Related papers: Scaling of the Thue-Morse diffraction measure
Dynamic optical sensors, as those based on the reflectivity of isotropic dielectrical interfaces, can be useful for measuring small changes in the refractive index of fluid media. Exact and approximated explicit formulas for their…
We show that scaling arguments are very useful to analyze the dynamics of periodically modulated noisy systems. Information about the behavior of the relevant quantities, such as the signal-to-noise ratio, upon variations of the noise…
For a class of (non-symmetric) diffusion processes on a length space, which in particular include the (reflecting) diffusion processes on a connected compact Riemannian manifold, the exact convergence rate is derived for $({\mathbb E}…
We study a class of dynamical systems given by measure preserving actions of the group $Z^d$ or $R^d$ and generating a set of spectral measures with an extremal rate of the Fourier coefficient decay: $\Hat\sigma(n) = O(|n|^{-1/2+\epsilon})$…
To our knowledge, the existing measure approximation theory requires the diffusion term of the stochastic delay differential equations (SDDEs) to be globally Lipschitz continuous. Our work is to develop a new explicit numerical method for…
The recently developed information-theoretic approach to crystallographic symmetry classifications and quantifications in two dimensions (2D) from digital transmission electron and scanning probe microscope images is adapted for the…
Light propagation through diffusive media can be described by the diffusion equation in a space-time domain. Further, fluorescence can be described by a system of coupled diffusion equations. This paper analyzes time-domain measurements,…
We study sparse recovery with structured random measurement matrices having independent, identically distributed, and uniformly bounded rows and with a nontrivial covariance structure. This class of matrices arises from random sampling of…
Let $A$ be a compact set in ${\mathbb R}^p$ of Hausdorff dimension $d$. For $s\in(0,d)$, the Riesz $s$-equilibrium measure $\mu^s$ is the unique Borel probability measure with support in $A$ that minimizes $$…
We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these…
We construct mesures supported on a compact subset E of the real line having zero principal value of their Cauchy integral a.e. on E with respect to Lebesgue measure and having singular components. E is sufficiently regular (Widom property…
The tip multifractal spectrum of a two-dimensional curve is one way to describe the behavior of the uniformizing conformal map of the complement near the tip. We give the tip multifractal spectrum for a Schramm-Loewner evolution (SLE)…
We propose a method to reconstruct the density of a luminescent source in a highly-scattering medium from ultrasound modulated optical measurements. Our approach is based on the solution to a hybrid inverse source problem for the diffusion…
In the pattern matching approach to imaging science, the process of ``metamorphosis'' is template matching with dynamical templates. Here, we recast the metamorphosis equations of into the Euler-Poincare variational framework of and show…
We provide an overview of standard "projective" quantum measurements with the goal of elucidating connections between theory and experiment. We make use of a unitary "Stinespring" representation of measurements on a dilated Hilbert space…
We present a measurement protocol and a data reduction workflow for obtaining single-crystal X-ray total-scattering datasets that capture both Bragg-peak and diffuse scattering intensities on an absolute (electrons2/atom) scale. We further…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
The \textit{Enriched Riemann Sphere} $\C P_*^1$ is $\C P^1$ plus a set of \textit{infinitesimals}, having the Newton-Puiseux field $\F$ as coordinates. Complex Analysis is extended to the $\F$-\textit{Analysis} (\textit{Newton-Puiseux…
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…
The value of the dynamic critical exponent $z$ is studied for two-dimensional superconducting, superfluid, and Josephson Junction array systems in zero magnetic field via the Fisher-Fisher-Huse dynamic scaling. We find $z\simeq5.6\pm0.3$, a…