On statistical bounds of heuristic solutions to location problems

Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region. 

Novel Statistical Methods in Quantitative Genetics : Modeling Genetic Variance for Quantitative Trait Loci Mapping and Genomic Evaluation

This thesis develops and evaluates statistical methods for different types of genetic analyses, including quantitative trait loci (QTL) analysis, genome-wide association study (GWAS), and genomic evaluation. The main contribution of the thesis is to provide novel insights in modeling genetic variance, especially via random effects models. In variance component QTL analysis, a full likelihood model accounting for uncertainty in the identity-by-descent (IBD) matrix was developed. It was found to be able to correctly adjust the bias in genetic variance component estimation and gain power in QTL mapping in terms of precision.  Double hierarchical generalized linear models, and a non-iterative simplified version, were implemented and applied to fit data of an entire genome. These whole genome models were shown to have good performance in both QTL mapping and genomic prediction. A re-analysis of a publicly available GWAS data set identified significant loci in Arabidopsis that control phenotypic variance instead of mean, which validated the idea of variance-controlling genes.  The works in the thesis are accompanied by R packages available online, including a general statistical tool for fitting random effects models (hglm), an efficient generalized ridge regression for high-dimensional data (bigRR), a double-layer mixed model for genomic data analysis (iQTL), a stochastic IBD matrix calculator (MCIBD), a computational interface for QTL mapping (qtl.outbred), and a GWAS analysis tool for mapping variance-controlling loci (vGWAS).

Parameter estimation of Poisson generalized linear mixed models based on three different statistical principles : a simulation study

Generalized linear mixed models are flexible tools for modeling non-normal data and are useful for accommodating overdispersion in Poisson regression models with random effects. Their main difficulty resides in the parameter estimation because there is no analytic solution for the maximization of the marginal likelihood. Many methods have been proposed for this purpose and many of them are implemented in software packages. The purpose of this study is to compare the performance of three different statistical principles - marginal likelihood, extended likelihood, Bayesian analysis-via simulation studies. Real data on contact wrestling are used for illustration.

Investigating The Sources Of Fresh Water Affecting The Hydrological Balance Of Lakes Enriquillo And Azuei (Hispaniola) – Data Analysis

The Enriquillo and Azuei are saltwater lakes located in a closed water basin in the southwestern region of the island of La Hispaniola, these have been experiencing dramatic changes in total lake-surface area coverage during the period 1980-2012. The size of Lake Enriquillo presented a surface area of approximately 276 km2 in 1984, gradually decreasing to 172 km2 in 1996. The surface area of the lake reached its lowest point in the satellite observation record in 2004, at 165 km2. Then the recent growth of the lake began reaching its 1984 size by 2006. Based on surface area measurement for June and July 2013, Lake Enriquillo has a surface area of ~358 km2. Sumatra sizes at both ends of the record are 116 km2 in 1984 and 134 km2in 2013, an overall 15.8% increase in 30 years. Determining the causes of lake surface area changes is of extreme importance due to its environmental, social, and economic impacts. The overall goal of this study is to quantify the changing water balance in these lakes and their catchment area using satellite and ground observations and a regional atmospheric-hydrologic modeling approach. Data analyses of environmental variables in the region reflect a hydrological unbalance of the lakes due to changing regional hydro-climatic conditions. Historical data show precipitation, land surface temperature and humidity, and sea surface temperature (SST), increasing over region during the past decades. Salinity levels have also been decreasing by more than 30% from previously reported baseline levels. Here we present a summary of the historical data obtained, new sensors deployed in the sourrounding sierras and the lakes, and the integrated modeling exercises. As well as the challenges of gathering, storing, sharing, and analyzing this large volumen of data in a remote location from such a diverse number of sources.

