Related papers: Spherical structure factor and classification of h…
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,…
In the previous paper [25], Stolarsky's invariance principle, known for point distributions on the Euclidean spheres [27], has been extended to the real, complex, and quaternionic projective spaces and the octonionic projective plane.…
Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting,…
The concept of hyperuniformity has been a useful tool in the study of large-scale density fluctuations in systems ranging across the natural and mathematical sciences. One can rank a large class of hyperuniform systems by their ability to…
Arrays of nanoparticles exploited in light scattering applications commonly only feature either a periodic or a rather random arrangement of its constituents. For the periodic case, light scattering is mostly governed by the strong spatial…
The random packing fraction of binary particles in D-dimensional Euclidean space R^D is studied using a geometric approach. First, the binary packing fraction of assemblies with small size difference are studied, using the excluded volume…
Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…
We give an explicit estimate of the distance of a closed, connected, oriented and immersed hypersurface of a space form to a geodesic sphere and show that the spherical closeness can be controlled by a power of an integral norm of the…
Reliable decision-making in complex multi-agent systems requires calibrated predictions and interpretable uncertainty. We introduce SphUnc, a unified framework combining hyperspherical representation learning with structural causal…
This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…
We prove rigidity for hypersurfaces with boundary in the unit $(n+1)$-sphere with scalar curvature bounded below by $n(n-1)$. Under appropriate boundary conditions, the hypersurfaces are shown to be part of the equatorial spheres. The lower…
In this paper, we characterize round spheres in the Euclidean space under some suitable conditions on the r-mean curvature.
Disordered hyperuniform structures are an exotic state of matter having vanishing long-wavelength density fluctuations similar to perfect crystals but without long-range order. Although its importance in materials science has been brought…
We present a pedagogical, but by no means complete, review of weak scale supersymmetry phenomenology. After a general introduction to the new particles that must be present in any supersymmetric framework, we describe how to write down…
Background: Saturation of nuclear density is a fundamental property of atomic nuclei but in reality, the nuclear internal density distribution is not uniform, e.g., some nuclei are known to have the so-called bubble structure, in which the…
By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
Hypersphere classification is a classical and foundational method that can provide easy-to-process explanations for the classification of real-valued and binary data. However, obtaining an (ideally concise) explanation via hypersphere…
In directional statistics, the von Mises-Fisher (vMF) distribution is one of the most basic and popular probability distributions for data on the unit hypersphere. Recently, the spherical normal (SN) distribution was proposed as an…
Detecting structures at the particle scale within plastically deformed crystalline materials allows a better understanding of the occurring phenomena. While previous approaches mostly relied on applying hand-chosen criteria on different…
We characterize model theoretic properties of the Urysohn sphere as a metric structure in continuous logic. In particular, our first main result shows that the theory of the Urysohn sphere is $\text{SOP}_n$ for all $n\geq 3$, but does not…