Dependence of the crossover exponent with the diffusion rate in the generalized contact process model

We study how the crossover exponent, phi, between the directed percolation (DP) and compact directed percolation (CDP) behaves as a function of the diffusion rate in a model that generalizes the contact process. Our conclusions are based in results pointed by perturbative series expansions and numerical simulations, and are consistent with a value phi = 2 for finite diffusion rates and phi = 1 in the limit of infinite diffusion rate.

The generalized inverse Weibull distribution

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.

The generalized log-gamma mixture model with covariates: local influence and residual analysis

In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure or relapse, may be indicated by a relatively high number of individuals with large censored survival times. In this paper the generalized log-gamma model is modified for the possibility that long-term survivors may be present in the data. The model attempts to separately estimate the effects of covariates on the surviving fraction, that is, the proportion of the population for which the event never occurs. The logistic function is used for the regression model of the surviving fraction. Inference for the model parameters is considered via maximum likelihood. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. Finally, a data set from the medical area is analyzed under the log-gamma generalized mixture model. A residual analysis is performed in order to select an appropriate model.

A generalized modified Weibull distribution for lifetime modeling

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution. (C) 2008 Elsevier B.V. All rights reserved.

The exponentiated generalized gamma distribution with application to lifetime data

A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.

Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

Some results on holomorphic generalized functions

In this note, we present three independent results within generalized complex analysis (in the Colombeau sense). The first of them deals with non-removable singularities; we construct a generalized function u on an open subset Omega of C(n), which is not a holomorphic generalized function on Omega but it is a holomorphic generalized function on Omega\S, where S is a hypersurface contained in Omega. The second result shows the existence of a holomorphic generalized function with prescribed values in the zero-set of a classical holomorphic function. The last result states the existence of a compactly supported solution to the (partial derivative) over bar operator.

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

A new family of generalized distributions

Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79-88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix `Kw`) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with an application to real data.

ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS

We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of (K) over bar and introduce several invariants of the ideals of 9(Q). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become Cl-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.

The exponentiated generalized inverse Gaussian distribution

The modeling and analysis of lifetime data is an important aspect of statistical work in a wide variety of scientific and technological fields. Good (1953) introduced a probability distribution which is commonly used in the analysis of lifetime data. For the first time, based on this distribution, we propose the so-called exponentiated generalized inverse Gaussian distribution, which extends the exponentiated standard gamma distribution (Nadarajah and Kotz, 2006). Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters. The usefulness of the new model is illustrated by means of a real data set. (c) 2010 Elsevier B.V. All rights reserved.

Self-perception and malocclusion and their relation to oral appearance and function

The aim of this study was to evaluate the relationship between malocclusion and self-perception of oral appearance/function, in 12/15-year-old Brazilian adolescents. The cluster sample consisted of 717 teenagers attending 24 urban public (n=611) and 5 rural public (n=107) schools in Maringá/PR. Malocclusion was measured using the Dental Aesthetic Index (DAI), in accordance with WHO recommendations. A parental questionnaire was applied to collect information on esthetic perception level and oral variables related to oral health. Univariate and multiple logistic regression analyses were performed. Multiple logistic regression confirmed that for 12-year-old, missing teeth (OR=2.865) and presence of openbite (open occlusal relationship) (OR=2.865) were risk indicators for speech capability. With regard to 15-year-old, presence of mandibular overjet (horizontal overlap) (OR=4.016) was a risk indicator for speech capability and molar relationship (OR=1.661) was a risk indicator for chewing capability. The impact of malocclusion on adolescents' life was confirmed in this study. Speech and chewing capability were associated with orthodontic deviations, which should be taken into consideration in oral health planning, to identify risk groups and improve community health services.

Dynamic and steady: shear rheological properties of xanthan and guar gums dispersed in yellow passion fruit pulp (Passiflora edulis f. flavicarpa)

Yellow passion fruit pulp is unstable, presenting phase separation that can be avoided by the addition of hydrocolloids. For this purpose, xanthan and guar gum [0.3, 0.7 and 1.0% (w/w)] were added to yellow passion fruit pulp and the changes in the dynamic and steady - shear rheological behavior evaluated. Xanthan dispersions showed a more pronounced pseudoplasticity and the presence of yield stress, which was not observed in the guar gum dispersions. Cross model fitting to flow curves showed that the xanthan suspensions also had higher zero shear viscosity than the guar suspensions, and, for both gums, an increase in temperature led to lower values for this parameter. The gums showed different behavior as a function of temperature in the range of 5 - 35ºC. The activation energy of the apparent viscosity was dependent on the shear rate and gum concentration for guar, whereas for xanthan these values only varied with the concentration. The mechanical spectra were well described by the generalized Maxwell model and the xanthan dispersions showed a more elastic character than the guar dispersions, with higher values for the relaxation time. Xanthan was characterized as a weak gel, while guar presented a concentrated solution behavior. The simultaneous evaluation of temperature and concentration showed a stronger influence of the polysaccharide concentration on the apparent viscosity and the G' and G" moduli than the variation in temperature.

Flow cytometry as a tool in the evaluation of blood leukocyte function in Chelonia mydas (Linnaeus, 1758) (Testudines, Cheloniidae)

Chelonia mydas is a sea turtle that feeds and nests on the Brazilian coast and a disease called fibropapillomatosis is a threat to this species. Because of this, it is extremely necessary to determine a methodology that would enable the analysis of blood leukocyte function in these sea turtles. In order to achieve this aim, blood samples were collected from C. mydas with or without fibropapillomas captured on the São Paulo north coast. Blood samples were placed in tubes containing sodium heparin and were transported under refrigeration to the laboratory in sterile RPMI 1640 cell culture medium. Leukocytes were separated by density gradient using Ficoll-PaqueTM Plus, Amershan Biociences®. The following stimuli were applied in the assessment of leukocyte function: Phorbol Miristate-Acetate (PMA) for oxidative burst activity evaluation and Zymosan A (Saccharomyces cerevisiae) Bio Particles®, Alexa Fluor® 594 conjugate for phagocytosis evaluation. Three cell populations were identified: heterophils, monocytes and lymphocytes. Monocytes were the cells responsible for phagocytosis and oxidative burst.