Magister Scientiae (Biodiversity and Conservation Biology) / Since the late 1970 there has been increased concern of amphibian decline and extinction. Several causes for the worldwide declines have been suggested and include ultraviolet radiation, predation, pollution, climate change, diseases and habitat modification. To counter this, more research on the subject has been encouraged of which long term monitoring has been suggested as a research method. The study was conducted in Kakamega Forest in Kenya, which is the country's remnant of the once vast Guineo-Congolian forest. A rectangular transect whose sides measured 600 m in total was established and transect walks were carried out every two weeks for two consecutive days between 2002 and 2006. 24 species were targeted in the study and were sampled through VES and AES and data recorded in a GPS and later downloaded. In this study I examined the influence of rainfall, temperature, habitat and moon phases on the activity of frogs in Kakamega Forest. I also determined under which weather conditions sampling was more efficient. When monitoring was carried out by two observers I tested whether their data were similar. Data were analysed using non-parametric methods (Kruskal-wallis and Tukey test), species abundances analysed using EstimateS..Out of the 24 targeted species only 14 were recorded, with a total of 535 specimens being counted mostly at night. Most frogs in Kakamega Forest were more active in temperatures between 20 and 25oC. There was not much variation and there was no frog activity when the temperature was extremely high. There was rainfall throughout the year and there was no significant differences in the number of frogs counted in rainfall above 200 mm or below 200 mm. There was no significant difference in the number of specimens found in the different vegetation segments in the forest. More amphibians were caught under cloudy, rainy and clear conditions at night than under any weather condition during the day. During the day, more amphibians were caught during cloudy conditions than when it rained or when there was no cloud cover. There was no difference in catch among night conditions and there was no difference between clear and rainy days In Kakamega Forest, night is the best time to sample amphibians. In terms of weather it is best to sample when it is cloudy both during the day and at night. There were no differences in sampling abilities between two observers tested under similar weather conditions.

The inadequacies of the current generation of deconvolution algorithms are rapidly becoming apparent as new, more sensitive radio interferometers are constructed. In light of these inadequacies, there is renewed interest in the field of deconvolution. Many new algorithms are being developed using the mathematical framework of compressed sensing. One such technique, MORESANE, has recently been shown to be a powerful tool for the recovery of faint difuse emission from synthetic and simulated data. However, the original implementation is not well-suited to large problem sizes due to its computational complexity. Additionally, its use of proprietary software prevents it from being freely distributed and used. This has motivated the development of a freely available Python implementation, PyMORESANE. This thesis describes the implementation of PyMORESANE as well as its subsequent augmentation with MPU and GPGPU code. These additions accelerate the algorithm and thus make it competitive with its legacy counterparts. The acceleration of the algorithm is verified by means of benchmarking tests for varying image size and complexity. Additionally, PyMORESANE is shown to work not only on synthetic data, but on real observational data. This verification means that the MORESANE algorithm, and consequently the PyMORESANE implementation, can be added to the current arsenal of deconvolution tools.

The thesis deals with brief introduction of the quantile regression theory. The thesis is divided into three thematic parts. In the first part the thesis deals with general introduction to the quantile regression, with theoretical aspects regarding quantile regression and with basic approaches to estimation of quantile regression parameters. The second part of the thesis focuses on general and asymptotic properties of the quantile regression. Goal of this part is to compare the quantile regression with traditional OLS regression and outline its possible application. In the third part the thesis describes statistical inference, construction of the confidence intervals and testing statistical hypotheses about quantile regression parameters. The goal of this part is to introduce traditional approach and the approach based on resampling procedures and in the end of the day perform mutual comparison of different approaches eventually propose partial modification.

abstract: This thesis addresses the following fundamental maximum throughput routing problem: Given an arbitrary edge-capacitated n-node directed network and a set of k commodities, with source-destination pairs (s_i,t_i) and demands d_i> 0, admit and route the largest possible number of commodities -- i.e., the maximum throughput -- to satisfy their demands. The main contributions of this thesis are three-fold: First, a bi-criteria approximation algorithm is presented for this all-or-nothing multicommodity flow (ANF) problem. This algorithm is the first to achieve a constant approximation of the maximum throughput with an edge capacity violation ratio that is at most logarithmic in n, with high probability. The approach used is based on a version of randomized rounding that keeps splittable flows, rather than approximating those via a non-splittable path for each commodity: This allows it to work for arbitrary directed edge-capacitated graphs, unlike most of the prior work on the ANF problem. The algorithm also works if a weighted throughput is considered, where the benefit gained by fully satisfying the demand for commodity i is determined by a given weight w_i>0. Second, a derandomization of the algorithm is presented that maintains the same approximation bounds, using novel pessimistic estimators for Bernstein's inequality. In addition, it is shown how the framework can be adapted to achieve a polylogarithmic fraction of the maximum throughput while maintaining a constant edge capacity violation, if the network capacity is large enough. Lastly, one important aspect of the randomized and derandomized algorithms is their simplicity, which lends to efficient implementations in practice. The implementations of both randomized rounding and derandomized algorithms for the ANF problem are presented and show their efficiency in practice. / Dissertation/Thesis / Masters Thesis Computer Science 2020

