Neste trabalho apresentamos uma demonstração detalhada para um conhecido teorema de I. J. Schoenberg que caracteriza certas funções positivas definidas em esferas. Analisamos ainda um critério para a obtenção de positividade definida de uma função a partir de condições de suavidade e convexidade dela, em uma tentativa de ratificar alguns resultados da literatura conhecidos como critérios de Pólya. / In this work we present a proof for a famous theorem of Schoenberg on positive definite functions on spheres. We analyze some results that deduce positive definiteness from diferentiability and convexity assumption on the function, an attempt to ratify some Pólya type conjectures found in the literature.

O principal objetivo deste trabalho e descrever o decaimento dos autovalores de operadores integrais gerados por núcleos definidos por séries de potências, mediante hipóteses sobre os coeficientes na série que representa o núcleo gerador. A análise e implementada em duas frentes: inicialmente, consideramos o caso em que o núcleo esta definido sobre a esfera unitária de \'R POT. m+1\', estendendo posteriormente a análise, para o caso da bola unitária do mesmo espaço. Em seguida, visando primordialmente o caso em que o núcleo esta definido sobre a esfera unitaria em \'C POT. m+1\', abordamos um caso mais geral, aquele no qual o núcleo esta definido por uma série de funções \'L POT. 2\'(X, u)-ortogonais, sendo (X, u) um espaço de medida arbitrário / The main target in this work is to deduce eigenvalue decay for integral operators generated by power series kernels, under general assumptions on the coefficients in the series representing the kernel. The analysis is twofold: firstly, we consider generating kernels defined on the unit sphere in \'R POT. m+1\', replacing the sphere with the unit ball in a subsequent stage. Secondly, we consider generating kernels defined on a general measure space (X, u) and possessing an \'L POT. 2\'(X, u)-orthogonal expansion there, an attempt to cover the case in which the kernel is defined on the unit sphere in \'C POT. m+1\'

Biological systems are driven by complex regulatory processes. Graphical models play a crucial role in the analysis and reconstruction of such processes. It is possible to derive regulatory models using network inference algorithms from high-throughput data, for example; from gene or protein expression data. A wide variety of network inference algorithms have been designed and implemented. Our aim is to explore the possibilities of using statistical independence criteria for biological network inference. The contributions of our work can be categorized into four sections. First, we provide a detailed overview of some of the most popular general independence criteria: distance covariance (dCov), kernel canonical variance (KCC), kernel generalized variance (KGV) and the Hilbert-Schmidt Independence Criterion (HSIC). We provide easy to understand geometrical interpretations for these criteria. We also explicitly show the equivalence of dCov, KGV and HSIC. Second, we introduce a new criterion for measuring dependence based on the signal to noise ratio (SNRIC). SNRIC is significantly faster to compute than other popular independence criteria. SNRIC is an approximate criterion but becomes exact under many popular modelling assumptions, for example for data from an additive noise model. Third, we compare the performance of the independence criteria on biological experimental data within the framework of the PC algorithm. Since not all criteria are available in a version that allows for testing conditional independence, we propose and test an approach which relies on residuals and requires only an unconditional version of an independence criterion. Finally we propose a novel method to infer networks with feedback loops. We use an MCMC sampler, which samples using a loss function based on an independence criterion. This allows us to find networks under very general assumptions, such as non-linear relationships, non-Gaussian noise distributions and feedback loops.

Heterogeneous platforms play an increasingly important role in modern computer systems. They combine high performance with low power consumption. From mobiles to supercomputers, we see an increasing number of computer systems that are heterogeneous. The most well-known heterogeneous system, CPU+GPU platforms have been widely used in recent years. As they become more mainstream, serving multiple tasks from multiple users is an emerging challenge. A good scheduler can greatly improve performance. However, indiscriminately allocating tasks based on availability leads to poor performance. As modern GPUs have a large number of hardware resources, most tasks cannot efficiently utilize all of them. Concurrent task execution on GPU is a promising solution, however, indiscriminately running tasks in parallel causes a slowdown. This thesis focuses on scheduling OpenCL kernels. A runtime framework is developed to determine where to schedule OpenCL kernels. It predicts the best-fit device by using a machine learning-based classifier, then schedules the kernels accordingly to either CPU or GPU. To improve GPU utilization, a kernel merging approach is proposed. Kernels are merged if their predicted co-execution can provide better performance than sequential execution. A machine learning based classifier is developed to find the best kernel pairs for co-execution on GPU. Finally, a runtime framework is developed to schedule kernels separately on either CPU or GPU, and run kernels in pairs if their co-execution can improve performance. The approaches developed in this thesis significantly improve system performance and outperform all existing techniques.

