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A new theoretical technique for understanding, analyzing and developing optical systems is presented. The approach is statistical in nature, where information about an object under investigation is discovered, by examining deviations from a…
Ascertaining the physical state of a system is vital in order to understand and predict its behaviour. Tomography is a standard approach used to determine the form of an unknown state. Here we show that an alternative approach, based on…
Quantitative thermodynamical, dynamical and magnetic properties of the solar and stellar plasmas are obtained by interpreting their emergent non-polarized and polarized spectrum. This inference requires the selection of a set of spectral…
Coherent diffraction imaging (CDI) of single molecules at atomic resolution is a major goal for the x-ray free electron lasers (XFELs). However, during an imaging pulse, the fast laser-induced ionization may strongly affect the recorded…
We proposed the modified version of quantum-mechanical theory of continuous measurements for the case of classical open systems. In our approach the influence of measurement on evolution of distribution function of an open system is…
Phase invariants are important pieces of information about the atomic structures of crystals. There are several mathematical methods in X-ray crystallography to estimate phase invariants. The multi-wave diffraction phenomenon offers a…
The measurement science in realizing and disseminating the unit for pressure in the International System of Units (SI), the pascal (Pa), has been the subject of much interest at the National Institute of Standards and Technology (NIST).…
The charging of insulating samples degrades the quality and complicates the interpretation of images in scanning electron microscopy and is important in other applications, such as particle detectors. In this paper we analyze this…
A method for estimating the relative content of crystalline phases of a multiphase sample, based on probabilistic analysis of the intensities of the diffraction pattern reflexes, has been developed. The method is based on the introduction…
We study random perturbations of multidimensional piecewise expanding maps. We characterize absolutely continuous stationary measures (acsm) of randomly perturbed dynamical systems in terms of pseudo-orbits linking the ergodic components of…
We describe a measurement device principle based on discrete iterations of Bayesian updating of system state probability distributions. Although purely classical by nature, these measurements are accompanied with a progressive collapse of…
We study non-local measures of spectral correlations and their utility in characterizing and distinguishing between the distinct eigenstate phases of quantum chaotic and many-body localized systems. We focus on two related quantities, the…
We develop novel methods to compute auto-correlation functions, or power spectral densities, for chaotic dynamical systems generated by an inverse method whose starting point is an invariant distribution and a two-form. In general, the…
We experimentally investigate the steady states of two granular assemblies differing in their material properties and allowed to exchange volume with each other under external agitation in the vicinity of their jamming transition. We…
Cyclic spectral analysis is a signal processing technique designed to deal with stochastic signals whose statistics vary periodically with time. Pulsar radio emission is a textbook example of this signal class, known as cyclostationary…
We study the spectrum of adjacency matrices of random graphs. We develop two techniques to lower bound the mass of the continuous part of the spectral measure or the density of states. As an application, we prove that the spectral measure…
Novel optical elements containing semitransparent wavelike films embedded into the bulk of transparent material, which form a reflection image without transmitted light distortion, are studied. The dynamic theory of light diffraction by a…
This article is devoted to the detection of parameters in anomalous diffusion from a single passive measurement. More precisely, we consider the simultaneous identification of coefficients as well as a time-dependent source term appearing…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
We consider impulsive dynamical systems defined on compact metric spaces and their respective impulsive semiflows. We establish sufficient conditions for the existence of probability measures which are invariant by such impulsive semiflows.…