Modified Paouris inequality

The Paouris inequality gives the large deviation estimate for Euclidean norms of log-concave vectors. We present a modified version of it and show how the new inequality may be applied to derive tail estimates of l_r-norms and suprema of norms of coordinate projections of isotropic log-concave vectors.Comment: 14 page

Die Bürgerversicherung: Die falsche Medizin für die Krankenversicherung. Zu den Vorschlägen von SPD und GRÜNEN

--

On the equivalence of modes of convergence for log-concave measures

An important theme in recent work in asymptotic geometric analysis is that many classical implications between different types of geometric or functional inequalities can be reversed in the presence of convexity assumptions. In this note, we explore the extent to which different notions of distance between probability measures are comparable for log-concave distributions. Our results imply that weak convergence of isotropic log-concave distributions is equivalent to convergence in total variation, and is further equivalent to convergence in relative entropy when the limit measure is Gaussian.Comment: v3: Minor tweak in exposition. To appear in GAFA seminar note

Alumina-zirconia coatings obtained by suspension plasma spraying from highly concentrated aqueous suspensions

Suspension plasma spraying (SPS) deposition represents an innovative technique to produce coatings that exhibit improved properties. However, the key to obtain coatings with superior functional properties relies on the investigation of the suspensions as starting materials. For this reason, the present work deals with the suspension preparation for SPS process and its influence on the resulting coatings. Laboratory-prepared 60/40 wt% alumina-zirconia suspensions were concentrated to avoid energy loss and were then successfully deposited by SPS technique. The liquid used was water instead of ethanol due to economical, environmental and safety reasons. The preparation of the suspension plays an important role in SPS process since stable and well-dispersed water suspensions are difficult to obtain. For this reason, colloidal behaviour characterisation of the starting particles as well as rheological optimisation of the feedstock suspensions were addressed in this research. Suspensions with different solid loadings (up to 30 vol.% or 72 wt%) were deposited using several spraying distances. All coatings displayed a bimodal microstructure consisting in partially melted zones surrounded by a fully melted matrix. α-Al2O3 and t’-ZrO2 constituted the main crystalline phases, but differences in the microstructure and properties of the coatings were observed. From these results, some relations between starting suspension and spraying parameters with coating characteristics were found. Thus the optimal spraying distance becomes shorter when the suspension solid loading increases.This work has been supported by the Spanish Ministry of Economy and Competitiveness, MINECO, (project MAT2015-67586-C3-R). M.D. Salvador thanks to CAPES – Programa Ciências sem Fronteiras (Brazil) for the concession of a PVE project Nº A086/2013. A. Borrell acknowledges the MINECO for her Juan de la Cierva-Incorporación contract (IJCI-2014-19839) and the Program to Support Research and Development (PAID-00-15) of the Universitat Politècnica de València

Logarithmically-concave moment measures I

We discuss a certain Riemannian metric, related to the toric Kahler-Einstein equation, that is associated in a linearly-invariant manner with a given log-concave measure in R^n. We use this metric in order to bound the second derivatives of the solution to the toric Kahler-Einstein equation, and in order to obtain spectral-gap estimates similar to those of Payne and Weinberger.Comment: 27 page

Optimal Concentration of Information Content For Log-Concave Densities

An elementary proof is provided of sharp bounds for the varentropy of random vectors with log-concave densities, as well as for deviations of the information content from its mean. These bounds significantly improve on the bounds obtained by Bobkov and Madiman ({\it Ann. Probab.}, 39(4):1528--1543, 2011).Comment: 15 pages. Changes in v2: Remark 2.5 (due to C. Saroglou) added with more general sufficient conditions for equality in Theorem 2.3. Also some minor corrections and added reference

Transference Principles for Log-Sobolev and Spectral-Gap with Applications to Conservative Spin Systems

