Regularity and convergence of stochastic convolutions in duals of nuclear Fréchet spaces

Let Φ′ be the strong dual of a nuclear Fréchet space Φ. In this paper we present regularity properties, weak convergence, and convergence in probability and in mean square of Φ′-valued stochastic evolution equations and convolutions with respect to Φ′-valued cadlag martingales.     

Wiener distributions and white noise analysis

The paper describes the structure of a new space of generalized Wiener functionals, , called the Wiener algebra, or space of Wiener distributions, and demonstrates its use in the white noise analysis. The concepts of derivatives and integrals for multi-time parameter generalized stochastic process:^N are introduced, and a derivative version of Itô's lemma is proved. The algebraic structure of and its lattice of subspaces is elaborated, and within this framework a generalized version of the Malliavin calculus is presented.     

Computation of efficient solutions of discretely distributed stochastic optimization problems

In engineering and economics often a certain vectorx of inputs or decisions must be chosen, subject to some constraints, such that the expected costs (or loss) arising from the deviation between the outputA() x of a stochastic linear systemxA()x and a desired stochastic target vectorb() are minimal. Hence, one has the following stochastic linear optimization problem minimizeF(x)=Eu(A()x b()) s.t.xD, (1) whereu is a convex loss function on ^m , (A(), b()) is a random (m,n + 1)-matrix, E denotes the expectation operator andD is a convex subset of ⁿ . Concrete problems of this type are e.g. stochastic linear programs with recourse, error minimization and optimal design problems, acid rain abatement methods, problems in scenario analysis and non-least square regression analysis.Solving (1), the loss functionu should be exactly known. However, in practice mostly there is some uncertainty in assigning appropriate penalty costs to the deviation between the outputA ()x and the targetb(). For finding in this situation solutions hedging against uncertainty a set of so-called efficient points of (1) is defined and a numerical procedure for determining these compromise solutions is derived. Several applications are discussed.     

Efficient solution of two-stage stochastic linear programs using interior point methods

Solving deterministic equivalent formulations of two-stage stochastic linear programs using interior point methods may be computationally difficult due to the need to factorize quite dense search direction matrices (e.g., AA ^T ). Several methods for improving the algorithmic efficiency of interior point algorithms by reducing the density of these matrices have been proposed in the literature. Reformulating the program decreases the effort required to find a search direction, but at the expense of increased problem size. Using transpose product formulations (e.g., A ^T A) works well but is highly problem dependent. Schur complements may require solutions with potentially near singular matrices. Explicit factorizations of the search direction matrices eliminate these problems while only requiring the solution to several small, independent linear systems. These systems may be distributed across multiple processors. Computational experience with these methods suggests that substantial performance improvements are possible with each method and that, generally, explicit factorizations require the least computational effort.     

Winning controllers and regions in competitive nonlinear dynamic games with two qualitative objectives and uncertain information

The Liapunov technique has been introduced in differential games in a sequence of works over the last decade. We discuss application of this technique to the interface between two competitive semi-games, each with different qualitative objective. The feedback information for controllers is provided from designed, analytically integrable state predictors with reduced dynamics, which considerably shortens the computing time. The case is illustrated on the scenario of target reaching before being intercepted, and intercepting before target is reached.Deceased.     

Stability of a class of transformations of distribution-valued processes and stochastic evolution equations

Stability of a class of linear transformations of distribution-valued stochastic processes is studied. Two types of applications to convergence of solutions of stochastic evolution equations are given. One of them, for the case of continuous limits, simplifies the tightness problem considerably due to a recent result of Aldous.Centro de Investigación y de Estudios Avanzados.     

Scattering of a Light Particle by a System of Harmonic Oscillators

We discuss the asymptotic wave function of a quantum system in ?³ composed by heavy and light particles, in the case where the light particles are in scattering states and no interaction is assumed among particles of the same kind. We first review a recent result concerning the case of K heavy and N light particles, where the one-particle potential acting on each heavy particle decays at infinity. Then we consider the case of one light particle interacting with a system of harmonic oscillators and prove the same kind of result following, with some modification, the proof of the previous case. A possible application to the analysis of the scattering of a light particle from condensed matter is also outlined.     

Molecular dynamics simulation of CH3 interaction with Si(1 0 0) surface

Molecular dynamics simulations of the CH₃ interaction with Si(1 0 0) were performed using the Tersoff-Brenner potential. The H/C ratio obtained from the simulations is in agreement with available experimental data. The results show that H atoms preferentially react with Si. SiH is the dominant form of SiH_x generated. The amount of hydrogen that reacts with silicon is essentially energy-independent. H atoms do not react with adsorbed carbon atoms. The presence of C-H bonds on the surface is due to molecular adsorption.     

Adsorbate motions induced by vibrational mode coupling

Adsorbate motions are discussed with a primary attention focused on the coupling between a vibrational mode excited by ultrafast laser heated hot-electrons or by inelastic tunneling electrons with scanning tunneling microscope and the reaction coordinate (RC) mode. Recent experimental results have demonstrated an efficient reaction pathways involving an indirect excitation of a frustrated translational mode, rather than its direct excitation for adsorbate hopping on surfaces. Elementary processes are briefly described for hopping of CO molecules on a laser heated stepped Pt surface, where excitation of the frustrated rotation mode has been found to plays an indispensable. Calculation of the inelastic tunneling current (ITC) for excitation of the C-O stretch mode of a CO molecule is combined with a theory of anharmonic mode coupling to activate the frustrated translation mode above the barrier. The hopping rate as a function of the bias voltage agrees with the experimental result. An unified theory of single-, and two-electron processes for ITC-induced motions induced by an indirect excitation of the RC-mode via mode coupling is also applied to reproduce a crossover from hopping to desorption of a single NH₃ molecule on Cu(1 0 0) with an increase in the tunneling current.     

New type of biosensor based on magnetic nanoparticle detection

A new type of biosensor has been developed based on detection of nanosized superparamagnetic particles that serve as labels in bioreactions. The method is based on non-linear magnetic material detection by a magnetic field having components at two frequencies f₁ and f₂. The response is measured at the combinatorial frequencies f_i=mf₁+nf₂, where m and n are integers, e.g., f_i=f₁±2f₂. Several highly sensitive readers of superparamagnetic particles have been designed and used for development of various formats of immunoassays, including those compatible with immunoconcentration and magnetic enrichment of antigens.