Related papers: Hyperuniform point sets on the sphere: probabilist…
Density-based clustering methodology has been widely considered in the statistical literature for classifying Euclidean observations. However, this approach has not been contemplated for directional data yet. In this work, directional…
In this paper we provide a framework for the study of isoperimetric problems in finitely generated group, through a combinatorial study of universal covers of compact simplicial complexes. We show that, when estimating filling functions,…
After a historical discussion of classical uniformisation results for Riemann surfaces, of problems appearing in higher dimensions, and of uniformisation results for projective manifolds with trivial or ample canonical bundle, we introduce…
We define a determinantal point process on the complex projective space that reduces to the so-called spherical ensemble for complex dimension 1 under identification of the 2-sphere with the Riemann sphere. Through this determinantal point…
We study hyperuniform properties in various two-dimensional periodic and quasiperiodic point patterns. Using the histogram of the two-point distances, we develop an efficient method to calculate the hyperuniformity order metric, which…
Hyperuniform materials, characterized by anomalously suppressed long-wavelength density fluctuations, exhibit unique optical and photonic properties distinct from both crystalline and random media. While most prior studies have focused on…
This paper introduces a new lifting method for analyzing convergence of continuous-time distributed synchronization/consensus systems on the unit sphere. Points on the d-dimensional unit sphere are lifted to the (d+1)-dimensional Euclidean…
We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases…
We present a conceptually simple, flexible, and universal visual perception head for variant visual tasks, e.g., classification, object detection, instance segmentation and pose estimation, and different frameworks, such as one-stage or…
With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral…
The spherical ensemble is a well-studied determinantal process with a fixed number of points on the sphere. The points of this process correspond to the generalized eigenvalues of two appropriately chosen random matrices, mapped to the…
Disordered hyperuniform dispersions are exotic amorphous two-phase materials characterized by an anomalous suppression of long-wavelength volume-fraction fluctuations, endowing them with novel physical properties. While such unusual…
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…
Consider the projection of a smooth irreducible surface in $\mathbb{P}^3$ from a point. The uniform position principle implies that the monodromy group of such a projection from a general point in $\mathbb{P}^3$ is the whole symmetric…
Estimating and disentangling epistemic uncertainty, uncertainty that is reducible with more training data, and aleatoric uncertainty, uncertainty that is inherent to the task at hand, is critically important when applying machine learning…
In previous work [Phys. Rev. X 5, 021020 (2015)], it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier-space in the sense that the the structure factor is exactly zero in a spherical region around 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…
Clustering on the unit hypersphere is a fundamental problem in various fields, with applications ranging from gene expression analysis to text and image classification. Traditional clustering methods are not always suitable for unit sphere…
Tilings based on the cut and project method are key model systems for the description of aperiodic solids. Typically, quantities of interest in crystallography involve averaging over large patches, and are well defined only in the…
A variety of performance demands are being placed on material systems, including desirable mechanical, thermal, electrical, optical, acoustic and flow properties. The purpose of the present article is to review the emerging field of…