Gaussian regression and optimal finite dimensional linear models

The problem of regression under Gaussian assumptions is treated generally. The relationship between Bayesian prediction, regularization and smoothing is elucidated. The ideal regression is the posterior mean and its computation scales as O(n³), where n is the sample size. We show that the optimal m-dimensional linear model under a given prior is spanned by the first m eigenfunctions of a covariance operator, which is a trace-class operator. This is an infinite dimensional analogue of principal component analysis. The importance of Hilbert space methods to practical statistics is also discussed.

Numerical study of the enlarged O(5) symmetry of the 3D antiferromagnetic RP^(2) spin model

We investigate by means of Monte Carlo simulation and finite-size scaling analysis the critical properties of the three dimensional O (5) non-linear σ model and of the antiferromagnetic RP^(2) model, both of them regularized on a lattice. High accuracy estimates are obtained for the critical exponents, universal dimensionless quantities and critical couplings. It is concluded that both models belong to the same universality class, provided that rather non-standard identifications are made for the momentum-space propagator of the RP^(2) model. We have also investigated the phase diagram of the RP^(2) model extended by a second-neighbor interaction. A rich phase diagram is found, where most of the phase transitions are of the first order.

Transferability of Regional Permafrost Disturbance Susceptibility Modelling Using Generalized Linear and Generalized Additive Models

To effectively assess and mitigate risk of permafrost disturbance, disturbance-p rone areas can be predicted through the application of susceptibility models. In this study we developed regional susceptibility models for permafrost disturbances using a field disturbance inventory to test the transferability of the model to a broader region in the Canadian High Arctic. Resulting maps of susceptibility were then used to explore the effect of terrain variables on the occurrence of disturbances within this region. To account for a large range of landscape charac- teristics, the model was calibrated using two locations: Sabine Peninsula, Melville Island, NU, and Fosheim Pen- insula, Ellesmere Island, NU. Spatial patterns of disturbance were predicted with a generalized linear model (GLM) and generalized additive model (GAM), each calibrated using disturbed and randomized undisturbed lo- cations from both locations and GIS-derived terrain predictor variables including slope, potential incoming solar radiation, wetness index, topographic position index, elevation, and distance to water. Each model was validated for the Sabine and Fosheim Peninsulas using independent data sets while the transferability of the model to an independent site was assessed at Cape Bounty, Melville Island, NU. The regional GLM and GAM validated well for both calibration sites (Sabine and Fosheim) with the area under the receiver operating curves (AUROC) N 0.79. Both models were applied directly to Cape Bounty without calibration and validated equally with AUROC's of 0.76; however, each model predicted disturbed and undisturbed samples differently. Addition- ally, the sensitivity of the transferred model was assessed using data sets with different sample sizes. Results in- dicated that models based on larger sample sizes transferred more consistently and captured the variability within the terrain attributes in the respective study areas. Terrain attributes associated with the initiation of dis- turbances were similar regardless of the location. Disturbances commonly occurred on slopes between 4 and 15°, below Holocene marine limit, and in areas with low potential incoming solar radiation

Modelo para distribuição de recursos nos municípios brasileiros baseado na lei de diretrizes orçamentárias, análise multicritério e programação linear

The municipal management in any country of the globe requires planning and allocation of resources evenly. In Brazil, the Law of Budgetary Guidelines (LDO) guides municipal managers toward that balance. This research develops a model that seeks to find the balance of the allocation of public resources in Brazilian municipalities, considering the LDO as a parameter. For this using statistical techniques and multicriteria analysis as a first step in order to define allocation strategies, based on the technical aspects arising from the municipal manager. In a second step, presented in linear programming based optimization where the objective function is derived from the preference of the results of the manager and his staff. The statistical representation is presented to support multicriteria development in the definition of replacement rates through time series. The multicriteria analysis was structured by defining the criteria, alternatives and the application of UTASTAR methods to calculate replacement rates. After these initial settings, an application of linear programming was developed to find the optimal allocation of enforcement resources of the municipal budget. Data from the budget of a municipality in southwestern Paraná were studied in the application of the model and analysis of results.

Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams

The milling of thin parts is a high added value operation where the machinist has to face the chatter problem. The study of the stability of these operations is a complex task due to the changing modal parameters as the part loses mass during the machining and the complex shape of the tools that are used. The present work proposes a methodology for chatter avoidance in the milling of flexible thin floors with a bull-nose end mill. First, a stability model for the milling of compliant systems in the tool axis direction with bull-nose end mills is presented. The contribution is the averaging method used to be able to use a linear model to predict the stability of the operation. Then, the procedure for the calculation of stability diagrams for the milling of thin floors is presented. The method is based on the estimation of the modal parameters of the part and the corresponding stability lobes during the machining. As in thin floor milling the depth of cut is already defined by the floor thickness previous to milling, the use of stability diagrams that relate the tool position along the tool-path with the spindle speed is proposed. Hence, the sequence of spindle speeds that the tool must have during the milling can be selected. Finally, this methodology has been validated by means of experimental tests.

Modelos linear e não linear em análises genéticas para sobrevivência de crias de ovinos da raça Santa Inês.

Resumo: Registros de sobrevivência do nascimento ao desmame de 3846 crias de ovinos da raça Santa Inês foram analisados por modelos de reprodutor linear e não linear (modelo de limiar), para estimar componentes de variância e herdabilidade. Os modelos usados para sobrevivência, analisada como característica da cria, incluíram os efeitos fixos de sexo, da combinação tipo de nascimento-criação da cria e da idade da ovelha ao parto, efeito da covariável peso da cria ao nascer e efeitos aleatórios de reprodutor, da classe rebanho-ano-estação e do resíduo. Componentes de variância para o modelo linear foram estimados pelo método da máxima verossimilhança restrita (REML) e para o modelo não linear por uma aproximação da máxima verossimilhança marginal (MML), pelo programa CMMAT2. O coeficiente de herdabilidade (h2) estimado pelo modelo de limiar foi de 0,29, e pelo modelo linear, 0,14. A correlação de ordem de Spearman entre as capacidades de transmissão dos reprodutores, com base nos dois modelos foi de 0,96. As estimativas de h2 obtidas indicam a possibilidade de se obter, por seleção, ganho genético para sobrevivência. [Linear and nonlinear models in genetic analyses of lamb survival in the Santa Inês hair sheep breed]. Abstract: Records of 3,846 lambs survival from birth to weaning of Santa Inês hair sheep breed, were analyzed by linear and non linear sire models (threshold model) to estimate variance components and heritability (h2). The models that were used to analyze survival, considered in this study as a lamb trait, included the fixed effects of sex of the lamb, combination of type of birth-rearing of lamb, and age of ewe, birth weight of lamb as covariate, and random effects of sire, herd-year-season and residual. Variance components were obtained using restricted maximum likelihood (REML), in linear model and marginal maximum likelihood in threshold model through CMMAT2 program. Estimate of heritability (h2) obtained by threshold model was 0.29 and by linear model was 0.14. Rank correlation of Spearman, between sire solutions based on the two models was 0.96. The obtained estimates in this study indicate that it is possible to acquire genetic gain to survival by selection.

Modeling and Model Predictive Control of an Industrial Hydraulic System

This thesis aims to illustrate the construction of a mathematical model of a hydraulic system, oriented to the design of a model predictive control (MPC) algorithm. The modeling procedure starts with the basic formulation of a piston-servovalve system. The latter is a complex non linear system with some unknown and not measurable effects that constitute a challenging problem for the modeling procedure. The first level of approximation for system parameters is obtained basing on datasheet informations, provided workbench tests and other data from the company. Then, to validate and refine the model, open-loop simulations have been made for data matching with the characteristics obtained from real acquisitions. The final developed set of ODEs captures all the main peculiarities of the system despite some characteristics due to highly varying and unknown hydraulic effects, like the unmodeled resistive elements of the pipes. After an accurate analysis, since the model presents many internal complexities, a simplified version is presented. The latter is used to linearize and discretize correctly the non linear model. Basing on that, a MPC algorithm for reference tracking with linear constraints is implemented. The results obtained show the potential of MPC in this kind of industrial applications, thus a high quality tracking performances while satisfying state and input constraints. The increased robustness and flexibility are evident with respect to the standard control techniques, such as PID controllers, adopted for these systems. The simulations for model validation and the controlled system have been carried out in a Python code environment.

