Invariances in variance estimates

We provide variants and improvements of the Brascamp-Lieb variance inequality which take into account the invariance properties of the underlying measure. This is applied to spectral gap estimates for log-concave measures with many symmetries and to non-interacting conservative spin systems

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

Closure properties of solutions to heat inequalities

We prove that if $u_1,u_2 : (0,\infty) \times \R^d \to (0,\infty)$ are sufficiently well-behaved solutions to certain heat inequalities on $\R^d$ then the function $u: (0,\infty) \times \R^d \to (0,\infty)$ given by $u^{1/p}=u_1^{1/p_1} * u_2^{1/p_2}$ also satisfies a heat inequality of a similar type provided $\tfrac{1}{p_1} + \tfrac{1}{p_2} = 1 + \tfrac{1}{p}$. On iterating, this result leads to an analogous statement concerning $n$-fold convolutions. As a corollary, we give a direct heat-flow proof of the sharp $n$-fold Young convolution inequality and its reverse form.Comment: 12 page

Metallicity determination in gas-rich galaxies with semiempirical methods

A study of the precision of the semiempirical methods used in the determination of the chemical abundances in gas-rich galaxies is carried out. In order to do this the oxygen abundances of a total of 438 galaxies were determined using the electronic temperature, the $R_{23}$ and the P methods. The new calibration of the P method gives the smaller dispersion for the low and high metallicity regions, while the best numbers in the turnaround region are given by the $R_{23}$ method. We also found that the dispersion correlates with the metallicity. Finally, it can be said that all the semiempirical methods studied here are quite insensitive to metallicity with a value of $8.0\pm0.2$ dex for more than 50% of the total sample. \keywords{ISM: abundances; (ISM): H {\sc ii} regions}Comment: 26 pages, 9 figures and 2 tables. To appear at AJ, January 200

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

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

Study of the optimal conditions for NV- center formation in type 1b diamond, using photoluminescence and positron annihilation spectroscopies

We studied the parameters to optimize the production of negatively-charged nitrogen-vacancy color centers (NV-) in type~1b single crystal diamond using proton irradiation followed by thermal annealing under vacuum. Several samples were treated under different irradiation and annealing conditions and characterized by slow positron beam Doppler-broadening and photoluminescence (PL) spectroscopies. At high proton fluences another complex vacancy defect appears limiting the formation of NV-. Concentrations as high as 2.3 x 10^18 cm^-3 of NV- have been estimated from PL measurements. Furthermore, we inferred the trapping coefficient of positrons by NV-. This study brings insight into the production of a high concentration of NV- in diamond, which is of utmost importance in ultra-sensitive magnetometry and quantum hybrid systems applications

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

Geometric inequalities from phase space translations

We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results from a certain convolution operation: the latter maps a classical probability distribution on phase space and a quantum state to a quantum state. We show that this inequality also gives rise to several related inequalities whose counterparts are well-known in the classical setting: in particular, it implies an entropy power inequality for the mentioned convolution operation as well as the isoperimetric inequality, and establishes concavity of the entropy power along trajectories of the quantum heat diffusion semigroup. As an application, we derive a Log-Sobolev inequality for the quantum Ornstein-Uhlenbeck semigroup, and argue that it implies fast convergence towards the fixed point for a large class of initial states.Comment: 37 pages; updated to match published versio