Related papers: Computing the Planar $\beta$-skeleton Depth

Classical results of Brent, Kuck and Maruyama (IEEE Trans. Computers 1973) and Brent (JACM 1974) show that any algebraic formula of size s can be converted to one of depth O(log s) with only a polynomial blow-up in size. In this paper, we…

For the first time, the calculation of the nuclear matrix element of the double-$\beta$ decay of $^{100}$Mo, with and without the emission of two neutrinos, is performed in the framework of the nuclear shell model. This task is accomplished…

A distance oracle (DO) with stretch $(\alpha, \beta)$ for a graph $G$ is a data structure that, when queried with vertices $s$ and $t$, returns a value $\widehat{d}(s,t)$ such that $d(s,t) \le \widehat{d}(s,t) \le \alpha \cdot d(s,t) +…

Finding the diameter of a graph in general cannot be done in truly subquadratic assuming the Strong Exponential Time Hypothesis (SETH), even when the underlying graph is unweighted and sparse. When restricting to concrete classes of graphs…

Tabular data learning has extensive applications in deep learning but its existing embedding techniques are limited in numerical and categorical features such as the inability to capture complex relationships and engineering. This paper…

Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…

A functional data depth provides a center-outward ordering criterion which allows the definition of measures such as median, trimmed means, central regions or ranks in a functional framework. A functional data depth can be global or local.…

A method to calculate the nuclear double beta decay ($2\nu\beta\beta$- and $0\nu\beta\beta$-) amplitudes within the continuum random phase approximation (cQRPA) is formulated. Calculations of the $\beta\beta$ transition amplitudes within…

The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an…

Limited DXA access hinders osteoporosis screening. This proof-of-concept study proposes using widely available knee X-rays for opportunistic Bone Mineral Density (BMD) estimation via deep learning, emphasizing robust uncertainty…

Nuclear $\beta$ decay is a key element of the astrophysical rapid neutron capture process ($r$-process). In this paper, we present state-of-the-art global $\beta$-decay calculations based on the quantified relativistic nuclear energy…

We discuss the structure of beta functions as determined by the recursive nature of Dyson--Schwinger equations turned into an analysis of ordinary differential equations, with particular emphasis given to quantum electrodynamics. In…

We noisily observe solutions of an ordinary differential equation $\dot u = f(u)$ at given times, where $u$ lives in a $d$-dimensional state space. The model function $f$ is unknown and belongs to a H\"older-type smoothness class with…

We study the sublinear multivariate mean estimation problem in $d$-dimensional Euclidean space. Specifically, we aim to find the mean $\mu$ of a ground point set $A$, which minimizes the sum of squared Euclidean distances of the points in…

Omnidirectional depth estimation presents a significant challenge due to the inherent distortions in panoramic images. Despite notable advancements, the impact of projection methods remains underexplored. We introduce Multi-Cylindrical…

We develop a phase estimation method with a distinct feature: its maximal runtime (which determines the circuit depth) is $\delta/\epsilon$, where $\epsilon$ is the target precision, and the preconstant $\delta$ can be arbitrarily close to…

For computing the exact value of the halfspace depth of a point w.r.t. a data cloud of $n$ points in arbitrary dimension, a theoretical framework is suggested. Based on this framework a whole class of algorithms can be derived. In all of…

Existing methods for rotation estimation between two spherical ($\mathbb{S}^2$) patterns typically rely on spherical cross-correlation maximization between two spherical function. However, these approaches exhibit computational complexities…

We provide a detailed estimate for the logical resource requirements of the quantum linear system algorithm (QLSA) [Phys. Rev. Lett. 103, 150502 (2009)] including the recently described elaborations [Phys. Rev. Lett. 110, 250504 (2013)].…

Quantitative computed tomography (QCT) is a standard method to determine bone mineral density (BMD) in the spine. Traditionally single 8 - 10 mm thick slices have been analyzed only. Current spiral CT scanners provide true 3D acquisition…