Statistical physics of power fluctuations in mode locked lasers

We present an analysis of the power fluctuations in the statistical steady state of a passively mode locked laser. We use statistical light-mode theory to map this problem to that of fluctuations in a reference equilibrium statistical physics problem, and in this way study the fluctuations non-perturbatively. The power fluctuations, being non-critical, are Gaussian and proportional in amplitude to the inverse square root of the number of degrees of freedom. We calculate explicit analytic expressions for the covariance matrix of the overall, pulse and cw power variables, providing complete information on the single-time power distribution in the laser, and derive a set of fluctuation-dissipation relations between them and the susceptibilities of the steady-state quantities.Comment: 7 pages, 1 figure, RevTe

Power-law size distributions in geoscience revisited

The size or energy of diverse structures or phenomena in geoscience appears to follow power-law distributions. A rigorous statistical analysis of such observations is tricky, though. Observables can span several orders of magnitude, but the range for which the power law may be valid is typically truncated, usually because the smallest events are too tiny to be detected and the largest ones are limited by the system size. We revisit several examples of proposed power-law distributions dealing with potentially damaging natural phenomena. Adequate fits of the distributions of sizes are especially important in these cases, given that they may be used to assess long-term hazard. After reviewing the theoretical background for power-law distributions, we improve an objective statistical fitting method and apply it to diverse data sets. The method is described in full detail and it is easy to implement. Our analysis elucidates the range of validity of the power-law fit and the corresponding exponent, and whether a power-law tail is improved by a truncated log-normal. We confirm that impact fireballs and Californian earthquakes show untruncated power-law behavior, whereas global earthquakes follow a double power law. Rain precipitation over space and time and tropical cyclones show a truncated power-law regime. Karst sinkholes and wildfires, in contrast, are better described by truncated log-normals, although wildfires also may show power-law regimes. Our conclusions only apply to the analyzed data sets, but show the potential of applying this robust statistical technique in the future

Chasing Unbiased Spectra of the Universe

The cosmological power spectrum of the coherent matter flow is measured exploiting an improved prescription for the apparent anisotropic clustering pattern in redshift space. New statistical analysis is presented to provide an optimal observational platform to link the improved redshift distortion theoretical model to future real datasets. The statistical power as well as robustness of our method are tested against 60 realizations of 8 Gpc/h^3 dark matter simulation maps mocking the precision level of upcoming wide--deep surveys. We showed that we can accurately extract the velocity power spectrum up to quasi linear scales of k~0.1 h/Mpc at z = 0.35 and up to k~0.15 h/Mpc at higher redshifts within a couple of percentage precision level. Our understanding of redshift space distortion is proved to be appropriate for precision cosmology, and our statistical method will guide us to righteous path to meet the real world.Comment: 9 pages, 7 figure

A Power Calculator for the Classical Twin Design

Power is a ubiquitous, though often overlooked, component of any statistical analyses. Almost every funding agency and institutional review board requires that some sort of power analysis is conducted prior to data collection. While there are several excellent on line power calculators for independent observations, twin studies pose unique challenges that are not incorporated into these algorithms. The goal of the current manuscript is to outline a general method for calculating power in twin studies, and to provide functions to allow researchers to easily conduct power analyses for a range of common twin models. Several scenarios are discussed to demonstrate the importance of various factors that influence the power within the classical twin design and to serve as examples for the provided functions

A rigorous and efficient asymptotic test for power-law cross-correlation

Podobnik and Stanley recently proposed a novel framework, Detrended Cross-Correlation Analysis, for the analysis of power-law cross-correlation between two time-series, a phenomenon which occurs widely in physical, geophysical, financial and numerous additional applications. While highly promising in these important application domains, to date no rigorous or efficient statistical test has been proposed which uses the information provided by DCCA across time-scales for the presence of this power-law cross-correlation. In this paper we fill this gap by proposing a method based on DCCA for testing the hypothesis of power-law cross-correlation; the method synthesizes the information generated by DCCA across time-scales and returns conservative but practically relevant p-values for the null hypothesis of zero correlation, which may be efficiently calculated in software. Thus our proposals generate confidence estimates for a DCCA analysis in a fully probabilistic fashion