Longitudinal Analysis Of Hippocampal T2 Relaxometry In Fmtle.

To investigate the degree of T2 relaxometry changes over time in groups of patients with familial mesial temporal lobe epilepsy (FMTLE) and asymptomatic relatives. We conducted both cross-sectional and longitudinal analyses of T2 relaxometry with Aftervoxel, an in-house software for medical image visualization. The cross-sectional study included 35 subjects (26 with FMTLE and 9 asymptomatic relatives) and 40 controls; the longitudinal study was composed of 30 subjects (21 with FMTLE and 9 asymptomatic relatives; the mean time interval of MRIs was 4.4 ± 1.5 years) and 16 controls. To increase the size of our groups of patients and relatives, we combined data acquired in 2 scanners (2T and 3T) and obtained z-scores using their respective controls. General linear model on SPSS21® was used for statistical analysis. In the cross-sectional analysis, elevated T2 relaxometry was identified for subjects with seizures and intermediate values for asymptomatic relatives compared to controls. Subjects with MRI signs of hippocampal sclerosis presented elevated T2 relaxometry in the ipsilateral hippocampus, while patients and asymptomatic relatives with normal MRI presented elevated T2 values in the right hippocampus. The longitudinal analysis revealed a significant increase in T2 relaxometry for the ipsilateral hippocampus exclusively in patients with seizures. The longitudinal increase of T2 signal in patients with seizures suggests the existence of an interaction between ongoing seizures and the underlying pathology, causing progressive damage to the hippocampus. The identification of elevated T2 relaxometry in asymptomatic relatives and in patients with normal MRI suggests that genetic factors may be involved in the development of some mild hippocampal abnormalities in FMTLE.

Cerebral Cortex Involvement In Machado-joseph Disease.

Machado-Joseph disease (MJD/SCA3) is the most frequent spinocerebellar ataxia, characterized by brainstem, basal ganglia and cerebellar damage. Few magnetic resonance imaging based studies have investigated damage in the cerebral cortex. The objective was to determine whether patients with MJD/SCA3 have cerebral cortex atrophy, to identify regions more susceptible to damage and to look for the clinical and neuropsychological correlates of such lesions. Forty-nine patients with MJD/SCA3 (mean age 47.7 ± 13.0 years, 27 men) and 49 matched healthy controls were enrolled. All subjects underwent magnetic resonance imaging scans in a 3 T device, and three-dimensional T1 images were used for volumetric analyses. Measurement of cortical thickness and volume was performed using the FreeSurfer software. Groups were compared using ancova with age, gender and estimated intracranial volume as covariates, and a general linear model was used to assess correlations between atrophy and clinical variables. Mean CAG expansion, Scale for Assessment and Rating of Ataxia (SARA) score and age at onset were 72.1 ± 4.2, 14.7 ± 7.3 and 37.5 ± 12.5 years, respectively. The main findings were (i) bilateral paracentral cortex atrophy, as well as the caudal middle frontal gyrus, superior and transverse temporal gyri, and lateral occipital cortex in the left hemisphere and supramarginal gyrus in the right hemisphere; (ii) volumetric reduction of basal ganglia and hippocampi; (iii) a significant correlation between SARA and brainstem and precentral gyrus atrophy. Furthermore, some of the affected cortical regions showed significant correlations with neuropsychological data. Patients with MJD/SCA3 have widespread cortical and subcortical atrophy. These structural findings correlate with clinical manifestations of the disease, which support the concept that cognitive/motor impairment and cerebral damage are related in disease.

Modeling The Effects Of Temperature And Ph On The Resistance Of Alicyclobacillus Acidoterrestris In Conventional Heat-treated Fruit Beverages Through A Meta-analysis Approach.

