Traces of functions in Fock spaces on lattices of critical density

Following a scheme of Levin we describe the values that functions in Fock spaces take on lattices of critical density in terms of both the size of the values and a cancelation condition that involves discrete versions of the Cauchy and Beurling-Ahlfors transforms.

A Fast Gradient Approximation for Nonlinear Blind Signal Processing

When dealing with nonlinear blind processing algorithms (deconvolution or post-nonlinear source separation), complex mathematical estimations must be done giving as a result very slow algorithms. This is the case, for example, in speech processing, spike signals deconvolution or microarray data analysis. In this paper, we propose a simple method to reduce computational time for the inversion of Wiener systems or the separation of post-nonlinear mixtures, by using a linear approximation in a minimum mutual information algorithm. Simulation results demonstrate that linear spline interpolation is fast and accurate, obtaining very good results (similar to those obtained without approximation) while computational time is dramatically decreased. On the other hand, cubic spline interpolation also obtains similar good results, but due to its intrinsic complexity, the global algorithm is much more slow and hence not useful for our purpose.

Equidistribution of Fekete Points on the Sphere

Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of Fekete points in the sphere. The way we proceed is by showing their connection to other arrays of points, the so-called Marcinkiewicz-Zygmund arrays and interpolating arrays, that have been studied recently.

Forecasting coal resources and reserves in heterogeneous coal zones using 3D facies models (As Pontes Basin, NW Spain)

Forecasting coal resources and reserves is critical for coal mine development. Thickness maps are commonly used for assessing coal resources and reserves; however they are limited for capturing coal splitting effects in thick and heterogeneous coal zones. As an alternative, three-dimensional geostatistical methods are used to populate facies distributionwithin a densely drilled heterogeneous coal zone in the As Pontes Basin (NWSpain). Coal distribution in this zone is mainly characterized by coal-dominated areas in the central parts of the basin interfingering with terrigenous-dominated alluvial fan zones at the margins. The three-dimensional models obtained are applied to forecast coal resources and reserves. Predictions using subsets of the entire dataset are also generated to understand the performance of methods under limited data constraints. Three-dimensional facies interpolation methods tend to overestimate coal resources and reserves due to interpolation smoothing. Facies simulation methods yield similar resource predictions than conventional thickness map approximations. Reserves predicted by facies simulation methods are mainly influenced by: a) the specific coal proportion threshold used to determine if a block can be recovered or not, and b) the capability of the modelling strategy to reproduce areal trends in coal proportions and splitting between coal-dominated and terrigenousdominated areas of the basin. Reserves predictions differ between the simulation methods, even with dense conditioning datasets. Simulation methods can be ranked according to the correlation of their outputs with predictions from the directly interpolated coal proportion maps: a) with low-density datasets sequential indicator simulation with trends yields the best correlation, b) with high-density datasets sequential indicator simulation with post-processing yields the best correlation, because the areal trends are provided implicitly by the dense conditioning data.