Methods to verify parameter equality in nonlinear regression models

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Bayesian longitudinal data analysis with mixed models and thick-tailed distributions using MCMC

Linear mixed effects models are frequently used to analyse longitudinal data, due to their flexibility in modelling the covariance structure between and within observations. Further, it is easy to deal with unbalanced data, either with respect to the number of observations per subject or per time period, and with varying time intervals between observations. In most applications of mixed models to biological sciences, a normal distribution is assumed both for the random effects and for the residuals. This, however, makes inferences vulnerable to the presence of outliers. Here, linear mixed models employing thick-tailed distributions for robust inferences in longitudinal data analysis are described. Specific distributions discussed include the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted, and the Gibbs sampler and the Metropolis-Hastings algorithms are used to carry out the posterior analyses. An example with data on orthodontic distance growth in children is discussed to illustrate the methodology. Analyses based on either the Student-t distribution or on the usual Gaussian assumption are contrasted. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process for modelling distributions of the random effects and of residuals in linear mixed models, and the MCMC implementation allows the computations to be performed in a flexible manner.

Finns growth dynamics, competition and power-law scaling

We study the growth dynamics of the size of manufacturing firms considering competition and normal distribution of competency. We start with the fact that all components of the system struggle with each other for growth as happened in real competitive business world. The detailed quantitative agreement of the theory with empirical results of firms growth based on a large economic database spanning over 20 years is good with a single set of the parameters for all the curves. Further, the empirical data of the variation of the standard deviation of the growth rate with the size of the firm are in accordance with the present theory rather than a simple power law. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Spatial variability of infiltration and its relationship to some physical properties

Water infiltration into soil is one of the basic factors for estimating irrigation intensity according to the plants' requirements; this is aimed at avoiding problems of surface run-off and degradation. The purpose of the present investigation was to determine the spatial variation of infiltration and its relationship to some physical properties of soil by means of geostatistical techniques in Typic Plinthaquult soils having average texture and flat relief. A 113 point mesh was designned, having a regular distance of 10 m between points, samples being taken from 0 to 0.20 meters depth. Sand, silt and clay content, bulk density, macroporosity, microporosity and total porosity were determined. Infiltration tests were carried out in the field by means of a 15 cm diameter ring. Descriptive statistics and geostatistics were used for analysing the data. Infiltration, silt and microporosity data did not fit a normal distribution curve. Infiltration had high variability, having an average 36.03 mm h(-1). Total porosity was 56.73%, this being the only property that did not show spatial dependency. The smallest ranges were observed for bulk density, macroporosity and microporosity, having values of less than 40 m. The smallest degrees of spatial dependence were observed for infiltration, silt and clay, evidence also being shown of the influence of silt and clay on infiltration rate. Contour maps were constructed; fitting them to the semivariogram models, together with studying the correlations, led to establishing relationships between the properties.

Experimental analysis of heat transfer in packed beds with air flow

Heat-transfer studies were carried out in a packed bed of glass beads, cooled by the wall, through which air percolated. Tube-to-particle diameter ratios (D/dp) ranged from 1.8 to 55, while the air mass flux ranged from 0.204 to 2.422 kg/m2·s. The outlet bed temperature (TL) was measured by a brass ring-shaped sensor and by aligned thermocouples. The resulting radial temperature profiles differed statistically. Angular temperature fluctuations were observed through measurements made at 72 angular positions. These fluctuations do not follow a normal distribution around the mean for low ratios D/dp. The presence of a restraining screen, as well as the increasing distance between the temperature measuring device and the bed surface, distorts TL. The radial temperature profile at the bed entrance (T0) was measured by a ring-shaped sensor, and T 0 showed to be a function of the radial position, the particle diameter, and the fluid flow rate.

