On confidence intervals from simulation of finite Markov chains

Consider a finite state irreducible Markov reward chain. It is shown that there exist simulation estimates and confidence intervals for the expected first passage times and rewards as well as the expected average reward, with 100% coverage probability. The length of the confidence intervals converges to zero with probability one as the sample size increases; it also satisfies a large deviations property.     

Charged cosmic strings interacting with gravitational and electromagnetic waves

Under a particular choice of the Ernst potential, we solve analytically the Einstein–Maxwell equations to derive a new exact solution depending on five parameters: the mass, the angular-momentum (per unit mass), α, the electromagnetic-field strength, k, the parameter-p and the Kerr-NUT parameter, l. This (Petrov Type D) solution is cylindrically symmetric and represents the curved background around a charged, rotating cosmic string, surrounded by gravitational and electromagnetic waves, under the influence of the Kerr-NUT parameter. A C-energy study in the radiation zone suggests that both the incoming and the outgoing radiation is gravitational, strongly focused around the null direction and preserving its profile. In this case, the absence of the k-parameter from the C-energy implies that, away from the linear defect the electromagnetic field is too weak to contribute to the energy-content of the cylindrically symmetric space-time under consideration. In order to explain this result, we have evaluated the Weyl and the Maxwell scalars near the axis of the linear defect and at the spatial infinity. Accordingly, we have found that the electromagnetic field is concentrated (mainly) in the vicinity of the axis, while falling-off prominently at large radial distances. However, as long as k ≠ 1, the non-zero Kerr-NUT parameter enhances those scalars, both near the axis and at the spatial infinity, introducing some sort of gravitomagnetic contribution.     

Detecting signatures of stochastic self-organization in US money and velocity measures

In this paper, we continue the research by Serletis [Random walks, breaking trend functions, and the chaotic structure of the velocity of money, J. Bus. Econ. Stat. 13 (1995) 453-458] and Serletis and Shintani [Chaotic monetary dynamics with confidence, J. Macroeconomics 28 (2006) 228-252] by applying the method of detrended fluctuation analysis (DFA)—introduced by Peng et al. [Mosaic organization of DNA nucleotides, Phys. Rev. E 49 (1994) 1685-1689] and adapted to the analysis of long-range correlations in economic data by Uritskaya [Forecasting of magnitude and duration of currency crises based on analysis of distortions of fractal scaling in exchange rate fluctuations, Noise and fluctuations in econophysics and finance, Proc. SPIE 5848 (2005) 17-26; Fractal methods for modeling and forecasting of currency crises, in: Proceedings of the fourth International Conference on Modeling and Analysis of Safety and Risk in Complex Systems, SPbSU Press, St.Petersburg, 2005, pp. 210-215]—to investigate the dynamical structure of United States money and velocity measures. We use monthly data over the time period from 1959:1 to 2006:2, at each of the four levels of monetary aggregation, M1, M2, M3, and MZM, making comparisons among simple-sum, Divisia, and currency equivalent (CE) methods of aggregation. The results suggest that the sum and Divisia monetary aggregates are more appropriate for measuring long-term tendencies in money supply dynamics while the CE aggregates are more sensitive measures of short-term processes in the economy.     

Biocompatible functionalisation of starch

The enzyme catalysed esterification of starch and fatty acids with terminal triple bonds is described. This material can be used as an acceptor for azide containing molecules, through azide/alkyne cycloaddition. The potential is illustrated by the production of fluorescently-labelled starch, and a biotinylated derivative which can bind streptavidin.