1,098 research outputs found
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,Ï). 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
A probabilistic approach to the geometry of the âᔚâż-ball
This article investigates, by probabilistic methods, various geometric questions on Bᔚâż, the unit ball of âᔚâż. We propose realizations in terms of independent random variables of several distributions on Bᔚâż, including the normalized volume measure. These representations allow us to unify and extend the known results of the sub-independence of coordinate slabs in Bᔚâż. As another application, we compute moments of linear functionals on Bᔚâż, which gives sharp constants in Khinchineâs inequalities on Bᔚ⿠and determines the Ïâ-constant of all directions on Bᔚâż. We also study the extremal values of several Gaussian averages on sections of Bᔚ⿠(including mean width and â-norm), and derive several monotonicity results as p varies. Applications to balancing vectors in ââ 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 lâautre. Du sauvage amĂ©ricain Ă lâhistoire comparĂ©e des religions
Lors dâun entretien, rĂ©alisĂ© dans le cadre du sĂ©minaire de lâĂ©quipe erasme et rapportĂ© dans le numĂ©ro 21 dâAnabases, Christian Jacob explicitait les enjeux des comparatismes (Anabases 21, 2015, p. 197-211). Ă cette occasion, Ă©taient rappelĂ©es la complexitĂ© et lâexigence des comparaisons historiques qui ne peuvent ĂȘtre menĂ©es quâĂ lâissue dâune solide rĂ©flexion mĂ©thodologique. Le bel ouvrage que proposent Ph. Borgeaud et S. Petrella sâinscrit parfaitement dans cette dĂ©marche rĂ©flexive sur les ..
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