Kinetic study of the plastoquinone pool availability correlated with H2O2 release in seawater and antioxidant responses in the red alga Kappaphycus alvarezii exposed to single or combined high light, chilling and chemical stresses

Under biotic/abiotic stresses, the red alga Kappaphycus alvarezii reportedly releases massive amounts of H2O2 into the surrounding seawater. As an essential redox signal, the role of chloroplast-originated H2O2 in the orchestration of overall antioxidant responses in algal species has thus been questioned. This work purported to study the kinetic decay profiles of the redox-sensitive plastoquinone pool correlated to H2O2 release in seawater, parameters of oxidative lesions and antioxidant enzyme activities in the red alga Kappaphycus alvarezii under the single or combined effects of high light, low temperature, and sub-lethal doses of 3-(3,4-dichlorophenyl)-1,1-dimethylurea (DCMU) and 2,5-dibromo-3-methyl-6-isopropyl-p-benzoquinone (DBMIB), which are inhibitors of the thylakoid electron transport system. Within 24 h, high light and chilling stresses distinctly affected the availability of the PQ pool for photosynthesis, following Gaussian and exponential kinetic profiles, respectively, whereas combined stimuli were mostly reflected in exponential decays. No significant correlation was found in a comparison of the PQ pool levels after 24 h with either catalase (CAT) or ascorbate peroxidase (APX) activities, although the H2O2 concentration in seawater (R = 0.673), total superoxide dismutase activity (R = 0.689), and particularly indexes of protein (R = 0.869) and lipid oxidation (R = 0.864), were moderately correlated. These data suggest that the release of H2O2 from plastids into seawater possibly impaired efficient and immediate responses of pivotal H2O2-scavenging activities of CAT and APX in the red alga K. alvarezii, culminating in short-term exacerbated levels of protein and lipid oxidation. These facts provided a molecular basis for the recognized limited resistance of the red alga K. alvarezii under unfavorable conditions, especially under chilling stress. © 2006 Elsevier B.V. All rights reserved.

Reliability of timber bridges using nailed plywood box beams

The Nailed Box Beam structural efficiency is directly dependent of the flange-web joint behavior, which determines the partial composition of the section, as the displacement between elements reduces the effective rigidity of the section and changes the stress distribution and the total displacement of the section. This work discusses the use of Nailed Plywood Box Beams in small span timber bridges, focusing on the reliability of the beam element. It is presented the results of tests carried out in 21 full scale Nailed Plywood Box Beams. The analysis of maximum load tests results shows that it presents a normal distribution, permitting the characteristic values calculation as the normal distribution theory specifies. The reliability of those elements was analyzed focusing on a timber bridge design, to estimate the failure probability in function of the load level.

Estudio de la compactación de un Ferralsol manejado con un sistema de no laboreo en Selvíria (MS, Brasil)

No tillage management is widely used by the Brazilian farmers and technicians like a soil conservation system, which reduces the soil losses by water erosion, increasing the infiltrated and stored water in soil, warranting environmental sustainability. No-tillage system does not invert the soil; it causes the creation of a compacted layer. The samples were taken in the agricultural year 2005/2006 in an Oxisoil at Selviria (MS/Brazil). The tillage management in the last 15 years was no-tillage system with crop rotation (maize -Zea mays L./bean - Phaseolus vulgaris L.). The analyzed soil physical properties were bulk density (BS), gravimetric water content (U) and mechanical resistance to penetration (RP) at three depths: 0-0.10 m, 0.10-0.20 m and 0.20-0.30 m. The samples were taken in a mesh with 117 sampled points covering an area of 0.16 ha. It was investigated the existence of compacted soil layer, using the mechanical resistance to penetration to 0.60 m depth with soil water content at field capacity. The data shows low coefficient of variation, except the resistance penetration data. Bulk density and gravimetric water content has a normal distribution. Only resistance to penetration at 0.10-0.20 m depth layer has a normal distribution. The correlation between different properties was low. The bulk density increases with depth; the increase of the values of soil bulk density are consistent with data in other papers, indicating there are not compaction problems for the crop development at the study area. Most of the values of resistance to penetration are lower than 2 MPa, being this value restrictive for root development. The analysis of resistance to penetration profile 0 to 0.60 m shows a compacted layer between 0.20-0.30 m. This compacted layer was caused by the conventional tillage system used at this area before the use of no-tillage system. The soil bulk density has higher values at the upper area, that it shows higher values of soil compaction. Although the values of bulk density and resistance to penetration are high, the area does not show great problems of soil compaction.

