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Within the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard…
The Kramers-Moyal analysis is a well established approach to analyze stochastic time series from complex systems. If the sampling interval of a measured time series is too low, systematic errors occur in the analysis results. These errors…
We investigate an interpolation/extrapolation method that, given scattered observations of the Fourier transform, approximates its inverse. The interpolation algorithm takes advantage of modelling the available data via a shape-driven…
The additivity principle allows a calculation of current fluctuations and associated density profiles in large diffusive systems. In order to test its validity in the weakly asymmetric exclusion process with open boundaries, we use a…
Verifying entanglement with experimental measurements requires that we take the limitations of experimental techniques into account, while still proving that the data obtained could not have been generated from a classical source. In the…
Richardson extrapolation is applied to a simple first-order upwind difference scheme for the approximation of solutions of singularly perturbed convection-diffusion problems in one dimension. Robust a posteriori error bounds are derived for…
This paper proposes semi-analytical methods to obtain the local permeability for granular soils based on indirect measurements of the local porosity profile in a large coaxial cell permeameter using spatial time-domain reflectometry. The…
A joint characterisation of the controllability and observability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…
A particular instance of the inverse magnetisation problem is considered. It is assumed that the support of a magnetic sample (a source term in the Poisson equation in $\mathbb{R}^3$) is contained in a bounded planar set parallel to the…
Polymer's network is treated as an anisotropic fractal with fractional dimensionality D = 1 + \epsilon close to one. Percolation model on such a fractal is studied. Using the real space renormalization group approach of Migdal and Kadanoff…
The frequency-dependent conductivity is studied for the one-dimensional Hubbard model, using a selection rule, the Bethe ansatz, and symmetries associated with conservation laws. For densities where the system is metallic the absorption…
This article focuses on the mathematical problem of reconstructing dynamic permeability $K(\omega)$ of two-phase composites from data at different frequencies, utilizing the analytic structure of the Stieltjes function representation of…
Time delay estimation has long been an active area of research. In this work, we show that compressive sensing with interpolation may be used to achieve good estimation precision while lowering the sampling frequency. We propose an…
Linear electromagnetic wave scattering systems can be characterized by an impedance matrix that relates the voltages and currents at the ports of the system. When the system size becomes greater than the wavelength of the fields involved,…
We develop a new probabilistic method for deriving deviation estimates in directed planar polymer and percolation models. The key estimates are for exit points of geodesics as they cross transversal down-right boundaries. These bounds are…
We consider residual-based a posteriori error estimators for Galerkin-type discretizations of time-harmonic Maxwell's equations. We focus on configurations where the frequency is high, or close to a resonance frequency, and derive…
This paper investigates the estimation of the self-similarity parameter in fractional processes. We re-examine the Kolmogorov-Smirnov (KS) test as a distribution-based method for assessing self-similarity, emphasizing its robustness and…
Using a recently introduced algorithm for simulating percolation in microcanonical (fixed-occupancy) samples, we study the convergence with increasing system size of a number of estimates for the percolation threshold for an open system…
We study long range density fluctuations (hyperuniformity) in two-dimensional jammed packings of bidisperse droplets. Taking advantage of microfluidics, we systematically span a large range of size and concentration ratios of the two…
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…