma formulação teórica que permite estudar num modelo estocástico, a influência dos erros de classificação na mensuração da prevalência da esquistossomose mansônica. Os erros de classificação são desagregados e identificados como: falhas de leitura por parte do examinador ou preparo inadequado da lâmina; contingências biológicas que possibilitam o aparecimento de ovos não viáveis e a eliminação de ovos contínua por parte dos indivíduos. É apresentada uma solução geral para o problema, bem como soluções para os casos em que se conhece a distribuição de probabilidades do número de ovos de S.mansoni. Uma solução aproximada e independente da forma e dependente dos dois primeiros momentos da distribuição do número de ovos é sugerida. A influência dos erros de classificação pode quantitativamente ser apreciada, através de um conjunto de tabelas elaboradas com diversos valores dos parâmetros intervenientes no problema. / The present paper is a theoretical approach which will, allow studying the influence - in a stochastic model - of errors in classifying the measurement of the prevalence of Schistosomiasis mansoni. The misclassification errors considered are due to: (A) failure of the examiner in either (1) reading or (2) poor technique. (B) biological contingences which will allow for the appearence of (1) sterile eggs, or (2) discontinuity in the elimination of eggs by the carriers. An exact general solution of the problem is presented, as well as solutions for the particular cases in which the probability distribution of S.mansoni eggs counts in known. An approximate solution is suggested, which is independent from the way in which the number of eggs is distributed, but depends upon the first two moments of the probability distribution of the eggs counts. The influence of misclassification errors can be judged in a quantitative way, by means of a set of tables mande up for the different parametric values of the problem.

Intelligent transportation systems aim to provide innovative applications and services relating to traffic management and enable ease of access to information for various system users. The intent to utilize the excessive on-board resources in the transportation system, along with the latest computing resource management technology in conventional clouds, has cultivated the concept of the Vehicular Cloud. Evolved from Vehicular Networks, the vehicular cloud can be formed by vehicles autonomously, and provides a large number of applications and services that can benefit the entire transportation system, as well as drivers, passengers, and pedestrians. However, due to high traffic mobility, the vehicular cloud is built on dynamic physical resources; as a result, it experiences several inherent challenges, which increase the complexity of its implementations. Having a detailed picture of the number of vehicles, as well as their time of availability in a given region through a model, works as a critical stepping stone for enabling vehicular clouds, as well as any other system involving vehicles moving over the traffic network. The number of vehicles represents the amount of computation capabilities available in this region and the navigation time indicates the period of validity for a specific compute node. Therefore, in this thesis, we carry out a comprehensive stochastic analysis of several traffic characteristics related to the implementation of vehicular cloud inside a road segment by adopting proper traffic models. According to the analytical results, we demonstrate the feasibility of running a certain class of applications or services on the vehicular cloud, even for highly dynamic scenarios. Specifically, two kinds of traffic scenarios are modeled: free-flow traffic and queueing-up traffic. We use a macroscopic traffic model to investigate the free-flow traffic and analyze the features such as traffic density, the number of vehicles and their residence time. Also, we utilize the queueing theory to model the queueing-up traffic; the queue length and the waiting time in the queue are analyzed. The results show the boundaries on enabling vehicular cloud, allowing to determine a range of parameters for simulating vehicular clouds.

As in the stock of trading business is allocated a large part of the capital resources, it is necessary to determine the manner of their control. For this purpose a number of models were developed. Before application to the specific case, these models must be properly adjusted to ensure conformity with reality. The aim of this thesis is to optimize the inventory management of electronic commerce. The stochastic model with loss from unfulfilled orders was chosen as default. First, the necessary adjustments were made to the model and defined input parameters. After filling model with real data, the optimum values of the monitored variables were obtained. The last part deals with the influence of changes in input parameters on the optimal value of variables. Use of the model is not limited to this particular case. Without major modifications, the model is also applicable to other similar problems.