We obtain new principles for transferring log-Sobolev and Spectral-Gap inequalities from a source metric-measure space to a target one, when the curvature of the target space is bounded from below. As our main application, we obtain explicit estimates for the log-Sobolev and Spectral-Gap constants of various conservative spin system models, consisting of non-interacting and weakly-interacting particles, constrained to conserve the mean-spin. When the self-interaction is a perturbation of a strongly convex potential, this partially recovers and partially extends previous results of Caputo, Chafa\"{\i}, Grunewald, Landim, Lu, Menz, Otto, Panizo, Villani, Westdickenberg and Yau. When the self-interaction is only assumed to be (non-strongly) convex, as in the case of the two-sided exponential measure, we obtain sharp estimates on the system's spectral-gap as a function of the mean-spin, independently of the size of the system.Comment: 57 page

Paraoxonase 2 protein is spatially expressed in the human placenta and selectively reduced in labour

Humans parturition involves interaction of hormonal, neurological, mechanical stretch and inflammatory pathways and the placenta plays a crucial role. The paraoxonases (PONs 1–3) protect against oxidative damage and lipid peroxidation, modulation of endoplasmic reticulum stress and regulation of apoptosis. Nothing is known about the role of PON2 in the placenta and labour. Since PON2 plays a role in oxidative stress and inflammation, both features of labour, we hypothesised that placental PON2 expression would alter during labour. PON2 was examined in placentas obtained from women who delivered by cesarean section and were not in labour and compared to the equivalent zone of placentas obtained from women who delivered vaginally following an uncomplicated labour. Samples were obtained from 12 sites within each placenta: 4 equally spaced apart pieces were sampled from the inner, middle and outer placental regions. PON2 expression was investigated by Western blotting and real time PCR. Two PON2 forms, one at 62 kDa and one at 43 kDa were found in all samples. No difference in protein expression of either isoform was found between the three sites in either the labour or non-labour group. At the middle site there was a highly significant decrease in PON2 expression in the labour group when compared to the non-labour group for both the 62 kDa form (p = 0.02) and the 43 kDa form (p = 0.006). No spatial differences were found within placentas at the mRNA level in either labour or non-labour. There was, paradoxically, an increase in PON2 mRNA in the labour group at the middle site only. This is the first report to describe changes in PON2 in the placenta in labour. The physiological and pathological significance of these remains to be elucidated but since PON2 is anti-inflammatory further studies are warranted to understand its role

Review: Assessment of completeness of reporting in intervention studies using livestock: an example from pain mitigation interventions in neonatal piglets

Accurate and complete reporting of study methods, results and interpretation are essential components for any scientific process, allowing end-users to evaluate the internal and external validity of a study. When animals are used in research, excellence in reporting is expected as a matter of continued ethical acceptability of animal use in the sciences. Our primary objective was to assess completeness of reporting for a series of studies relevant to mitigation of pain in neonatal piglets undergoing routine management procedures. Our second objective was to illustrate how authors can report the items in the Reporting guidElines For randomized controLled trials for livEstoCk and food safety (REFLECT) statement using examples from the animal welfare science literature. A total of 52 studies from 40 articles were evaluated using a modified REFLECT statement. No single study reported all REFLECT checklist items. Seven studies reported specific objectives with testable hypotheses. Six studies identified primary or secondary outcomes. Randomization and blinding were considered to be partially reported in 21 and 18 studies, respectively. No studies reported the rationale for sample sizes. Several studies failed to report key design features such as units for measurement, means, standard deviations, standard errors for continuous outcomes or comparative characteristics for categorical outcomes expressed as either rates or proportions. In the discipline of animal welfare science, authors, reviewers and editors are encouraged to use available reporting guidelines to ensure that scientific methods and results are adequately described and free of misrepresentations and inaccuracies. Complete and accurate reporting increases the ability to apply the results of studies to the decision-making process and prevent wastage of financial and animal resources

Towards a unified theory of Sobolev inequalities

We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities. In particular, we discuss our recent papers on fractional order inequalities, Coulhon type inequalities, transference and dimensionless inequalities and our forthcoming work on sharp higher order Sobolev inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1