Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry

We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general $F$-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide criteria for these Sobolev type inequalities and for related properties. In particular, we implement in the context of probability measures the ideas of Maz'ja's capacity theory, and present equivalent forms relating the capacity of sets to their measure. Orlicz hypercontractivity efficiently describes the integrability improving properties of the Heat semigroup associated to the Boltzmann measures $\mu_\alpha (dx) = (Z_\alpha)^{-1} e^{-2|x|^\alpha} dx$, when $\alpha\in (1,2)$. As an application we derive accurate isoperimetric inequalities for their products. This completes earlier works by Bobkov-Houdr\'e and Talagrand, and provides a scale of dimension free isoperimetric inequalities as well as comparison theorems.Comment: 76 pages, 1 figur

Letter to the Editor: 1H, 15N, and 13C chemical shift assignments of the resuscitation promoting factor domain of Rv1009 from Mycobacterium tuberculosis

International audienceNo abstract availabl

Numerical study of tracers transport by a mesoscale convective system over West Africa

A three-dimensional cloud-resolving model is used to investigate the vertical transport from the lower to the upper troposphere in a mesoscale convective system (MCS) that occurred over Niger on 15 August 2004. The redistribution of five passive tracers initially confined in horizontally homogeneous layers is analyzed. The monsoon layer tracer (0–1.5 km) is the most efficiently transported in the upper troposphere with concentrations 3 to 4 times higher than the other tracers in the anvil. On the contrary the African Easterly Jet tracer (~3 km) has the lowest contribution above 5 km. The vertical profiles of the mid-troposphere tracers (4.5–10 km) in the MCS exhibit two peaks: one in their initial layers, and the second one at 13–14 km altitude, underlying the importance of mid-tropospheric air in feeding the upper troposphere. Mid-tropospheric tracers also experience efficient transport by convective downdrafts with a consequent increase of their concentrations at the surface. The concentration of the upper troposphere–lower stratosphere tracer exhibits strong gradients at the edge of the cloud, meaning almost no entrainment of this tracer into the cloud. No downward transport from the upper troposphere is simulated below 5 km. A proxy for lightning produced NO_x is transported preferentially in the forward anvil in the upper troposphere. Additionally, lateral inflows significantly contribute to the updraft and downdraft airflows emphasizing the three-dimensional structure of the West African MCSs

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

SpecCert: Specifying and Verifying Hardware-based Security Enforcement

Over time, hardware designs have constantly grown in complexity and modern platforms involve multiple interconnected hardware components. During the last decade, several vulnerability disclosures have proven that trust in hardware can be misplaced. In this article, we give a formal definition of Hardware-based Security Enforcement (HSE) mechanisms, a class of security enforcement mechanisms such that a software component relies on the underlying hardware platform to enforce a security policy. We then model a subset of a x86-based hardware platform specifications and we prove the soundness of a realistic HSE mechanism within this model using Coq, a proof assistant system

Isoperimetry and stability of hyperplanes for product probability measures

International audienceWe investigate stationarity and stability of half-spaces as isoperimetric sets for product probability measures, considering the cases of coordinate and non-coordinate half-spaces. Moreover, we present several examples to which our results can be applied, with a particular emphasis on the logistic measure

Strong Coupling of a Spin Ensemble to a Superconducting Resonator

We report the realization of a quantum circuit in which an ensemble of electronic spins is coupled to a frequency tunable superconducting resonator. The spins are Nitrogen-Vacancy centers in a diamond crystal. The achievement of strong coupling is manifested by the appearance of a vacuum Rabi splitting in the transmission spectrum of the resonator when its frequency is tuned through the NV center electron spin resonance.Comment: 4 pages, 3 figure

A Pre-expectation Calculus for Probabilistic Sensitivity

Sensitivity properties describe how changes to the input of a program affect the output, typically by upper bounding the distance between the outputs of two runs by a monotone function of the distance between the corresponding inputs. When programs are probabilistic, the distance between outputs is a distance between distributions. The Kantorovich lifting provides a general way of defining a distance between distributions by lifting the distance of the underlying sample space; by choosing an appropriate distance on the base space, one can recover other usual probabilistic distances, such as the Total Variation distance. We develop a relational pre-expectation calculus to upper bound the Kantorovich distance between two executions of a probabilistic program. We illustrate our methods by proving algorithmic stability of a machine learning algorithm, convergence of a reinforcement learning algorithm, and fast mixing for card shuffling algorithms. We also consider some extensions: using our calculus to show convergence of Markov chains to the uniform distribution over states and an asynchronous extension to reason about pairs of program executions with different control flow

PULSED AND CW LASER TREATMENTS OF IMPLANTED POLYSILICON SOLAR CELLS

Conventional ion implantation and unanalyzed ion bombardment have been used to elaborate the rectifying N+ contact of polycrystalline silicon (Wacker, HEM, CGE) solar cells. Two surface laser annealing in the liquid phase (Nd : YAG laser) and in the solid phase (CO2 laser) regimes have been used. The properties of the solar cells so processed have been investigated. For both doping procedures and both annealing techniques, the cells (conversion) efficiencies under AM1 illumination exceeded 11% for the various polysilicon substrates

Hypercontractive measures, Talagrand's inequality, and influences

We survey several Talagrand type inequalities and their application to influences with the tool of hypercontractivity for both discrete and continuous, and product and non-product models. The approach covers similarly by a simple interpolation the framework of geometric influences recently developed by N. Keller, E. Mossel and A. Sen. Geometric Brascamp-Lieb decompositions are also considered in this context