Related papers: Computing the Planar $\beta$-skeleton Depth
The numerical calculation of optical properties (extinction, absorption, scattering and polarisation efficiencies) is often time-consuming for non-spherical and inhomogeneous particles. Where possible analytical methods are therefore to be…
We focus on the high-dimensional linear regression problem, where the algorithmic goal is to efficiently infer an unknown feature vector $\beta^*\in\mathbb{R}^p$ from its linear measurements, using a small number $n$ of samples. Unlike most…
The complexity of the following numerical problem is studied in the quantum model of computation: Consider a general elliptic partial differential equation of order 2m in a smooth, bounded domain Q\subset \R^d with smooth coefficients and…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
We introduce a new jet substructure technique called "soft drop declustering", which recursively removes soft wide-angle radiation from a jet. The soft drop algorithm depends on two parameters--a soft threshold $z_\text{cut}$ and an angular…
In quantum information processing, one often considers inserting a barrier into a box containing a particle to generate one bit of Shannon entropy. We formulate this problem as a one-dimensional Schr\"{o}dinger equation with a…
Monocular depth estimation is an ambiguous problem, thus global structural cues play an important role in current data-driven single-view depth estimation methods. Panorama images capture the complete spatial information of their…
In this paper we explore several applications of the recently introduced spaces of functions of bounded $\beta$-dimensional mean oscillation for $\beta \in (0,n]$ to regularity theory of critical exponent elliptic equations. We first show…
By applying a 2014 result on the distribution of full cylinders, we give a proof of the useful folklore: for any $\beta>1$, the Hausdorff dimension of an arbitrary set in the shift space $S_\beta$ is equal to the Hausdorff dimension of its…
Kernel mean embeddings -- integrals of a kernel with respect to a probability distribution -- are essential in Bayesian quadrature, but also widely used in other computational tools for numerical integration or for statistical inference…
We study the problem of finding confidence ellipsoids for an arbitrary distribution in high dimensions. Given samples from a distribution $D$ and a confidence parameter $\alpha$, the goal is to find the smallest volume ellipsoid $E$ which…
Over the past few years, monocular depth estimation and completion have been paid more and more attention from the computer vision community because of their widespread applications. In this paper, we introduce novel physics…
The regression depth of a hyperplane with respect to a set of n points in R^d is the minimum number of points the hyperplane must pass through in a rotation to vertical. We generalize hyperplane regression depth to k-flats for any k between…
We present SiLU network constructions whose approximation efficiency depends critically on proper hyperparameter tuning. For the square function $x^2$, with optimally chosen shift $a$ and scale $\beta$, we achieve approximation error…
We investigate several computational problems related to the stochastic convex hull (SCH). Given a stochastic dataset consisting of $n$ points in $\mathbb{R}^d$ each of which has an existence probability, a SCH refers to the convex hull of…
Monocular depth foundation models generalize well across scenes, yet they are typically optimized with uniform pixel-wise objectives that do not distinguish user-specified or task-relevant target regions from the surrounding context. We…
Statistical analysis of functional data is challenging due to their complex patterns, for which functional depth provides an effective means of reflecting their ordering structure. In this work, we investigate practical aspects of the…
Let $\R$ be a real closed field, $ {\mathcal Q} \subset \R[Y_1,...,Y_\ell,X_1,...,X_k], $ with $ \deg_{Y}(Q) \leq 2, \deg_{X}(Q) \leq d, Q \in {\mathcal Q}, #({\mathcal Q})=m$, and $ {\mathcal P} \subset \R[X_1,...,X_k] $ with $\deg_{X}(P)…
State-of-the-art monocular depth estimation (MDE) models often struggle in challenging environments, primarily because they overlook robust physical information. To demonstrate this, we first conduct an empirical study by computing the…
Spatial modelling often uses Gaussian random fields to capture the stochastic nature of studied phenomena. However, this approach incurs significant computational burdens (O(n3)), primarily due to covariance matrix computations. In this…