POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

Generic hyperbolicity of stationary solutions for a reaction-diffusion system

In this paper, we study the generic hyperbolicity of equilibria of a reaction-diffusion system with respect to nonlinear terms in the set of C(2)-functions equipped with the Whitney Topology. To accomplish this, we combine Baire`s Lemma and the usual Transversality Theorem. (C) 2010 Elsevier Ltd. All rights reserved.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

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.

SELF-SIMILARITY AND LAMPERTI CONVERGENCE FOR FAMILIES OF STOCHASTIC PROCESSES

We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to certain important families of processes that are not self-similar in the conventional sense. This includes Hougaard Levy processes such as the Poisson processes, Brownian motions with drift and the inverse Gaussian processes, and some new fractional Hougaard motions defined as moving averages of Hougaard Levy process. Such families have many properties in common with ordinary self-similar processes, including the form of their covariance functions, and the fact that they appear as limits in a Lamperti-type limit theorem for families of stochastic processes.

Leaf area index estimation with MODIS reflectance time series and model inversion during full rotations of Eucalyptus plantations

The leaf area index (LAI) of fast-growing Eucalyptus plantations is highly dynamic both seasonally and interannually, and is spatially variable depending on pedo-climatic conditions. LAI is very important in determining the carbon and water balance of a stand, but is difficult to measure during a complete stand rotation and at large scales. Remote-sensing methods allowing the retrieval of LAI time series with accuracy and precision are therefore necessary. Here, we tested two methods for LAI estimation from MODIS 250m resolution red and near-infrared (NIR) reflectance time series. The first method involved the inversion of a coupled model of leaf reflectance and transmittance (PROSPECT4), soil reflectance (SOILSPECT) and canopy radiative transfer (4SAIL2). Model parameters other than the LAI were either fixed to measured constant values, or allowed to vary seasonally and/or with stand age according to trends observed in field measurements. The LAI was assumed to vary throughout the rotation following a series of alternately increasing and decreasing sigmoid curves. The parameters of each sigmoid curve that allowed the best fit of simulated canopy reflectance to MODIS red and NIR reflectance data were obtained by minimization techniques. The second method was based on a linear relationship between the LAI and values of the GEneralized Soil Adjusted Vegetation Index (GESAVI), which was calibrated using destructive LAI measurements made at two seasons, on Eucalyptus stands of different ages and productivity levels. The ability of each approach to reproduce field-measured LAI values was assessed, and uncertainty on results and parameter sensitivities were examined. Both methods offered a good fit between measured and estimated LAI (R(2) = 0.80 and R(2) = 0.62 for model inversion and GESAVI-based methods, respectively), but the GESAVI-based method overestimated the LAI at young ages. (C) 2010 Elsevier Inc. All rights reserved.

Generalized Pustular Psoriasis in Childhood

Generalized pustular psoriasis is a rare form of psoriasis consisting of a generalized eruption of sudden onset with erythema and sterile pustules. In children, generalized pustular psoriasis is even more uncommon and may present as a severe and potentially life-threatening disorder. In this study, we present demographics, clinical aspects, treatment response, and follow-up of seven children with generalized pustular psoriasis. Retrospective study reviewing the records of seven children with generalized pustular psoriasis including age, gender, age of onset, presence of scalp and nail involvement, family history, concomitant diseases, precipitating factors, treatment modalities, and outcome. Age of first symptoms ranged from 1 month to 11 years. All patients received systemic retinoids at one time of the follow-up period. Other treatment modalities included immunosuppressive drugs, biologics, phototherapy, and sulfasalazine. Two patients presented with severe constitutional illness, secondary infection and septic shock, including one fatal outcome. All further cases have remained free of recurrences for a mean period of up to 3 years. In our study, generalized pustular psoriasis presented a wide clinical spectrum in children ranging from mild, asymptomatic outbreaks to more severe, life-threatening episodes. One fatality was observed. Children generally responded well to systemic retinoids. Further studies and long-term follow-up periods are needed to define potential trigger factors, efficacy and safety of different treatment modalities in children with generalized pustular psoriasis.

