No description available.

In solving noise-free and noisy optimization problems, candidate initialization and sampling play a key role, but are not deeply investigated. It is of interest to know if the entire search space has the same quality for candidate-solutions during solving different type of optimization problems. In this thesis, a comprehensive investigation is conducted in order to clear those doubts, and to examine the effects of variant sampling methods on solving challenging optimization problems, such as large-scale, noisy, and multi-modal problems. As a result, the search space is segmented by using seven segmentation schemes, namely: Center-Point, Center-Based, Modula-Opposite, Quasi-Opposite, Quasi-Reflection, Supper- Opposite, and Opposite-Random. The introduced schemes are studied using Monte-Carlo simulation, on various types of noise-free optimization problems, and ultimately ranked based on their performance in terms of probability of closeness, average distance to unknown solution, number of solutions found, and diversity. Based on the results of the experiments, high-ranked schemes are selected and utilized on well-known metaheuristic algorithms, as case studies. Two categories of case studies are targeted; one for a singlesolution- based metaheuristic (S-metaheuristic) and another one for a population based metaheuristic (P-metaheuristic). A high-ranked single-solution-based scheme is utilized to accelerate Simulated Annealing (SA) algorithm, as a noise-free S-metaheuristic case study. Similarly, for noise-free P-metaheuristic case study, an effective population-based algorithm, Differential Evolution (DE), has been utilized. The experiments confirm that the new algorithms outperform the parent algorithm (DE) on large-scale problems. In the same direction, with regards to solving noisy problems more efficiently, a Shaking-based sampling method is introduced, in which the original noise is tackled by adding an additional noise into the search process. As a case study, the Shaking-based sampling is utilized on the DE algorithm, from which two variant algorithms have been developed and showed impressive performance in comparison to the classical DE, in tackling noisy largescale problems. This thesis has created an opportunity for a comprehensive investigation on search space segmentation schemes and proposed new sampling methods. The current study has provided a guide to use appropriate sampling schemes for a given types of problems such as noisy, large-scale and multi-modal optimization problems. Furthermore, this thesis questions the effectiveness of uniform-random sampling method, which is widely used in of S-Metaheuristic and P-Metaheuristic algorithms. / UOIT

Master of Science / Department of Statistics / Perla E. Reyes Cuellar / The term network has become part of our everyday vocabulary. The more popular are perhaps the social ones, but the concept also includes business partnerships, literature citations, biological networks, among others. Formally, networks are defined as sets of items and their connections. Often modeled as the mathematic object known as a graph, networks have been studied extensively for several years, and research is widely available. In statistics, a variety of modeling techniques and statistical terms have been developed to analyze them and predict individual behaviors. Specifically, certain statistics like degree distribution, clustering coefficient, and so on are considered important indicators in traditional social network studies. However, while conventional network models assume that the whole network population is known, complete information is not always available. Thus, different sampling methods are often required when the population data is inaccessible. Less time has been dedicated to studying the accuracy of these sampling methods to produce a representative sample. As such, the aim of this report is to identify the capacity of sampling techniques to reflect the features of the original network. In particular, we study Anti-cluster Respondent Driven Sampling (AC-RDS). We also explore whether standard modeling techniques paired with sample data could estimate statistics often used in the study of social networks. Respondent Driven Sampling (RDS) is a chain referral approach to study rare and/or hidden populations. Originating from the link-tracing design, RDS has been further developed into a series of methods utilized in social network studies, such as locating target populations or estimating the number and proportion of needle-sharing among drug addicts. However, RDS does not always perform as well as expected. When the social network contains tight communities (or clusters) with few connections between them, traditional RDS tends to oversample one community, introducing bias. AC-RDS is a special Markov chain process that collects samples across communities, capturing the whole network. With special referral requests, the initial seeds are more likely to refer to the individuals that are outside their communities. In this report, we fitted the Exponential Random Graph Model (ERGM) and a Stochastic Block Model (SBM) to an empirical study of the Facebook friendship network of 1034 participants. Then, given our goal of identifying techniques that will produce a representative sample, we decided to compare two version of AC-RDSs, in addition to traditional RDS, with Simple Random Sampling (SRS). We compared the methods by drawing 100 network samples using each sampling technique, then fitting an SBM to each sample network we used the results to project the network into one of population size. We calculated essential network statistics, such as degree distribution, of each sampling method and then compared the result to the original network observed statistics.

