Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

The new class of Kummer beta generalized distributions

Ng and Kotz (1995) introduced a distribution that provides greater flexibility to extremes. We define and study a new class of distributions called the Kummer beta generalized family to extend the normal, Weibull, gamma and Gumbel distributions, among several other well-known distributions. Some special models are discussed. The ordinary moments of any distribution in the new family can be expressed as linear functions of probability weighted moments of the baseline distribution. We examine the asymptotic distributions of the extreme values. We derive the density function of the order statistics, mean absolute deviations and entropies. We use maximum likelihood estimation to fit the distributions in the new class and illustrate its potentiality with an application to a real data set.

On the generalized canonical equations of Hamilton for a time-dependent mass particle

Fundamental principles of mechanics were primarily conceived for constant mass systems. Since the pioneering works of Meshcherskii (see historical review in Mikhailov (Mech. Solids 10(5):32-40, 1975), efforts have been made in order to elaborate an adequate mathematical formalism for variable mass systems. This is a current research field in theoretical mechanics. In this paper, attention is focused on the derivation of the so-called 'generalized canonical equations of Hamilton' for a variable mass particle. The applied technique consists in the consideration of the mass variation process as a dissipative phenomenon. Kozlov's (Stek. Inst. Math 223:178-184, 1998) method, originally devoted to the derivation of the generalized canonical equations of Hamilton for dissipative systems, is accordingly extended to the scenario of variable mass systems. This is done by conveniently writing the flux of kinetic energy from or into the variable mass particle as a 'Rayleigh-like dissipation function'. Cayley (Proc. R Soc. Lond. 8:506-511, 1857) was the first scholar to propose such an analogy. A deeper discussion on this particular subject will be left for a future paper.

On the Hilbert transform in the framework of generalized functions

In this paper, a definition of the Hilbert transform operating on Colombeau's temperated generalized functions is given. Similar results to some theorems that hold in the classical theory, or in certain subspaces of Schwartz distributions, have been obtained in this framework.

Fish Oil Supplementation Reduces Cachexia and Tumor Growth While Improving Renal Function in Tumor-Bearing Rats

The objective of the present work was to study the renal function of healthy and tumor-bearing rats chronically supplemented with fish oil (FO), a source of n-3 polyunsaturated fatty acids. Weanling male rats were divided in two groups, one control (C) and another orally supplemented for 70 days with FO (1 g/kg body weight). After this time, half the animals of each group were injected in the right flank with a suspension of Walker 256 tumor cells (W and WFO). The W group had less proteinemia reflecting cachectic proteolysis, FO reversed this fact. Tumor weight gain was also reduced in WFO. Glomerular filtration rate (GFR) was not different in FO or W compared to C, but was higher in WFO. Renal plasma flow (RPF) was higher in the FO supplemented groups. The W group had lower plasma osmolality than the C group, but FO supplementation resulted in normalization of this parameter. Fractional sodium excretion (FENa+) of FO rats was similar to C. Proximal Na+ reabsorption, evaluated by lithium clearance, was similar among the groups. Urinary thromboxane B-2 (TXB2) excretion was lower in the supplemented groups. The number of macrophages in renal tissue was higher in W compared to C rats, but was lower in WFO rats compared to W rats. In conclusion, FO supplementation resulted in less tumor growth and cachexia, and appeared to be renoprotective, as suggested by higher RPF and GFR.

Extracellular matrix in airway smooth muscle is associated with dynamics of airway function in asthma

Background: Altered deposition of extracellular matrix (ECM) in the airway smooth muscle (ASM) layer as observed in asthma may influence ASM mechanical properties. We hypothesized that ECM in ASM is associated with airway function in asthma. First, we investigated the difference in ECM expression in ASM between asthma and controls. Second, we examined whether ECM expression is associated with bronchoconstriction and bronchodilation in vivo. Methods: Our cross-sectional study comprised 19 atopic mild asthma patients, 15 atopic and 12 nonatopic healthy subjects. Spirometry, methacholine responsiveness, deep-breath-induced bronchodilation (Delta R-rs) and bronchoscopy with endobronchial biopsies were performed. Positive staining of elastin, collagen I, III and IV, decorin, versican, fibronectin, laminin and tenascin in ASM was quantified as fractional area and mean density. Data were analysed using Pearson's or Spearman's correlation coefficient. Results: Extracellular matrix expression in ASM was not different between asthma and controls. In asthmatics, fractional area and mean density of collagen I and III were correlated with methacholine dose-response slope and DRrs, respectively (r = 0.71, P < 0.01; r = 0.60, P = 0.02). Furthermore, ASM collagen III and laminin in asthma were correlated with FEV1 reversibility (r = -0.65, P = 0.01; r = -0.54, P = 0.04). Conclusion: In asthma, ECM in ASM is related to the dynamics of airway function in the absence of differences in ECM expression between asthma and controls. This indicates that the ASM layer in its full composition is a major structural component in determining variable airways obstruction in asthma.