The reactions of specific neuron types to intestinal ischemia in the guinea pig enteric nervous system

Damage following ischemia and reperfusion (I/R) is common in the intestine and can be caused during abdominal surgery, in several disease states and following intestinal transplantation. Most studies have concentrated on damage to the mucosa, although published evidence also points to effects on neurons. Moreover, alterations of neuronally controlled functions of the intestine persist after I/R. The present study was designed to investigate the time course of damage to neurons and the selectivity of the effect of I/R damage for specific types of enteric neurons. A branch of the superior mesenteric artery supplying the distal ileum of anesthetised guinea pigs was occluded for 1 h and the animals were allowed to recover for 2 h to 4 weeks before tissue was taken for the immunohistochemical localization of markers of specific neuron types in tissues from sham and I/R animals. The dendrites of neurons with nitric oxide synthase (NOS) immunoreactivity, which are inhibitory motor neurons and interneurons, were distorted and swollen by 24 h after I/R and remained enlarged up to 28 days. The total neuron profile areas (cell body plus dendrites) increased by 25%, but the sizes of cell bodies did not change significantly. Neurons of type II morphology (intrinsic primary afferent neurons), revealed by NeuN immunoreactivity, were transiently reduced in cell size, at 24 h and 7 days. These neurons also showed signs of minor cell surface blebbing. Calretinin neurons, many of which are excitatory motor neurons, were unaffected. Thus, this study revealed a selective damage to NOS neurons that was observed at 24 h and persisted up to 4 weeks, without a significant change in the relative numbers of NOS neurons.

Impaired dendritic cell differentiation and maturation in the absence of C3

Human monocytes can be differentiated into immature dendritic cells (DCs) in the presence of serum and cytokines. One of the main functions of immature DCs is to capture and process antigens. Following maturation, they differentiate into antigen presenting cells. The role of complement in the differentiation process from monocytes towards immature DCs remains elusive. Here we demonstrate that complement 3 (C3) has a regulatory impact on the expression of specific DC surface molecules and DC-derived cytokine production during DC differentiation. We isolated human adherent peripheral blood mononuclear cells, which were cultured in the presence of GM-CSF plus IL-4 in medium supplemented with normal human serum or C3 deficient serum. The lack of C3 during DC differentiation negatively impacted the expression of C-type lectin receptor DC-SIGN, the antigen presenting molecules HLA-DR and CD1a, and the costimulatory molecules CD80 and CD86. Further, the spontaneous production of IL-6 and IL-12 was reduced in the absence of C3. Moreover, the maturation of immature DCs in response to LPS challenge was impaired in the absence of C3 as evidenced by reduced MHC-II, co-stimulatory molecule expression as well as modulated IL-12 and TNF-alpha production. Collectively, our results provide evidence for a novel role of C3 as a critical cofactor in human DC differentiation and maturation. (C) 2007 Elsevier Ltd. All rights reserved.

Immune response to cytolethal distending toxin of Aggregatibacter actinomycetemcomitans in periodontitis patients

