Derivation of the Blackbody Radiation Spectrum from a Natural Maximum-Entropy Principle Involving Casimir Energies and Zero-Point Radiation

By numerical calculation, the Planck spectrum with zero-point radiation is shown to satisfy a natural maximum-entropy principle whereas alternative choices of spectra do not. Specifically, if we consider a set of conducting-walled boxes, each with a partition placed at a different location in the box, so that across the collection of boxes the partitions are uniformly spaced across the volume, then the Planck spectrum correspond to that spectrum of random radiation (having constant energy kT per normal mode at low frequencies and zero-point energy (1/2)hw per normal mode at high frequencies) which gives maximum uniformity across the collection of boxes for the radiation energy per box. The analysis involves Casimir energies and zero-point radiation which do not usually appear in thermodynamic analyses. For simplicity, the analysis is presented for waves in one space dimension.Comment: 11 page

The Pareto-Frontier in a simple Mirrleesian model of income taxation

We characterize the Pareto-frontier in a simple Mirrleesian model of income taxation. We show how the second-best frontier which incorporates incentive constraints due to private information on productive abilities relates to the first-best frontier which takes only resource constraints into account. In particular, we argue that the second-best frontier can be interpreted as a Laer-curve. We also use this second-best frontier for a comparative statics analysis of how optimal income tax rates vary with the degree of inequity aversion, and for a characterization of optimal public-good provision. We show that a more inequity averse policy maker chooses tax schedules that are more redistributive and involve higher marginal tax rates, but chooses a lower public-goods provision level.Optimal Income Taxation, Public-good provision, Laer-Curve

Grover's quantum searching algorithm is optimal

I improve the tight bound on quantum searching by Boyer et al. (quant-ph/9605034) to a matching bound, thus showing that for any probability of success Grovers quantum searching algorithm is optimal. E.g. for near certain success we have to query the oracle pi/4 sqrt{N} times, where N is the size of the search space. I also show that unfortunately quantum searching cannot be parallelized better than by assigning different parts of the search space to independent quantum computers. Earlier results left open the possibility of a more efficient parallelization.Comment: 13 pages, LaTeX, essentially published versio

Political Competition and Mirrleesian Income Taxation: A First Pass

We study Downsian competition in a Mirrleesian model of income taxation. The competing politicians may differ in competence. If politicians engage in vote-share maximization, the less competent politician’s policy proposals are attractive to the minority of rich agents, whereas those of the competent politician are attractive to the majority of poor agents. The less competent politician wins with positive probability, which gives rise to a political failure in the sense of Besley and Coate (1998). Political failures are avoided if politicians maximize winning probabilities. Nevertheless, the two equilibria cannot be Pareto-ranked, the minority may be better off under vote-share maximization.electoral competition, non-linear income taxation, candidate quality

Scaling Symmetries of Scatterers of Classical Zero-Point Radiation

Classical radiation equilibrium (the blackbody problem) is investigated by the use of an analogy. Scaling symmetries are noted for systems of classical charged particles moving in circular orbits in central potentials V(r)=-k/r^n when the particles are held in uniform circular motion against radiative collapse by a circularly polarized incident plane wave. Only in the case of a Coulomb potential n=1 with fixed charge e is there a unique scale-invariant spectrum of radiation versus frequency (analogous to zero-point radiation) obtained from the stable scattering arrangement. These results suggest that non-electromagnetic potentials are not appropriate for discussions of classical radiation equilibrium.Comment: 13 page

CIXL2: A Crossover Operator for Evolutionary Algorithms Based on Population Features

In this paper we propose a crossover operator for evolutionary algorithms with real values that is based on the statistical theory of population distributions. The operator is based on the theoretical distribution of the values of the genes of the best individuals in the population. The proposed operator takes into account the localization and dispersion features of the best individuals of the population with the objective that these features would be inherited by the offspring. Our aim is the optimization of the balance between exploration and exploitation in the search process. In order to test the efficiency and robustness of this crossover, we have used a set of functions to be optimized with regard to different criteria, such as, multimodality, separability, regularity and epistasis. With this set of functions we can extract conclusions in function of the problem at hand. We analyze the results using ANOVA and multiple comparison statistical tests. As an example of how our crossover can be used to solve artificial intelligence problems, we have applied the proposed model to the problem of obtaining the weight of each network in a ensemble of neural networks. The results obtained are above the performance of standard methods