Moran's genetics model via electric networks

Using the electric approach, we derive exact and asymptotic closed form formulas for hitting times in symmetric cases of the Moran's genetics model.     

Combinatorial solutions to normal ordering of bosons

We present a combinatorial method of constructing solutions to the normal ordering of boson operators. Generalizations of standard combinatorial notions — the Stirling and Bell numbers, Bell polynomials and Dobinski relations — lead to calculational tools, which allow to find explicitly normally ordered forms for a large class of operator functions. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Triggered single photons and entangled photons from a quantum dot microcavity

Current quantum cryptography systems are limited by the attenuated coherent pulses they use as light sources: a security loophole is opened up by the possibility of multiple-photon pulses. By replacing the source with a single-photon emitter, transmission rates of secure information can be improved. We have investigated the use of single self-assembled InAs/GaAs quantum dots as such single-photon sources, and have seen a tenfold reduction in the multi-photon probability as compared to Poissonian pulses. An extension of our experiment should also allow for the generation of triggered, polarization-entangled photon pairs. The utility of these light sources is currently limited by the low efficiency with which photons are collected. However, by fabricating an optical microcavity containing a single quantum dot, the spontaneous emission rate into a single mode can be enhanced. Using this method, we have seen 78% coupling of single-dot radiation into a single cavity resonance. The enhanced spontaneous decay should also allow for higher photon pulse rates, up to about 3 GHz. Received 8 July 2001 and Received in final form 25 August 2001     

Information guided noise reduction for Monte Carlo integration of oscillatory functions

A simple procedure for decreasing the statistical error associated with Monte Carlo integration of oscillatory functions is presented. The method uses available information about the integral of a similar oscillatory function to correlate the estimates of the positive and negative components of the integral. Numerical tests show that information guided noise reduction (IGNoR) leads to substantial decrease of the statistical error, allowing meaningful results to be obtained with a fraction of the cost required to attain similar precision from the raw Monte Carlo estimate.     

Optimization of separations of alkyl-substituted phenolate anions by capillary zone electrophoresis

Anions of alkylphenols have very similar electrophoretic mobilities in CZE owing to their very small differences in size and the narrow range of their pK_a values. By studying electrophoretic mobility as a function both of pH and of the amount of acetonitrile in the electrolyte solution, optimum separation conditions were determined. It was possible to separate a group of methyl-substituted phenols, including several positional isomers. Mixtures containing n-propyl and isopropyl phenols and 1°, 2°, and 3° butylphenols could be resolved.     

The Forbes 400, the Pareto power-law and efficient markets

Statistical regularities at the top end of the wealth distribution in the United States are examined using the Forbes 400 lists of richest Americans, published between 1988 and 2003. It is found that the wealths are distributed according to a power-law (Pareto) distribution. This result is explained using a simple stochastic model of multiple investors that incorporates the efficient market hypothesis as well as the multiplicative nature of financial market fluctuations.     

Model-dependent nature of blowtorch effect on the escape and equilibration rates

We analyze the relaxation behavior of a bistable system when the background temperature profile is inhomogeneous due to the presence of a localized hot region (blowtorch) on one side of the potential barrier. Since the diffusion equation for inhomogeneous medium is model-dependent, we consider two physical models to study the kinetics of such system. Using a conventional stochastic method, we obtain the escape and equilibration rates of the system for the two physical models. For both models, we find that the hot region enhances the escape rate from the well where it is placed while it retards the escape rate from the other well. However, the value of the escape rate from the well where the hot region is placed differs for the two models while that of the escape rate from the other well is identical for both. This work, for the first time, gives a detailed report of the similarities and differences of the escape rates and, hence, exposes the common and distinct features of the two known physical models in determining the way the bistable system relaxes. Received 25 September 2001