Related papers: A Sparse Multicover Bifiltration of Linear Size

Future cellular systems will likely employ massive bi-dimensional arrays to improve performance by large array gain and more accurate spatial filtering, motivating the design of low-complexity signal processing methods. We propose…

Diversity maximization is an important geometric optimization problem with many applications in recommender systems, machine learning or search engines among others. A typical diversification problem is as follows: Given a finite metric…

Two-sample feature selection is the problem of finding features that describe a difference between two probability distributions, which is a ubiquitous problem in both scientific and engineering studies. However, existing methods have…

For any two point sets $A,B \subset \mathbb{R}^d$ of size up to $n$, the Chamfer distance from $A$ to $B$ is defined as $\text{CH}(A,B)=\sum_{a \in A} \min_{b \in B} d_X(a,b)$, where $d_X$ is the underlying distance measure (e.g., the…

We consider the problem of matching a metric space $(X,d_X)$ of size $k$ with a subspace of a metric space $(Y,d_Y)$ of size $n \geq k$, assuming that these two spaces have constant doubling dimension $\delta$. More precisely, given an…

Consider the strata of primitive $k$-differentials on the Riemann sphere whose singularities, except for two, are poles of order divisible by $k$. The map that assigns to each $k$-differential the $k$-residues at these poles is a ramified…

Scalar wave scattering by many small particles of arbitrary shapes with impedance boundary condition is studied. The problem is solved asymptotically and numerically under the assumptions a << d << lambda, where k = 2pi/lambda is the wave…

Recently, cross-source point cloud registration from different sensors has become a significant research focus. However, traditional methods confront challenges due to the varying density and structure of cross-source point clouds. In order…

We investigate minimal-perimeter configurations of two finite sets of points on the square lattice. This corresponds to a lattice version of the classical double-bubble problem. We give a detailed description of the fine geometry of…

As a popular representation of 3D data, point cloud may contain noise and need to be filtered before use. Existing point cloud filtering methods either cannot preserve sharp features or result in uneven point distribution in the filtered…

Clustering is an important technique for identifying structural information in large-scale data analysis, where the underlying dataset may be too large to store. In many applications, recent data can provide more accurate information and…

Let $P$ be a set of points in $\mathbb{R}^d$, $B$ a bicoloring of $P$ and $\Oo$ a family of geometric objects (that is, intervals, boxes, balls, etc). An object from $\Oo$ is called balanced with respect to $B$ if it contains the same…

It is a common contention that it is an ``impossible mission'' to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level. In this paper, we investigate such…

This paper introduces the notion of $k$-isoparametric hypersurface in an $(n+1)$-dimensional Riemannian manifold for $k=0,1,...,n$. Many fundamental and interesting results (towards the classification of homogeneous hypersurfaces among…

Accurate monocular depth estimation is crucial for 3D scene understanding, but existing methods often blur depth at object boundaries, introducing spurious intermediate 3D points. While achieving sharp edges usually requires very…

We use confocal microscopy to study a random close packed sample of colloidal particles. We introduce an algorithm to estimate the size of each particle. Taking into account their sizes, we compute the compressibility of the sample as a…

We apply state-of-the-art computational geometry methods to the problem of reconstructing a time-varying sea surface from tide gauge records. Our work builds on a recent article by Nitzke et al.~(Computers \& Geosciences, 157:104920, 2021)…

We create mechanically stable (MS) packings of bidisperse disks using an algorithm in which we successively grow or shrink soft repulsive disks followed by energy minimization until the overlaps are vanishingly small. We focus on small…

We consider quasi-interpolation with a main application in radial basis function approximations and compression in this article. Constructing and using these quasi-interpolants, we consider wavelet and compression-type approximations from…

We formalize the notion of sampling a function using k-d darts. A k-d dart is a set of independent, mutually orthogonal, k-dimensional subspaces called k-d flats. Each dart has d choose k flats, aligned with the coordinate axes for…