Importância do modelo animal para testar hipóteses sobre a fisiopatologia do binômio diabetes e incontinência urinária feminina

Aims: To discuss the importance of studying animal models to test hypotheses about the mechanisms of urinary continence and pathophysiology of diabetes and urinary incontinence. Source of Data: A literature review was conducted in PubMed and SciELO. The key words used were diabetes, urinary incontinence, urethra, human and rats. Summary of Findings: There is a strong relation between the genesis of urinary incontinence and diabetes mellitus. Due to the similarity of normal distribution of skeletal muscle and urethra anatomy between humans and rats, these animal models have been used in current research about these disorders. Conclusions: The use of rats as an animal model is suitable for experimental studies that test hypotheses about the mechanisms of continence and pathophysiology of the binomial diabetes mellitus and urinary incontinence, thus enabling solutions of great value in clinical practice.

Determinação de GMP e CMP* no leite por métodos espectrofotométrico (ANSM) e cromatográfico (HPLC) - parâmetros metodológicos (*glicomacropeptídeo e caseinomacropeptídeo)

Glycomacropeptide is a glycosilated fraction of bovine kappa-casein that remains soluble when milk is clotted by rennin. Determinations of milk sialic acid content are useful because its concentration reflects the amount of free GMP of milk. In normal milk these amounts are very low, 12 to 16 times lower than in sweet whey. Therefore, its determination may be applied to verify possible frauds with whey addictions, since it works as a fingerprint. With the description of a new spectrophotometric method for determination of free GMP (ANSM) occurred a simplification of procedures, being faster than others (HPLC method), without loss of accuracy. However, due to variations of glycosilation in kappa-casein between animals, during the lactation period, due to mastitis and yet due to proteolysis on milk, it was necessary to know these variations to interpret correctly the analytical results. It was analyzed 1,703 samples of producer's raw milk and 1,189 samples of processed milk (HTST and UHT). The results showed that normal milk from herd (producer's milk) have only small amounts of free GMP, with A470nm = 0.232±0.088 or 3.89±1.25 mg of sialic acid/L. The upper limit of this distribution was A = 0.496; thus every bigger value may represent a problem, being outside of normal distribution.

Effects of probiotic bacteria on Candida presence and IgA anti-Candida in the oral cavity of elderly

Imbalance in the resident microbiota may promote the growth of opportunistic microorganisms, such as yeasts of Candida genus and the development of diseases, especially in aged people. This study evaluated whether the consumption of the probiotic Yakult LB® (Lactobacillus casei and Bifidobacterium breve) was able to influence on the specific immunological response against Candida and on the presence of these yeasts in the oral cavity of 42 healthy aged individuals. Saliva samples were collected before and after the probiotic use for 30 days, 3 times a week. The samples were plated in Dextrose Saboraud Agar with chloramphenicol, the colony-forming units (CFU/mL) were counted and the Candida species were identified. Anti-Candida IgA analysis was conducted using the ELISA technique. ANOVA and Student's t-test were used for normally distributed data and the Wilcoxon test was used for data with non-normal distribution (α=0.05). The results showed a statistically significant reduction (p<0.05) in Candida prevalence (from 92.9% to 85.7%), in CFU/mL counts of Candida and in the number of non-albicans species after consumption of the probiotic. Immunological analysis demonstrated a significant increase (p<0.05) in anti-Candida IgA levels. In conclusion, probiotic bacteria reduced Candida numbers in the oral cavity of the elderly and increased specific secretory immune response against these yeasts, suggesting its possible use in controlling oral candidosis.

