Fictitious play applied to sequences of games and discounted stochastic games

In this paper, we show that the iterative method of Brown and Robinson, for solving a matrix game, is also applicable to a converging sequence of matrices, where the players choose at staget a row and a column of thet-th matrix in the sequence. As an application of this result, we describe a new solution method for discounted stochastic games with finite state and action spaces.     

Penalized likelihood regression for generalized linear models with non-quadratic penalties

One of the popular method for fitting a regression function is regularization: minimizing an objective function which enforces a roughness penalty in addition to coherence with the data. This is the case when formulating penalized likelihood regression for exponential families. Most of the smoothing methods employ quadratic penalties, leading to linear estimates, and are in general incapable of recovering discontinuities or other important attributes in the regression function. In contrast, non-linear estimates are generally more accurate. In this paper, we focus on non-parametric penalized likelihood regression methods using splines and a variety of non-quadratic penalties, pointing out common basic principles. We present an asymptotic analysis of convergence rates that justifies the approach. We report on a simulation study including comparisons between our method and some existing ones. We illustrate our approach with an application to Poisson non-parametric regression modeling of frequency counts of reported acquired immune deficiency syndrome (AIDS) cases in the UK.     

Bromo-Derivatives of 2′-NHR-3,4-methylenedioxychalcone and Its 4-Quinolone Isomer

Bromination reaction of 2′-NHR-3,4′-methylenedioxychalcone (1) and 2,3-dihydro-2-(3′,4′-methylenedioxyphenyl)-4(1H)-quinolone (7) with bromine and N-bromosuccinimide are discussed. Depending on the character of the R group and on the reagent used nuclear or side-chain brominated or side-chain bromo-methoxylated products were obtained.     

Quantum Nuclear Delocalization and its Rovibrational Fingerprints

Quantum mechanics dictates that nuclei must undergo some delocalization. In this work, emergence of quantum nuclear delocalization and its rovibrational fingerprints are discussed for the case of the van der Waals complex . The equilibrium structure of is planar and T-shaped, one He atom solvating the quasi-linear He−H⁺−He core. The dynamical structure of , in all of its bound states, is fundamentally different. As revealed by spatial distribution functions and nuclear densities, during the vibrations of the molecule the solvating He is not restricted to be in the plane defined by the instantaneously bent chomophore, but freely orbits the central proton, forming a three-dimensional torus around the chromophore. This quantum delocalization is observed for all vibrational states, the type of vibrational excitation being reflected in the topology of the nodal surfaces in the nuclear densities, showing, for example, that intramolecular bending involves excitation along the circumference of the torus.