Monomial Testing and Applications

In this paper, we devise two algorithms for the problem of testing $q$-monomials of degree $k$ in any multivariate polynomial represented by a circuit, regardless of the primality of $q$. One is an $O^*(2^k)$ time randomized algorithm. The other is an $O^*(12.8^k)$ time deterministic algorithm for the same $q$-monomial testing problem but requiring the polynomials to be represented by tree-like circuits. Several applications of $q$-monomial testing are also given, including a deterministic $O^*(12.8^{mk})$ upper bound for the $m$-set $k$-packing problem.Comment: 17 pages, 4 figures, submitted FAW-AAIM 2013. arXiv admin note: substantial text overlap with arXiv:1302.5898; and text overlap with arXiv:1007.2675, arXiv:1007.2678, arXiv:1007.2673 by other author

Steady-state phase error for a phase-locked loop subjected to periodic Doppler inputs

The performance of a carrier phase locked loop (PLL) driven by a periodic Doppler input is studied. By expanding the Doppler input into a Fourier series and applying the linearized PLL approximations, it is easy to show that, for periodic frequency disturbances, the resulting steady state phase error is also periodic. Compared to the method of expanding frequency excursion into a power series, the Fourier expansion method can be used to predict the maximum phase error excursion for a periodic Doppler input. For systems with a large Doppler rate fluctuation, such as an optical transponder aboard an Earth orbiting spacecraft, the method can be applied to test whether a lower order tracking loop can provide satisfactory tracking and thereby save the effect of a higher order loop design

Enhanced collimated GeV monoenergetic ion acceleration from a shaped foil target irradiated by a circularly polarized laser pulse

Using multi-dimensional particle-in-cell (PIC) simulations we study ion acceleration from a foil irradiated by a circularly polarized laser pulse at 1022W/cm^2 intensity. When the foil is shaped initially in the transverse direction to match the laser intensity profile, the center part of the target can be uniformly accelerated for a longer time compared to a usual flat target. Target deformation and undesirable plasma heating are effectively suppressed. The final energy spectrum of the accelerated ion beam is improved dramatically. Collimated GeV quasi-mono-energetic ion beams carrying as much as 18% of the laser energy are observed in multi-dimensional simulations. Radiation damping effects are also checked in the simulations.Comment: 4 pages, 4 figure

Effect of C60_{60} giant resonance on the photoabsorption of encaged atoms

The absolute differential oscillator strengths (DOS's) for the photoabsorption of the Ne, Ar, and Xe atoms encapsulated in the C$_{60}$ have been evaluated using the time-dependent-density-functional-theory, which solves the quantum Liouvillian equation with the Lanczos chain method. The calculations are performed in the energy regions both inside and outside the C$_{60}$ giant resonance. The photoabsorption spectra of the atoms encaged in the C$_{60}$ demonstrate strong oscillations inside the energy range of the C$_{60}$ giant resonance. This type of oscillation cannot be explained by the confinement resonance, but is due to the energy transfer from the C$_{60}$ valence electrons to the photoelectron through the intershell coupling

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