Related papers: Support of Continuous Smeary Measures on Spheres

Starting with the spherical Jeans equation, we show that there exists a radius where the mass enclosed depends only on the projected tangential velocity dispersion, assuming that the anisotropy profile slowly varies. This is…

We investigate the asymptotic normality of the posterior distribution in the discrete setting, when model dimension increases with sample size. We consider a probability mass function $\theta_0$ on $\mathbbm{N}\setminus \{0\}$ and a…

Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…

X-ray observations of galaxy clusters are routinely used to derive radial distributions of ICM thermdynamical properties such as density and temperature. However, observations allow us to access quantities projected on the celestial sphere…

We study the flow of equal-volume binary granular mixtures of spheres and dumbbells with different aspect ratios down a rough inclined plane, using the discrete element method. We consider two types of mixtures -- in the first type the…

We analyze the creeping flow generated by a spherical particle moving through a viscous fluid with nematic directional order, in which momentum diffusivity is anisotropic and which opposes resistance to bending. Specifically, we provide…

The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…

In this paper, we study the spherical cardioid distribution, a higher-dimensional and higher-order generalization of the circular cardioid distribution. This distribution is rotationally symmetric and generates unimodal, multimodal, axial,…

Distinguishing between uniform and non-uniform sample distributions is a common problem in directional data analysis; however for many tests, non-uniform distributions exist that fail uniformity rejection. By merging directional statistics…

We prove that a homeomorphism of a compact metric space has an expansive measure \cite{ms} if and only if it has many ones with invariant support. We also study homeomorphisms for which the expansive measures are dense in the space of Borel…

Within the framework of hierarchical clustering we show that a simple Press-Schechter-like approximation, based on spherical dynamics, provides a good estimate of the evolution of the density field in the quasi-linear regime up to $\Sigma…

One of the basic aims of this paper is to study the relationship between the geometry of ``hypersurface like'' subsets of Euclidean space and the properties of the measures they support. In this context we show that certain doubling…

Motivated by the fact that circular or spherical data are often much concentrated around a location $\pmb\theta$, we consider inference about $\pmb\theta$ under "high concentration" asymptotic scenarios for which the probability of any…

We quantify the stellar rotation of galaxies by computing the $\lambda_{R}$ parameter, a proxy for the stellar angular momentum in a sample of 106 galaxies with redshift 0.1 $<$ z $<$ 0.8 and stellar masses from $\sim$10$^{7.5}$ to…

A variety of tools can be used for spreading metal, ceramic, and polymer feedstocks in powder bed additive manufacturing methods. Rollers are often employed when spreading powders with limited flowability, as arises in powders comprising…

Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static…

For $d \ge 2$, let $X$ be a random vector having a Bingham distribution on $\mathcal{S}^{d-1}$, the unit sphere centered at the origin in $\R^d$, and let $\Sigma$ denote the symmetric matrix parameter of the distribution. Let $\Psi(\Sigma)$…

We prove the scalar curvature rigidity for $L^\infty$ metrics on $\mathbb S^n\backslash\Sigma$, where $\mathbb S^n$ is the $n$-dimensional sphere with $n\geq 3$ and $\Sigma$ is a closed subset of $\mathbb S^n$ of codimension at least…

Two drastically different theories predict the marginal criticality of jamming. The full replica symmetry breaking (fullRSB) theory [1-4] predicts the power-law distributions of weak contact forces and small inter-particle gaps in…

We propose a new probabilistic characterization of the uniform distribution on the hypersphere in terms of the distribution of pairwise inner products, extending the ideas of \citep{cuesta2009projection,cuesta2007sharp} in a data-driven…