Eigenvalue estimates for submanifolds of warped product spaces

We give lower bounds for the fundamental tone of open sets in minimal submanifolds immersed into warped product spaces of type $N^n \times_f Q^q$, where $f \in C^\infty(N)$. We also study the essential spectrum of these minimal submanifolds.Comment: 17 page

Effect of obesity and metabolic syndrome on plasma oxysterols and fatty acids in human

BACKGROUND: Obesity and the related entity metabolic syndrome are characterized by altered lipid metabolism and associated with increased morbidity risk for cardiovascular disease and cancer. Oxysterols belong to a large family of cholesterol-derived molecules known to play crucial role in many signaling pathways underlying several diseases. Little is known on the potential effect of obesity and metabolic syndrome on oxysterols in human. OBJECTIVES: In this work, we questioned whether circulating oxysterols might be significantly altered in obese patients and in patients with metabolic syndrome. We also tested the potential correlation between circulating oxysterols and fatty acids. METHODS: 60 obese patients and 75 patients with metabolic syndrome were enrolled in the study along with 210 age- and sex-matched healthy subjects, used as control group. Plasma oxysterols were analyzed by isotope dilution GC/MS, and plasma fatty acids profiling was assessed by gas chromatography coupled with flame ionization detection. RESULTS: We found considerable differences in oxysterols profiling in the two disease groups that were gender-related. Compared to controls, males showed significant differences only in 4α- and 4β-hydroxycholesterol levels in obese and metabolic syndrome patients. In contrast, females showed consistent differences in 7-oxocholesterol, 4α-hydroxycholesterol, 25-hydroxycholesterol and triol. Concerning fatty acids, we found minor differences in the levels of these variables in males of the three groups. Significant changes were observed in plasma fatty acid profile of female patients with obesity or metabolic syndrome. We found significant correlations between various oxysterols and fatty acids. In particular, 4β-hydroxycholesterol, which is reduced in obesity and metabolic syndrome, correlated with a number of saturated and mono-unsaturated fatty acids that are end-products of de novo lipogenesis. CONCLUSIONS: Our data provide the first evidence that obesity and metabolic syndrome are associated with major, gender-specific, changes in circulating oxysterols and fatty acids. These findings suggest a metabolic link between oxysterols and fatty acids, and that oxysterols may contribute to the epidemic diseases associated with obesity and metabolic syndrome in female

Universal mean-field upper bound for the generalization gap of deep neural networks

Modern deep neural networks (DNNs) represent a formidable challenge for theorists: according to the commonly accepted probabilistic framework that describes their performance, these architectures should overfit due to the huge number of parameters to train, but in practice they do not. Here we employ results from replica mean field theory to compute the generalization gap of machine learning models with quenched features, in the teacher-student scenario and for regression problems with quadratic loss function. Notably, this framework includes the case of DNNs where the last layer is optimized given a specific realization of the remaining weights. We show how these results-combined with ideas from statistical learning theory-provide a stringent asymptotic upper bound on the generalization gap of fully trained DNN as a function of the size of the dataset P. In particular, in the limit of large P and N-out (where N-out is the size of the last layer) and N-out << P, the generalization gap approaches zero faster than 2N(out)/P, for any choice of both architecture and teacher function. Notably, this result greatly improves existing bounds from statistical learning theory. We test our predictions on a broad range of architectures, from toy fully connected neural networks with few hidden layers to state-of-the-art deep convolutional neural networks

BIOMEX (Biology and Mars Experiment): Preliminary results on Antarctic black cryptoendolithic fungi in ground based experiments

The main goal for astrobiologists is to find traces of present or past life in extraterrestrial environment or in meteorites. Biomolecules, such as lipids, pigments or polysaccharides, may be useful to establish the presence of extant or extinct life (Simoneit, B et al., 1998). BIOMEX (Biology and Mars Experiment) aims to measure to what extent biomolecules, such as pigments and cellular components, preserve their stability under space and Mars-like conditions. The experiment has just been launched in the space and will be exposed on EXPOSE-R payload to the outside of the International Space Station (ISS) for about 2 years. Among a number of extremophilic microorganisms tested, the Antarctic cryptoendolithic black fungus Cryomyces antarcticus CCFEE 515 was included in the experiment. The fungus, living in the airspaces of porous rocks, was already chosen in previous astrobiological investigation for studying the interplanetary transfer of life via meteorites. In that context, the fungus survived 18 months of exposure outside of the ISS (Onofri al., 2012); for all these reasons it is considered an optimal eukaryotic model for astrobiological exploration. Before launch dried samples were exposed, in ground based experiments, to extreme conditions, including vacuum, irradiation and temperature cycles.Upon sample re-hydration and survival analysis, including colony forming ability, Propidium MonoAzide (PMA) assay-coupled quantitative PCR (Mohapatra and La Duc, 2012) all the test systems survived, neither any DNA damage was detectable. Our analyses focused also on mineral-microorganisms interactions and stability/degradation of typical fungal macromolecules, in particular melanin, when exposed to space and simulated Martian conditions, contributing to the development of libraries of biosignatures in rocks, supporting future exploration missions

