Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

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A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel densityestimation techniques in the context of compositional data analysis. Indeed, they gavetwo options for the choice of the kernel to be used in the kernel estimator. One ofthese kernels is based on the use the alr transformation on the simplex SD jointly withthe normal distribution on RD-1. However, these authors themselves recognized thatthis method has some deficiencies. A method for overcoming these dificulties based onrecent developments for compositional data analysis and multivariate kernel estimationtheory, combining the ilr transformation with the use of the normal density with a fullbandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu-Figueras (2006). Here we present an extensive simulation study that compares bothmethods in practice, thus exploring the finite-sample behaviour of both estimators

Kernel-based methods for change detection in remote sensing images

Nowadays, the joint exploitation of images acquired daily by remote sensing instruments and of images available from archives allows a detailed monitoring of the transitions occurring at the surface of the Earth. These modifications of the land cover generate spectral discrepancies that can be detected via the analysis of remote sensing images. Independently from the origin of the images and of type of surface change, a correct processing of such data implies the adoption of flexible, robust and possibly nonlinear method, to correctly account for the complex statistical relationships characterizing the pixels of the images. This Thesis deals with the development and the application of advanced statistical methods for multi-temporal optical remote sensing image processing tasks. Three different families of machine learning models have been explored and fundamental solutions for change detection problems are provided. In the first part, change detection with user supervision has been considered. In a first application, a nonlinear classifier has been applied with the intent of precisely delineating flooded regions from a pair of images. In a second case study, the spatial context of each pixel has been injected into another nonlinear classifier to obtain a precise mapping of new urban structures. In both cases, the user provides the classifier with examples of what he believes has changed or not. In the second part, a completely automatic and unsupervised method for precise binary detection of changes has been proposed. The technique allows a very accurate mapping without any user intervention, resulting particularly useful when readiness and reaction times of the system are a crucial constraint. In the third, the problem of statistical distributions shifting between acquisitions is studied. Two approaches to transform the couple of bi-temporal images and reduce their differences unrelated to changes in land cover are studied. The methods align the distributions of the images, so that the pixel-wise comparison could be carried out with higher accuracy. Furthermore, the second method can deal with images from different sensors, no matter the dimensionality of the data nor the spectral information content. This opens the doors to possible solutions for a crucial problem in the field: detecting changes when the images have been acquired by two different sensors.

Time Series Input Selection using Multiple Kernel Learning

In this paper we study the relevance of multiple kernel learning (MKL) for the automatic selection of time series inputs. Recently, MKL has gained great attention in the machine learning community due to its flexibility in modelling complex patterns and performing feature selection. In general, MKL constructs the kernel as a weighted linear combination of basis kernels, exploiting different sources of information. An efficient algorithm wrapping a Support Vector Regression model for optimizing the MKL weights, named SimpleMKL, is used for the analysis. In this sense, MKL performs feature selection by discarding inputs/kernels with low or null weights. The approach proposed is tested with simulated linear and nonlinear time series (AutoRegressive, Henon and Lorenz series).

Exploração da Implementação Actual de IPv6 no Kernel do Linux

A presente dissertação visa retratar a exploração do suporte do protocolo internet versão seis (IPv6) no kernel do Linux, conjuntamente com a análise detalhada do estado de implementação dos diferentes aspectos em que se baseia o protocolo. O estudo incide na experimentação do funcionamento em geral do stack, a identificação de inconsistências deste em relação RFC’s respectivos, bem como a simulação laboratorial de cenários que reproduzam casos de utilização de cada uma das facilidades analisadas. O objecto desta dissertação não é explicar o funcionamento do novo protocolo IPv6, mas antes, centrar-se essencialmente na exploração do IPv6 no kernel do Linux. Não é um documento para leigos em IPv6, no entanto, optou-se por desenvolver uma parte inicial onde é abordado o essencial do protocolo: a sua evolução até à aprovação e a sua especificação. Com base no estudo realizado, explora-se o suporte do IPv6 no kernel do Linux, fazendo uma análise detalhada do estudo de implementação dos diferentes aspectos em que se baseia o protocolo. Bem como a realização de testes de conformidade IPv6 em relação aos RFC’s.

Mapping of Environmental Data Using Kernel-Based Methods

Recently, kernel-based Machine Learning methods have gained great popularity in many data analysis and data mining fields: pattern recognition, biocomputing, speech and vision, engineering, remote sensing etc. The paper describes the use of kernel methods to approach the processing of large datasets from environmental monitoring networks. Several typical problems of the environmental sciences and their solutions provided by kernel-based methods are considered: classification of categorical data (soil type classification), mapping of environmental and pollution continuous information (pollution of soil by radionuclides), mapping with auxiliary information (climatic data from Aral Sea region). The promising developments, such as automatic emergency hot spot detection and monitoring network optimization are discussed as well.

