Here we apply a recently developed maximum likelihood method for determining best-fit parameterised lens models to observations of the rich lensing cluster Abell 1689. The observations that we use were taken with the ESO/MPG Wide Field Imager. The wide field-of-view enables us to use the weakly lensed images of faint background objects on an unsurpassed range of scales, 0.12 h−1 Mpc < R < 1.8 h...

We report on an analytical study of the statistics of conductance, g, and shot-noise power, p, for a chaotic cavity with arbitrary numbers N1,2 of channels in two leads and symmetry parameter β = 1, 2, 4. With the theory of Selberg’s integral the first four cumulants of g and first two cumulants of p are calculated explicitly. We give analytical expressions for the conductance and shot-noise di...

We report our efforts to constrain the form of the low-mass star and brown dwarf mass function via Bayesian inference. Recent surveys of M, L, and T dwarfs in the local solar neighborhood are an essential component of our study. Uncertainties in the age distribution of local field stars make reliable inference complicated. We adopt a wide range of plausible assumptions about the rate of galacti...

The distribution of many real discrete random variables (e.g., the frequency of words, the population of cities) can be approximated by a zeta distribution, that is known popularly as Zipf’s law, or power law in physics. Here we revisit the relationship between power law distribution of a magnitude and the corresponding power relationship between the magnitude of a certain element and its rank....

We measure the power spectrum of galaxy clustering in real space from the APM Galaxy Survey. We present an improved technique for the numerical inversion of Limber’s equation that relates the angular clustering of galaxies to an integral over the power spectrum in three dimensions. Our approach is underpinned by a large ensemble of mock galaxy catalogues constructed from the Hubble Volume N-bod...

We report empirical studies on the personal income distribution, and clarify that the distribution pattern of the lognormal with power law tail is the universal structure. We analyze the temporal change of Pareto index and Gibrat index to investigate the change of the inequality of the income distribution. In addition some mathematical models which are proposed to explain the power law distribu...

It is generally recognized that economical systems, and more in general complex systems, are characterized by power law distributions. Sometime, these distributions show a changing of the slope in the tail so that, more appropriately, they show a multi-power law behavior. We present a method to derive analytically a two-power law distribution starting from a single power law function recently o...

Nanoflares have been proposed as the main source of heating of the solar corona. However, detecting them directly has so far proved elusive, and extrapolating to them from the properties of larger brightenings gives unreliable estimates of the power-law exponent α characterising their distribution. Here we take the approach of statistically modelling light curves representative of the quiet Sun...

In this paper we study Copy Number Variation (CNV) data. The underlying process generating CNV segments is generally assumed to be memory-less, giving rise to an exponential distribution of segment lengths. In this paper, we provide evidence from cancer patient data, which suggests that this generative model is too simplistic, and that segment lengths follow a power-law distribution instead. We...

We consider a generalization of homogeneous and isotropic Çinlar velocity fields to capture power-law spectra. The random velocity field is non-Gaussian with a representation motivated by Lagrangian and Eulerian observations. A wide range of turbulent flows can be generated by varying the stochastic parameters of the model. The velocity field being a functional version of Poisson shot-noise is ...