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 …

$k$-Approval Veto: A Spectrum of Voting Rules Balancing Metric Distortion and Minority Protection
Fatih Erdem Kizilkaya, David Kempe
https://arxiv.org/abs/2507.17981 https://

$k$-Approval Veto: A Spectrum of Voting Rules Balancing Metric Distortion and Minority Protection
In the context of single-winner ranked-choice elections between $m$ candidates, we explore the tradeoff between two competing goals in every democratic system: the majority principle (maximizing the social welfare) and the minority principle (safeguarding minority groups from overly bad outcomes).To measure the social welfare, we use the well-established framework of metric distortion subject to various objectives: utilitarian (i.e., total cost), $α$-percentile (e.g., median cost for $α= 1/2$…

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…

Connected k-Median with Disjoint and Non-disjoint Clusters
Jan Eube, Kelin Luo, Dorian Reineccius, Heiko R\"oglin, Melanie Schmidt
https://arxiv.org/abs/2507.02774

Connected k-Median with Disjoint and Non-disjoint Clusters
The connected $k$-median problem is a constrained clustering problem that combines distance-based $k$-clustering with connectivity information. The problem allows to input a metric space and an unweighted undirected connectivity graph that is completely unrelated to the metric space. The goal is to compute $k$ centers and corresponding clusters such that each cluster forms a connected subgraph of $G$, and such that the $k$-median cost is minimized. The problem has applications in very differe…

JWST COMPASS: A NIRSpec G395H Transmission Spectrum of the Super-Earth GJ 357 b
Jea Adams Redai, Nicholas Wogan, Nicole L. Wallack, Munazza K. Alam, Artyom Aguichine, Angie Wolfgang, Hannah R. Wakeford, Johanna Teske, Nicholas Scarsdale, Sarah E. Moran, Mercedes Lopez Morales, Annabella Meech, Peter Gao, Anna Gagnebin, Natasha E. Batalha, Natalie M. Batalha, Lili Alderson

JWST COMPASS: A NIRSpec G395H Transmission Spectrum of the Super-Earth GJ 357 b
We present JWST NIRSpec/G395H transmission spectroscopy observations of GJ 357 b, a warm ($T_{\mathrm{eq}} \approx 525$ K) super-Earth ($1.2\ \mathrm{R_{\oplus}} $, $1.84\ \mathrm{M_{\oplus}} $) orbiting a nearby M3-type star, with a median precision of 18 ppm and 27 ppm in NRS1 and NRS2, respectively. These precisions are obtained by binning the spectrum into 53 spectroscopic channels with a resolution of 60 pixels (around 0.02 $μ$m) each. Our analysis of the transmission spectrum reveals no …