Speculative bubbles and contagion: analysis of volatility's clusters during the DotCom bubble based on the dynamic conditional correlation model

Reviewing the de nition and measurement of speculative bubbles in context of contagion, this paper analyses the DotCom bubble in American and European equity markets using the dynamic conditional correlation (DCC) model proposed by (Engle and Sheppard 2001) as on one hand as an econometrics explanation and on the other hand the behavioral nance as an psychological explanation. Contagion is de ned in this context as the statistical break in the computed DCCs as measured by the shifts in their means and medians. Even it is astonishing, that the contagion is lower during price bubbles, the main nding indicates the presence of contagion in the di¤erent indices among those two continents and proves the presence of structural changes during nancial crisis

Statistical modelling of extreme rainfall in Madeira Island

Extreme rainfall events have triggered a significant number of flash floods in Madeira Island along its past and recent history. Madeira is a volcanic island where the spatial rainfall distribution is strongly affected by its rugged topography. In this thesis, annual maximum of daily rainfall data from 25 rain gauge stations located in Madeira Island were modelled by the generalised extreme value distribution. Also, the hypothesis of a Gumbel distribution was tested by two methods and the existence of a linear trend in both distributions parameters was analysed. Estimates for the 50– and 100–year return levels were also obtained. Still in an univariate context, the assumption that a distribution function belongs to the domain of attraction of an extreme value distribution for monthly maximum rainfall data was tested for the rainy season. The available data was then analysed in order to find the most suitable domain of attraction for the sampled distribution. In a different approach, a search for thresholds was also performed for daily rainfall values through a graphical analysis. In a multivariate context, a study was made on the dependence between extreme rainfall values from the considered stations based on Kendall’s τ measure. This study suggests the influence of factors such as altitude, slope orientation, distance between stations and their proximity of the sea on the spatial distribution of extreme rainfall. Groups of three pairwise associated stations were also obtained and an adjustment was made to a family of extreme value copulas involving the Marshall–Olkin family, whose parameters can be written as a function of Kendall’s τ association measures of the obtained pairs.

Multivariate analysis for the classification and differentiation of Madeira wines according to main grape varieties

In order to differentiate and characterize Madeira wines according to main grape varieties, the volatile composition (higher alcohols, fatty acids, ethyl esters and carbonyl compounds) was determined for 36 monovarietal Madeira wine samples elaborated from Boal, Malvazia, Sercial and Verdelho white grape varieties. The study was carried out by headspace solid-phase microextraction technique (HS-SPME), in dynamic mode, coupled with gas chromatography–mass spectrometry (GC–MS). Corrected peak area data for 42 analytes from the above mentioned chemical groups was used for statistical purposes. Principal component analysis (PCA) was applied in order to determine the main sources of variability present in the data sets and to establish the relation between samples (objects) and volatile compounds (variables). The data obtained by GC–MS shows that the most important contributions to the differentiation of Boal wines are benzyl alcohol and (E)-hex-3-en-1-ol. Ethyl octadecanoate, (Z)-hex-3-en-1-ol and benzoic acid are the major contributions in Malvazia wines and 2-methylpropan-1-ol is associated to Sercial wines. Verdelho wines are most correlated with 5-(ethoxymethyl)-furfural, nonanone and cis-9-ethyldecenoate. A 96.4% of prediction ability was obtained by the application of stepwise linear discriminant analysis (SLDA) using the 19 variables that maximise the variance of the initial data set.

Reduction capability of soil humic substances from the Rio Negro basin, Brazil, towards Hg(II) studied by a multimethod approach and principal component analysis (PCA)

This paper characterizes humic substances (HS) extracted from soil samples collected in the Rio Negro basin in the state of Amazonas, Brazil, particularly investigating their reduction capabilities towards Hg(II) in order to elucidate potential mercury cycling/volatilization in this environment. For this reason, a multimethod approach was used, consisting of both instrumental methods (elemental analysis, EPR, solid-state NMR, FIA combined with cold-vapor AAS of Hg(0)) and statistical methods such as principal component analysis (PCA) and a central composite factorial planning method. The HS under study were divided into groups, complexing and reducing ones, owing to different distribution of their functionalities. The main functionalities (cor)related with reduction of Hg(II) were phenolic, carboxylic and amide groups, while the groups related with complexation of Hg(II) were ethers, hydroxyls, aldehydes and ketones. The HS extracted from floodable regions of the Rio Negro basin presented a greater capacity to retain (to complex, to adsorb physically and/or chemically) Hg(II), while nonfloodable regions showed a greater capacity to reduce Hg(II), indicating that HS extracted from different types of regions contribute in different ways to the biogeochemical mercury cycle in the basin of the mid-Rio Negro, AM, Brazil. (c) 2007 Published by Elsevier B.V.

