Universiẗat, Diss., 2003--Dortmund.

Fechamento de loops é um dos principais processos das estratégias de SLAM baseadas em grafos, usadas para estimar o erro de deslocamento acumulado à ser minimizado pela técnica. Neste sentido, boas correspondências de cenas permitem criar uma conexão entre dois nós do grafo que está sendo construído para representar o ambiente. Contudo, falsas correspondências podem levar essas estratégias a um estado irreversível de falsa representação do ambiente. Neste trabalho, um método robusto baseado em features que usa sequências de imagens para reconhecer áreas revisitadas é apresentado. Este método usa a abordagem de Bag-of-Words para reduzir efeitos de iluminação e uma ponderação TF-IDF para ressaltar as principais features que descrevem cada cena. Além disso, um algoritmo baseado na técnica de Mean Shift é usado sobre uma matriz de similaridade para identificar a possível trajetória seguida pelo robô e melhorar a detecção de fechamento de loop. O método apresentado foi testado em um ambiente aberto usando sequências de imagens coletadas com usando uma câmera de mão e um drone modelo Parrot ArDrone 2.0. / Loop closure recognition is one of the main processes of graph-based SLAM strategies, used to estimate the accumulated motion error to be minimized by the technique. Good scene correspondences allow to create constraints between two nodes in the graph that is currently being built to represent the environment that the robot is immersed. However, false correspondences can lead these strategies to an irreversible wrong environment representation. In this work, we present a robust feature-based loop closure approach that uses image sequence matching to recognize revisited areas. This approach uses Bag-of- Words to reduce the effects of lightning changes and a TF-IDF weighting to enhance the main features that describe each scene. Besides, an algorithm based on Mean Shift is used over a similarity matrix to identify the possible trajectory followed by the robot and improve the loop closure detection. Our method is tested in a GPS-denied outdoor environment using image sequences collected using a handheld camera and a Parrot ArDrone 2.0.

Fechamento de loops é um dos principais processos das estratégias de SLAM baseadas em grafos, usadas para estimar o erro de deslocamento acumulado à ser minimizado pela técnica. Neste sentido, boas correspondências de cenas permitem criar uma conexão entre dois nós do grafo que está sendo construído para representar o ambiente. Contudo, falsas correspondências podem levar essas estratégias a um estado irreversível de falsa representação do ambiente. Neste trabalho, um método robusto baseado em features que usa sequências de imagens para reconhecer áreas revisitadas é apresentado. Este método usa a abordagem de Bag-of-Words para reduzir efeitos de iluminação e uma ponderação TF-IDF para ressaltar as principais features que descrevem cada cena. Além disso, um algoritmo baseado na técnica de Mean Shift é usado sobre uma matriz de similaridade para identificar a possível trajetória seguida pelo robô e melhorar a detecção de fechamento de loop. O método apresentado foi testado em um ambiente aberto usando sequências de imagens coletadas com usando uma câmera de mão e um drone modelo Parrot ArDrone 2.0. / Loop closure recognition is one of the main processes of graph-based SLAM strategies, used to estimate the accumulated motion error to be minimized by the technique. Good scene correspondences allow to create constraints between two nodes in the graph that is currently being built to represent the environment that the robot is immersed. However, false correspondences can lead these strategies to an irreversible wrong environment representation. In this work, we present a robust feature-based loop closure approach that uses image sequence matching to recognize revisited areas. This approach uses Bag-of- Words to reduce the effects of lightning changes and a TF-IDF weighting to enhance the main features that describe each scene. Besides, an algorithm based on Mean Shift is used over a similarity matrix to identify the possible trajectory followed by the robot and improve the loop closure detection. Our method is tested in a GPS-denied outdoor environment using image sequences collected using a handheld camera and a Parrot ArDrone 2.0.

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Mean-field games (MFGs) model the behavior of large populations of rational agents. Each agent seeks to minimize an individual cost that depends on the statistical distribution of the population. Roughly speaking, MFGs are given by the limit of differential games with N agents as N goes to infinity. This limit describes an average effect of the population’s behavior. Instead of modeling large systems for all agents, we consider two coupled equations: the Hamilton–Jacobi equation and the Fokker–Planck equation. A solution to MFGs is given by two functions: a value function and a population density. From the point of view of mathematics, monotonicity conditions for MFGs are a natural way to obtain the uniqueness of solutions and the stability of systems. In this thesis, we develop a new framework to establish the existence of solutions to MFGs through monotonicity. First, we study first-order stationary monotone MFGs with Dirichlet boundary conditions. In MFGs, boundary conditions arise when agents can leave the domain. There are exit costs for agents given by Dirichlet boundary conditions. Here, we establish the existence of solutions to MFGs that fulfill those boundary conditions in the trace sense. In particular, our solution is continuous up to the boundary in the one-dimensional case. Second, we consider time-dependent monotone MFGs with space-periodic boundary conditions. To solve the time-dependent monotone MFG, we introduce a mono- tone high-order regularized elliptic problem in Rn+1, although the original MFG is a parabolic type. To preserve monotonicity, we need to determine the specific boundary conditions for the time variable. Then, we can apply our method of stationary MFGs to this regularization. In particular, we prove that a solution to the problem exists for any terminal time. Third, we investigate stationary MFGs with hypoelliptic operators that are degenerate differential operators. Those models arise from stochastic control problems with the Stratonovich integration. We study a hypoelliptic MFG with the standard quadratic Hamiltonian. Under standard assumptions, although there is no uniform elliptic condition in hypoelliptic operators, we verify that there is a unique solution to our hypoelliptic MFG.

