A remark on a conjecture on the symmetric Gaussian Problem

In this paper we study the functional given by the integral of the mean curvature of a convex set with Gaussian weight with Gaussian volume constraint. It was conjectured that the ball centered at the origin is the only minimizer of such a functional for certain value of the mass. We give a positive answer in dimension two while in higher dimension the situation is different. In fact, for small value of mass the ball centered at the origin is a local minimizer while for large values the ball is a maximizer among convex sets with uniform bound on the curvature

Some weighted isoperimetric inequalities in quantitative form

In this paper we study two different weighted isoperimetric inequalities. In the first part of the paper we prove a sharp stability result for the isoperimetric inequality with a log-convex weight. In the second part we analize the behavior of a negative power weight for the perimeter thus providing a complete picture of the isoperimetric problem in this context.Comment: We spotted a mistake in the proof of lemma 3.

Abnormal hippocampal melatoninergic system: a potential link between absence epilepsy and depression-like behavior in WAG/Rij rats?

Absence epilepsy and depression are comorbid disorders, but the molecular link between the two disorders is unknown. Here, we examined the role of the melatoninergic system in the pathophysiology of spike and wave discharges (SWDs) and depression-like behaviour in the Wistar Albino Glaxo from Rijswijk (WAG/Rij) rat model of absence epilepsy. In WAG/Rij rats, SWD incidence was higher during the dark period of the light-dark cycle, in agreement with previous findings. However, neither pinealectomy nor melatonin administration had any effect on SWD incidence, suggesting that the melatoninergic system was not involved in the pathophysiology of absence-like seizures. Endogenous melatonin levels were lower in the hippocampus of WAG/Rij rats as compared to non-epileptic control rats, and this was associated with higher levels of melatonin receptors in the hippocampus, but not in the thalamus. In line with the reduced melatonin levels, cell density was lower in the hippocampus ofWAG/Rij rats and was further reduced by pinealectomy. As expected, WAG/Rij rats showed an increased depression-like behaviour in the sucrose preference and forced swim tests, as compared to non-epileptic controls. Pinealectomy abolished the difference between the two strains of rats by enhancing depression-like behaviour in non-epileptic controls. Melatonin replacement displayed a significant antidepressant-like effect in bothWAG/Rij and control rats. These findings suggest that a defect of hippocampal melatoninergic system may be one of the mechanisms underlying the depression-like phenotype inWAG/Rij rats and that activation of melatonin receptors might represent a valuable strategy in the treatment of depression associated with absence epilepsy

Effects of antioxidant supplementation on the aging process

The free radical theory of aging hypothesizes that oxygen-derived free radicals are responsible for the age-related damage at the cellular and tissue levels. In a normal situation, a balanced-equilibrium exists among oxidants, antioxidants and biomolecules. Excess generation of free radicals may overwhelm natural cellular antioxidant defences leading to oxidation and further contributing to cellular functional impairment. The identification of free radical reactions as promoters of the aging process implies that interventions aimed at limiting or inhibiting them should be able to reduce the rate of formation of aging changes with a consequent reduction of the aging rate and disease pathogenesis. Even if antioxidant supplementation is receiving growing attention and is increasingly adopted in Western countries, supporting evidence is still scarce and equivocal. Major limitations in literature are still needed to be addressed to better evaluate the potential benefits from antioxidant supplementation: 1) an improved understanding of oxidation mechanisms possibly at the basis of the aging process, 2) the determination of reliable markers of oxidative damage and antioxidant status, 3) the identification of a therapeutic window in which an eventual antioxidant supplementation may be beneficial, 4) a deeper knowledge of the antioxidant molecules which in several conditions act as pro-oxidants. In the present paper, after a preliminary introduction to the free radical theory of aging and the rationale of antioxidant supplementation as an anti-aging intervention, we will present an overview of evidence relating antioxidant supplementations with clinical conditions typical of older age (ie, cardiovascular disease, Alzheimer’s disease, cancer). We will also discuss studies that have evaluated whether antioxidant supplementation might improve major outcomes of interest in older persons (ie, physical performance, muscle strength, longevity). Given the large amount of data available on the antioxidant supplementation topic, this overview is not intended to be exhaustive. The aim of this paper is to provide the main basis from which future studies should start and indicate which the main limitations that need to be addressed are