Comparison of the population biology of Epialtus bituberculatus from two rocky shores with distinct hydrodynamic patterns

The population biology of Epialtus bituberculatus was compared between two different intertidal localities with differing levels of wave exposure. Sampling was conducted monthly between January and December, 2001 on seaweed banks of Sargassum cymosum in the intertidal zone of the rocky shores Grande (GR) (23°23′S-45°03′W) and Domingas Dias (DD) (23°29′S-45°08′W). Four hundred and twenty-eight crabs were captured at the GR site: 111 juvenile males, 106 adult males, 57 juvenile females, 17 adult females and 137 ovigerous females; while 455 specimens were obtained at the DD site: 76 juvenile males, 113 adult males, 37 juvenile females, 40 adult females and 189 ovigerous females. The population from GR showed a non-normal distribution and from DD a normal distribution. The sex-ratio (female/male) was 1:0.97 at GR (χ2 = 0.77, P = 0.084), whereas it was 1:1.41 at DD (χ2 = 13.03, P < 0.001). The largest individuals occurred at DD (U = 78249.0, P < 0.001). The estimated size at sexual maturity was 6.3 and 5.0 mm carapace width (CW) for males, and 5.4 and 5.2 mm CW for females, from GR and DD, respectively. The observed differences in E. bituberculatus between the studied localities might be explained by the different degrees of wave exposure between sites. However, other factors that might also explain the observed differences (e.g. temperature, salinity and food availability) cannot be discarded as relevant in influencing the population structure between sites herein studied. © 2012 Marine Biological Association of the United Kingdom.

Improving methods in gap ecology: Revisiting size and shape distributions using a model selection approach

Questions: We assess gap size and shape distributions, two important descriptors of the forest disturbance regime, by asking: which statistical model best describes gap size distribution; can simple geometric forms adequately describe gap shape; does gap size or shape vary with forest type, gap age or the method used for gap delimitation; and how similar are the studied forests and other tropical and temperate forests? Location: Southeastern Atlantic Forest, Brazil. Methods: Analysing over 150 gaps in two distinct forest types (seasonal and rain forests), a model selection framework was used to select appropriate probability distributions and functions to describe gap size and gap shape. The first was described using univariate probability distributions, whereas the latter was assessed based on the gap area-perimeter relationship. Comparisons of gap size and shape between sites, as well as size and age classes were then made based on the likelihood of models having different assumptions for the values of their parameters. Results: The log-normal distribution was the best descriptor of gap size distribution, independently of the forest type or gap delimitation method. Because gaps became more irregular as they increased in size, all geometric forms (triangle, rectangle and ellipse) were poor descriptors of gap shape. Only when small and large gaps (> 100 or 400m2 depending on the delimitation method) were treated separately did the rectangle and isosceles triangle become accurate predictors of gap shape. Ellipsoidal shapes were poor descriptors. At both sites, gaps were at least 50% longer than they were wide, a finding with important implications for gap microclimate (e.g. light entrance regime) and, consequently, for gap regeneration. Conclusions: In addition to more appropriate descriptions of gap size and shape, the model selection framework used here efficiently provided a means by which to compare the patterns of two different types of forest. With this framework we were able to recommend the log-normal parameters μ and σ for future comparisons of gap size distribution, and to propose possible mechanisms related to random rates of gap expansion and closure. We also showed that gap shape varied highly and that no single geometric form was able to predict the shape of all gaps, the ellipse in particular should no longer be used as a standard gap shape. © 2012 International Association for Vegetation Science.

Basic ingredients for mathematical modeling of tumor growth in vitro: Cooperative effects and search for space

Based on the literature data from HT-29 cell monolayers, we develop a model for its growth, analogous to an epidemic model, mixing local and global interactions. First, we propose and solve a deterministic equation for the progress of these colonies. Thus, we add a stochastic (local) interaction and simulate the evolution of an Eden-like aggregate by using dynamical Monte Carlo methods. The growth curves of both deterministic and stochastic models are in excellent agreement with the experimental observations. The waiting times distributions, generated via our stochastic model, allowed us to analyze the role of mesoscopic events. We obtain log-normal distributions in the initial stages of the growth and Gaussians at long times. We interpret these outcomes in the light of cellular division events: in the early stages, the phenomena are dependent each other in a multiplicative geometric-based process, and they are independent at long times. We conclude that the main ingredients for a good minimalist model of tumor growth, at mesoscopic level, are intrinsic cooperative mechanisms and competitive search for space. © 2013 Elsevier Ltd.