The Kardar-Parisi-Zhang (KPZ) equation is a stochastic PDE describing various objects in statistical mechanics such as random interface growth, directed polymers, interacting particle systems. We study large deviations of the KPZ equation, both in the short time and long time regime. We prove the first short time large deviations for the KPZ equation and detects a Gaussian - 5/2 power law crossover in the lower tail rate function. In the long-time regime, we study the upper tail large deviations of the KPZ equation starting from a wide range of initial data and explore how the rate function depends on the initial data. The KPZ equation plays a role as the weak scaling limit of various models in the KPZ universality class. We show the stochastic higher spin six vertex model, a class of models which sit on top of the KPZ integrable systems, converges weakly to the KPZ equation under certain scaling. This extends the weak universality of the KPZ equation. On the other hand, we show that under a different scaling, the stochastic higher spin six vertex model converges to a hyperbolic stochastic PDE called stochastic telegraph equation. One key tool behind the proof of these two stochastic PDE limits is a property called Markov duality.

abstract: This dissertation addresses access management problems that occur in both emergency and outpatient clinics with the objective of allocating the available resources to improve performance measures by considering the trade-offs. Two main settings are considered for estimating patient willingness-to-wait (WtW) behavior for outpatient appointments with statistical analyses of data: allocation of the limited booking horizon to patients of different priorities by using time windows in an outpatient setting considering patient behavior, and allocation of hospital beds to admitted Emergency Department (ED) patients. For each chapter, a different approach based on the problem context is developed and the performance is analyzed by implementing analytical and simulation models. Real hospital data is used in the analyses to provide evidence that the methodologies introduced are beneficial in addressing real life problems, and real improvements can be achievable by using the policies that are suggested. This dissertation starts with studying an outpatient clinic context to develop an effective resource allocation mechanism that can improve patient access to clinic appointments. I first start with identifying patient behavior in terms of willingness-to-wait to an outpatient appointment. Two statistical models are developed to estimate patient WtW distribution by using data on booked appointments and appointment requests. Several analyses are conducted on simulated data to observe effectiveness and accuracy of the estimations. Then, this dissertation introduces a time windows based policy that utilizes patient behavior to improve access by using appointment delay as a lever. The policy improves patient access by allocating the available capacity to the patients from different priorities by dividing the booking horizon into time intervals that can be used by each priority group which strategically delay lower priority patients. Finally, the patient routing between ED and inpatient units to improve the patient access to hospital beds is studied. The strategy that captures the trade-off between patient safety and quality of care is characterized as a threshold type. Through the simulation experiments developed by real data collected from a hospital, the achievable improvement of implementing such a strategy that considers the safety-quality of care trade-off is illustrated. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2019

Thesis (PhD (Applied Mathematics))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: In many applications, an accurate, robust and fast tracker is needed, for example in surveillance, gesture recognition, tracking lips for lip-reading and creating an augmented reality by embedding a tracked object in a virtual environment. In this dissertation we investigate the viability of a tracker that combines the accuracy of active appearancemodels with the robustness of the particle lter (a stochastic process)—we call this combination the PFAAM. In order to obtain a fast system, we suggest local optimisation as well as using active appearance models tted with non-linear approaches. Active appearance models use both contour (shape) and greyscale information to build a deformable template of an object. ey are typically accurate, but not necessarily robust, when tracking contours. A particle lter is a generalisation of the Kalman lter. In a tutorial style, we show how the particle lter is derived as a numerical approximation for the general state estimation problem. e algorithms are tested for accuracy, robustness and speed on a PC, in an embedded environment and by tracking in ìD. e algorithms run real-time on a PC and near real-time in our embedded environment. In both cases, good accuracy and robustness is achieved, even if the tracked object moves fast against a cluttered background, and for uncomplicated occlusions. / AFRIKAANSE OPSOMMING: ’nAkkurate, robuuste en vinnige visuele-opspoorderword in vele toepassings benodig. Voorbeelde van toepassings is bewaking, gebaarherkenning, die volg van lippe vir liplees en die skep van ’n vergrote realiteit deur ’n voorwerp wat gevolg word, in ’n virtuele omgewing in te bed. In hierdie proefskrif ondersoek ons die lewensvatbaarheid van ’n visuele-opspoorder deur die akkuraatheid van aktiewe voorkomsmodellemet die robuustheid van die partikel lter (’n stochastiese proses) te kombineer—ons noem hierdie kombinasie die PFAAM. Ten einde ’n vinnige visuele-opspoorder te verkry, stel ons lokale optimering, sowel as die gebruik van aktiewe voorkomsmodelle wat met nie-lineêre tegnieke gepas is, voor. Aktiewe voorkomsmodelle gebruik kontoer (vorm) inligting tesamemet grysskaalinligting om ’n vervormbaremeester van ’n voorwerp te bou. Wanneer aktiewe voorkomsmodelle kontoere volg, is dit normaalweg akkuraat,maar nie noodwendig robuust nie. ’n Partikel lter is ’n veralgemening van die Kalman lter. Ons wys in tutoriaalstyl hoe die partikel lter as ’n numeriese benadering tot die toestand-beramingsprobleem afgelei kan word. Die algoritmes word vir akkuraatheid, robuustheid en spoed op ’n persoonlike rekenaar, ’n ingebedde omgewing en deur volging in ìD, getoets. Die algoritmes loop intyds op ’n persoonlike rekenaar en is naby intyds op ons ingebedde omgewing. In beide gevalle, word goeie akkuraatheid en robuustheid verkry, selfs as die voorwerp wat gevolg word, vinnig, teen ’n besige agtergrond beweeg of eenvoudige okklusies ondergaan.

