Characterization of ellipses as uniformly dense sets with respect to a family of convex bodies

Let K \subset R^N be a convex body containing the origin. A measurable set G \subset R^N with positive Lebesgue measure is said to be uniformly K-dense if, for any fixed r > 0, the measure of G \cap (x + rK) is constant when x varies on the boundary of G (here, x + rK denotes a translation of a dilation of K). We first prove that G must always be strictly convex and at least C1,1-regular; also, if K is centrally symmetric, K must be strictly convex, C1,1-regular and such that K = G - G up to homotheties; this implies in turn that G must be C2,1- regular. Then for N = 2, we prove that G is uniformly K-dense if and only if K and G are homothetic to the same ellipse. This result was already proven by Amar, Berrone and Gianni in [3]. However, our proof removes their regularity assumptions on K and G and, more importantly, it is susceptible to be generalized to higher dimension since, by the use of Minkowski's inequality and an affine inequality, avoids the delicate computations of the higher-order terms in the Taylor expansion near r = 0 for the measure of G\cap(x+rK) (needed in [3])

Dynamical friction in multi-component evolving globular clusters

We use the Chandrasekhar formalism and direct N-body simulations to study the effect of dynamical friction on a test object only slightly more massive than the field stars, orbiting a spherically symmetric background of particles with a mass spectrum. The main goal is to verify whether the dynamical friction time (t_DF) develops a non-monotonic radial-dependence that could explain the bimodality of the Blue Straggler radial distributions observed in globular clusters. In these systems, in fact, relaxation effects lead to a mass and velocity radial segregation of the different mass components, so that mass-spectrum effects on t_DF are expected to be dependent on radius. We find that, in spite of the presence of different masses, t_DF is always a monotonic function of radius, at all evolutionary times and independently of the initial concentration of the simulated cluster. This because the radial dependence of t_DF is largely dominated by the total mass density profile of the background stars (which is monotonically decreasing with radius). Hence, a progressive temporal erosion of the BSS population at larger and larger distances from the cluster center remains the simplest and the most likely explanation of the shape of the observed BSS radial distributions, as suggested in previous works. We also confirm the theoretical expectation that approximating a multi-mass globular cluster as made of (averaged) equal-mass stars can lead to significant overestimates of t_DF within the half-mass radius.Comment: In press on Ap

Reducing total and saturated fat for lowering food energy density: potential health impacts of a gradual reformulation strategy in the UK

Background: Manufactured and out-of-home (MOOH) foods contribute to excessive calories and have a critical role in fuelling the obesity epidemic. Aims: 1) To show policymakers and food producers that reducing food energy density through a 20% fat reduction in MOOH food categories is a realistic and feasible public health nutrition strategy; 2) To predict the health impacts of a fat reformulation strategy to persuade UK policymakers to implement it in the MOOH food sector to reduce obesity prevalence in the UK. Methods: Firstly, I carried out a survey of cakes and biscuits sold in UK supermarkets to evaluate the variation of total fat, SFA, and energy/100g. Secondly, I evaluated the energy reduction in the NDNS population resulting from the proposed strategy. I predicted the bodyweight reduction by using a weight loss model. I scaled up the resulting bodyweight reduction to the UK adult population. I estimated the reductions in overweight/obesity and type 2 diabetes cases, ischemic heart disease (IHD), and strokes deaths that could be prevented from the strategy. Results: There was a 40% average fat variation in cakes and biscuits. The proposed fat reformulation strategy in MOOH foods would reduce mean energy intake by 67.6 kcal/d/person and mean bodyweight by 2.7 kg/person. Obesity and overweight prevalence would be reduced by 6.8%, corresponding to 4.5 million cases of obesity/overweight being reduced in the UK. The bodyweight reduction could prevent 180,000 cases of type 2 diabetes over two decades. The SFA reduction would prevent 97,000 IHD and stroke deaths over 20 years. Conclusions: Fat reformulation is a feasible strategy to reduce fat and energy density in cakes and biscuits. A 20% fat reduction (particularly SFA) in MOOH foods would prevent obesity, type 2 diabetes, and cardiovascular disease and bring SFA intake within the recommended intakes

Influence of Blackberry Plants on the Aroma Profile of Vitis vinifera L. cv. Pinot Noir

V. vinifera cv. Pinot noir vines were grown in pots together with blackberry plants and the effect of this association on the grape aroma was assessed. Preliminary data showed that vines that cohabited with blackberry had a different aroma profile compared to vine grown alone. The association with blackberry increased the concentration of 30 out 74 free aroma compounds and of 24 out 95 bound ones. No aroma compound was identified exclusively in the treated grapes

Impaired postural control in patients affected by tension-type headache.

