Approximation of quadratic irrationals and their pierce expansions

In this article two aims are pursued: on the one hand, to present arapidly converging algorithm for the approximation of square roots; on theother hand and based on the previous algorithm, to find the Pierce expansionsof a certain class of quadratic irrationals as an alternative way to themethod presented in 1984 by J.O. Shallit; we extend the method to findalso the Pierce expansions of quadratic irrationals of the form $2 (p-1)(p - \sqrt{p^2 - 1})$ which are not covered in Shallit's work.

A generalization of Hull and White formula and applications to option pricing approximation

By means of Malliavin Calculus we see that the classical Hull and White formulafor option pricing can be extended to the case where the noise driving thevolatility process is correlated with the noise driving the stock prices. Thisextension will allow us to construct option pricing approximation formulas.Numerical examples are presented.

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

By means of classical Itô's calculus we decompose option prices asthe sum of the classical Black-Scholes formula with volatility parameterequal to the root-mean-square future average volatility plus a term dueby correlation and a term due to the volatility of the volatility. Thisdecomposition allows us to develop first and second-order approximationformulas for option prices and implied volatilities in the Heston volatilityframework, as well as to study their accuracy. Numerical examples aregiven.

Motivation and content Language Integrated Learning : an impulse for Second Language Teaching

“Estudiantes motivados producen profesores motivados y viceversa” (Lesley Denham)La cita refleja el efecto recíproco que tiene el comportamiento del profesor en el compromiso de los estudiantes a lo largo del año y viceversa. Es sorprendente como, destacando las fortalezas de cada estudiante en lugar de sus debilidades, nunca comparándolos entre ellos sino con su propio rendimiento, puede despertar una motivación intrínseca en el estudiante, y una merecida satisfacción personal para el profesor.Sin embargo, no existen botones motivacionales mágicos que podamos pulsar y hacer que el alumno quiera aprender. Como profesores, tomar la iniciativa será crucial: dar a nuestros estudiantes el espacio suficiente para experimentar, realzar su autonomía, e intuir las respuestas a través de un proceso inductivo. En definitiva, hacerles protagonistas de su proceso de aprendizaje.Incluir AICLE en la clase de inglés es una metodología que nos ayudará a conseguirlo. Los estudiantes asocian AICLE con algo interesante y divertido, diferente a las sesiones teóricas. Como resultado, al utilizar la lengua, lo hacen movidos por sus sentimientos, aprendiendo de forma implícita.“Estudiants motivats produeixen professors motivats i viceversa” (Lesley Denham)La cita reflecteix l'efecte recíproc que té el comportament del professor en el compromís dels estudiants al llarg de l'any i viceversa. És sorprenent com, destacant les fortaleses de cada estudiant en lloc de les seves debilitats, mai comparant-los entre ells sinó amb el seu propi rendiment, pot despertar una motivació intrínseca a l'estudiant, i una merescuda satisfacció personal per al professor.No obstant això, no existeixen botons motivacionals màgics que puguem prémer i fer que l'alumne vulgui aprendre. Com a professors, prendre la iniciativa serà crucial: donar als nostres estudiants l'espai suficient per experimentar, realçar la seva autonomia, i intuir les respostes a través d'un procés inductiu. En definitiva, fer-los protagonistes del seu procés d'aprenentatge.Incloure AICLE en la classe d'anglès és una metodologia que ens ajudarà a aconseguir-ho. Els estudiants consideren AICLE interessant i divertit, diferent a les sessions teòriques. Com a resultat, en utilitzar la llengua, ho fan moguts pels seus sentiments, aprenent de forma implícita.

Incremental neural networks for function approximation

A new strategy for incremental building of multilayer feedforward neural networks is proposed in the context of approximation of functions from R-p to R-q using noisy data. A stopping criterion based on the properties of the noise is also proposed. Experimental results for both artificial and real data are performed and two alternatives of the proposed construction strategy are compared.

A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion

An epidemic model is formulated by a reactionâeuro"diffusion system where the spatial pattern formation is driven by cross-diffusion. The reaction terms describe the local dynamics of susceptible and infected species, whereas the diffusion terms account for the spatial distribution dynamics. For both self-diffusion and cross-diffusion, nonlinear constitutive assumptions are suggested. To simulate the pattern formation two finite volume formulations are proposed, which employ a conservative and a non-conservative discretization, respectively. An efficient simulation is obtained by a fully adaptive multiresolution strategy. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation.

