Tootfinder

Homotopy Iterators
Paul Breiding, Taylor Brysiewicz, Hannah Friedman
https://arxiv.org/abs/2509.08084 https://arxiv.org/pdf/2509.08084

Homotopy Iterators
We introduce the concept of homotopy iterators for performing polynomial homotopy continuation tasks in a memory efficient manner. The main idea is to push forward an iterator for the start solutions of a homotopy via the function which tracks them along the homotopy. Doing so produces a representation of the target solutions, bypassing the need to hold all solutions in memory. We discuss several applications of this datatype ranging from solution counting to data compression.

#Beagle-Dame #Stella mit #Hundeblick beim Abendessen: "Kriege ich wirklich nix von dem Futter auf dem Tisch wo so lecker riecht? Büdde!" (Es gab übrigens Zwiebelkuchen.)

#SteadySupporter
Eine neue KI-Technologie könnte die #Früherkennung von #Augenkrankheiten bei Kindern revolutionieren.
Forscher in

Mit KI zur besseren Früherkennung: Augenkrankheiten bei Kindern durch Handyfotos diagnostizieren
Chinesische Forscher haben eine KI entwickelt, die Augenkrankheiten bei Kindern anhand von Handyfotos erkennt. Mehr über die Studie und ihre Ergebnisse.

I went to the store and said “sell me your cheapest barolos, I need to stock up”.
This one is incredible. Will have to go back tomorrow and see if I can score a handful more before the long night:

Niedersachsen: CDU fordert pauschales Handyverbot an Schulen, SPD dagegen
In Niedersachsen will die Oppositionspartei CDU ein striktes Handyverbot in Schulen bis zur Oberstufe. Die regierende SPD lehnt die Forderungen ab.

#replyGuys Handbook

🇺🇦 #NowPlaying on KEXP's #DriveTime
Hand Habits:
🎵 Wheel of Change
#HandHabits
https://handhabits.bandcamp.com/track/wheel-of-change
https://open.spotify.com/track/3Pt9wTo0ls4aSGg7EtWh7w

Crisis averted!
https://mastodon.gamedev.place/@jbevain/115183884840190959

The condensed homotopy type of a scheme
Peter J. Haine, Tim Holzschuh, Marcin Lara, Catrin Mair, Louis Martini, Sebastian Wolf with an appendix by Bogdan Zavyalov
https://arxiv.org/abs/2510.07443

The condensed homotopy type of a scheme
We study a condensed version of the étale homotopy type of a scheme, which refines both the usual étale homotopy type of Friedlander-Artin-Mazur and the proétale fundamental group of Bhatt-Scholze. In the first part of this paper, we prove that this condensed homotopy type satisfies descent along integral morphisms and that the expected fiber sequences hold. We also provide explicit computations, for example, for rings of continuous functions. A key ingredient in many of our arguments is a d…