Study of the Wealth Inequality in the Minority Game

To demonstrate the usefulness of physical approaches for the study of realistic economic systems, we investigate the inequality of players' wealth in one of the most extensively studied econophysical models, namely, the minority game (MG). We gauge the wealth inequality of players in the MG by a well-known measure in economics known as the modified Gini index. From our numerical results, we conclude that the wealth inequality in the MG is very severe near the point of maximum cooperation among players, where the diversity of the strategy space is approximately equal to the number of strategies at play. In other words, the optimal cooperation between players comes hand in hand with severe wealth inequality. We also show that our numerical results in the asymmetric phase of the MG can be reproduced semi-analytically using a replica method.Comment: 9 pages in revtex 4 style with 3 figures; minor revision with a change of title; to appear in PR

Semi-Finite Forms of Bilateral Basic Hypergeometric Series

We show that several classical bilateral summation and transformation formulas have semi-finite forms. We obtain these semi-finite forms from unilateral summation and transformation formulas. Our method can be applied to derive Ramanujan's $_1\psi_1$ summation, Bailey's $_2\psi_2$ transformations, and Bailey's $_6\psi_6$ summation.Comment: 8 pages. accepted by Proc. Amer. Math. So

Properties of TiO2 thin films and a study of the TiO2-GaAs interface

Titanium dioxide (TiO2) films prepared by chemical vapor deposition were investigated in this study for the purpose of the application in the GaAs metal-insulator-semiconductor field-effect transistor. The degree of crystallization increases with the deposition temperature. The current-voltage study, utilizing an Al-TiO2-Al MIM structure, reveals that the d-c conduction through the TiO2 film is dominated by the bulk-limited Poole-Frenkel emission mechanism. The dependence of the resistivity of the TiO2 films on the deposition environment is also shown. The results of the capacitance-voltage study indicate that an inversion layer in an n-type substrate can be achieved in the MIS capacitor if the TiO2 films are deposited at a temperature higher than 275 C. A process of low temperature deposition followed by the pattern definition and a higher temperature annealing is suggested for device fabrications. A model, based on the assumption that the surface state densities are continuously distributed in energy within the forbidden band gap, is proposed to interpret the lack of an inversion layer in the Al-TiO2-GaAs MIS structure with the TiO2 films deposited at 200 C

Lattice Gluon Propagator in the Landau Gauge: A Study Using Anisotropic Lattices

Lattice gluon propagators are studied using tadpole and Symanzik improved gauge action in Landau gauge. The study is performed using anisotropic lattices with asymmetric volumes. The Landau gauge dressing function for the gluon propagator measured on the lattice is fitted according to a leading power behavior: $Z(q^2)\simeq (q^2)^{2\kappa}$ with an exponent $\kappa$ at small momenta. The gluon propagators are also fitted using other models and the results are compared. Our result is compatible with a finite gluon propagator at zero momentum in Landau gauge.Comment: 14 pages, 4 figure

Anti-lecture Hall Compositions and Overpartitions

We show that the number of anti-lecture hall compositions of n with the first entry not exceeding k-2 equals the number of overpartitions of n with non-overlined parts not congruent to $0,\pm 1$ modulo k. This identity can be considered as a refined version of the anti-lecture hall theorem of Corteel and Savage. To prove this result, we find two Rogers-Ramanujan type identities for overpartition which are analogous to the Rogers-Ramanjan type identities due to Andrews. When k is odd, we give an alternative proof by using a generalized Rogers-Ramanujan identity due to Andrews, a bijection of Corteel and Savage and a refined version of a bijection also due to Corteel and Savage.Comment: 16 page