A model is proposed to describe the spike-frequency adaptation observed in many neuronal systems. We assume that adaptation is mainly due to a calcium-activated potassium current, and we consider two coupled stochastic differential equations for which an analytical approach combined with simulation techniques and numerical methods allow to obtain both qualitative and quantitative results about asymptotic mean firing rate, mean calcium concentration and the firing probability density. A related algorithm, based on the Hazard Rate Method, is also devised and described.

Conformational heterogeneity is key to the function of many biomacromolecules, but only a few groups have tried to characterize it until recently. Now, thanks to the increased throughput of experimental data and the increased computational power, the problem of the characterization of protein structural variability has become more and more popular. Several groups have devoted their efforts in trying to create quantitative, reliable and accurate protocols for extracting such information from averaged data. We analyze here different approaches, discussing strengths and weaknesses of each.

Linear combinations of iterates of Bernstein polynomials exponentially converging to the Lagrange interpolating polynomial are given. The results are applied in CAGD to get an exponentially fast weighted progressive iterative approximation technique to fit data with finer and finer precision.

In this paper, we present the results of an experiment aiming to compare measurements of atmospheric delay by synthetic aperture radar (SAR) interferometry and GPS techniques to estimates by numerical weather prediction. Maps of the differential atmospheric delay are generated by processing a set of interferometric SAR images acquired by the ENVISAT-ASAR mission over the Lisbon region from April to November 2009. GPS measurements of the wet zenith delay are carried out over the same area, covering the time interval between the first and the last SAR acquisition.

A hydro-kinetic scheme for water-like fluids, based on a lattice version of the Boltzmann equation, is presented and applied to the popular TIP3P model of liquid water. By proceeding in much larger steps than molecular dynamics, the scheme proves to be very effective in attaining global minima of classical pair potentials with directional and radial interactions, as confirmed by further simulations using the three-dimensional Ben-Naim water potential.

We prove a dimension-invariant imbedding estimate for Sobolev spaces of first order into a small Lebesgue space, and we establish the optimality of its fundamental function. Namely, for any 1 < p < ?, the inequality with a constant c_p, related to the imbedding of W_0^{1,p}(B_n) into Y_p(0,1), where Yp(0,1) is a rearrangement-invariant Banach function space independent of the dimension n, B_n is the ball in R^n of measure 1 and c_p is a constant independent of n, is satisfied by the small Lebesgue space L(p,p? /2 (0, 1).

A defect occurs on the inaccessible side of a metallic thin plate . We detect and evaluate from real thermal data collected.

Even though the Hartley-entropy-based contrast function guarantees an unmixing local minimum, the reported nonsmooth optimization techniques that minimize this nondifferentiable function encounter computational bottlenecks. Toward this, Powell's derivative-free optimization method has been extended to a Riemannian manifold, namely, oblique manifold, for the recovery of quasi-correlated sources by minimizing this contrast function.

Direct numerical approximation of a continuous-time infinite horizon control problem, requires to recast the model as a discrete-time, finite-horizon control model. The quality of the optimization results can be heavily degraded if the discretization process does not take into account features of the original model to be preserved.

We discuss the current status of the modifications to the ESA ORM scientific processor in view of the release of the ORM v8