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

Recombinant gamma interferon provokes resistance of human breast cancer cells to spontaneous and IL-2 activated non-MHC restricted cytotoxicity.

Natural and lymphokine activated killer cells (NK and LAK) are believed to play an important role in the control of tumour progression and metastasis. Their specific receptors on tumours cells are still unknown. Several studies suggest that these cells recognise and eliminate abnormal cells with deleted or reduced expression of MHC class I molecules. Previous reports suggest that interferons (IFN), by increasing MHC class I expression on target cells, induce resistance to killing by NK cells. We investigated the role of MHC molecule expression by two human breast cancer cell lines T47D and ZR75-1 in their susceptibility to NK and LAK cells. These two cell lines spontaneously express low levels of HLA class I antigens but no HLA class II molecules. After IFN-gamma treatment they both overexpressed MHC class I and de novo expressed class II molecules as detected by flow cytometry, quantified by a radioimmunoassay and analysed by two-dimensional gel electrophoresis. Opposed to untreated cells these IFN-gamma treated cells were resistant to NK and LAK lysis. Furthermore, preincubation of IFN-gamma treated breast cancer cells with F(ab')2 fragments of monoclonal antibodies to HLA class I and HLA class II molecules was unable to restore lysis. In contrast, several complete monoclonal antibodies including anti-HLA class I and HLA class II induced the lysis of target cells whether or not they had been treated by IFN-gamma. The therapeutic use of monoclonal antibodies directed against antigens expressed on tumour cells (ADCC) in conjunction with interferon therapy should be discussed in lymphokine-based strategies for treatment of cancer patients

Soft Listeria: actin-based propulsion of liquid drops

We study the motion of oil drops propelled by actin polymerization in cell extracts. Drops deform and acquire a pear-like shape under the action of the elastic stresses exerted by the actin comet. We solve this free boundary problem and calculate the drop shape taking into account the elasticity of the actin gel and the variation of the polymerization velocity with normal stress. The pressure balance on the liquid drop imposes a zero propulsive force if gradients in surface tension or internal pressure are not taken into account. Quantitative parameters of actin polymerization are obtained by fitting theory to experiment.Comment: 5 pages, 4 figure

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

Identification of Quantitative Trait Loci responsible for embryonic lethality in mice assessed by ultrasonography.

Recurrent Spontaneous Abortion (RSA) is a frequent pathology affecting 1 to 5% of couples. In approximately 50 % of cases, the aetiology is unknown suggesting a subtle interaction between genetic and environmental factors. Previous attempts to describe genetic factors using the candidate gene approach have been relatively unsuccessful due to the physiological, cellular and genetic complexity of mammalian reproduction. Indeed, fertility can be considered as a quantitative feature resulting from the interaction of genetic, epigenetic and environmental factors. Herein, we identified Quantitative Trait Loci (QTL) associated with diverse embryonic lethality phenotypes and the subsequent embryonic resorption in 39 inter-specific recombinant congenic mice strains, using in vivo ultrasound bio-microscopy. The short chromosomal intervals related to the phenotypes will facilitate the study of a restricted number of candidate genes which are potentially dysregulated in patients affected by RSA

Two remarks on generalized entropy power inequalities

This note contributes to the understanding of generalized entropy power inequalities. Our main goal is to construct a counter-example regarding monotonicity and entropy comparison of weighted sums of independent identically distributed log-concave random variables. We also present a complex analogue of a recent dependent entropy power inequality of Hao and Jog, and give a very simple proof.Comment: arXiv:1811.00345 is split into 2 papers, with this being on

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