Multi-spectral imagery provides a robust and low-cost dataset for assessing wetland extent and quality over broad regions and is frequently used for wetland inventories. However in forested wetlands, hydrology is obscured by tree canopy making it difficult to detect with multi-spectral imagery alone. Because of this, classification of forested wetlands often includes greater errors than that of other wetlands types. Elevation and terrain derivatives have been shown to be useful for modelling wetland hydrology. But, few studies have addressed the use of LiDAR intensity data detecting hydrology in forested wetlands. Due the tendency of LiDAR signal to be attenuated by water, this research proposed the fusion of LiDAR intensity data with LiDAR elevation, terrain data, and aerial imagery, for the detection of forested wetland hydrology. We examined the utility of LiDAR intensity data and determined whether the fusion of Lidar derived data with multispectral imagery increased the accuracy of forested wetland classification compared with a classification performed with only multi-spectral image. Four classifications were performed: Classification A - All Imagery, Classification B - All LiDAR, Classification C - LiDAR without Intensity, and Classification D - Fusion of All Data. These classifications were performed using random forest and each resulted in a 3-foot resolution thematic raster of forested upland and forested wetland locations in Vermilion County, Illinois. The accuracies of these classifications were compared using Kappa Coefficient of Agreement. Importance statistics produced within the random forest classifier were evaluated in order to understand the contribution of individual datasets. Classification D, which used the fusion of LiDAR and multi-spectral imagery as input variables, had moderate to strong agreement between reference data and classification results. It was found that Classification A performed using all the LiDAR data and its derivatives (intensity, elevation, slope, aspect, curvatures, and Topographic Wetness Index) was the most accurate classification with Kappa: 78.04%, indicating moderate to strong agreement. However, Classification C, performed with LiDAR derivative without intensity data had less agreement than would be expected by chance, indicating that LiDAR contributed significantly to the accuracy of Classification B.

The biological datasets produced as a result of high-throughput genomic research such as specifically microarrays, contain vast amounts of knowledge for entire genome and their expression affiliations. Gene clustering from such data is a challenging task due to the huge data size and high complexity of the algorithms as well as the visualization needs. Most of the existing analysis methods for genome-wide gene expression profiles are sequential programs using greedy algorithms and require subjective human decision. Recently, Zhu et al. proposed a parallel Random matrix theory (RMT) based approach for generating transcriptional networks, which is much more resistant to high level of noise in the data [9] without human intervention. Nowadays GPUs are designed to be used more efficiently for general purpose computing [1] and are vastly superior to CPUs [6] in terms of threading performance. Our kernel functions running on GPU utilizes the functions from both the libraries of Compute Unified Basic Linear Algebra Subroutines (CUBLAS) and Compute Unified Linear Algebra (CULA) which implements the Linear Algebra Package (LAPACK). Our experiment results show that GPU program can achieve an average speed-up of 2~3 times for some simulated datasets.

vi, 48 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / We compare the relaxation times of two random walks - the simple random walk and the metropolis walk - on an arbitrary finite multigraph G. We apply this result to the random graph with n vertices, where each edge is included with probability p = [Special characters omitted.] where λ > 1 is a constant and also to the Newman-Watts small world model. We give a bound for the reconstruction problem for general trees and general 2 × 2 matrices in terms of the branching number of the tree and some function of the matrix. Specifically, if the transition probabilities between the two states in the state space are a and b , we show that we do not have reconstruction if Br( T ) [straight theta] < 1, where [Special characters omitted.] and Br( T ) is the branching number of the tree in question. This bound agrees with a result obtained by Martin for regular trees and is obtained by more elementary methods. We prove an inequality closely related to this problem. / Committee in charge: David Levin, Chairperson, Mathematics; Christopher Sinclair, Member, Mathematics; Marcin Bownik, Member, Mathematics; Hao Wang, Member, Mathematics; Van Kolpin, Outside Member, Economics

We study a family of random walks defined on certain Euclidean lattices that are related to incidence matrices of balanced incomplete block designs. We estimate the return probability of these random walks and use it to determine the asymptotics of the number of balanced incomplete block design matrices. We also consider the problem of collisions of independent simple random walks on graphs. We prove some new results in the collision problem, improve some existing ones, and provide counterexamples to illustrate the complexity of the problem.

