Essential collections for equilibrium concepts

The aim of this study is to identify and characterize the parts of an extensive form game that are ??relevant?? to determining whether the outcome of a certain strategy profile is an equilibrium outcome. We formally define what we mean by ??relevant?? and refer to the associated collection of information sets as essential. We apply this idea to a number of classic equilibrium concepts and discuss some implications of our approach.     

Numerical analysis of TOF measurements in pulsed laser ablation

The results of numerical simulation of pulsed laser ablation both in vacuum and into a background gas are presented. The influences of different processes, such as time evolution of the surface temperature, interspecies interactions (elastic collisions, recombination-dissociation reaction), interaction with an ambient gas, and excitations-relaxation processes on time-of-flight (TOF) distributions are examined. Experimentally obtained time-of-flight distributions are further analyzed, based on the results of numerical simulation. It is found that with the aid of numerical results one can explain not only the shape of the TOF distribution, but also the distance dependency of its maximum position (mean delay time). In addition, the mechanisms leading to the appearance of bimodal time-of-flight distribution are revealed. The study presents particular interest for the analysis of experimental results obtained during pulsed laser ablation.     

A potential approach for ordinal games

We introduce the class of ordinal games with a potential, which are characterized by the absence of weak improvement cycles, the same condition used by Voorneveld and Norde (1997) for ordinal potential games.     

Improved diffusion Monte Carlo propagators for bosonic systems using Itô calculus

The construction of importance sampled diffusion Monte Carlo (DMC) schemes accurate to second order in the time step is discussed. A central aspect in obtaining efficient second order schemes is the numerical solution of the stochastic differential equation (SDE) associated with the Fokker-Plank equation responsible for the importance sampling procedure. In this work, stochastic predictor-corrector schemes solving the SDE and consistent with It? calculus are used in DMC simulations of helium clusters. These schemes are numerically compared with alternative algorithms obtained by splitting the Fokker-Plank operator, an approach that we analyze using the analytical tools provided by Ito; calculus. The numerical results show that predictor-corrector methods are indeed accurate to second order in the time step and that they present a smaller time step bias and a better efficiency than second order split-operator derived schemes when computing ensemble averages for bosonic systems. The possible extension of the predictor-corrector methods to higher orders is also discussed.     

On the optimal control for variational inequalities

We prove an existence theorem for the optimal control of variational inequalities governed by a pseudomonotone operator: the cost is assumed to be quadratic. Then, we give an extension of the theorem to more general costs (assuming the operator to be monotone); we also give a result on a perturbation problem.This work is an extended part of the author's thesis, written under the direction of Professor T. Zolezzi. This research was partially supported by the Consiglio Nazionale delle Ricerche (CNR), Rome, Italy.     

Characterizing properties of approximate solutions for optimization problems

Approximate solutions for optimization problems become of interest if the ‘true’ optimum cannot be found: this may happen for the simple reason that an optimum does not exist or because of the ‘bounded rationality’ (or bounded accuracy) of the optimizer. This paper characterizes several approximate solutions by means of consistency and additional requirements. In particular we consider invariance properties. We prove that, where the domain contains optimization problems without maximum, there is no non-trivial consistent solution satisfying non-emptiness, translation and multiplication invariance. Moreover, we show that the class of ‘satisficing’ solutions is obtained, if the invariance axioms are replaced with Chernoff’s Choice Axiom.     

A surface enhanced Raman spectroscopy study of aminothiophenol and aminothiophenol-C60 self-assembled monolayers: evolution of Raman modes with experimental parameters

P-aminothiophenol (PATP) is a well-known molecule for the preparation of self-assembled monolayers on gold via its thiol functional group. After adsorption, it has been demonstrated that this molecule is anchored to gold through its thiol group, and standing nearly upright at the surface with the amino functional group on top. This molecule has been extensively studied by surface enhanced Raman spectroscopy but its exact SERS spectrum remains unclear. Here, we demonstrate that it can be strongly affected by at least two experimental parameters: laser power and layer density. Those features are discussed in terms of a dimerization of the PATP molecules. The free amino group affords the adsorption of other molecules such as C(60). In this case, a complex multilayer system is formed and the question of its precise characterisation remains a key point. In this article, we demonstrate that surface enhanced Raman spectroscopy combined with x ray photoelectron spectroscopy can bring very important information about the organization of such a self-assembled multilayer on gold. In our study, the strong evolution of Raman modes after C(60) adsorption suggests a change in the organization of aminothiophenol molecules during C(60) adsorption. These changes, also observed when the aminothiophenol layer is annealed in toluene, do not prevent the adsorption of C(60) molecules.