In this work, all publicly-accessible published findings on Alicyclobacillus acidoterrestris heat resistance in fruit beverages as affected by temperature and pH were compiled. Then, study characteristics (protocols, fruit and variety, °Brix, pH, temperature, heating medium, culture medium, inactivation method, strains, etc.) were extracted from the primary studies, and some of them incorporated to a meta-analysis mixed-effects linear model based on the basic Bigelow equation describing the heat resistance parameters of this bacterium. The model estimated mean D* values (time needed for one log reduction at a temperature of 95 °C and a pH of 3.5) of Alicyclobacillus in beverages of different fruits, two different concentration types, with and without bacteriocins, and with and without clarification. The zT (temperature change needed to cause one log reduction in D-values) estimated by the meta-analysis model were compared to those ('observed' zT values) reported in the primary studies, and in all cases they were within the confidence intervals of the model. The model was capable of predicting the heat resistance parameters of Alicyclobacillus in fruit beverages beyond the types available in the meta-analytical data. It is expected that the compilation of the thermal resistance of Alicyclobacillus in fruit beverages, carried out in this study, will be of utility to food quality managers in the determination or validation of the lethality of their current heat treatment processes.

Análise bayesiana do modelo de herança monogênica no melhoramento vegetal: um exemplo com abobrinha

A common breeding strategy is to carry out basic studies to investigate the hypothesis of a single gene controlling the trait (major gene) with or without polygenes of minor effect. In this study we used Bayesian inference to fit genetic additive-dominance models of inheritance to plant breeding experiments with multiple generations. Normal densities with different means, according to the major gene genotype, were considered in a linear model in which the design matrix of the genetic effects had unknown coefficients (which were estimated in individual basis). An actual data set from an inheritance study of partenocarpy in zucchini (Cucurbita pepo L.) was used for illustration. Model fitting included posterior probabilities for all individual genotypes. Analysis agrees with results in the literature but this approach was far more efficient than previous alternatives assuming that design matrix was known for the generations. Partenocarpy in zucchini is controlled by a major gene with important additive effect and partial dominance.

Adaptação de protocolos invasivos e não invasivos para avaliações aeróbias e anaeróbias específicas ao basquetebol feminino

OBJECTIVE: To adapted the critical velocity (CV), RAST test and lactate minimum (LM) to evaluation of female basketball players. METHODS: Twelve well-trained female basketball players (19 ± 1yrs) were submitted to four intensities running (10 - 14 km/h) at shuttle exercise until exhaustion, applied on alternate days. The linear model 'velocity vs. 1/tlim' was adopted to determine the aerobic (CV) and anaerobic (CCA) parameters. The lactate minimum test consisted of two phases: 1) hiperlactatemia induction using the RAST test and 2) incremental test composed by five shuttle run (20-m) at 7, 8, 9, 10, and 12 km/h. Blood samples were collected at the end of each stage. RESULTS: The velocity (vLM) and blood lactate concentration at LM were obtained by two polynomial adjustments: lactate vs. intensity (LM1) and lactate vs. time (LM2). ANOVA one-way, Student t-test and Pearson correlation were used for statistical analysis. The CV was obtained at 10.3 ± 0.2 km/h and the CCA estimated at 73.0 ± 3.4 m. The RAST was capable to induce the hiperlactatemia and to determine the Pmax (3.6 ± 0.2 W/kg), Pmed (2.8 ± 0.1 W/kg), Pmin (2.3 ± 0.1 W/kg) and FI (30 ± 3%). The vLM1 and vLM2 were obtained, respectively, at 9.47 ±0.13 km/h and 9.8 ± 0.13 km/h, and CV was higher than vLM1. CONCLUSION: The results suggest that the non-invasive model can be used to determine the aerobic and anaerobic parameters. Furthermore, the LM test adapted to basketball using RAST and progressive phase was effective to evaluate female athletes considering the specificity of modality, with high success rates observed in polynomial adjustment 'lactate vs. time' (LM2).