Use of the FACTS solvation model for protein-ligand docking calculations. Application to EADock.

Protein-ligand docking has made important progress during the last decade and has become a powerful tool for drug development, opening the way to virtual high throughput screening and in silico structure-based ligand design. Despite the flattering picture that has been drawn, recent publications have shown that the docking problem is far from being solved, and that more developments are still needed to achieve high successful prediction rates and accuracy. Introducing an accurate description of the solvation effect upon binding is thought to be essential to achieve this goal. In particular, EADock uses the Generalized Born Molecular Volume 2 (GBMV2) solvent model, which has been shown to reproduce accurately the desolvation energies calculated by solving the Poisson equation. Here, the implementation of the Fast Analytical Continuum Treatment of Solvation (FACTS) as an implicit solvation model in small molecules docking calculations has been assessed using the EADock docking program. Our results strongly support the use of FACTS for docking. The success rates of EADock/FACTS and EADock/GBMV2 are similar, i.e. around 75% for local docking and 65% for blind docking. However, these results come at a much lower computational cost: FACTS is 10 times faster than GBMV2 in calculating the total electrostatic energy, and allows a speed up of EADock by a factor of 4. This study also supports the EADock development strategy relying on the CHARMM package for energy calculations, which enables straightforward implementation and testing of the latest developments in the field of Molecular Modeling.

Ab initio study of NOx compounds adsorption on SnO2 surface

An ab initio study of the adsorption processes on NOx compounds on (1 1 0) SnO2 surface is presented with the aim of providing theoretical hints for the development of improved NOx gas sensors. From first principles calculations (DFT¿GGA approximation), the most relevant NO and NO2 adsorption processes are analyzed by means of the estimation of their adsorption energies. The resulting values and the developed model are also corroborated with experimental desorption temperatures for NO and NO2, allowing us to explain the temperature-programmed desorption experiments. The interference of the SO2 poisoning agent on the studied processes is discussed and the adsorption site blocking consequences on sensing response are analyzed.

Multipole surface-plasmon modes on simple metals

The average multipole surface-plasmon energy for simple metals, as well as that of ordinary surface and bulk plasmons, is obtained using energy-weighted moments of the electronic response to sufficiently general external perturbations. A local approximation of exchange and correlation effects is used within a jellium model. Band-structure effects are incorporated through an effective electronic mass. Taking advantage of the transparency of the method, we analyze under what circumstances such modes might be observable. It is shown that due to an interplay between Coulomb and kinetic energies, the multipole modes become unobservable for increasing values of the transferred momentum (q) parallel to the surface. The value of q at which the multipole mode becomes unobservable is much smaller than the cutoff value for Landau damping. The effect of the electronic surface diffuseness is also analyzed. We compare our results with previous density-functional calculations and with recent experimental data for Na, K, and Cs.

Systematics of properties of the electron gas in deep-etched quantum wires

An efficient method is developed for an iterative solution of the Poisson and Schro¿dinger equations, which allows systematic studies of the properties of the electron gas in linear deep-etched quantum wires. A much simpler two-dimensional (2D) approximation is developed that accurately reproduces the results of the 3D calculations. A 2D Thomas-Fermi approximation is then derived, and shown to give a good account of average properties. Further, we prove that an analytic form due to Shikin et al. is a good approximation to the electron density given by the self-consistent methods.

Spin and density longitudinal response of quantum dots in the time-dependent local-spin-density approximation

The longitudinal dipole response of a quantum dot has been calculated in the far-infrared regime using local-spin-density-functional theory. We have studied the coupling between the collective spin and density modes as a function of the magnetic field. We have found that the spin dipole mode and single-particle excitations have a sizable overlap, and that the magnetoplasmon modes can be excited by the dipole spin operator if the dot is spin polarized. The frequency of the dipole spin edge mode presents an oscillation which is clearly filling factor (v) related. We have found that the spin dipole mode is especially soft for even-n values. Results for selected numbers of electrons and confining potentials are discussed.

Density-functional calculations of magnetoplasmons in quantum rings

We have studied the structure and dipole charge-density response of nanorings as a function of the magnetic field using local-spin-density-functional theory. Two small rings consisting of 12 and 22 electrons confined by a positively charged background are used to represent the cases of narrow and wide rings. The results are qualitatively compared with experimental data existing on microrings and on antidots. A smaller ring containing five electrons is also analyzed to allow for a closer comparison with a recent experiment on a two-electron quantum ring.