Tootfinder

Review of Three Variants of the k-d Tree
Russell A. Brown
https://arxiv.org/abs/2506.20687 https://arxiv.org/pdf/2506.20687

Review of Three Variants of the k-d Tree
The original description of the k-d tree recognized that rebalancing techniques, such as used to build an AVL tree or a red-black tree, are not applicable to a k-d tree. Hence, in order to build a balanced k-d tree, it is necessary to find the median of a set of data for each recursive subdivision of that set. The sort or selection used to find the median, and the technique used to partition the set about that median, strongly influence the computational complexity of building a k-d tree. This …

Uniform Mean Estimation for Heavy-Tailed Distributions via Median-of-Means
Mikael M{\o}ller H{\o}gsgaard, Andrea Paudice
https://arxiv.org/abs/2506.14673 h…

Uniform Mean Estimation for Heavy-Tailed Distributions via Median-of-Means
The Median of Means (MoM) is a mean estimator that has gained popularity in the context of heavy-tailed data. In this work, we analyze its performance in the task of simultaneously estimating the mean of each function in a class $\mathcal{F}$ when the data distribution possesses only the first $p$ moments for $p \in (1,2]$. We prove a new sample complexity bound using a novel symmetrization technique that may be of independent interest. Additionally, we present applications of our result to $k$…

The ASAS-SN Low Surface Brightness Survey I: Proof-of-Concept and Potential Applications
Evan Jennerjahn, Michael A. Tucker, Benjamin J. Shappee, Christopher S. Kochanek, Subo Dong, Annika H. G. Peter, Jose L. Prieto, K. Z. Stanek, Todd A. Thompson
https://arxiv.org/abs/2506.14873

The ASAS-SN Low Surface Brightness Survey I: Proof-of-Concept and Potential Applications
The ASAS-SN Low Surface Brightness Survey utilizes the $\sim7$ years of g-band CCD data from ASAS-SN (The All-Sky Automated Survey for Supernovae) to create stacked images of the entire sky. It is significantly deeper than previous photographic surveys. Our median/95th percentile cumulative exposure time per field is 58.1/86.8 hours, and our median $3σ$ g-band surface brightness limit off the Galactic plane ($|b| > 20°$) is 26.1 mag arcsec$^{-2}$. We image large-scale diffuse struct…