Background and Objective: Cytolethal distending toxin (CDT) is a genotoxin produced by Aggregatibacter actinomycetemcomitans. In spite of its association with pathogenesis, little is known about the humoral immune response against the CDT. This study aimed to test whether subgingival colonization and humoral response to A. actinomycetemcomitans would lead to a response against CDT. Material and Methods: Sera from periodontally healthy, localized and generalized aggressive periodontitis and chronic periodontitis subjects (n = 80) were assessed for immunoglobulin G titers to A. actinomycetemcomitans serotypes a/b/c and to each CDT subunit (CdtA, CdtB and CdtC) by ELISA. A. actinomycetemcomitans subgingival levels and neutralization of CDT activity were also analyzed. Results: Sera from 75.0% localized and 81.8% generalized aggressive periodontitis patients reacted to A. actinomycetemcomitans. A response to serotype b was detected in localized (66.7%) and generalized aggressive periodontitis (54.5%). Reactivity to A. actinomycetemcomitans correlated with subgingival colonization (R = 0.75, p < 0.05). There was no correlation between A. actinomycetemcomitans colonization or response to serotypes and the immunoglobulin G response to CDT subunits. Titers of immunoglobulin G to CdtA and CdtB did not differ among groups; however, sera of all generalized aggressive periodontitis patients reacted to CdtC. Neutralization of CDT was not correlated with levels of antibodies to CDT subunits. Conclusion: Response to CdtA and CdtB did not correlate with the periodontal status of the subject in the context of an A. actinomycetemcomitans infection. However, a response to CdtC was found in sera of generalized but not of localized aggressive periodontitis subjects. Differences in response to CdtC between generalized and localized aggressive periodontitis subjects indicate that CDT could be expressed differently by the infecting strains. Alternatively, the antibody response to CdtC could require the colonization of multiple sites.

Using non-homogeneous Poisson models with multiple change-points to estimate the number of ozone exceedances in Mexico City

In this paper, we consider some non-homogeneous Poisson models to estimate the probability that an air quality standard is exceeded a given number of times in a time interval of interest. We assume that the number of exceedances occurs according to a non-homogeneous Poisson process (NHPP). This Poisson process has rate function lambda(t), t >= 0, which depends on some parameters that must be estimated. We take into account two cases of rate functions: the Weibull and the Goel-Okumoto. We consider models with and without change-points. When the presence of change-points is assumed, we may have the presence of either one, two or three change-points, depending of the data set. The parameters of the rate functions are estimated using a Gibbs sampling algorithm. Results are applied to ozone data provided by the Mexico City monitoring network. In a first instance, we assume that there are no change-points present. Depending on the adjustment of the model, we assume the presence of either one, two or three change-points. Copyright (C) 2009 John Wiley & Sons, Ltd.

C(0) and bi-Lipschitz K-equivalence of mappings

In this paper we investigate the classification of mappings up to K-equivalence. We give several results of this type. We study semialgebraic deformations up to semialgebraic C(0) K-equivalence and bi-Lipschitz K-equivalence. We give an algebraic criterion for bi-Lipschitz K-triviality in terms of semi-integral closure (Theorem 3.5). We also give a new proof of a result of Nishimura: we show that two germs of smooth mappings f, g : R(n) -> R(n), finitely determined with respect to K-equivalence are C(0)-K-equivalent if and only if they have the same degree in absolute value.

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Transformed generalized linear models

The estimation of data transformation is very useful to yield response variables satisfying closely a normal linear model, Generalized linear models enable the fitting of models to a wide range of data types. These models are based on exponential dispersion models. We propose a new class of transformed generalized linear models to extend the Box and Cox models and the generalized linear models. We use the generalized linear model framework to fit these models and discuss maximum likelihood estimation and inference. We give a simple formula to estimate the parameter that index the transformation of the response variable for a subclass of models. We also give a simple formula to estimate the rth moment of the original dependent variable. We explore the possibility of using these models to time series data to extend the generalized autoregressive moving average models discussed by Benjamin er al. [Generalized autoregressive moving average models. J. Amer. Statist. Assoc. 98, 214-223]. The usefulness of these models is illustrated in a Simulation study and in applications to three real data sets. (C) 2009 Elsevier B.V. All rights reserved.

Power series generalized nonlinear models

We introduce in this paper a new class of discrete generalized nonlinear models to extend the binomial, Poisson and negative binomial models to cope with count data. This class of models includes some important models such as log-nonlinear models, logit, probit and negative binomial nonlinear models, generalized Poisson and generalized negative binomial regression models, among other models, which enables the fitting of a wide range of models to count data. We derive an iterative process for fitting these models by maximum likelihood and discuss inference on the parameters. The usefulness of the new class of models is illustrated with an application to a real data set. (C) 2008 Elsevier B.V. All rights reserved.