Esse trabalho tem dois objetivos principais: o primeiro deles consiste em apresentar o estado da arte sobre processos de otimização combinatorial dando uma ênfase especial ao método Simulated Annealing (SA). São apresentados seu histórico, funcionalidades, algoritmo genérico e propostas de paralelização presentes na literatura. Além disso, é apresentado o algoritmo de geração de redes aleatórias contínuas, algoritmo, esse, projetado por pesquisadores do Instituto de Física da UFRGS que utiliza o método SA para gerar redes que atendam certas restrições. O segundo objetivo consiste empropor a paralelização desse algoritmo visando diminuir significativamente o tempo de geração de cada rede, que com o algoritmo seqüencial chega a demorar mais de um mês. Nessa etapa foi utilizada uma adaptação de um dos métodos propostos pela literatura juntamente com a técnica de divisão de domínio. Os resultados obtidos mostraram-se satisfatórios tanto em relação à qualidade numérica quanto à diminuição do tempo de processamento. Além disso, discute-se no trabalho a genericidade da proposta de paralelização a outros problemas baseados em SA. / This work has two main goals: the first one is to present the state of the art on combinatorial optimization processes, with a special emphasis to the Simulated Annealing (SA) method. The work presents its history, features, generic algorithm and proposed parallelization present in the literature. Moreover, the algorithm to generate random networks continued is presented. This algorithm was designed by researchers of the UFRGS Physics Institute and it uses the SA method. The second goal of this work is to propose a parallelization for this algorithm in order to decrease significantly the generation time of each network, that with the sequential algorithm reaches more than months. To do that was used an adaptation of one of the methods proposed by literature together with the domain partitioning technical. The results were satisfactory in terms of the numerical quality and in the decrease of the processing time. In addition, this work discusses the genericity of the proposed parallelization to other problems based on SA.

abstract: The purpose of information source detection problem (or called rumor source detection) is to identify the source of information diffusion in networks based on available observations like the states of the nodes and the timestamps at which nodes adopted the information (or called infected). The solution of the problem can be used to answer a wide range of important questions in epidemiology, computer network security, etc. This dissertation studies the fundamental theory and the design of efficient and robust algorithms for the information source detection problem. For tree networks, the maximum a posterior (MAP) estimator of the information source is derived under the independent cascades (IC) model with a complete snapshot and a Short-Fat Tree (SFT) algorithm is proposed for general networks based on the MAP estimator. Furthermore, the following possibility and impossibility results are established on the Erdos-Renyi (ER) random graph: $(i)$ when the infection duration $<\frac{2}{3}t_u,$ SFT identifies the source with probability one asymptotically, where $t_u=\left\lceil\frac{\log n}{\log \mu}\right\rceil+2$ and $\mu$ is the average node degree, $(ii)$ when the infection duration $>t_u,$ the probability of identifying the source approaches zero asymptotically under any algorithm; and $(iii)$ when infection duration $<t_u,$ the breadth-first search (BFS) tree starting from the source is a fat tree. Numerical experiments on tree networks, the ER random graphs and real world networks show that the SFT algorithm outperforms existing algorithms. In practice, other than the nodes' states, side information like partial timestamps may also be available. Such information provides important insights of the diffusion process. To utilize the partial timestamps, the information source detection problem is formulated as a ranking problem on graphs and two ranking algorithms, cost-based ranking (CR) and tree-based ranking (TR), are proposed. Extensive experimental evaluations of synthetic data of different diffusion models and real world data demonstrate the effectiveness and robustness of CR and TR compared with existing algorithms. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2015