Most problems in engineering and natural sciences involve parametric equations in which the parameters are not known exactly due to measurement errors, lack of measurement data, or even intrinsic variability. In such problems, one objective is to compute point or aggregate values, called “quantities of interest”. A rapidly growing research area that tries to tackle this problem is Uncertainty Quantification (UQ). As the name suggests, UQ aims to accurately quantify the uncertainty in quantities of interest. To that end, the approach followed in this thesis is to describe the parameters using probabilistic measures and then to employ probability theory to approximate the probabilistic information of the quantities of interest. In this approach, the parametric equations must be accurately solved for multiple values of the parameters to explore the dependence of the quantities of interest on these parameters, using various so-called “sampling methods”. In almost all cases, the parametric equations cannot be solved exactly and suitable numerical discretization methods are required. The high computational complexity of these numerical methods coupled with the fact that the parametric equations must be solved for multiple values of the parameters make UQ problems computationally intensive, particularly when the dimensionality of the underlying problem and/or the parameter space is high. This thesis is concerned with optimizing existing sampling methods and developing new ones. Starting with the Multilevel Monte Carlo (MLMC) estimator, we first prove its normality using the Lindeberg-Feller CLT theorem. We then design the Continuation Multilevel Monte Carlo (CMLMC) algorithm that efficiently approximates the parameters required to run MLMC. We also optimize the hierarchies of one-dimensional discretization parameters that are used in MLMC and analyze the tolerance splitting parameter between the statistical error and the bias constraints. An important contribution of this thesis is the novel Multi-index Monte Carlo (MIMC) method which is an extension of MLMC in high dimensional problems with significant computational savings. Under reasonable assumptions on the weak and variance convergence, which are related to the mixed regularity of the underlying problem and the discretization method, the order of the computational complexity of MIMC is, at worst up to a logarithmic factor, independent of the dimensionality of the underlying parametric equation. We also apply the same multi-index methodology to another sampling method, namely the Stochastic Collocation method. Hence, the novel Multi-index Stochastic Collocation method is proposed and is shown to be more efficient in problems with sufficient mixed regularity than our novel MIMC method and other standard methods. Finally, MIMC is applied to approximate quantities of interest of stochastic particle systems in the mean-field when the number of particles tends to infinity. To approximate these quantities of interest up to an error tolerance, TOL, MIMC has a computational complexity of O(TOL-2log(TOL)2). This complexity is achieved by building a hierarchy based on two discretization parameters: the number of time steps in an Milstein scheme and the number of particles in the particle system. Moreover, we use a partitioning estimator to increase the correlation between two stochastic particle systems with different sizes. In comparison, the optimal computational complexity of MLMC in this case is O(TOL-3) and the computational complexity of Monte Carlo is O(TOL-4).

