Tese de mestrado. Engenharia Electrotécnica e de Computadores (Especialização em Energias Renováveis). Faculdade de Engenharia. Universidade do Porto. 2007

<p>I present an application to visualization of GPS data and Linear Correlations and models. A collection of data for each vehicle is used to compute correlations. Deviating correlations can be indicative of a faulty vehicle.</p><p> The correlation values for each vehicle are computed with use linear regression algorithms using up to 4 signals in the data (with varied time window), and display the model parameters in a window next to the GPS map. Multiple measurements (multiple drive routes and multiple model parameters) are displayed at the same time, allowing tracking over time and comparison of different vehicles.</p><p> </p><p> The whole technique is demonstrated on three data which is set on first frame by user. The results are displayed with a java application and Google Map.</p>

This dissertation considers two approaches for testing hypotheses in unbalanced mixed linear models. The first approach is to construct a design with some type of structure or "partial" balance, so that some of the optimal properties of a completely balanced design hold. It is shown that for a particular type of partially balanced design certain hypothesis tests are optimal. The second approach is to study how the unbalancedness of a design affects a hypothesis test in terms of level and power. Measures of imbalance are introduced and simulation results are presented that demonstrate the relationship of the level and power of a test and the measures. The first part of this thesis focuses on error orthogonal designs which are a type of partially balanced design. It is shown that with an error orthogonal design and under certain additional conditions, ANOVA F-tests about certain linear combinations of the variance components and certain linear combinations of the fixed effects are uniformly most powerful (UMP) similar and UMP unbiased. The ANOVA F-tests for the variance components are also invariant, so that the tests are also UMP invariant similar and UMP invariant unbiased. For certain simultaneous hypotheses about linear combinations of the fixed effects, the ANOVA F-tests are UMP invariant unbiased. The second part of this thesis considers a mixed model with a random nested effect, and studies the effects of an unbalanced design on the level and power of a hypothesis test of the nested variance component being equal to zero. Measures of imbalance are introduced for each of the four conditions necessary to obtain an exact test. Simulations are done for two different models to determine if there is a relationship between any of the measures and the level and power for both a naive test and a test using Satterthwaite's approximation. It is found that a measure based on the coefficients of the expected mean squares is indicative of how a test is performing. This measure is also simple to compute, so that it can easily be employed to determine the validity of the expected level and power. / Graduation date: 1999

Graduation date: 1994

Responding to Joint Attention (RJA) involves an infant's ability to follow a gaze or point by a partner. Prenatal cocaine exposure (PCE), which places a child in danger of numerous risks, has been accepted as having subtle effects on developmental outcomes such as social competence and associated socio-emotional outcomes. The current study looked at a sample of 166 children prenatally exposed to cocaine who were attending an early intervention program. The study established group and individual trajectories of responding to joint attention from 12, 15, and 18 months of age. Hierarchical modeling identified two groups, a delay group and an average group, while individual trajectories identified a linear pattern of growth of RJA. Both individual and group trajectories indicated that children with higher RJA from 12 to 18 months demonstrated better social competence at three years of age and first grade. The delay and average group showed significant differences on later social competence measures, but not problem behaviors, such that RJA, a positive behavior, may connect more closely with later positive behaviors than with behavior problems. RJA may therefore be useful in a preventative intervention targeted at enhancing positive social behaviors and as an important and simple screening tool for possible delay early in a child's life, helping to deliver early intervention services in a targeted and effective manner.

The following study utilizes data from the High School and Beyond Study in order to predict mathematics achievement using both student characteristics and school level characteristics. Utilizing Hierarchical Linear Modeling, this study extends the body of literature by exploring how race, socio-economic status, and gender, as well as the percentage of minority students in a school, whether or not the school is Catholic, the proportion of students in the academic track, and the mean socioeconomic status of the school all affect mathematics achievement. Through this methodology, it was possible to see the direct effects of both student level and school level variables on achievement, as well as the cross-level interaction of all of these variables. Findings suggest that there are discrepancies in how different types of students achieve, as well as how those students achieve in varying contexts. Many of the variables were statistically significant in their effect on mathematics achievement. Implications for this research are discussed and considerations for future research are presented.

