Tootfinder

@… it’s Kiril Vatev 😅 https://www.kirilv.com/canvas-confetti/

This https://arxiv.org/abs/2402.07980 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Lanczos spectrum for random operator growth
Krylov methods have reappeared recently, connecting physically sensible notions of complexity with quantum chaos and quantum gravity. In these developments, the Hamiltonian and the Liouvillian are tridiagonalized so that Schrodinger/Heisenberg time evolution is expressed in the Krylov basis. In the context of Schrodinger evolution, this tridiagonalization has been carried out in Random Matrix Theory. We extend these developments to Heisenberg time evolution, describing how the Liouvillian can b…

From @scottduncanwx@instagram.com
Too many records to count. Yet another astonishing weekend of warmth for Europe.
April national records exceeded in Slovenia 🇸🇮, Bosnia & Herzegovina 🇧🇦 and Croatia 🇭🇷 but many other notable site records fell.
Change is already on its way though...
https://www.instagram…

This https://arxiv.org/abs/2312.11677 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Krylov complexity for non-local spin chains
Building upon recent research in spin systems with non-local interactions, this study investigates operator growth using the Krylov complexity in different non-local versions of the Ising model. We find that the non-locality results in a faster scrambling of the operator to all sites. While the saturation value of Krylov complexity of local integrable and local chaotic theories differ by a significant margin, this difference is much suppressed when non-local terms are introduced in both regimes…

Stability and Multigroup Fairness in Ranking with Uncertain Predictions
Siddartha Devic, Aleksandra Korolova, David Kempe, Vatsal Sharan
https://arxiv.org/abs/2402.09326

An upper bound for the second moment of the length of the period of the continued fraction expansion for $\sqrt{d}$
M. A. Korolev
https://arxiv.org/abs/2403.08616

An upper bound for the second moment of the length of the period of the continued fraction expansion for $\sqrt{d}$
If $d$ is not a perfect square, we define $T(d)$ as the length of the minimal period of the simple continued fraction expansion for $\sqrt{d}$. Otherwise, we put $T(d) = 0$. In the recent paper (2024), F.Battistoni, L.Grenié and G.Molteni established (in particular) an upper bound for the second moment of $T(d)$ over the segment $xα\sqrt{x}$. In this paper, we improve slightly this result …

Knowledge Graph Embedding in Intent-Based Networking
Kashif Mehmood, Katina Kralevska, David Palma
https://arxiv.org/abs/2405.07850 https://

On the representations of a family of pointed Hopf algebras
Agustin Garcia Iglesias, Alfio Antonio Rodriguez
https://arxiv.org/abs/2403.08945 https://

On the representations of a family of pointed Hopf algebras
For each $\ell\geq 1$ and $λ,μ\in\Bbbk$, we study the representations of a family of pointed Hopf algebras $\mathcal{A}_{λ,μ}$. These arise as Hopf cocycle deformations of the graded algebra $\mathcal{FK}_3\#\Bbbk \mathbb{G}_{3,\ell}$, where $\mathcal{FK}_3$ is the Fomin-Kirillov algebra and $\mathbb{G}_{3,\ell}$ is a given non-abelian finite group. We compute the simple modules, their projective covers and formulate a description of tensor products. We observe that our results are fundam…

Mechanically-driven growth and competition in a Voronoi model of tissues
Louis Brezin, Kirill S. Korolev
https://arxiv.org/abs/2405.07899 https://

Mechanically-driven growth and competition in a Voronoi model of tissues
Louis Brezin, Kirill S. Korolev
https://arxiv.org/abs/2405.07899 https://