Correlations among behavior, performance and environment in broiler breeders using multivariate analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Discrimination of geomorphic surfaces with multivariate analysis of soil attributes in sandstone - basalt lithosequence

O conceito de superfície geomórfica permite uma interligação entre os diferentes ramos da ciência do solo, tais como geologia, geomorfologia e pedologia. Esta associação favorece a compreensão da distribuição espacial dos solos na paisagem, e torna possível compreender o comportamento dos atributos do solo, que estão principalmente relacionadas com a estratigrafia e formas do relevo. Assim, este estudo visa à aplicação da estatística multivariada para categorizar superfícies geomórficas em uma litossequência arenito-basalto, de modo a fornecer uma base para a avaliação do solo em áreas afins. A área de estudo está localizada no município de Pereira Barreto, São Paulo, Brasil. A área escolhida possui 530 hectares, onde foram localizadas e mapeadas três superfícies geomórficas (I, II e III). Na área, 134 amostras foram coletadas nas profundidades de 0,0-0,2 m e 0,8-1,0 m, foram determinados os conteúdos de areia, silte e argila, pH em CaCl2, conteúdo de MO, P, Ca, Mg, K, Al e H+Al. Com base nos resultados, foram realizadas a análise univariada e multivariada de variância, clusters e principal componente, a fim de comparar as três superfícies geomórficas. A análise estatística univariada dos atributos do solo não foi eficiente na identificação das três superfícies geomórficas. Utilizando-se os atributos físicos e químicos do solo, as técnicas estatísticas multivariada permitiram à separação dos três grupos de corpos naturais do solo que foram equivalentes as três superfícies geomórficas mapeadas. Estes resultados são interessantes, pois demonstram a viabilidade da utilização de classificação numérica das superfícies geomórficas para ajudar no mapeamento de solo.

RAPD analysis of genetic variability in a multiprovenance base population of Eucalyptus grandis hill ex maiden

Este estudo visou avaliar a variabilidade e distância genética dentro de uma população-base de melhoramento genético de Eucalyptus grandis. A avaliação da variabilidade genética tem como objetivos principais analisar a base genética da população-base e montar um banco de dados marcadores moleculares da população em análise. Essa população é formada por 327 indivíduos, principalmente das procedências de Coff's Harbour, Atherton e Rio Claro. Devido à heterozigosidade natural dessa população, ela pode ser dividida em diversas subpopulações, de acordo com a latitude e longitude de origem; e dentro de subpopulações, em função do grau de melhoramento genético já realizado do material analisado no Brasil. Isso permitiu avaliar quanto da variabilidade detectada dentro da população-base foi devido a esses fatores: procedência e grau de melhoramento. A aplicação da técnica RAPD permitiu avaliar 70 locos polimórficos, que foram analisados utilizando-se o coeficiente de Jaccard, o que resultou em matrizes de similaridade genética entre os indivíduos. Os dados de similaridade genética posteriormente foram submetidos à análise estatística. Osdados indicaram que a população-base apresenta ampla base genética, com média de similaridade genética de 0,328. O subgrupo denominado Região 3, composto por material selvagem da macrorregião de Atherton, juntamente com material de APS da macrorregião de Coff's Harbour, foi um dos que mais contribuíram para a ampla base genética da população-base. Foi possível detectar diferença estatística entre as populações selvagens das procedências de Atherton e Coff's Harbour, assim como entre essas procedências e a de Rio Claro.

Analysis of cardiac autonomic modulation in obese and eutrophic children

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Image analysis of modified cellulose fibers from sugarcane bagasse by zirconium oxychloride

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Determination of Population Size of Glass-like Carbon Sampling Used in Weibull Analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Determining the Optimum Processing Parameters of Glass-like Carbon Using Weibull Analysis of its Fracture Behaviour

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)