L_p moments of random vectors via majorizing measures

For a random vector X in R^n, we obtain bounds on the size of a sample, for which the empirical p-th moments of linear functionals are close to the exact ones uniformly on an n-dimensional convex body K. We prove an estimate for a general random vector and apply it to several problems arising in geometric functional analysis. In particular, we find a short Lewis type decomposition for any finite dimensional subspace of L_p. We also prove that for an isotropic log-concave random vector, we only need about n^{p/2} \log n sample points so that the empirical p-th moments of the linear functionals are almost isometrically the same as the exact ones. We obtain a concentration estimate for the empirical moments. The main ingredient of the proof is the construction of an appropriate majorizing measure to bound a certain Gaussian process.Comment: 32 pages, to appear in Advances in Mathematic

The Discrete radon transform: A more efficient approach to image reconstruction

The Radon transform and its inversion are the mathematical keys that enable tomography. Radon transforms are defined for continuous objects with continuous projections at all angles in [0,π). In practice, however, we pre-filter discrete projections take

A probabilistic approach to the geometry of the \ell_p^n-ball

This article investigates, by probabilistic methods, various geometric questions on B_p^n, the unit ball of \ell_p^n. We propose realizations in terms of independent random variables of several distributions on B_p^n, including the normalized volume measure. These representations allow us to unify and extend the known results of the sub-independence of coordinate slabs in B_p^n. As another application, we compute moments of linear functionals on B_p^n, which gives sharp constants in Khinchine's inequalities on B_p^n and determines the \psi_2-constant of all directions on B_p^n. We also study the extremal values of several Gaussian averages on sections of B_p^n (including mean width and \ell-norm), and derive several monotonicity results as p varies. Applications to balancing vectors in \ell_2 and to covering numbers of polyhedra complete the exposition.Comment: Published at http://dx.doi.org/10.1214/009117904000000874 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

MicroBio team objectives

MicroBio team objectives. STLOpenday

A probabilistic approach to the geometry of the ℓᵨⁿ-ball

This article investigates, by probabilistic methods, various geometric questions on Bᵨⁿ, the unit ball of ℓᵨⁿ. We propose realizations in terms of independent random variables of several distributions on Bᵨⁿ, including the normalized volume measure. These representations allow us to unify and extend the known results of the sub-independence of coordinate slabs in Bᵨⁿ. As another application, we compute moments of linear functionals on Bᵨⁿ, which gives sharp constants in Khinchine’s inequalities on Bᵨⁿ and determines the ψ₂-constant of all directions on Bᵨⁿ. We also study the extremal values of several Gaussian averages on sections of Bᵨⁿ (including mean width and ℓ-norm), and derive several monotonicity results as p varies. Applications to balancing vectors in ℓ₂ and to covering numbers of polyhedra complete the exposition

Hydrocarbon Pay zone Prediction using AI Neural Network Modeling.

This paper captures the ability of AI neural network technology to analyze petrophysical datasets for pattern recognition and accurate prediction of the pay zone of a vertical well from the Santa Fe field in Kansas. During this project, data from 10 completed wells in the Santa Fe field were gathered, resulting in a dataset with 25,580 records, ten predictors (logs data), and a single binary output (Yes or No) to identify the availability of Hydrocarbon over a half feet depth segment in the well. Several models composed of different predictors combinations were also tested to determine how impactful some logs were compared to others for the prediction process. With 32 tested models using a base set of 5 logs (X, Y GR, DEPT, and CALI) and different combinations of 5 other logs ( RT90, RHOB, NPHI, PE, DT). All models containing RT90, NP, or DT led to a better prediction matching the pay zone established based on a petrophysical analysis and completion data from the well. Results from this project could be used as another support to help and justify decision-making for a Petro physicist regarding work in the field with less experience

Order statistics and concentration of l_r norms for log-concave vectors

We establish upper bounds for tails of order statistics of isotropic log-concave vectors and apply them to derive a concentration of l_r norms of such vectors.Comment: 17 page

Thin shell implies spectral gap up to polylog via a stochastic localization scheme

We consider the isoperimetric inequality on the class of high-dimensional isotropic convex bodies. We establish quantitative connections between two well-known open problems related to this inequality, namely, the thin shell conjecture, and the conjecture by Kannan, Lovasz, and Simonovits, showing that the corresponding optimal bounds are equivalent up to logarithmic factors. In particular we prove that, up to logarithmic factors, the minimal possible ratio between surface area and volume is attained on ellipsoids. We also show that a positive answer to the thin shell conjecture would imply an optimal dependence on the dimension in a certain formulation of the Brunn-Minkowski inequality. Our results rely on the construction of a stochastic localization scheme for log-concave measures.Comment: 33 page

Annular gap bubble column: Experimental investigation and computational fluid dynamics modeling

This paper investigates the countercurrent gas-liquid flow in an annular gap bubble column with a 0.24 m inner diameter by using experimental and numerical investigations. The two-phase flow is studied experimentally using flow visualizations, gas holdup measurements, and double fiber optical probes in the following range of operating conditions: superficial air velocities up to 0.23 m/s and superficial water velocities up to -0.11 m/s, corresponding to gas holdups up to 29%. The flow visualizations were used to observe the flow patterns and to obtain the bubble size distribution (BSD). The gas holdup measurements were used for investigating the flow regime transitions, and the double fiber optical probes were used to study the local flow phenomena. A computational fluid dynamics (CFD) Eulerian two-fluid modeling of the column operating in the bubbly flow regime is proposed using the commercial software ansys fluent. The three-dimensional (3D) transient simulations have been performed considering a set of nondrag forces and polydispersity. It is shown that the errors in the global holdup and in the local properties are below 7% and 16%, respectively, in the range considered. Copyright © 2016 by ASME

Philippe Borgeaud et Sara Petrella, Le singe de l’autre. Du sauvage américain à l’histoire comparée des religions

Lors d’un entretien, réalisé dans le cadre du séminaire de l’équipe erasme et rapporté dans le numéro 21 d’Anabases, Christian Jacob explicitait les enjeux des comparatismes (Anabases 21, 2015, p. 197-211). À cette occasion, étaient rappelées la complexité et l’exigence des comparaisons historiques qui ne peuvent être menées qu’à l’issue d’une solide réflexion méthodologique. Le bel ouvrage que proposent Ph. Borgeaud et S. Petrella s’inscrit parfaitement dans cette démarche réflexive sur les ..