Related papers: Support of Continuous Smeary Measures on Spheres
We use numerical simulation to investigate and analyze the way that rigid disks and spheres arrange themselves when compressed next to incommensurate substrates. For disks, a movable set is pressed into a jammed state against an ordered…
The Sobolev regularity of invariant measures for diffusion processes is proved on non-smooth metric measure spaces with synthetic lower Ricci curvature bounds. As an application, the symmetrizability of semigroups is characterized, and the…
The wall shear rate distribution P(gamma) is investigated for pressure-driven Stokes flow through random arrangements of spheres at packing fractions 0.1 <= phi <= 0.64. For dense packings, P(gamma) is monotonic and approximately…
Self-gravitating stellar disks with random motion support both exponentially growing and, in some cases, purely oscillatory axisymmetric bending modes, unlike their cold disk counterparts. A razor-thin disk with even a very small degree of…
Discrepancy measures between probability distributions, often termed statistical distances, are ubiquitous in probability theory, statistics and machine learning. To combat the curse of dimensionality when estimating these distances from…
We study the absolute continuity with respect to the Lebesgue measure of the distribution of the nodal volume associated with a smooth, non-degenerated and stationary Gaussian field $(f(x), {x \in \mathbb R^d})$. Under mild conditions, we…
We investigate confined shear thickening suspensions for which the sample thickness is comparable to the particle dimensions. Rheometry measurements are presented for densely packed suspensions of spheres and rods with aspect ratios 6 and…
We consider a geometrically finite discrete group of conformal transformations of the sphere. Further we consider distributions which are supported on the limit set and are invariant with conformal weight. We estimate their regularity in…
The problem of estimating the support of a distribution is of great importance in many areas of machine learning, computer science, physics and biology. Most of the existing work in this domain has focused on settings that assume perfectly…
We consider the filtering and smoothing problems for an infinite-dimensional diffusion process X, observed through a finite-dimensional representation at discrete points in time. At the heart of our proposed methodology lies the…
We derive fundamental asymptotic results for the expected covering radius $\rho(X_N)$ for $N$ points that are randomly and independently distributed with respect to surface measure on a sphere as well as on a class of smooth manifolds. For…
A first measurement of beam spin asymmetries for $\pi^+\pi^0$ and $\pi^-\pi^0$ pairs in semi-inclusive deep inelastic scattering is reported. The asymmetries in the dihadron angular distributions were measured from the scattering of a 10.6…
We consider complete non-compact manifolds with either a sub-quadratic growth of the norm of the Riemann curvature, or a sub-quadratic growth of both the norm of the Ricci curvature and the squared inverse of the injectivity radius. We show…
We study turbulent channel flows of monodisperse and polydisperse suspensions of finite-size spheres by means of Direct Numerical Simulations using an immersed boundary method to account for the dispersed phase. Suspensions with 3 different…
The directional precision of the sample mean estimator was calculated analytically for the offset exponential and normal distributions in three-dimensional space both for a finite sample and for limiting cases. It was shown that the…
Various substances in the liquid state tend to form droplets. In this paper the shape of such droplets is investigated within the spherical model of a lattice gas. We show that in this case the droplet boundary is always diffusive, as…
We present new explicit upper bounds for the smoothness of the distribution of the random diagonal sum $S_n=\sum_{j=1}^nX_{j,\pi(j)}$ of a random $n\times n$ matrix $X=(X_{j,r})$, where the $X_{j,r}$ are independent integer valued random…
We develop a test for spherical symmetry of a multivariate distribution $\Pr$ that works well even when the dimension of the data $d$ is larger than the sample size $n$. We propose a non-negative measure of spherical asymmetry $\zeta(\Pr)$…
We derive fundamental sampling bounds for smooth signals in continuous settings without sparsity assumptions. By introducing the Fourier ratio as a measure of spectral compressibility induced by smoothness, we obtain explicit, deterministic…
We investigate the properties of forced inertial modes of a rotating fluid inside a spherical shell. Our forcing is tidal like, but its main property is that it is on the large scales. Our solutions first confirm some analytical results…