Phase transitions in biodegradable films based on blends of gelatin and poly (vinyl alcohol)

The aim of this work was to study the effect of the hydrolysis degree (HD) and the concentration (C PVA) of two types of poly (vinyl alcohol) (PVA) and the effect of the type and the concentration of plasticizers on the phase properties of biodegradable films based on blends of gelatin and PVA, using a response-surface methodology. The films were made by casting and the studied properties were their glass (Tg) and melting (Tm) transition temperatures, which were determined by diferential scanning calorimetry (DSC). For the data obtained on the first scan, the fitting of the linear model was statistically significant and predictive only for the second melting temperature. In this case, the most important effect on the second Tm of the first scan was due to the HD of the PVA. In relation to the second scan, the linear model could be fit to Tg data with only two statistically significant parameters. Both the PVA and plasticizer concentrations had an important effect on Tg. Concerning the second Tm of the second scan, the linear model was fit to data with two statistically significant parameters, namely the HD and the plasticizer concentration. But, the most important effect was provoked by the HD of the PVA.

Prevalência de hipertensão arterial em militares jovens e fatores associados

OBJETIVO: Estimar a prevalência de hipertensão arterial entre militares jovens e fatores associados. MÉTODOS: Estudo transversal realizado com amostra de 380 militares do sexo masculino de 19 e 35 anos de idade em uma unidade da Força Aérea Brasileira em São Paulo, SP, entre 2000 e 2001. Os pontos de corte para hipertensão foram: >140mmHg para pressão sistólica e > 90mmHg para pressão diastólica. As variáveis estudadas incluíram fatores de risco e de proteção para hipertensão, como características comportamentais e nutricionais. Para análise das associações, utilizou-se regressão linear generalizada múltipla, com família binomial e ligação logarítmica, obtendo-se razões de prevalências com intervalo de 90% de confiança e seleção hierarquizada das variáveis. RESULTADOS: A prevalência de hipertensão arterial foi de 22% (IC 90%: 21;29). No modelo final da regressão múltipla verificou-se prevalência de hipertensão 68% maior entre os ex-fumantes em relação aos não fumantes (IC 90%: 1,13;2,50). Entre os indivíduos com sobrepeso (índice de massa corporal - IMC de 25 a 29kg/m2) e com obesidade (IMC>29kg/m2) as prevalências foram, respectivamente, 75% (IC 90%: 1,23;2,50) e 178% (IC 90%: 1,82;4,25) maiores do que entre os eutróficos. Entre os que praticavam atividade física regular, comparado aos que não praticavam, a prevalência foi 52% menor (IC 90%: 0,30;0,90). CONCLUSÕES: Ser ex-fumante e ter sobrepeso ou obesidade foram situações de risco para hipertensão, enquanto que a prática regular de atividade física foi fator de proteção em militares jovens.

Bovine gene polymorphisms related to fat deposition and meat tenderness

Leptin, thyroglobulin and diacylglycerol O-acyltransferase play important roles in fat metabolism. Fat deposition has an influence on meat quality and consumers' choice. The aim of this study was to determine allele and genotype frequencies of polymorphisms of the bovine genes, which encode leptin (LEP), thyroglobulin (TG) and diacylglycerol O-acyltransferase (DGAT1). A further objective was to establish the effects of these polymorphisms on meat characteristics. We genotyped 147 animals belonging to the Nelore (Bos indicus), Canchim (5/8 Bos taurus + 3/8 Bos indicus), Rubia Gallega X Nelore (1/2 Bos taurus + 1/2 Bos indicus), Brangus Three-way cross (9/16 Bos taurus + 7/16 Bos indicus) and Braunvieh Three-way cross (3/4 Bos taurus + 1/4 Bos indicus) breeds. Backfat thickness, total lipids, marbling score, ribeye area and shear force were fitted, using the General Linear Model (GLM) procedure of the SAS software. The least square means of genotypes and genetic groups were compared using Tukey's test. Allele frequencies vary among the genetic groups, depending on Bos indicus versus Bos taurus influence. The LEP polymorphism segregates in pure Bos indicus Nelore animals, which is a new finding. The T allele of TG is fixed in Nelore, and DGAT1 segregates in all groups, but the frequency of allele A is lower in Nelore animals. The results showed no association between the genotypes and traits studied, but a genetic group effect on these traits was found. So, the genetic background remains relevant for fat deposition and meat tenderness, but the gene markers developed for Bos taurus may be insufficient for Bos indicus.