Inicialmente, estudamos alguns resultados clássicos da teoria dos núcleos positivos definidos e alguns resultados pertinentes. Estudamos em seguida, o Teorema de Mercer e algumas de suas generalizações e conseqüências, incluindo a caracterização da transformada de Fourier de um núcleo positivo definido com domínio Rm£Rm, m ¸ 1. O trabalho traz um enfoque especial nos núcleos cujo domínio é um subconjunto não-compacto de Rm £ Rm, uma vez que os demais casos são considerados de maneira extensiva na literatura. Aplicamos esses estudos na análise do decaimento dos autovalores de operadores integrais gerados por núcleos positivos definidos / Firstly, we study some classical results from the theory of positive definite kernels along with some related results. Secondly, we focus on generalizations of Mercer\'s theorem and some of their implications. Special attention is given to the cases where the domain of the kernel is not compact, once the other cases are considered consistently in the literature. We include a characterization for the Fourier transform of a positive definite kernel on Rm£Rm, m ¸ 1. Finally, we apply the previous study in the analysis of decay rates for eigenvalues of integral operators generated by positive definite kernels

Neste trabalho apresentamos uma demonstração detalhada para um conhecido teorema de I. J. Schoenberg que caracteriza certas funções positivas definidas em esferas. Analisamos ainda um critério para a obtenção de positividade definida de uma função a partir de condições de suavidade e convexidade dela, em uma tentativa de ratificar alguns resultados da literatura conhecidos como critérios de Pólya. / In this work we present a proof for a famous theorem of Schoenberg on positive definite functions on spheres. We analyze some results that deduce positive definiteness from diferentiability and convexity assumption on the function, an attempt to ratify some Pólya type conjectures found in the literature.

This thesis focuses particularly on the application of chemometrics in the field of analytical chemistry. Chemometrics (or multivariate analysis) consists in finding a relationship between two groups of variables, often called dependent and independent variables. In infrared spectroscopy for instance, chemometrics consists in the prediction of a quantitative variable (the obtention of which is delicate, requiring a chemical analysis and a qualified operator), such as the concentration of a component present in the studied product from spectral data measured on various wavelengths or wavenumbers (several hundreds, even several thousands). In this research we propose a methodology in the field of chemometrics to handle the chemical data (spectrophotometric data) which are often in high dimension. To handle these data, we first propose a new incremental method (step-by-step) for the selection of spectral data using linear and non-linear regression based on the combination of three principles: linear or non-linear regression, incremental procedure for the variable selection, and use of a validation set. This procedure allows on one hand to benefit from the advantages of non-linear methods to predict chemical data (there is often a non-linear relationship between dependent and independent variables), and on the other hand to avoid the overfitting phenomenon, one of the most crucial problems encountered with non-linear models. Secondly, we propose to improve the previous method by a judicious choice of the first selected variable, which has a very important influence on the final performances of the prediction. The idea is to use a measure of the mutual information between the independent and dependent variables to select the first one; then the previous incremental method (step-by-step) is used to select the next variables. The variable selected by mutual information can have a good interpretation from the spectrochemical point of view, and does not depend on the data distribution in the training and validation sets. On the contrary, the traditional chemometric linear methods such as PCR or PLSR produce new variables which do not have any interpretation from the spectrochemical point of view. Four real-life datasets (wine, orange juice, milk powder and apples) are presented in order to show the efficiency and advantages of both proposed procedures compared to the traditional chemometric linear methods often used, such as MLR, PCR and PLSR.

Caribbean spiny lobster (Panulirus argus) is a popular and heavily exploited seafood throughout its range. This species supports the primary fishery in many Caribbean countries, especially in the Bahamas, which reports the highest catches and where spiny lobster serves as the number one food export. P. argus possesses one of the longest pelagic larval durations of any marine species, ranging from 6-12 months. This allows for the possibility of long-range dispersal, which would make it difficult to determine if local adult populations originate from areas close-by or within the same countries/jurisdictions, thus presenting implications for conservation and management of the species. This project seeks to explore the policy implications of lobster larval dispersal in the Bahamas by examining the larval connectivity of locally spawned P. argus in order to determine the mean dispersal kernel and to identify hotspots of settlement within the area. A coupled biophysical model was used to simulate larval transport from scaled egg production of 47 release locations within the Bahamas. The model was initialized bi-weekly from April through May, the highest months of larvae production in the Bahamas, with each model run occurring for a maximum of 180 days. The dispersal kernel for the Bahamas was calculated to be an average of 100-300 km, indicating that the larvae released within its boundaries typically settled there as well. Due to the long pelagic larval duration, larval particles were able to travel extensive distances, averaging trajectories covering distances of 4000 km and greater from the source locations. Yet, those same larval particles still settled in locations within the Bahamas, suggesting local retention, which varies from the common perception that lobster in the Bahamas originate elsewhere. This knowledge can be used to assess and perhaps reevaluate conservation and management strategies related to the Bahamian P. argus fishery, including the implementation of MPAs and/or MPA networks, input and output management controls, and other management tools.

In the study of the Degasperis-Procesi dierential equation, an eigenvalue problem called the cubic string occurs. This is a third order generalization of the second order problem describing the eigenmodes of a vibrating string. In this thesis we study the eigenfunctions of the cubic string for discrete and continuous mass distributions, using the theory of total positivity, via a combinatorial approach with planar networks.

<p>This Master thesis describes the benchmarking of a DSP processor. Benchmarking means measuring the performance in some way. In this report, we have focused on the number of instruction cycles needed to execute certain algorithms. The algorithms we have used in the benchmark are all very common in signal processing today. </p><p>The results we have reached in this thesis have been compared to benchmarks for other processors, performed by Berkeley Design Technology, Inc. </p><p>The algorithms were programmed in assembly code and then executed on the instruction set simulator. After that, we proposed changes to the instruction set, with the aim to reduce the execution time for the algorithms. </p><p>The results from the benchmark show that our processor is at the same level as the ones tested by BDTI. Probably would a more experienced programmer be able to reduce the cycle count even more, especially for some of the more complex benchmarks.</p>