Variable Kernel estimates: On the impossibility of tuning the parameters

For the standard kernel density estimate, it is known that one can tune the bandwidth such that the expected L1 error is within a constant factor of the optimal L1 error (obtained when one is allowed to choose the bandwidth with knowledge of the density). In this paper, we pose the same problem for variable bandwidth kernel estimates where the bandwidths are allowed to depend upon the location. We show in particular that for positive kernels on the real line, for any data-based bandwidth, there exists a densityfor which the ratio of expected L1 error over optimal L1 error tends to infinity. Thus, the problem of tuning the variable bandwidth in an optimal manner is ``too hard''. Moreover, from the class of counterexamples exhibited in the paper, it appears thatplacing conditions on the densities (monotonicity, convexity, smoothness) does not help.

Weighted Kernel regression

In the fixed design regression model, additional weights areconsidered for the Nadaraya--Watson and Gasser--M\"uller kernel estimators.We study their asymptotic behavior and the relationships between new andclassical estimators. For a simple family of weights, and considering theIMSE as global loss criterion, we show some possible theoretical advantages.An empirical study illustrates the performance of the weighted estimatorsin finite samples.

Transformation kernel density estimation of actuarial loss functions

[cat] Es presenta un estimador nucli transformat que és adequat per a distribucions de cua pesada. Utilitzant una transformació basada en la distribució de probabilitat Beta l’elecció del paràmetre de finestra és molt directa. Es presenta una aplicació a dades d’assegurances i es mostra com calcular el Valor en Risc.

The Lorenz-maximal core allocations and the kernel in some classes of assignment games

En aquest treball demostrem que en la classe de jocs d'assignació amb diagonal dominant (Solymosi i Raghavan, 2001), el repartiment de Thompson (que coincideix amb el valor tau) és l'únic punt del core que és maximal respecte de la relació de dominància de Lorenz, i a més coincideix amb la solucié de Dutta i Ray (1989), també coneguda com solució igualitària. En segon lloc, mitjançant una condició més forta que la de diagonal dominant, introduïm una nova classe de jocs d'assignació on cada agent obté amb la seva parella òptima almenys el doble que amb qualsevol altra parella. Per aquests jocs d'assignació amb diagonal 2-dominant, el repartiment de Thompson és l'únic punt del kernel, i per tant el nucleolo.

Transformation kernel density estimation of actuarial loss functions

[cat] Es presenta un estimador nucli transformat que és adequat per a distribucions de cua pesada. Utilitzant una transformació basada en la distribució de probabilitat Beta l’elecció del paràmetre de finestra és molt directa. Es presenta una aplicació a dades d’assegurances i es mostra com calcular el Valor en Risc.

NPK fertilization on initial growth of physic nut seedlings in Quartzarenic Neossol

Balanced fertilization is important for plant growth. There is little information on physic nut (Jatropha curcas L.) and tests with the fertilization of the species are very recent. This study evaluated the initial growth of physic nut seedlings in response to NPK rates to Quartzarenic Neossol in a greenhouse and estimated P and K critical soil levels and N, P and K in shoot dry matter after 120 days of evaluation. The treatments were arranged in a randomized, fractional factorial design (4 x 4 x 4)½, totalizing 32 treatments with three replicates, 96 experimental plots and N rates (0, 75, 150 and 300 mg dm-3) as urea; P rates (0, 45, 90 and 180 mg dm-3) as triple superphosphate and K rates (0, 50, 100 and 200 mg dm-3) as potassium chloride. After 120 days, the plants were harvested and some variables evaluated: plant height, stem diameter, shoot and root dry weight, macro and micronutrient levels in plant shoots, and soil chemical properties. The physic nut seedlings responded to NPK fertilizer in the initial growth phase; the response to N was negative. The recommended P and K rates were 25 and 67 mg dm-3, respectively. The critical levels, corresponding to the recommended P rate were 13 and 74 mg dm-3 for K in soil (Mehlich-1). The N, P and K levels in the shoot dry matter of physic nut were 37.4, 2.1 and 35.7 g kg-1, respectively.

Mycorrhizal effectiveness on physic nut as influenced by phosphate fertilization levels

In recent years, physic nut (Jatropha curcas L.) has attracted attention because of its potential for biofuel production. Although it is adapted to low-fertility soils, physic nut requires soil acidity corrections and addition of a considerable amount of fertilizer for high productivity. The objective of this research was to evaluate the effectiveness of arbuscular mycorrhizal fungi (AMF) (control without AMF inoculation, Gigaspora margarita inoculation or Glomus clarum inoculation) on increasing growth and yield of physic nut seedlings under different rates of P fertilization (0, 25, 50, 100, 200, and 400 mg kg-1 P soil) in greenhouse. The experiment was arranged in a completely randomized, block in a factorial scheme design with four replications. The physic nut plants were harvested 180 days after the beginning of the experiment. Mycorrhizal inoculation increased physic nut growth, plant P concentration and root P uptake efficiency at low soil P concentrations. The P use quotient of the plants decreased as the amount of P applied increased, and the P use efficiency index increased at low P levels and decreased at high P levels. Mycorrhizal root colonization and AMF sporulation were negatively affected by P addition. The highest mycorrhizal efficiency was observed when the soil contained between 7.8 and 25 mgkg-1 of P. The physic nut plants responded strongly to P application, independent of mycorrhizal inoculation.