abstract: Random forest (RF) is a popular and powerful technique nowadays. It can be used for classification, regression and unsupervised clustering. In its original form introduced by Leo Breiman, RF is used as a predictive model to generate predictions for new observations. Recent researches have proposed several methods based on RF for feature selection and for generating prediction intervals. However, they are limited in their applicability and accuracy. In this dissertation, RF is applied to build a predictive model for a complex dataset, and used as the basis for two novel methods for biomarker discovery and generating prediction interval. Firstly, a biodosimetry is developed using RF to determine absorbed radiation dose from gene expression measured from blood samples of potentially exposed individuals. To improve the prediction accuracy of the biodosimetry, day-specific models were built to deal with day interaction effect and a technique of nested modeling was proposed. The nested models can fit this complex data of large variability and non-linear relationships. Secondly, a panel of biomarkers was selected using a data-driven feature selection method as well as handpick, considering prior knowledge and other constraints. To incorporate domain knowledge, a method called Know-GRRF was developed based on guided regularized RF. This method can incorporate domain knowledge as a penalized term to regulate selection of candidate features in RF. It adds more flexibility to data-driven feature selection and can improve the interpretability of models. Know-GRRF showed significant improvement in cross-species prediction when cross-species correlation was used to guide selection of biomarkers. The method can also compete with existing methods using intrinsic data characteristics as alternative of domain knowledge in simulated datasets. Lastly, a novel non-parametric method, RFerr, was developed to generate prediction interval using RF regression. This method is widely applicable to any predictive models and was shown to have better coverage and precision than existing methods on the real-world radiation dataset, as well as benchmark and simulated datasets. / Dissertation/Thesis / Doctoral Dissertation Biomedical Informatics 2017

abstract: Scattering from random rough surface has been of interest for decades. Several methods were proposed to solve this problem, and Kirchho approximation (KA) and small perturbation method (SMP) are among the most popular. Both methods provide accurate results on rst order scattering, and the range of validity is limited and cross-polarization scattering coecient is zero for these two methods unless these two methods are carried out for higher orders. Furthermore, it is complicated for higher order formulation and multiple scattering and shadowing are neglected in these classic methods. Extension of these two methods has been made in order to x these problems. However, it is usually complicated and problem specic. While small slope approximation is one of the most widely used methods to bridge KA and SMP, it is not easy to implement in a general form. Two scale model can be employed to solve scattering problems for a tilted perturbation plane, the range of validity is limited. A new model is proposed in this thesis to deal with cross-polarization scattering phenomenon on perfect electric conducting random surfaces. Integral equation is adopted in this model. While integral equation method is often combined with numerical method to solve the scattering coecient, the proposed model solves the integral equation iteratively by analytic approximation. We utilize some approximations on the randomness of the surface, and obtain an explicit expression. It is shown that this expression achieves agreement with SMP method in second order. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2017

This thesis mainly addresses two issues: 1) to investigate how to perform the lip segmentation without knowing the true number of segments in advance, and 2) to investigate how to select the local optimal observation scale for each structure from the viewpoint of lip segmentation e.ectively. Regarding the .rst issue, two number of prede.ned segments independent lip segmentation methods are proposed. In the .rst one, a multi-layer model is built up, in which each layer corresponds to one segment cluster. Subsequently, a Markov random .eld (MRF) derived from this model is obtained such that the segmenta­tion problem is formulated as a labeling optimization problem under the maximum a posteriori-Markov random .eld (MAP-MRF) framework. Suppose the pre-assigned number of segments may over-estimate the ground truth, whereby leading to the over-segmentation. An iterative algorithm capable of performing segment clusters and over-segmentation elimination simultaneously is presented. Based upon this algorithm, a lip segmentation scheme is proposed, featuring the robust performance to the estimate of the number of segment clusters. In the second method, a fuzzy clustering objective function which is a variant of the partition entropy (PE) and implemented using Havrda-Charvat’s structural a-entropy is presented. This objec­tive function features that the coincident cluster centroids in pattern space can be equivalently substituted by one centroid with the function value unchanged. The minimum of the proposed objective function can be reached provided that: (1) the number of positions occupied by cluster centroids in pattern space is equal to the truth cluster number, and (2) these positions are coincident with the optimal cluster centroids obtained under PE criterion. In the implementation, the clusters provided that the number of clusters is greater than or equal to the ground truth are ran­domly initialized. Then, an iterative algorithm is utilized to minimize the proposed objective function. The initial over-partition will be gradually faded out with the redundant centroids superposed over the convergence of the algorithm. For the second issue, an MRF based method with taking local scale variation into account to deal with the lip segmentation problem is proposed. Supposing each pixel of the target image has an optimal local scale from the segmentation viewpoint, the lip segmentation problem can be treated as a combination of observation scale selection and observed data classi.cation. Accordingly, a multi-scale MRF model is proposed to represent the membership map of each input pixel to a speci.c segment and local-scale map simultaneously. The optimal scale map and the correspond­ing segmentation result are obtained by minimizing the objective function via an iterative algorithm. Finally, based upon the three proposed methods, some lip segmentation exper­iments are conducted, respectively. The results show the e.cacy of the proposed methods in comparison with the existing counterparts.

