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Lagrangian descriptors provide a global dynamical picture of the geometric structures for arbitrarily time-dependent flows with broad applications. This paper develops a mathematical framework for computing Lagrangian descriptors when…
We describe a statistical method to avoid biased estimation of the content of different particle species. We consider the case when the particle identification information strongly depends on some kinematical variables, whose distributions…
The Fourier spectral techniques that are common in Astronomy for analyzing periodic or multi-periodic light-curves lose their usefulness when they are applied to unsteady light-curves. We review some of the novel techniques that have been…
Measures of discordance between datasets have become an essential part of cosmological analyses. It is important to accurately evaluate the significance of such discordances when present. We propose here a Bayesian interpretation of…
The well-known diffusion theory describes propagation of light and electromagnetic waves in complex media. While diffusion theory is known to fail both for predominant forward scattering or strong absorption, its precise range of validity…
Computer representations of real numbers are necessarily discrete, with some finite resolution, discreteness, quantization, or minimum representable difference. We perform astrometric and photometric measurements on stars and co-add…
When fitting theory to data in the presence of background uncertainties, the question of whether the spectral shape of the background happens to be similar to that of the theoretical model of physical interest has not generally been…
The massive data sets from today's particle physics experiments present a variety of challenges amenable to the tools developed by the statistics community. From the real-time decision of what subset of data to record on permanent storage,…
In this article: a) a method is developed for calculating volumetric diagrams of elastic scattering of microparticles (in particular, electrons and photons) on single-layer and multi-layer statistically uneven surfaces; b) the diffraction…
We analyse the covariance of the one-dimensional mass power spectrum along lines of sight. The covariance reveals the correlation between different modes of fluctuations in the cosmic density field and gives the sample variance error for…
Many existing approaches for estimating parameters in settings with distributional shifts operate under an invariance assumption. For example, under covariate shift, it is assumed that $p(y|x)$ remains invariant. We refer to such…
Searches for variations of fundamental constants require accurate measurement errors. There are several potential sources of errors and quantifying each one accurately is essential. This paper addresses one source of uncertainty relating to…
The surface brightness fluctuations (SBF) method is a statistical method applied on image pixels in different bands. This contribution aims to distinguish between the observational (statistical) method and the theoretical (probabilistic)…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
The determination of chemical abundances from stellar spectra is considered a mature field of astrophysics. Digital spectra of stars are recorded and processed with standard techniques, much like samples in the biological sciences.…
We study evolution equations of drift-diffusion type when various parameters are random. Motivated by applications in pedestrian dynamics, we focus on the case when the total mass is, due to boundary or reaction terms, not conserved. After…
Ptychography, as an essential tool for high-resolution and nondestructive material characterization, presents a challenging large-scale nonlinear and non-convex inverse problem; however, its intrinsic photon statistics create clear…
We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…
Description of detection and emission in terms of the photon localization is discussed. It is shown that the standard representation of plane waves of photons should be revised to take into consideration the boundary conditions caused by…
A number of physical processes show some form of bifurcation or periodic splintering of a single distribution into two new ones. Recently, it has been noted that cavity searches for interactions between photons and exotic fields may also…