Sixteen subjects, affected by chronic tension-type headache (TTH) accordingly to the International Headache Society Classification (1988) criteria, in presence of tenderness in pericranial muscles,with a mean age of 37+/-11.8 years, and ten healthy volunteer subjects, age and sex matched, were submitted to postural analysis by Static Posturography (S.Ve.P. Amplaid). Aim of the study was to evaluate whether patients with TTH have disturbed postural control, as compared to normal subjects. Postural analysis considered all posturographic variables but focused on spectral frequency analysis of body sway. In both open (OE) and closed eyes (CE) condition, spectral frequency analysis showed a significantly increased body sway at low (OE= p < or = 0.01; CE= p < or = 0.01) and middle (OE= p < or = 0.01; CE= p < or = 0.01) frequencies on the antero-posterior (y) plane and at low frequencies (OE= p < or = 0.05; CE= p < or = 0.05) on the lateral (x) plane. Statistical analysis was performed using the Student's t test for unpaired data, p value 0.05 defined significant. The proprioceptive input seems to be predominant at middle and high frequencies in maintaining posture, our results seem then to suggest a proprioceptive disturbance in TTH patients. The disturbance is likely related to chronic pericranial muscle contraction and tenderness. Posturography and spectral analysis may help not only in the diagnosis of a postural disturbance but even more in the follow-up of TTH patients, during and after a medical and/or a rehabilitative treatment

Suitability of miRNA assessment in postmortem interval estimation

OBJECTIVE: The aim of this review was to explore recent pieces of evidence focused on the use of miRNAs for PMI estimation both in humans and animal experiments, with particular interest on the best miRNAs to use as reference/target markers in different tissues or biological fluids. MiRNAs are innovative biomarkers used in clinical and research field: they appear very attractive, being introduced in forensic research scenarios even for PMI estimation.MATERIALS AND METHODS: Data from PubMed and Scopus were analyzed from January 2013 to August 2020. Based on inclusion/exclusion criteria, high-quality articles have been selected to become the subject of this review.RESULTS: A total of 737 papers were found but, after titles/abstracts screening for inclusion criteria and a full-text careful selection, 33 papers were deeply studied. After the exclusion of 19 papers, 15 articles remained. Eight papers dealt with animals (mice/rats), two both with animals and humans (for method validation previously built), while 5 exclusively with humans. Myocardium (6/15) and brain (6/15) were the most studied tissues. respectively in mice/rats and humans. PMI considered was up to 7.5 days in mouse studies and less than 3 days in human models.CONCLUSIONS: Because of their significant stability in both early and long PMI, miRNAs are the cleverest reference markers to be used. Temperature and environmental conditions influence mostly mRNA, while miRNAs are less susceptible to them. The best miRNA to choose depends on its tissue specificity, i.e., miR-9 and miR-125 in brain or miR-1 and miR-133 in skeletal muscle/heart

Effects of the Fractionation of the Nitrogen Fertilization on Root Nitrate Uptake and Vine Agronomic Performance in Pinot Gris Grapevines in a Temperate Climate

The study aims to investigate at a physiological and molecular level the root absorption of nitrogen (N) during the annual cycle of grapevine. The study was performed on potted Pinot Gris plants grafted on Kober 5BB and grown for two consecutive years in a semi-controlled environment (Northeast, Italy). The study compared the response of plants N-fertilized in spring (T1), or in spring and in post-harvest (T2) or no-N fertilized (C). Results showed that under our climate conditions nitrate was taken up by the grapevines when applied both in spring or in spring and post-harvest. The nitrate acquisition in T1 roots is mediated at molecular and physiological level by a higher activation of high-affinity nitrate-transport system to take up nitrate in comparison to no-fertilized plants. Comparing the two N fertilization managements, the dynamic of nitrate uptake rates showed different patterns with an overall late response of High-Affinity Transport System when the application of part of N-fertilization was delayed to post-harvest (T2) in comparison to T1. Nevertheless, during the 2 years of the trial the fractionation of N fertilization applied in spring and post-harvest did not negatively affect the yield and quality parameters of vines. An increase of N concentration in T2 roots after two consecutive growing seasons may suggest that the fractionation can lead to beneficial effects on long period. Results of this work contribute to improve the comprehension of N acquisition in grapevine in order to optimize the use of N inputs in vineyard

Quantitative uniqueness for elliptic equations with singular lower order terms

We use a Carleman type inequality of Koch and Tataru to obtain quantitative estimates of unique continuation for solutions of second order elliptic equations with singular lower order terms. First we prove a three sphere inequality and then describe two methods of propagation of smallness from sets of positive measure.Comment: 23 pages, v2 small changes are done and some mistakes are correcte