In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested in MFGs with a nonmonotonic behavior, which corresponds to situations where agents tend to aggregate. First, we derive the MFG equations from control theory. Then, we compute explicit solutions using the current formulation and examine their behavior. Finally, we represent the solutions and analyze the results. This thesis main contributions are the following: First, we develop the current method to solve MFG explicitly. Second, we analyze in detail non-monotonic MFGs and discover new phenomena: non-uniqueness, discontinuous solutions, empty regions and unhappiness traps. Finally, we address several regularization procedures and examine the stability of MFGs.

Abstract Nuclear Medicine (NM) images inherently suffer from large amounts of noise and blur. The purpose of this research is to reduce the noise and blur while maintaining image integrity for improved diagnosis. The proposal is to further improve image quality after the standard pre- and post-processing undertaken by a gamma camera system. Mean Field Annealing (MFA), the image processing technique used in this research is a well known image processing approach. The MFA algorithm uses two techniques to achieve image restoration. Gradient descent is used as the minimisation technique, while a deterministic approximation to Simulated Annealing (SA) is used for optimisation. The algorithm anisotropically diffuses an image, iteratively smoothing regions that are considered non-edges and still preserving edge integrity until a global minimum is obtained. A known advantage of MFA is that it is able to minimise to this global minimum, skipping over local minima while still providing comparable results to SA with significantly less computational effort. Image blur is measured using either a point or line source. Both allow for the derivation of a Point Spread Function (PSF) that is used to de-blur the image. The noise variance can be measured using a flood source. The noise is due to the random fluctuations in the environment as well as other contributors. Noisy blurred NM images can be difficult to diagnose particularly at regions with steep intensity gradients and for this reason MFA is considered suitable for image restoration. From the literature it is evident that MFA can be applied successfully to digital phantom images providing improved performance over Wiener filters. In this paper MFA is shown to yield image enhancement of planar NM images by implementing a sharpening filter as a post MFA processing technique.

Background: Cervical cancer is the most common gynecological malignant disorder worldwide. Activated platelets play a key role in cancer development and progression. Mean platelet volume (MPV) is an early indicator of platelet activation. The aim of the present study was to evaluate MPV levels in patients with cervical cancer. Materials and methods: A total of 181 patients with cervical cancer and 181 controls between January 2015 and June 2015 were included in the study. Patient characteristics and hematologic test data at initial diagnosis were collected and odds ratios (ORs) and 95% confidence intervals (CIs) for risk of cervical cancer were calculated using multivariate logistic regression analyses across MPV quartiles. Results: MPV levels were decreased in patients with cervical cancer compared with control subjects. A significant correlation between MPV and FIGO stage was found. Moreover, after adjusting for other risk factors, the ORs (95%CIs) for cervical cancer according to MPV quartiles were 4.450 (1.975-10.026), 2.505 (1.206-5.202), 0.573 (0.261-1.259), and 1.000, respectively. Conclusions: MPV was found to be independently associated with the presence of cervical cancer. Our results suggest that MPV could be potential diagnostic screening tool.

The educational system in the United States is meant for the native speakers of English. As a result, students who are limited English proficient do not succeed academically in this educational system.

In this thesis, we present three projects. First, we investigate the numerical approximation of Hamilton-Jacobi equations with the Caputo time-fractional derivative. We introduce an explicit in time discretization of the Caputo derivative and a finite-difference scheme for the approximation of the Hamiltonian. We show that the approximation scheme so obtained is stable under an appropriate condition on the discretization parameters and converges to the unique viscosity solution of the Hamilton-Jacobi equation. Also, we study the numerical approximation of a system of PDEs which arises from an optimal control problem for the time-fractional Fokker-Planck equation with time-dependent drift. The system is composed of a backward time-fractional Hamilton-Jacobi-Bellman equation and a forward time-fractional Fokker-Planck equation. We approximate Caputo derivatives in the system by means of L1 schemes and the Hamiltonian by finite differences. The scheme for the Fokker-Planck equation is constructed in such a way that the duality structure of the PDE system is preserved on the discrete level. We prove the well-posedness of the scheme and the convergence to the solution of the continuous problem. Finally, we study a particle approximation for one-dimensional first-order Mean-Field-Games with local interactions with planning conditions. Our problem comprises a system of a Hamilton-Jacobi equation coupled with a transport equation. As we are dealing with the planning problem, we prescribe initial and terminal distributions for the transport equation. The particle approximation builds on a semi-discrete variational problem. First, we address the existence and uniqueness of the semi-discrete variational problem. Next, we show that our discretization preserves some conserved quantities. Finally, we prove that the approximation by particle systems preserves displacement convexity. We use this last property to establish uniform estimates for the discrete problem. All results for the discrete problem are illustrated with numerical examples.