Sequential data are encountered in many contexts of everyday life and in numerous scientific applications. They can for instance be SMS typeset on mobile phones, web pages reached while crossing hyperlinks, system logs or DNA samples, to name a few. Generating such data defines a sequential process. This thesis is concerned with the modeling of sequential processes from observed data. Sequential processes are here modeled using probabilistic models, namely discrete time Markov chains (MC), Hidden Markov Models (HMMs) and Partially Observable Markov Models (POMMs). Such models can answer questions such as (i) Which event will occur a couple of steps later? (ii) How many times will a particular event occur? and (iii) When does an event occur for the first time given the current situation? The last question is of particular interest in this thesis and is mathematically formalized under the notion of First Passage Times (FPT) dynamics of a process. The FPT dynamics is used here to solve the three following problems related to machine learning and data mining: (i) HMM/POMM induction, (ii) supervised sequence classification and (iii) relevant subgraph mining. Firstly, we propose a novel algorithm, called POMMStruct, for learning the structure and the parameters of POMMs to best fit the empirical FPT dynamics observed in the samples. Experimental results illustrate the benefit of POMMStruct in the modeling of sequential processes with a complex temporal dynamics while compared to classical induction approaches. Our second contribution is concerned with the classification of sequences. We propose to model the FPT in sequences with discrete phase-type (PH) distributions using a novel algorithm called PHit. These distributions are used to devise a new string kernel and a probabilistic classifier. Experimental results on biological data shows that our methods provides state-of-the-art classification results. Finally, we address the problem of mining subgraphs, which are relevant to model the relationships between selected nodes of interest, in large graphs such as biological networks. A new relevance criterion based on particular random walks called K-walks is proposed as well as efficient algorithms to compute this criterion. Experiments on the KEGG metabolic network and on randomly generated graphs are presented.

The mechanisms that control growth processes in biology tissues have attracted continuous research interest despite their complexity. With the emergence of big data experimental approaches there is an urgent need to develop statistical and computational models to fit the experimental data and that can be used to make predictions to guide future research. In this work we apply statistical methods on growth process of different biological tissues, focusing on development of neuron dendrites and tumor cells. We first examine the neuron cell growth process, which has implications in neural tissue regenerations, by using a computational model with uniform branching probability and a maximum overall length constraint. One crucial outcome is that we can relate the parameter fits from our model to real data from our experimental collaborators, in order to examine the usefulness of our model under different biological conditions. Our methods can now directly compare branching probabilities of different experimental conditions and provide confidence intervals for these population-level measures. In addition, we have obtained analytical results that show that the underlying probability distribution for this process follows a geometrical progression increase at nearby distances and an approximately geometrical series decrease for far away regions, which can be used to estimate the spatial location of the maximum of the probability distribution. This result is important, since we would expect maximum number of dendrites in this region; this estimate is related to the probability of success for finding a neural target at that distance during a blind search. We then examined tumor growth processes which have similar evolutional evolution in the sense that they have an initial rapid growth that eventually becomes limited by the resource constraint. For the tumor cells evolution, we found an exponential growth model best describes the experimental data, based on the accuracy and robustness of models. Furthermore, we incorporated this growth rate model into logistic regression models that predict the growth rate of each patient with biomarkers; this formulation can be very useful for clinical trials. Overall, this study aimed to assess the molecular and clinic pathological determinants of breast cancer (BC) growth rate in vivo.

