Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

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.

Genetic aspects of adolescent idiopathic scoliosis in a family with multiple affected members: a research article

Abstract Background The etiology of idiopathic scoliosis remains unknown and different factors have been suggested as causal. Hereditary factors can also determine the etiology of the disease; however, the pattern of inheritance remains unknown. Autosomal dominant, X-linked and multifactorial patterns of inheritances have been reported. Other studies have suggested possible chromosome regions related to the etiology of idiopathic scoliosis. We report the genetic aspects of and investigate chromosome regions for adolescent idiopathic scoliosis in a Brazilian family. Methods Evaluation of 57 family members, distributed over 4 generations of a Brazilian family, with 9 carriers of adolescent idiopathic scoliosis. The proband presented a scoliotic curve of 75 degrees, as determined by the Cobb method. Genomic DNA from family members was genotyped. Results Locating a chromosome region linked to adolescent idiopathic scoliosis was not possible in the family studied. Conclusion While it was not possible to determine a chromosome region responsible for adolescent idiopathic scoliosis by investigation of genetic linkage using microsatellites markers during analysis of four generations of a Brazilian family with multiple affected members, analysis including other types of genomic variations, like single nucleotide polymorphisms (SNPs) could contribute to the continuity of this study.

Homogeneous structures and rigidity of isoparametric submanifolds in Hilbert space

We study isoparametric submanifolds of rank at least two in a separable Hilbert space, which are known to be homogeneous by the main result in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181], and with such a submanifold M and a point x in M we associate a canonical homogeneous structure I" (x) (a certain bilinear map defined on a subspace of T (x) M x T (x) M). We prove that I" (x) , together with the second fundamental form alpha (x) , encodes all the information about M, and we deduce from this the rigidity result that M is completely determined by alpha (x) and (Delta alpha) (x) , thereby making such submanifolds accessible to classification. As an essential step, we show that the one-parameter groups of isometries constructed in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181] to prove their homogeneity induce smooth and hence everywhere defined Killing fields, implying the continuity of I" (this result also seems to close a gap in [U. Christ, J. Differential Geom., 62 (2002), 1-15]). Here an important tool is the introduction of affine root systems of isoparametric submanifolds.

Average control of Markov decision processes with Feller transition probabilities and general action spaces

This paper studies the average control problem of discrete-time Markov Decision Processes (MDPs for short) with general state space, Feller transition probabilities, and possibly non-compact control constraint sets A(x). Two hypotheses are considered: either the cost function c is strictly unbounded or the multifunctions A(r)(x) = {a is an element of A(x) : c(x, a) <= r} are upper-semicontinuous and compact-valued for each real r. For these two cases we provide new results for the existence of a solution to the average-cost optimality equality and inequality using the vanishing discount approach. We also study the convergence of the policy iteration approach under these conditions. It should be pointed out that we do not make any assumptions regarding the convergence and the continuity of the limit function generated by the sequence of relative difference of the alpha-discounted value functions and the Poisson equations as often encountered in the literature. (C) 2012 Elsevier Inc. All rights reserved.

Relationships between gender, age, family conditions, physical and mental health, and social isolation of elderly caregivers

Background: In an aging population an increasing number of elderly caregivers will be called upon to provide care over a long period, during which time they will be burdened both by caregiving and by the physiological effects of their own aging. Among them there will be more aged male caregivers, who will probably be less prepared than women to become caregivers. The aim of this study was to investigate the relationship between caregivers' gender, age, family income, living arrangements and social support as independent variables, and depressive symptoms, comorbidities, level of frailty, grip strength, walking speed and social isolation, as dependent variables. Methods: 176 elderly people (123 women) were selected from a sample of a population-based study on frailty (n = 900), who had cared for a spouse (79.3%) and/or parents (31.4%) in the past five years (mean age = 71.8 +/- 4.86 years; mean monthly family income in minimum wages = 4.64 +/- 5.14). The study used questionnaires and self-report scales, grip strength and walking speed tests. Results: 65% of participants evaluated caregiving as being very stressful. Univariate analyses of regression showed low family income as a risk factor for depression; being female and low perceived social support as a risk for comorbidities; being 80 years of age and above for low grip strength; and being male for social isolation indicated by discontinuity of activities and social roles. In multivariate analyses of regression, poverty arose as a risk factor for depression and being female for comorbidities. Conclusions: Gender roles, age, income and social support interacted with physical and emotional health, and with the continuity of social participation of elderly caregivers. Special attention must be given to male caregivers.

Equity and women's health services for contraception, abortion and childbirth in Brazil

This paper addresses equity in health and health care in Brazil, examining unjust disparities between women and men, and between women from different social strata, with a focus on services for contraception, abortion and pregnancy. In 2010 women's life expectancy was 77.6 years, men's was 69.7 years. Women are two-thirds of public hospital services users and assess their health status less positively than men. The total fertility rate was 1.8 in 2011, and contraceptive prevalence has been high among women at all income levels. The proportion of sterilizations has decreased; lower-income women are more frequently sterilized. Abortions are mostly illegal; women with more money have better access to safe abortions in private clinics. Poorer women generally self-induce abortion with misoprostol, seeking treatment of complications from public clinics. Institutional violence on the part of health professionals is reported by half of women receiving abortion care and a quarter of women during childbirth. Maternity care is virtually universal. The public sector has fewer caesarean sections, fewer low birth weight babies, and more rooming-in, but excessive episiotomies and inductions. Privacy, continuity of care and companionship during birth are more common in the private sector. To achieve equity, the health system must go beyond universal, unregulated access to technology, and move towards safe, effective and transparent care. (C) 2012 Reproductive Health Matters

Integrodifference model for blowfly invasion

We propose a stage-structured integrodifference model for blowflies' growth and dispersion taking into account the density dependence of fertility and survival rates and the non-overlap of generations. We assume a discrete-time, stage-structured, model. The spatial dynamics is introduced by means of a redistribution kernel. We treat one and two dimensional cases, the latter on the semi-plane, with a reflexive boundary. We analytically show that the upper bound for the invasion front speed is the same as in the one-dimensional case. Using laboratory data for fertility and survival parameters and dispersal data of a single generation from a capture-recapture experiment in South Africa, we obtain an estimate for the velocity of invasion of blowflies of the species Chrysomya albiceps. This model predicts a speed of invasion which was compared to actual observational data for the invasion of the focal species in the Neotropics. Good agreement was found between model and observations.