A presente Tese de Doutorado é composta de quatro artigos científicos em duas áreas distintas. Em Horta, Guerre e Fernandes (2015), o qual constitui o Capítulo 2 desta Tese, é proposto um estimador suavizado no contexto de modelos de regressão quantílica linear (Koenker e Basset, 1978). Uma representação de Bahadur-Kiefer uniforme é obtida, a qual apresenta uma ordem assintótica que domina aquela correspondente ao estimador clássico. Em seguida, prova-se que o viés associado à suavização é negligenciável, no sentido de que o termo de viés é equivalente, em primeira ordem, ao verdadeiro parâmetro. A taxa precisa de convergência é dada, a qual pode ser controlada uniformemente pela escolha do parâmetro de suavização. Em seguida, são estudadas propriedades de segunda ordem do estimador proposto, em termos do seu erro quadrático médio assintótico, e mostra-se que o estimador suavizado apresenta uma melhoria em relação ao usual. Como corolário, tem-se que o estimador é assintoticamente normal e consistente à ordem p n. Em seguida, é proposto um estimador consistente para a matriz de covariância assintótica, o qual não depende de estimação de parâmetros auxiliares e a partir do qual pode-se obter diretamente intervalos de confiança assintóticos. A qualidade do método proposto é por fim ilustrada em um estudo de simulação. Os artigos Horta e Ziegelmann (2015a, 2015b, 2015c) se originam de um ímpeto inicial destinado a generalizar os resultados de Bathia et al. (2010). Em Horta e Ziegelmann (2015a), Capítulo 3 da presente Tese, é investigada a questão de existência de certos processos estocásticos, ditos processos conjugados, os quais são conduzidos por um segundo processo cujo espaço de estados tem como elementos medidas de probabilidade. Através dos conceitos de coerência e compatibilidade, obtémse uma resposta afirmativa à questão anterior. Baseado nas noções de medida aleatória (Kallenberg, 1973) e desintegração (Chang e Pollard, 1997; Pollard, 2002), é proposto um método geral para construção de processos conjugados. A teoria permite um rico conjunto de exemplos, e inclui uma classe de modelos de mudança de regime. Em Horta e Ziegelmann (2015b), Capítulo 4 desta Tese, é proposto – em relação com a construção obtida em Horta e Ziegelmann (2015a) – o conceito de processo fracamente conjugado: um processo estocástico real a tempo contínuo, conduzido por uma sequência de funções de distribuição aleatórias, ambos conectados por uma condição de compatibilidade a qual impõe que aspectos da distribuição do primeiro processo são divisíveis em uma quantidade enumerável de ciclos, dentro dos quais este tem como marginais, precisamente, o segundo processo. Em seguida, mostra-se que a metodologia de Bathia et al. (2010) pode ser aplicada para se estudar a estrutura de dependência de processos fracamente conjugados, e com isso obtém-se resultados de consistência à ordem p n para os estimadores que surgem naturalmente na teoria. Adicionalmente, a metodologia é ilustrada através de uma implementação a dados financeiros. Especificamente, o método proposto permite que características da dinâmica das distribuições de processos de retornos sejam traduzidas em termos de um processo escalar latente, a partir do qual podem ser obtidas previsões de quantidades associadas a essas distribuições. Em Horta e Ziegelmann (2015c), Capítulo 5 da presente Tese, são obtidos resultados de consistência à ordem p n em relação à estimação de representações espectrais de operadores de autocovariância de séries de tempo Hilbertianas estacionárias, em um contexto de medições imperfeitas. Os resultados são uma generalização do método desenvolvido em Bathia et al. (2010), e baseiam-se no importante fato de que elementos aleatórios em um espaço de Hilbert separável são quase certamente ortogonais ao núcleo de seu respectivo operador de covariância. É dada uma prova