In this thesis, it is proposed to examine the difference equation:(z-h) ∆-hW(z) = A(z)W(z)(1) where W(z) is a vector with two components,∆-hW(h) = W(z) – W(z-h)/h(2)Here, A(z) is a 2x2 matrix, whose elements admit factorial series representations:A (z) = R + Σ∞s=0 As+1S!/z(z+h) ••• (z+sh)(3)R and As+l are square matrices of order two and independent of z. We also assume that eigen values of R do not differ by an integer. We hope to show that if (3) converges in some half plane, then (1) will have a fundamental matris solution of the form: W(z) = S(z)ZR where S(z) is a 2x2 matrix, whose elements have convergent factorial representation in some half plane.

Data in the form of counts or proportions often exhibit more variability than that predicted by a Poisson or binomial distribution. Many different models have been proposed to account for extra-Poisson or extra-binomial variation. A simple model includes a single heterogeneity factor (dispersion parameter) in the variance. Other models that allow the dispersion parameter to vary between groups or according to a continuous covariate also exist but require a more complicated analysis. This thesis is concerned with (1) understanding the consequences of using an oversimplified model for overdispersion, (2) presenting diagnostic tools for detecting the dependence of overdispersion on covariates in regression settings for counts and proportions and (3) presenting diagnostic tools for distinguishing between some commonly used models for overdispersed data. The double exponential family of distributions is used as a foundation for this work. A double binomial or double Poisson density is constructed from a binomial or Poisson density and an additional dispersion parameter. This provides a completely parametric framework for modeling overdispersed counts and proportions. The first issue above is addressed by exploring the properties of maximum likelihood estimates obtained from incorrectly specified likelihoods. The diagnostic tools are based on a score test in the double exponential family. An attractive feature of this test is that it can be computed from the components of the deviance in the standard generalized linear model fit. A graphical display is suggested by the score test. For the normal linear model, which is a special case of the double exponential family, the diagnostics reduce to those for heteroscedasticity presented by Cook and Weisberg (1983). / Graduation date: 1990

The asymptotically fastest algorithms for many linear algebra problems on integer matrices, including solving a system of linear equations and computing the determinant, use high-order lifting. For a square nonsingular integer matrix A, high-order lifting computes B congruent to A^{-1} mod X^k and matrix R with AB = I + RX^k for non-negative integers X and k. Here, we present a deterministic method -- "double-plus-one" lifting -- to compute the high-order residue R as well as a succinct representation of B. As an application, we give a fully deterministic algorithm to certify the unimodularity of A. The cost of the algorithm is O((log n) n^{omega} M(log n + log ||A||)) bit operations, where ||A|| denotes the largest entry in absolute value, M(t) the cost of multiplying two integers bounded in bit length by t, and omega the exponent of matrix multiplication. Unimodularity certification is then applied to give a heuristic, but certified, algorithm for computing the determinant and Hermite normal form of a square, nonsingular integer matrix. Though most effective on random matrices, a highly optimized implementation of the latter algorithm demonstrates the techniques' effectiveness across a variety of inputs: empirical running times grow as O(n^3log n). A comparison against the fastest known Hermite normal algorithms -- those available in Sage and Magma -- show our implementation is, in all cases, highly competitive, and often surpasses existing, state-of-the-art implementations.

I present an application to visualization of GPS data and Linear Correlations and models. A collection of data for each vehicle is used to compute correlations. Deviating correlations can be indicative of a faulty vehicle. The correlation values for each vehicle are computed with use linear regression algorithms using up to 4 signals in the data (with varied time window), and display the model parameters in a window next to the GPS map. Multiple measurements (multiple drive routes and multiple model parameters) are displayed at the same time, allowing tracking over time and comparison of different vehicles. The whole technique is demonstrated on three data which is set on first frame by user. The results are displayed with a java application and Google Map.