Bounds on the deficit in the logarithmic Sobolev inequality

The de cit in the logarithmic Sobolev inequality for the Gaussian measure is considered and estimated by means of transport and information-theoretic distances

Characterization of Talagrand's transport-entropy inequalities in metric spaces

We give a characterization of transport-entropy inequalities in metric spaces. As an application we deduce that such inequalities are stable under bounded perturbation (Holley-Stroock perturbation Lemma)

Deviation inequalities for convex functions motivated by the Talagrand conjecture

Motivated by Talagrand's conjecture on regularization properties of the natural semigroup on the Boolean hypercube, and in particular its continuous analogue involving regularization properties of the Ornstein-Uhlenbeck semigroup acting on in-tegrable functions, we explore deviation inequalities for log-semiconvex functions under Gaussian measure

A new characterization of Talagrand's transport-entropy inequalities and applications

We show that Talagrand's transport inequality is equivalent to a restricted logarithmic Sobolev inequality. This result clarifies the links between these two important functional inequalities. As an application, we give the first proof of the fact that Talagrand's inequality is stable under bounded perturbations.Comment: Published in at http://dx.doi.org/10.1214/10-AOP570 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Infimum-convolution description of concentration properties of product probability measures, with applications

International audienceThis paper is devoted to the concentration properties of product probability measures mu = mu(1) circle times(...)circle times mu(n), expressed in term of dimension-free functional inequalities of the form [GRAPHICS] where a is a parameter, 0 < alpha < 1, and Q(alpha)f is an appropriate infimum-convolution operator. This point of view has been introduced by Maurey [B. Maurey, Some deviation inequalities, Geom. Funct: Anal. 1 (1991) 188-197]. It has its origins in concentration inequalities by Talagrand where the enlargement of sets is done in accordance with the cost function of the operator Q alpha f (see [M. Talagrand, Concentration of measure and isoperimetric, inequalities in product spaces, Publ. Math. Inst. Hautes Etudes Sci. 81 (1995) 73-205, M. Talagrand, New concentration inequalities in product spaces, Invent. Math. 126 *(1996) 505-563, M. Talagrand, A new look at independence, Ann. Probab. 24 (1996) 1-34]). A main application of the functional inequalities obtained here is optimal deviations inequalities for suprema of sums of independent random variables. As example, we also derive classical deviations bounds for the one-dimensional bin packing problem. (c) 2006 Elsevier Masson SAS. All rights reserved

Effects of reflux laryngitis on laryngeal chemoreflexes in newborn lambs

It has been suggested that reflux laryngitis (RL) is involved in apneas-bradycardias of the newborn. The aim of the present study was to develop a unique RL model in newborn lambs to test the hypothesis that RL enhances the cardiorespiratory components of the laryngeal chemoreflexes (LCR) in the neonatal period. Gastric juice surrogate (2 ml of normal saline solution with HCl pH 2 + pepsin 300 U/ml) (RL group, n = 6) or normal saline (control group, n = 6) was repeatedly injected onto the posterior aspect of the larynx, 3 times a day for 6 consecutive days, via a retrograde catheter introduced into the cervical esophagus. Lambs instilled with gastric juice surrogate presented clinical signs of RL, as well as moderate laryngitis on histological observation. Laryngeal chemoreflexes were thereafter induced during sleep by injection of 0.5 ml of HCl (pH 2), ewe's milk, distilled water or saline into the laryngeal vestibule via a chronic, transcutaneous supraglottal catheter. Overall, RL led to a significantly greater respiratory inhibition compared with the control group during LCR, including longer apnea duration (P = 0.01), lower minimal respiratory rate (P = 0.002), and a more prominent decrease in arterial hemoglobin saturation (SpO(2)) (P = 0.03). No effects were observed on cardiac variables. In conclusion, 1) our unique neonatal ovine model presents clinical and histological characteristics of RL; and 2) the presence of RL in newborn lambs increases the respiratory inhibition observed with LCR, at times leading to severe apneas and desaturations

Effects of moderate hyperbilirubinemia on nutritive swallowing and swallowing-breathing coordination in preterm lambs

Background: Hyperbilirubinemia (HB) occurs in 90% of preterm newborns. HB induces acute neurological disorders (somnolence, abnormal tone, feeding difficulties, auditory dysfunction) and alterations in respiratory control. These findings suggest brainstem neurotoxicity that could also affect swallowing centers. Objective: To test the hypothesis that HB impairs nutritive swallowing (NS) and swallowing-breathing coordination. Methods: Two groups of preterm lambs (born 14 days prior to term), namely control (n = 6) and HB (n = 5), were studied. On day 5 of life (D0), moderate HB (150-250 µmol/l) was induced during 17 h in the HB group. Swallowing was assessed via recording of pharyngeal pressure and respiration by respiratory inductance plethysmography and pulse oximetry. The effect of HB on NS was assessed during standardized bottle-feeding. A second recording was performed 48 h after recovery from HB (D3). Results: Swallows were less frequent (p = 0.003) and of smaller volume (p = 0.01) in HB lambs while swallowing frequency was decreased (p = 0.004). These differences disappeared after HB normalization. Swallowing-breathing coordination was impaired in HB lambs, with a decrease in percent time with NS burst-related apneas/hypopneas at D0 and D3. Simultaneously, HB lambs tended to experience more severe desaturations (<80%) during bottle-feeding. Finally, following bottle-feeding, the respiratory rate was significantly lower, along with an increased apnea duration in HB lambs. Conclusions: Swallowing and swallowing-breathing coordination are altered by acute moderate HB in preterm lambs. Decreased efficiency at bottle-feeding is accompanied by continuation of breathing during swallow bursts, which may promote lung aspiration

Criteria for entropic curvature on graph spaces

This paper presents local criteria for lower bounds on entropic curvature of graph spaces along Schr\"odinger bridges at zero temperature, according to the definition given by the second named author in [31], in the continuity of the work by C. L\'eonard [19] inspired by the Lott-Sturm-Villani theory. A graph space is defined as a quadruple $(\mathcal{X},d,L,m)$ where $\mathcal{X}$ is the set of vertices, $d$ is the combinatorial distance and $m$ is a reversible reference measure with respect to a generator $L$ of a Markov semi-group on $\mathcal{X}$. The criteria are given by local optimization problems on balls of radius two, depending only on the generator $L$ and on the discrete structure of these balls. General tensorization properties of the criteria are presented for the study of the Cartesian product of graphs. This approach is robust since it applies to a wide range of graph spaces and also for any measure $m$, including measures with interaction potential like Ising models. We introduce a very large class of structured graphs, for which the local criteria give non-negative entropic curvature for the uniform measure. A Bonnet-Myers type of theorem also ensures that any such graph with positive entropic curvature is finite. On any graph space, positive entropic curvature provides transport-entropy inequalities with so-called weak optimal transport costs, as well as Poincar\'e or modified log-Sobolev inequalities for the renormalized probability measure $\mu = m/m(\mathcal{X})$. These inequalities are related to refined concentration properties of the measure $\mu$, speed of convergence of semi-groups to the measure $\mu$. We also present examples of graphs with negative curvature. Some comparisons of our results with other notions of curvature are established, such as Bakry-Emery curvature conditions [7,8], Ollivier or Lin-Lu-Yau's curvature [28,20].Comment: 62 pages, 2 figure