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We study the flow harmonic distribution in deformed nuclei. To do this, we use the standard Gram-Charlier method to find the higher-order correction to the well-known Bessel-Gaussian distribution. We find that, apart from the necessity of…
Object detection is a critical part of visual scene understanding. The representation of the object in the detection task has important implications on the efficiency and feasibility of annotation, robustness to occlusion, pose, lighting,…
The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit…
The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…
The level curvature distribution function is studied both analytically and numerically for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the curvature distribution beyond the…
Transforms using random matrices have been found to have many applications. We are concerned with the projection of a signal onto Gaussian-distributed random orthogonal bases. We also would like to easily invert the process through…
In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…
We investigate statistical distributions of differences in gravitational-lensing deflections between two light rays, the so-called lensing excursion angles. A probability distribution function of the lensing excursion angles, which plays a…
The lensing cross section of triaxial halos depends on the relative orientation between a halo's principal axes and its line of sight. Consequently, a lensing subsample of randomly oriented halos is not, in general,randomly oriented. Using…
A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…
Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geometry. Indeed, the theory of distributions is a fundamental…
Simplicial distributions provide a framework for studying quantum contextuality, a generalization of Bell's non-locality. Understanding extremal simplicial distributions is of fundamental importance with applications to quantum computing.…
In this paper we obtain the density function and the distribution function of the distance between two uniformly and independently distributed random points in any right-angled triangle. The density function is derived from the chord length…
Sliced optimal transport reduces optimal transport on multi-dimensional domains to transport on the line. More precisely, sliced optimal transport is the concatenation of the well-known Radon transform and the cumulative density transform,…
An analytical model of a thick asymmetric Gaussian ring is presented for which the visibility function is calculated in two perpendicular directions for baselines up to 6 of the Earth's diameter.
Angular differential imaging (ADI) (Marois et al. 2006) is an observational technique in high contrast imaging where the telescope is used in pupil tracking mode so that the image of the sky rotates with respect to the optical surfaces.…
Distance Geometry is based on the inverse problem that asks to find the positions of points, in a Euclidean space of given dimension, that are compatible with a given set of distances. We briefly introduce the field, and discuss some open…
Correlated ${\cal G}$ distributions can be used to describe the clutter seen in images obtained with coherent illumination, as is the case of B-scan ultrasound, laser, sonar and synthetic aperture radar (SAR) imagery. These distributions…
Divergence measures play a central role and become increasingly essential in deep learning, yet efficient measures for multiple (more than two) distributions are rarely explored. This becomes particularly crucial in areas where the…
We propose dual regression as an alternative to the quantile regression process for the global estimation of conditional distribution functions under minimal assumptions. Dual regression provides all the interpretational power of the…