Indiana University-Purdue University Indianapolis (IUPUI) / Social dysfunction is a hallmark of schizophrenia and leads to significant disability and distress. Decreased positive and increased negative affect predict poorer social functioning in those with schizophrenia. Social functioning and affect have traditionally been measured in the laboratory; yet, these methods are limited. Experience sampling methods (ESM) offer more immediate, ecologically valid assessments of these constructs. The purpose of this study was to examine social functioning and affect in schizophrenia using a novel form of ESM that passively collects audio data. The two primary hypotheses were: 1) clinical status (schizophrenia versus control) will predict social functioning, level of positive affect, and level of negative affect; and 2) the relationship between clinical status and affect will be moderated by context (social versus non-social). Additional exploratory aims tested the convergent validity between traditional, laboratory-based assessments of social functioning and this novel ESM. Data was collected from 38 people with schizophrenia and 36 control participants; Results partially supported the hypotheses. As expected, laboratory measures of social functioning revealed that those with schizophrenia performed worse than controls. ESM measures of social functioning found that the schizophrenia group interacted with others at the same rate as the control group but did not exhibit as much social engagement. ESM measures of affect revealed the schizophrenia group reported more negative affect than controls, but no differences in positive affect were found. Social context did not moderate the relationship between clinical status and affect. Lastly, correlations between laboratory measures and ESM measures of social functioning were significant for the schizophrenia group but not the control group. Results further our understanding of social functioning and affect in those with schizophrenia and yield important implications for future work.

L'objet de cette thèse est le développement et l'étude des algorithmes de planification de mouvement pour les systèmes hautement dimensionnés que sont les robots humanoïdes et les acteurs virtuels. Plusieurs adaptations des méthodes génériques de planification de mouvement randomisées sont proposées et discutées. Une première contribution concerne l'utilisation de techniques de réduction de dimension linéaire pour accélérer les algorithmes d'échantillonnage. Cette méthode permet d'identifier en ligne quand un processus de planification passe par un passage étroit de l'espace des configurations et adapte l'exploration en fonction. Cet algorithme convient particulièrement bien aux problèmes difficiles de la planification de mouvement pour l'animation graphique. La deuxième contribution est le développement d'algorithmes randomisés de planification sous contraintes. Il s'agit d'une intégration d'outils de cinématique inverse hiérarchisée aux algorithmes de planification de mouvement randomisés. On illustre cette méthode sur différents problèmes de manipulation pour robots humanoïdes. Cette contribution est généralisée à la planification de mouvements corps-complet nécessitant de la marche. La dernière contribution présentée dans cette thèse est l'utilisation des méthodes précédentes pour résoudre des tâches de manipulation complexes par un robot humanoïde. Nous présentons en particulier un formalisme destiné à représenter les informations propres à l'objet manipulé utilisables par un planificateur de mouvement. Ce formalisme est présenté sous le nom d'« objets documentés». / This thesis deals with the development and analysis of motion planning algorithms for high dimensional systems: humanoid robots and digital actors. Several adaptations of generic randomized motion planning methods are proposed and discussed. A first contribution concerns the use of linear dimensionality reduction techniques to speed up sampling algorithms. This method identifies on line when a planning process goes through a narrow passage of some configuration space, and adapts the exploration accordingly. This algorithm is particularly suited to difficult problems of motion planning for computer animation. The second contribution is the development of randomized algorithms for motion planning under constraints. It consists in the integration of prioritized inverse kinematics tools within randomized motion planning. We demonstrate the use of this method on different manipulation planning problems for humanoid robots. This contribution is generalized to whole-body motion planning with locomotion. The last contribution of this thesis is the use of previous methods to solve complex manipulation tasks by humanoid robots. More specifically, we present a formalism that represents information specific to a manipulated object usable by a motion planner. This formalism is presented under the name of "documented object".