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Cette thèse porte sur l'étude probabiliste et statistique de populations sans interactions structurées par un trait. Elle est motivée par la compréhension des mécanismes de division et de vieillissement cellulaire. On modélise la dynamique de ces populations à l'aide d'un processus de Markov branchant à valeurs mesures. Chaque individu dans la population est caractérisé par un trait (l'âge, la taille, etc...) dont la dynamique au cours du temps suit un processus de Markov. Ce trait détermine le cycle de vie de chaque individu : sa durée de vie, son nombre de descendants et le trait à la naissance de ses descendants. Dans un premier temps, on s'intéresse à la question de l'échantillonnage uniforme dans la population. Nous décrivons le processus pénalisé, appelé processus auxiliaire, qui correspond au trait d'un individu "typique" dans la population en donnant son générateur infinitésimal. Dans un second temps, nous nous intéressons au comportement asymptotique de la mesure empirique associée au processus de branchement. Sous des hypothèses assurant l'ergodicité du processus auxiliaire, nous montrons que le processus auxiliaire correspond asymptotiquement au trait le long de sa lignée ancestrale d'un individu échantillonné uniformément dans la population. Enfin, à partir de données composées des traits à la naissance des individus dans l'arbre jusqu'à une génération donnée, nous proposons des estimateurs à noyau de la densité de transition de la chaine correspondant au trait le long d'une lignée ainsi que de sa mesure invariante. De plus, dans le cas d'une diffusion réfléchie sur un compact, nous estimons par maximum de vraisemblance le taux de division du processus. Nous montrons la consistance de cet estimateur ainsi que sa normalité asymptotique. L'implémentation numérique de l'estimateur est par ailleurs réalisée. / We study structured populations without interactions from a probabilistic and a statistical point of view. The underlying motivation of this work is the understanding of cell division mechanisms and of cell aging. We use the formalism of branching measure-valued Markov processes. In our model, each individual is characterized by a trait (age, size, etc...) which moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event occurs, the trait of the descendants at birth depends on the trait of the mother and on the number of descendants. First, we study the trait of a uniformly sampled individual in the population. We explicitly describe the penalized Markov process, named auxiliary process, corresponding to the dynamic of the trait of a "typical" individual by giving its associated infinitesimal generator. Then, we study the asymptotic behavior of the empirical measure associated with the branching process. Under assumptions assuring the ergodicity of the auxiliary process, we prove that the auxiliary process asymptotically corresponds to the trait along its ancestral lineage of a uniformly sampled individual in the population. Finally, we address the problem of parameter estimation in the case of a branching process structured by a diffusion. We consider data composed of the trait at birth of all individuals in the population until a given generation. We give kernel estimators for the transition density and the invariant measure of the chain corresponding to the trait of an individual along a lineage. Moreover, in the case of a reflected diffusion on a compact set, we use maximum likelihood estimation to reconstruct the division rate. We prove consistency and asymptotic normality for this estimator. We also carry out the numerical implementation of the estimator.

The development of adaptive mesh refinement capabilities in the field of computational fluid dynamics is an essential tool for enabling the simulation of larger and more complex physical problems. While such techniques have been known for a long time, most simulations do not make use of them because of the lack of a robust implementation. In this work, we present recent progresses that have been made to develop adaptive mesh refinement features in Nek5000, a code based on the spectral element method. These developments are driven by the algorithmic challenges posed by future exascale supercomputers. First, we perform the study of the strong scaling of Nek5000 on three petascale machines in order to assess the scalability of the code and identify the current bottlenecks. It is found that strong scaling limit ranges between 5, 000 and 220, 000 degrees of freedom per core depending on the machine and the case. The need for synchronized and low latency communication for efficient computational fluid dynamics simulation is also confirmed. Additionally, we present how Hypre, a library for linear algebra, is used to develop a new and efficient code for performing the setup step required prior to the use of an algebraic multigrid solver for preconditioning the pressure equation in Nek5000. Finally, the main objective of this work is to develop new methods for estimating the error on a numerical solution of the Navier–Stokes equations via the resolution of an adjoint problem. These new estimators are compared to existing ones, which are based on the decay of the spectral coefficients. Then, the estimators are combined with newly implemented capabilities in Nek5000 for automatic grid refinement and adaptive mesh adaptation is carried out. The applications considered so far are steady and two-dimensional, namely the lid-driven cavity at Re = 7, 500 and the flow past a cylinder at Re = 40. The use of adaptive mesh refinement techniques makes mesh generation easier and it is shown that a similar accuracy as with a static mesh can be reached with a significant reduction in the number of degrees of freedom. / <p>QC 20171114</p>

Segmented regression is a type of nonlinear regression that allows differing functional forms to be fit over different ranges of the explanatory variable. This paper considers the simple segmented regression case of two linear segments that are constrained to meet, often called the linear-linear model. Parameter estimation in the case where the joinpoint between the regimes is unknown can be tricky. Using a simulation study, four estimators for the parameters of the linear-linear model are evaluated. The bias and mean squared error of the estimators are considered under differing parameter combinations and sample sizes. Parameters estimated in the model are the location of the change-point, the slope and intercept of the first segment, the change in slope from the first segment to the second, and the variance over both segments.

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