Linear compartment models describe the transport of a given material through a set of compartments and can be represented by a directed graph. The parameters of a linear compartment model correspond to the transport rates between different compartments. These parameters are usually estimated from experimental input-output data, by solving the parameter estimation problem. A fundamental prerequi...

We derive a three-term asymptotic expansion for the expected lifetime of Brownian motion and for the torsional rigidity on thin domains in R, and a two-term expansion for the maximum (and corresponding maximizer) of the expected lifetime. The approach is similar to that which we used previously to study the eigenvalues of the Dirichlet Laplacian and consists of scaling the domain in one directi...

By means of Monte Carlo simulations we show that there are two qualitatively different modes of localization of classical waves in 1-D random periodic-on-average systems. States from pass bands and band edges of the underlying band structure demonstrate single parameter scaling with universal behavior. States from the interior of the band gaps do not have universal behavior and require two para...

An adaptive visible/invisible watermarking scheme is done to prevent the privacy and preserving copyright protection of digital data using Hadamard transform based on the scaling factor of the image. The value of scaling factor depends on the control parameter. The scaling factor is calculated to embedded the watermark. Depend upon the control parameter the visible and invisible watermarking is...

By means of Monte Carlo simulations we show that there are two qualitatively different modes of localization of classical waves in 1D random periodic-on-average systems. States from pass bands and band edges of the underlying band structure demonstrate single parameter scaling with universal behavior. States from the interior of the band gaps do not have universal behavior and require two param...

In this paper we investigate the asymptotic properties of nonparametric bayesian mixtures of Betas for estimating a smooth density on [0, 1]. We consider a parameterisation of Betas distributions in terms of mean and scale parameters and construct a mixture of these Betas in the mean parameter, while either fixing the scaling parameter (as a function on the number of observations) or putting a ...

In this work we consider the steady state scaling behavior of directed percolation around the upper critical dimension. In particular we determine numerically the order parameter, its fluctuations as well as the susceptibility as a function of the control parameter and the conjugated field. Additionally to the universal scaling functions, several universal amplitude combinations are considered....

The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We find a new significant scaling parameter in the system, and derive an exact analytical criterion for single parameter scaling which differs from the commonly used condition of phase randomization. The results obtained ar...

We consider the pair correlation functions of both the order parameter field and its square for phase ordering in the O(n) model with nonconserved order parameter, in spatial dimension 2 ≤ d ≤ 3 and spin dimension 1 ≤ n ≤ d. We calculate, in the scaling limit, the exact short-distance singularities of these correlation functions and compare these predictions to numerical simulations. Our result...