O Estado de São Paulo é o principal produtor de uvas de mesa do país, sendo a Niágara Rosada (Vitis Labrusca) a cultivar predominante. Para se oferecer produtos de qualidade ao mercado, os produtores necessitam determinar, periodicamente, o estado de maturação das uvas, sendo o teor de sólidos solúveis (tss), a principal variável avaliada. Para essa determinação, utilizase a amostragem dos frutos na área cultivada. O presente trabalho discute, assim, os métodos de amostragem estratificado e aleatório, e o tamanho adequado da amostra de baga individual, para avaliar o estado de maturação da uva Niágara Rosada, com base no teor de sólidos solúveis. O tamanho adequado da amostra de baga individual foi encontrado para os dois métodos de amostragem, separadamente, utilizando-se os métodos Máxima Curvatura, Máxima Curvatura Modificado e Curva da Variancia. Os métodos de amostragem foram comparados utilizando-se uma análise univariada para dados com medidas repetidas, através dos procedimentos GLM e MIXED do SAS. Foram utilizados dois procedimentos, para que se produzisse resultados confiáveis. Os tamanhos mínimos de amostra de baga individual requeridos, para os métodos estratificado e aleatório foram aproximadamente 30 e 27 bagas por área, respectivamente. Os métodos de amostragem estudados apresentaram diferença significativa, e o método aleatório apresentou grande variação máxima e mínima por planta, devendo assim, ser evitado para esse tipo de estudo. / Sao Paulo state is the main table grape producer in Brazil, being the Niágara Rosada (Vitis Labrusca) the predominant cultivar. To offer quality products to the market, the producers need to determine, periodically, the grapes maturation state, being the content of soluble solids the main variable measured. To determine this content, a sample of fruits in an area is collected. This work approaches the random and the stratified sampling methods and the appropriate sample size of individual berry to evaluate the maturation state of the Niágara Rosada based on the content of soluble solids. The appropriate sample size for individual berry was obtained for two sampling methods, separately, using the Maximum Curvature, Modified Maximum Curvature and Variance Curve methods. The sampling methods were compared using a univariate analysis for repeated measures data using the SAS GLM and MIXED procedures. Two different procedures were used to attain reliable results. The minimum berry sample size required for stratified and random methods were approximately 30 and 27 berries by area, respectively. The sampling methods investigated present significantly different results, and the random method presented high maximum and minimum variation by plant and should be avoided for this kind of study.

Métodos de amostragem no levantamento da comunidade arbórea em floresta estacional semidecidual foram comparados. Primeiro foi testado o método de Bitterlich a fim de selecionar o fator de área basal mais adequado para o estudo da comunidade arbórea. O critério de inclusão adotado foi todas as árvores com DAP > 10 cm. Os fatores de área basal de 2, 3 e 4 m 2 ha -1 amostraram 596, 408 e 297 indivíduos e 59, 57 e 50 espécies, respectivamente. As estimativas de área basal, DAP médio, diversidade e equabilidade não apresentaram diferenças significativas. O fator de área basal igual a 3 foi selecionado porque mostrou melhor resultado em relação ao tempo gasto e facilidade de campo. Em uma segunda análise, os métodos de parcelas de área fixa (100 parcelas contíguas), pontos quadrantes e pontos de Bitterlich foram comparados para o levantamento da comunidade arbórea. O critério de inclusão adotado foi todas as árvores > 10cm. As 100 parcelas contíguas de 10x10m amostraram 59 espécies. Os 177 pontos de quadrantes amostraram 69 espécies e os 45 pontos de Bitterlich (fator de área basal = 3 m 2 ha -1 ) amostraram 57 espécies. Ocotea indecora foi favorecida pelo método de Bitterlich. O método de Bitterlich apresentou dificuldades no trabalho de campo devido a falta de visibilidade em algum pontos. Entretanto esse método apresentou melhor resultado na amostragem de espécies quando o esforço amostral é analisado por unidades amostrais. O método de quadrantes foi melhor na análise do esforço amostral por tempo. Na terceira análise o efeito de desvios da completa aleatoriedade espacial sobre a estimativa de densidade produzida pelo método de quadrantes foi analisada através de simulação de Monte Carlo. Foram geradas florestas hipotéticas com padrão espacial regular e agrupado com diferentes densidades. O efeito do tamanho da amostra também foi analisado, porém não mostrou efeito significativo na redução do viés. Os valores de viés relativo da estimativa da densidade variaram desde +70,3% (florestas regulares) até -75,7% (florestas fortemente agrupadas). A densidade de árvores não causou efeito na estimativa do viés, com exceção para as florestas completamente aleatórias e regulares em lattice aleatorizado. O método de quadrantes superestima a densidade arbórea para as florestas com padrão regular e subestima a densidade para as florestas com padrão espacial agrupado. É importante saber a priori o padrão espacial da floresta a fim de se aplicar o método de quadrantes e saber interpretar os seus resultados. / Sampling methods for surveying in tree species community in a semideciduos forest were compared. First was applied the angle count sampling method and select the best basal area factor to study the tree community. The criterion of inclusion adopted was all trees with DBH > 10cm. The basal factors 2, 3 and 4 m 2 ha -1 sampled 596, 408 and 297 individuals and 59, 57 and 50 species. The estimates of basal area, mean DBH, density, diversity and equability are not significantly differents among basal area factors. The basal area factor 3 was selected because showed better performance in terms of time spent and field operation. In a second analysis three sampling methods were compared for survey tree species community: fixed area plot (100 contiguos plots), point centered quarter method and Bitterlich method. The criterion of inclusion adopted was all trees with DBH > 10cm. The 100 contiguous plots of 10x10m showed 59 species. The 177 centered quarter method sampled 69 species and the 45 angle count points (basal area factor = 3 m 2 ha -1 ) showed 57 species. Ocotea indecora was favored by the Bitterlich method. Bitterlich method presented difficulty in field operation due to the lack of visibility in some sample points. However it better presented performance in the sampling of species in the amostral effort for plots. The centered quarter method was better in the amostral effort for time. In a third analysis the effect of deviation from the complete spatial randomness on point centered quarter method estimate of forest density was analysed through Monte Carlo simulation of hypothetical forests with regular and clustered spatial patterns and with diferent densities. The influence of sample size was also analysed, but showed no marked effect on estimation biases. The relative bias on the tree density estimation varied from +70.3% (regular lattice spatial pattern) to -75.7% (strongly clustered spatial pattern). Tree density did not affected estimation bias, except for completely spatial pattern and randomized regular lattice pattern. Point-centered quarter method overestimate (positive bias) tree density for regular patterns and underestimate (negative bias) for clustered patterns. Knowledge of tree spatial pattern in a forest is necessary for correct implementation and results interpretation in this method.