Anti-VEGF Therapy in Breast and Lung Mouse Models of Cancers

Cancer is the second leading cause of death in the world after cardiovascular diseases. Some types of cancer cells often travel to other parts of the body through blood circulation or lymph vessels, where they begin to grow. This process is recognized as metastasis. Angiogenesis is the formation of new blood vessels from existing vessel. Normally angiogenesis is a healthy process, that helps the body to heal wounds and repair damaged body tissues, whereas in cancerous condition this process supports new blood vessels formation that provide a tumor with its own blood supply, nutrients and allow it to grow. The most important proximal factor for angiogenesis is the vascular endothelial growth factor VEGF. Angioinhibition is a form of targeted therapy that uses drugs to stop tumors from making new blood vessels. Therefore, in this paper we analyse the importance of VEGF as target of cancer therapy, analysing murine models

Susceptibility mapping of shallow landslides inducing debris flows: a comparison of physics-based approaches

The assessment of timing and potential locations of rainfallinduced shallow landslides through mathematical models represents a challenge for the assessment of landslide hazard, especially in cases with limited or not available data. In fact, modeling slope hydrological response and stability requires accurate estimates of unsaturated/saturated hydraulic and geotechnical properties of materials involved in landsliding, as well as climate and topography. Such aspect is relevant for the prediction of location and timing of landslide events, which is greatly needed to reduce their catastrophic effects in terms of economic losses and casualties. To such a scope, we present the comparison of results of two physics-based models applied to the assessment of susceptibility to shallow rainfall-induced landslides in Valtellina region (northern Italy). The analyses were carried out considering effects of availability, resolution and type of data concerning spatial distribution, thickness and properties of soils coverings. For such a scope, the Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability (TRIGRS) and the Climatic Rainfall Hydrogeological Modeling Experiment (CHRyME) models were considered. The study emphasizes issues in performing distributed numerical slope stability modeling depending on the availability of spatially distributed soil properties which hamper the quality of physic-based models. Further analyses aimed at the probabilistic assessment of landslide spatial distribution, related to a specific value of rainfall threshold, can be considered as potentially applicable to multi-scale landslide hazard mapping and extendable to other similar mountainous frameworks

Response to Letter by Tsuda

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Physically based estimation of rainfall thresholds triggering shallow landslides in volcanic slopes of Southern Italy

On the 4th and 5th of March 2005, about 100 rainfall-induced landslides occurred along volcanic slopes of Camaldoli Hill in Naples, Italy. These started as soil slips in the upper substratum of incoherent and welded volcaniclastic deposits, then evolved downslope according to debris avalanche and debris flow mechanisms. This specific case of slope instability on complex volcaniclastic deposits remains poorly characterized and understood, although similar shallow landsliding phenomena have largely been studied in other peri-volcanic areas of the Campania region underlain by carbonate bedrock. Considering the landslide hazard in this urbanized area, this study focused on quantitatively advancing the understanding of the predisposing factors and hydrological conditions contributing to the initial landslide triggering. Borehole drilling, trial pits, dynamic penetrometer tests, topographic surveys, and infiltration tests were conducted on a slope sector of Camaldoli Hill to develop a geological framework model. Undisturbed soil samples were collected for laboratory testing to further characterize hydraulic and geotechnical properties of the soil units identified. In situ soil pressure head monitoring probes were also installed. A numerical model of two-dimensional variably saturated subsurface water flow was parameterized for the monitored hillslope using field and laboratory data. Based on the observed soil pressure head dynamics, the model was calibrated by adjusting the evapotranspiration parameters. This physically based hydrologic model was combined with an infinite-slope stability analysis to reconstruct the critical unsaturated/saturated conditions leading to slope failure. This coupled hydromechanical numerical model was then used to determine intensity–duration (I-D) thresholds for landslide initiation over a range of plausible rainfall intensities and topographic slope angles for the region. The proposed approach can be conceived as a practicable method for defining a warning criterion in urbanized areas threatened by rainfall-induced shallow landslides, given the unavailability of a consistent inventory of past landslide events that prevents a rigorous empirical analysis