A second order minimality condition for the Mumford-Shah functional

A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\Gamma)$, $\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.Comment: 30 page

Stability estimates for resolvents, eigenvalues and eigenfunctions of elliptic operators on variable domains

We consider general second order uniformly elliptic operators subject to homogeneous boundary conditions on open sets $\phi (\Omega)$ parametrized by Lipschitz homeomorphisms $\phi$ defined on a fixed reference domain $\Omega$. Given two open sets $\phi (\Omega)$, $\tilde \phi (\Omega)$ we estimate the variation of resolvents, eigenvalues and eigenfunctions via the Sobolev norm $\|\tilde \phi -\phi \|_{W^{1,p}(\Omega)}$ for finite values of $p$, under natural summability conditions on eigenfunctions and their gradients. We prove that such conditions are satisfied for a wide class of operators and open sets, including open sets with Lipschitz continuous boundaries. We apply these estimates to control the variation of the eigenvalues and eigenfunctions via the measure of the symmetric difference of the open sets. We also discuss an application to the stability of solutions to the Poisson problem.Comment: 34 pages. Minor changes in the introduction and the refercenes. Published in: Around the research of Vladimir Maz'ya II, pp23--60, Int. Math. Ser. (N.Y.), vol. 12, Springer, New York 201

Multiplicity of Positive Solutions for an Obstacle Problem in R

In this paper we establish the existence of two positive solutions for the obstacle problem \displaystyle \int_{\Re}\left[u'(v-u)'+(1+\lambda V(x))u(v-u)\right] \geq \displaystyle \int_{\Re} f(u)(v-u), \forall v\in \Ka where $f$ is a continuous function verifying some technical conditions and \Ka is the convex set given by \Ka =\left\{v\in H^{1}(\Re); v \geq \varphi \right\}, with $\varphi \in H^{1}(\Re)$ having nontrivial positive part with compact support in $\Re$. \vspace{0.2cm} \noindent \emph{2000 Mathematics Subject Classification} : 34B18, 35A15, 46E39. \noindent \emph{Key words}: Obstacle problem, Variational methods, Positive solutions.Comment: To appear in Progress in Nonlinear Differential Equations and their Application

The PRIAMO study: age- and sex-related relationship between prodromal constipation and disease phenotype in early Parkinson's disease.

OBJECTIVES: To explore the impact of sex and age on relationship between prodromal constipation and disease phenotype in Parkinson's disease at early stages. METHODS: A total of 385 Parkinson's disease patients from the PRIAMO study were classified according to the presence of prodromal constipation and followed for 24 months. Multivariable mixed-effect models were applied. All analyses were performed separately for sex (64.1% men) and median age (different by sex: 67 years-old in men and 68 years-old in women). RESULTS: As for sex, prodromal constipation was associated with greater odds of attention/memory complaints and apathy symptoms in women only. As for age, prodromal constipation was associated with lower cognitive and higher apathy scores in older patients only. CONCLUSIONS: Prodromal constipation anticipates lower cognitive performances and more severe apathy since the earliest stages in women and older patients. Sex- and age-related heterogeneity of prodromal markers of Parkinson's disease may impact disease phenotype

Translation-program of the first Hungarian periodical in the late 18th century

International audienc

Impact of different spray-drying conditions on the viability of wine Saccharomyces cerevisiae strains

Spray-drying (SD) is widely considered a suitable method to preserve microorganisms, but data regarding yeasts are still scanty. In this study, the effect of growing media, process variables and carriers over viability of a wild wine Saccharomyces (S.) cerevisiae LM52 was evaluated. For biomass production, the strain was grown (batch and fed-batch fermentation) in a synthetic, as well as in a beet sugar molasses based-medium. Drying of cells resuspended in several combinations of soluble starch and maltose was performed at different inlet and outlet temperatures. Under the best conditions–suspension in soluble starch plus maltose couplet to inlet and outlet temperatures of 110 and 55 C, respectively—the loss of viability of S. cerevisiae LM52 was 0.8 ± 0.1 and 0.5 ± 0.2 Log c.f.u. g-1 for synthetic and molasses-based medium, respectively. Similar results were obtained when S. cerevisiae strains Zymoflore F15 and EC1118, isolated from commercial active dry yeast (ADY), were tested. Moreover, powders retained a high vitality and showed good fermentation performances up to 6 month of storage, at both 4 and -20 C. Finally, fermentation performances of different kinds of dried formulates (SD and ADY) compared with fresh cultures did not show significant differences. The procedure proposed allowed a small-scale production of yeast in continuous operation with relatively simple equipment, and may thus represent a rapid response-on-demand for the production of autochthonous yeasts for local wine-making

Methylation Dynamics on 5′-UTR of DAT1 Gene as a Bio-Marker to Recognize Therapy Success in ADHD Children

Attention-deficit/hyperactivity disorder (ADHD), a neuropsychiatric condition characterized by inattention, hyperactivity, and impulsivity, afflicts 5% of children worldwide. Each ADHD patient presents with individual cognitive and motivational peculiarities. Furthermore, choice of appropriate therapy is still up to clinicians, who express somewhat qualitative advice on whether a child is being successfully cured or not: it would be more appropriate to use an objective biomarker to indicate whether a treatment led to benefits or not. The aim of our work is to search for such clinical biomarkers. We recruited 60 ADHD kids; psychopathological scales were administered at recruitment and after six weeks of therapy. Out of such a cohort of ADHD children, we rigorously extracted two specific subgroups; regardless of the initial severity of their disease, we compared those who obtained the largest improvement (ΔCGAS > 5) vs. those who were still characterized by a severe condition (CGAS < 40). After such a therapy, methylation levels of DNA extracted from buccal swabs were measured in the 5′-UTR of the DAT1 gene. CpGs 3 and 5 displayed, in relation to the other CpGs, a particular symmetrical pattern; for “improving” ADHD children, they were methylated together with CpG 2 and CpG 6; instead, for “severe” ADHD children, they accompanied a methylated CpG 1. These specific patterns of methylation could be used as objective molecular biomarkers of successful cures, establishing if a certain therapy is akin to a given patient (personalized medicine). Present data support the use of post-therapy molecular data obtained with non-invasive techniques