Evaluation of physiologic complexity in time series using generalized sample entropy and surrogate data analysis

Complexity in time series is an intriguing feature of living dynamical systems, with potential use for identification of system state. Although various methods have been proposed for measuring physiologic complexity, uncorrelated time series are often assigned high values of complexity, errouneously classifying them as a complex physiological signals. Here, we propose and discuss a method for complex system analysis based on generalized statistical formalism and surrogate time series. Sample entropy (SampEn) was rewritten inspired in Tsallis generalized entropy, as function of q parameter (qSampEn). qSDiff curves were calculated, which consist of differences between original and surrogate series qSampEn. We evaluated qSDiff for 125 real heart rate variability (HRV) dynamics, divided into groups of 70 healthy, 44 congestive heart failure (CHF), and 11 atrial fibrillation (AF) subjects, and for simulated series of stochastic and chaotic process. The evaluations showed that, for nonperiodic signals, qSDiff curves have a maximum point (qSDiff(max)) for q not equal 1. Values of q where the maximum point occurs and where qSDiff is zero were also evaluated. Only qSDiff(max) values were capable of distinguish HRV groups (p-values 5.10 x 10(-3); 1.11 x 10(-7), and 5.50 x 10(-7) for healthy vs. CHF, healthy vs. AF, and CHF vs. AF, respectively), consistently with the concept of physiologic complexity, and suggests a potential use for chaotic system analysis. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4758815]

Generalized beta-generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets. (c) 2011 Elsevier B.V. All rights reserved.

The log-exponentiated generalized gamma regression model for censored data

For the first time, we introduce a generalized form of the exponentiated generalized gamma distribution [Cordeiro et al. The exponentiated generalized gamma distribution with application to lifetime data, J. Statist. Comput. Simul. 81 (2011), pp. 827-842.] that is the baseline for the log-exponentiated generalized gamma regression model. The new distribution can accommodate increasing, decreasing, bathtub- and unimodal-shaped hazard functions. A second advantage is that it includes classical distributions reported in the lifetime literature as special cases. We obtain explicit expressions for the moments of the baseline distribution of the new regression model. The proposed model can be applied to censored data since it includes as sub-models several widely known regression models. It therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data. We show that our extended regression model is very useful by means of two applications to real data.

On Wald Residuals in Generalized Linear Models

A rigorous asymptotic theory for Wald residuals in generalized linear models is not yet available. The authors provide matrix formulae of order O(n(-1)), where n is the sample size, for the first two moments of these residuals. The formulae can be applied to many regression models widely used in practice. The authors suggest adjusted Wald residuals to these models with approximately zero mean and unit variance. The expressions were used to analyze a real dataset. Some simulation results indicate that the adjusted Wald residuals are better approximated by the standard normal distribution than the Wald residuals.

Renal function evaluation in patients with American Cutaneous Leishmaniasis after specific treatment with pentavalent antimonial

Background: Renal evaluation studies are rare in American Cutaneous Leishmaniasis (ACL). The aim of this study is to investigate whether specific treatment reverts ACL-associated renal dysfunction. Methods: A prospective study was conducted with 37 patients with ACL. Urinary concentrating and acidification ability was assessed before and after treatment with pentavalent antimonial. Results: The patients mean age was 35.6 +/- 12 years and 19 were male. Before treatment, urinary concentrating defect (U/P-osm < 2.8) was identified in 27 patients (77%) and urinary acidification defect in 17 patients (46%). No significant glomerular dysfunction was observed before and after specific ACL treatment. There was no reversion of urinary concentrating defects, being observed in 77% of the patients before and in 88% after treatment (p = 0.344). Urinary acidification defect was corrected in 9 patients after treatment, reducing its prevalence from 40% before to only 16% after treament, (p = 0.012). Microalbuminuria higher than 30 mg/g was found in 35% of patients before treatment and in only 8% after treatment. Regarding fractional excretion of sodium, potassium, calcium, phosphorus and magnesium, there was no significant difference between pre and post-treatment period. Conclusion: As previously described, urinary concentrating and acidification defects were found in an important number of patients with ACL. Present results demonstrate that only some patients recover urinary acidification capacity, while no one returned to normal urinary concentration capacity.

Renal function evaluation in patients with American Cutaneous Leishmaniasis after specific treatment with pentavalent antimonial

Background Renal evaluation studies are rare in American Cutaneous Leishmaniasis (ACL). The aim of this study is to investigate whether specific treatment reverts ACL-associated renal dysfunction. Methods A prospective study was conducted with 37 patients with ACL. Urinary concentrating and acidification ability was assessed before and after treatment with pentavalent antimonial. Results The patients mean age was 35.6 ± 12 years and 19 were male. Before treatment, urinary concentrating defect (U/Posm <2.8) was identified in 27 patients (77%) and urinary acidification defect in 17 patients (46%). No significant glomerular dysfunction was observed before and after specific ACL treatment. There was no reversion of urinary concentrating defects, being observed in 77% of the patients before and in 88% after treatment (p = 0.344). Urinary acidification defect was corrected in 9 patients after treatment, reducing its prevalence from 40% before to only 16% after treament, (p = 0.012). Microalbuminuria higher than 30 mg/g was found in 35% of patients before treatment and in only 8% after treatment. Regarding fractional excretion of sodium, potassium, calcium, phosphorus and magnesium, there was no significant difference between pre and post-treatment period. Conclusion As previously described, urinary concentrating and acidification defects were found in an important number of patients with ACL. Present results demonstrate that only some patients recover urinary acidification capacity, while no one returned to normal urinary concentration capacity.