Made available in DSpace on 2015-03-04T18:51:13Z (GMT). No. of bitstreams: 1 thesisRosa.pdf: 2324244 bytes, checksum: e7604311281924e9c68f2886457323e8 (MD5) Previous issue date: 2009-01-10 / Conselho Nacional de Desenvolvimento Cientifico e Tecnologico / In the context of the stochastic perturbations theories we analyze the accuracy of two linear poroelastic models applied to highly heterogeneous porous media subject to uncertainties in the permeability and the elastic constants. The poroelastic models completely and weakly coupled analized arise characterized by the degree of intensity coupling between the hydrodinamics, governor of the percolation of the fluid and poromechanics which governs the deformation of the porous matrix. New equations for the moments of effective solutions using techniques of asymptotic expansion. In light of the perturbation theory are set simplifying assumptions that clarify clearly the domain of validity of weakly coupled model, widely used in simulation of oil reservoirs in the presence of heterogeneities and correlation in poroelastic coefficients. Computational simulations of the primary extraction of oil process are carried out using Monte Carlo techniques in conjunction with finite element methods. Results obtained clearly confirm the conjecture established by the perturbation theorie related with the inaccuracy of the weakly coupled model in the presence of variability in the elastic constants. The methodology used allows to quantify the distance between the two poroelastics models and therefore propose the appropriate model for different conditions of loading and variability of the geological formation. / No contexto das teorias de perturbação estocástica, analisamos a acurácia de dois modelos poroelásticos lineares aplicados a meios porosos altamente heterogêneos sujeitos as incertezas na permeabilidade e nas constantes elásticas. Os modelos poroelásticos completamente e fracamente acoplados analisados surgem caracterizados pelo grau de intensidade de acoplamento entre a hidrodinámica governante da percolação o do fluido e a poromecânica que rege as deformações da matriz porosa. Novas equações efetivas para os momentos das soluções são obtidas fazendo uso de técnicas de expansão assintótica. À luz da teoria de perturbação, são estabelecidas hipóteses simplificadoras que elucidam o domínio de validade do modelo fracamente acoplado, amplamente utilizado nos simuladores de Reservatórios de Petróleo, na presença de heterogeneidades e correlação nos coeficientes poroelásticos. Simulações computacionais do processo de extração primária de petróleo são realizadas utilizando técnicas de Monte Carlo em conjunção com métodos de elementos finitos. Resultados numéricos obtidos confirmam pela teoria de perturbação relacionada com a inacurácia do modelo fracamente acoplado na presença de variabilidade nas constantes elásticas. A metodologia empregada permite quantificar a distância entre os dois modelos poroelásticos, e consequentemente, propor a escolha do modelo apropriado para diferentes condições de carregamento e variabilidade da formação geológica.

Cette thèse examine une nouvelle façon d'étudier l'impact d'une voie de signalisation donnée sur l'évolution d'un tissu grâce à l'analyse multi-niveaux. Cette analyse est divisée en deux parties principales: La première partie considère les modèles décrivant la voie au niveau cellulaire. A l'aide de ces modèles, on peut calculer de manière résoluble la dynamique d'un groupe de cellules, en le représentant par une distribution multivariée sur des concentrations de molécules clés. La deuxième partie propose un modèle 3d de croissance tissulaire qui considère la population de cellules comme un ensemble de sous-populations, partitionnée de façon à ce que chaque sous-population partage les mêmes conditions externes. Pour chaque sous-population, le modèle résoluble présenté dans la première partie peut être utilisé. Cette thèse se concentre principalement sur la première partie, tandis qu'un chapitre couvre un projet de modèle pour la deuxième partie. / This thesis examines a new way to study the impact of a given pathway on the dynamics of a tissue through Multi-Level Analysis. The analysis is split in two main parts: The first part considers models describing the pathway at the cellular level. Using these models, one can compute in a tractable manner the dynamics of a group of cells, representing it by a multivariate distribution over concentrations of key molecules. % of the distribution of the states of this pathway through groups of cells. The second part proposes a 3d model of tissular growth that considers the population of cell as a set of subpopulations, partitionned such as each subpopulation shares the same external conditions. For each subpopulation, the tractable model presented in the first part can be used. This thesis focuses mainly on the first part, whereas a chapter covers a draft of a model for the second part.