direta deste fato. / The present Thesis is composed of 4 research papers in two distinct areas. In Horta, Guerre, and Fernandes (2015), which constitutes Chapter 2 of this Thesis, we propose a smoothed estimator in the framework of the linear quantile regression model of Koenker and Bassett (1978). A uniform Bahadur-Kiefer representation is provided, with an asymptotic rate which dominates the standard quantile regression estimator. Next, we prove that the bias introduced by smoothing is negligible in the sense that the bias term is firstorder equivalent to the true parameter. A precise rate of convergence, which is controlled uniformly by choice of bandwidth, is provided. We then study second-order properties of the smoothed estimator, in terms of its asymptotic mean squared error, and show that it improves on the usual estimator when an optimal bandwidth is used. As corollaries to the above, one obtains that the proposed estimator is p n-consistent and asymptotically normal. Next, we provide a consistent estimator of the asymptotic covariance matrix which does not depend on ancillary estimation of nuisance parameters, and from which asymptotic confidence intervals are straightforwardly computable. The quality of the method is then illustrated through a simulation study. The research papers Horta and Ziegelmann (2015a;b;c) are all related in the sense that they stem from an initial impetus of generalizing the results in Bathia et al. (2010). In Horta and Ziegelmann (2015a), Chapter 3 of this Thesis, we address the question of existence of certain stochastic processes, which we call conjugate processes, driven by a second, measure-valued stochastic process. We investigate primitive conditions ensuring existence and, through the concepts of coherence and compatibility, obtain an affirmative answer to the former question. Relying on the notions of random measure (Kallenberg (1973)) and disintegration (Chang and Pollard (1997), Pollard (2002)), we provide a general approach for construction of conjugate processes. The theory allows for a rich set of examples, and includes a class of Regime Switching models. In Horta and Ziegelmann (2015b), Chapter 4 of the present Thesis, we introduce, in relation with the construction in Horta and Ziegelmann (2015a), the concept of a weakly conjugate process: a continuous time, real valued stochastic process driven by a sequence of random distribution functions, the connection between the two being given by a compatibility condition which says that distributional aspects of the former process are divisible into countably many cycles during which it has precisely the latter as marginal distributions. We then show that the methodology of Bathia et al. (2010) can be applied to study the dependence structure of weakly conjugate processes, and therewith provide p n-consistency results for the natural estimators appearing in the theory. Additionally, we illustrate the methodology through an implementation to financial data. Specifically, our method permits us to translate the dynamic character of the distribution of an asset returns process into the dynamics of a latent scalar process, which in turn allows us to generate forecasts of quantities associated to distributional aspects of the returns process. In Horta and Ziegelmann (2015c), Chapter 5 of this Thesis, we obtain p n-consistency results regarding estimation of the spectral representation of the zero-lag autocovariance operator of stationary Hilbertian time series, in a setting with imperfect measurements. This is a generalization of the method developed in Bathia et al. (2010). The generalization relies on the important property that centered random elements of strong second order in a separable Hilbert space lie almost surely in the closed linear span of the associated covariance operator. We provide a straightforward proof to this fact.