The mean curvature of cylindrically bounded submanifolds

We give an estimate of the mean curvature of a complete submanifold lying inside a closed cylinder $B(r)\times\R^{\ell}$ in a product Riemannian manifold $N^{n-\ell}\times\R^{\ell}$. It follows that a complete hypersurface of given constant mean curvature lying inside a closed circular cylinder in Euclidean space cannot be proper if the circular base is of sufficiently small radius. In particular, any possible counterexample to a conjecture of Calabion complete minimal hypersurfaces cannot be proper. As another application of our method, we derive a result about the stochastic incompleteness of submanifolds with sufficiently small mean curvature.Comment: First version (December 2008). Final version, including new title (February 2009). To appear in Mathematische Annale

Elevated Mitochondrial Bioenergetics and Axonal Arborization Size Are Key Contributors to the Vulnerability of Dopamine Neurons

SummaryAlthough the mechanisms underlying the loss of neurons in Parkinson’s disease are not well understood, impaired mitochondrial function and pathological protein aggregation are suspected as playing a major role. Why DA (dopamine) neurons and a select small subset of brain nuclei are particularly vulnerable to such ubiquitous cellular dysfunctions is presently one of the key unanswered questions in Parkinson’s disease research. One intriguing hypothesis is that their heightened vulnerability is a consequence of their elevated bioenergetic requirements. Here, we show for the first time that vulnerable nigral DA neurons differ from less vulnerable DA neurons such as those of the VTA (ventral tegmental area) by having a higher basal rate of mitochondrial OXPHOS (oxidative phosphorylation), a smaller reserve capacity, a higher density of axonal mitochondria, an elevated level of basal oxidative stress, and a considerably more complex axonal arborization. Furthermore, we demonstrate that reducing axonal arborization by acting on axon guidance pathways with Semaphorin 7A reduces in parallel the basal rate of mitochondrial OXPHOS and the vulnerability of nigral DA neurons to the neurotoxic agents MPP+ (1-methyl-4-phenylpyridinium) and rotenone. Blocking L-type calcium channels with isradipine was protective against MPP+ but not rotenone. Our data provide the most direct demonstration to date in favor of the hypothesis that the heightened vulnerability of nigral DA neurons in Parkinson’s disease is directly due to their particular bioenergetic and morphological characteristics

Effect of chicken bone extracts on metabolic and mitochondrial functions of K562 cell line

Background: Tetracyclines’ use in intensive animal farming has raised some concerns regarding the biosafety for humans. Increasing evidences have revealed the presence of these drugs in processed animal by-products, such as bone, throughout the food chain. A potential off-target of tetracyclines is the bacterial-like mitochondrial translational machinery, thereby causing proteostatic alterations in mitochondrial DNA-encoded components of the oxidative phosphorylation system. Methods: The Seahorse methodology, confocal microscopy imaging of mitochondrial potential and reactive oxygen species, and q-RT-PCR analysis of the expression of genes involved in mitochondrial biogenesis and mitophagy were carried out on human lymphoblast derived K562 cell line challenged with bone powder derived from chicken treated with or without oxytetracycline and pure oxytetracycline. Results: A complex dose-dependent profile was attained with a low dosage of bone powder extracts causing a metabolic adaptation hallmarked by stimulation of the mitochondrial respiration and enhanced expression of mitochondriogenic factors in particular in cells challenged with oxytetracycline-free bone extract. Conversely, a higher dosage of bone powder extracts, regardless of their source, caused a progressive inhibition of mitochondrial respiration and glycolysis, ultimately leading to cell death. No significant effects of the pure oxytetracycline were observed. Conclusion: Bone powder, regardless of chicken treatment, contains and releases factors/chemicals responsible for the observed effects on energy metabolism. Quantitative differential effects appear to depend on biochemical alterations in the bone matrix caused by antibiotics rather than antibiotics themselves