Willmore minimizers with prescribed isoperimetric ratio

Motivated by a simple model for elastic cell membranes, we minimize the Willmore functional among two-dimensional spheres embedded in R^3 with prescribed isoperimetric ratio

Lifespan theorem for constrained surface diffusion flows

We consider closed immersed hypersurfaces in $\R^{3}$ and $\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for which a smooth solution exists, and a small upper bound on a power of the total curvature during this time. By phrasing the theorem in terms of the concentration of curvature in the initial surface, our result holds for very general initial data and has applications to further development in asymptotic analysis for these flows.Comment: 29 pages. arXiv admin note: substantial text overlap with arXiv:1201.657

On well-posedness, stability, and bifurcation for the axisymmetric surface diffusion flow

In this article, we study the axisymmetric surface diffusion flow (ASD), a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2 + \alpha)-little-H\"older regular surfaces of revolution embedded in R^3 and satisfying periodic boundary conditions. We also give conditions for global existence of solutions and prove that solutions are real analytic in time and space. Further, we investigate the geometric properties of solutions to ASD. Utilizing a connection to axisymmetric surfaces with constant mean curvature, we characterize the equilibria of ASD. Then, focusing on the family of cylinders, we establish results regarding stability, instability and bifurcation behavior, with the radius acting as a bifurcation parameter for the problem.Comment: 37 pages, 6 figures, To Appear in SIAM J. Math. Ana

The Conformal Willmore Functional: a Perturbative Approach

The conformal Willmore functional (which is conformal invariant in general Riemannian manifold $(M,g)$) is studied with a perturbative method: the Lyapunov-Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3, g_\epsilon)$ -where $g_\epsilon$ is a metric close and asymptotic to the euclidean one. With the same technique a non existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.Comment: 34 pages; Journal of Geometric Analysis, on line first 23 September 201

Exendin-4 Improves Glycemic Control, Ameliorates Brain and Pancreatic Pathologies, and Extends Survival in a Mouse Model of Huntington's Disease

OBJECTIVE—The aim of this study was to find an effective treatment for the genetic form of diabetes that is present in some Huntington's disease patients and in Huntington's disease mouse models. Huntington's disease is a neurodegenerative disorder caused by a polyglutamine expansion within the huntingtin protein. Huntington's disease patients exhibit neuronal dysfunction/degeneration, chorea, and progressive weight loss. Additionally, they suffer from abnormalities in energy metabolism affecting both the brain and periphery. Similarly to Huntington's disease patients, mice expressing the mutated human huntingtin protein also exhibit neurodegenerative changes, motor dysfunction, perturbed energy metabolism, and elevated blood glucose levels

Family violence, war, and natural disasters: A study of the effect of extreme stress on children's mental health in Sri Lanka

Catani C, Jacob N, Schauer E, Kohila M, Neuner F. Family violence, war, and natural disasters: a study of the effect of extreme stress on children's mental health in Sri Lanka. BMC Psychiatry. 2008;8(1): 33.BACKGROUND: The consequences of war violence and natural disasters on the mental health of children as well as on family dynamics remain poorly understood. Aim of the present investigation was to establish the prevalence and predictors of traumatic stress related to war, family violence and the recent Tsunami experience in children living in a region affected by a long-lasting violent conflict. In addition, the study looked at whether higher levels of war violence would be related to higher levels of violence within the family and whether this would result in higher rates of psychological problems in the affected children. METHODS: 296 Tamil school children in Sri Lanka's North-Eastern provinces were randomly selected for the survey. Diagnostic interviews were carried out by extensively trained local Master level counselors. PTSD symptoms were established by means of a validated Tamil version of the UCLA PTSD Index. Additionally, participants completed a detailed checklist of event types related to organized and family violence. RESULTS: 82.4% of the children had experienced at least one war-related event. 95.6% reported at least one aversive experience out of the family violence spectrum. The consequences are reflected in a 30.4% PTSD and a 19.6% Major Depression prevalence. Linear regression analyses showed that fathers' alcohol intake and previous exposure to war were significantly linked to the amount of maltreatment reported by the child. A clear dose-effect relationship between exposure to various stressful experiences and PTSD was found in the examined children. CONCLUSION: Data argue for a relationship between war violence and violent behavior inflicted on children in their families. Both of these factors, together with the experience of the recent Tsunami, resulted as significant predictors of PTSD in children, thus highlighting the detrimental effect that the experience of cumulative stress can have on children's mental health

On shape dependence of holographic entanglement entropy in AdS4/CFT3

We study the finite term of the holographic entanglement entropy of finite domains with smooth shapes and for four dimensional gravitational backgrounds. Analytic expressions depending on the unit vectors normal to the minimal area surface are obtained for both stationary and time dependent spacetimes. The special cases of AdS4, asymptotically AdS4 black holes, domain wall geometries and Vaidya-AdS backgrounds have been analysed explicitly. When the bulk spacetime is AdS4, the finite term is the Willmore energy of the minimal area surface viewed as a submanifold of the three dimensional flat Euclidean space. For the static spacetimes, some numerical checks involving spatial regions delimited by ellipses and non convex domains have been performed. In the case of AdS4, the infinite wedge has been also considered, recovering the known analytic formula for the coefficient of the logarithmic divergence

Early Energy Deficit in Huntington Disease: Identification of a Plasma Biomarker Traceable during Disease Progression

Huntington disease (HD) is a fatal neurodegenerative disorder, with no effective treatment. The pathogenic mechanisms underlying HD have not been elucidated, but weight loss, associated with chorea and cognitive decline, is a characteristic feature of the disease that is accessible to investigation. We, therefore, performed a multiparametric study exploring body weight and the mechanisms of its loss in 32 presymptomatic carriers and HD patients in the early stages of the disease, compared to 21 controls. We combined this study with a multivariate statistical analysis of plasma components quantified by proton nuclear magnetic resonance (1H NMR) spectroscopy. We report evidence of an early hypermetabolic state in HD. Weight loss was observed in the HD group even in presymptomatic carriers, although their caloric intake was higher than that of controls. Inflammatory processes and primary hormonal dysfunction were excluded. 1H NMR spectroscopy on plasma did, however, distinguish HD patients at different stages of the disease and presymptomatic carriers from controls. This distinction was attributable to low levels of the branched chain amino acids (BCAA), valine, leucine and isoleucine. BCAA levels were correlated with weight loss and, importantly, with disease progression and abnormal triplet repeat expansion size in the HD1 gene. Levels of IGF1, which is regulated by BCAA, were also significantly lower in the HD group. Therefore, early weight loss in HD is associated with a systemic metabolic defect, and BCAA levels may be used as a biomarker, indicative of disease onset and early progression. The decreased plasma levels of BCAA may correspond to a critical need for Krebs cycle energy substrates in the brain that increased metabolism in the periphery is trying to provide