Inference for dynamic systems and conformational sampling for protein folding are two problems motivated by applied data, which pose computational challenges from a statistical perspective. Dynamic systems are often described by a set of coupled differential equations, and methods of parametric estimation for these models from noisy data can require repeatedly solving the equations numerically. Many of these models also lead to rough likelihood surfaces, which makes sampling difficult. We introduce a method for Bayesian inference on these models, using a multiple chain framework that exploits the underlying mathematical structure and interpolates the posterior to improve efficiency. In protein folding, a large conformational space must be searched for low energy states, where any energy function constructed on the states is at best approximate. We propose a method for sampling fragment conformations that accounts for geometric and energetic constraints, and explore ideas for folding entire proteins that account for uncertain energy landscapes and learning from data more effectively. These ingredients are combined into a framework for tackling the problem of generating improvements to protein structure predictions. / Statistics

Saproxylic insects rely on dead or dying wood at some point in their development and appear to be sensitive to forest management. In 2005 and 2006, I sampled saproxylic insects in mixedwood boreal forests in northeastern Ontario to assess effects of: 1) different logging practices, 2) variations in woody debris (WD) qualities, and 3) different sampling methods. I also compared insect communities between heavily decayed WD and soil. Although I collected data on all arthropod orders, I focused on the families of the Diptera and parasitic Hymenoptera and the morphospecies of the Scelionidae and Diapriidae. These insects showed clear responses to the WD quality treatments, but not to the different logging treatments. A few families were affected by ex situ sampling. I also found that the faunas of soil and WD are rather distinct from each other. This study shows that WD is a source of forest biodiversity. Consequently, sustainable forest management will rely on studies like this to conserve and maintain the biodiversity of Canada's largest group of eco-zones.