Tootfinder

#LB Só porque eu achei bonita a imagem.
https://mathstodon.xyz/@ngons/114636901870731820

Undecidability of Translational Tiling of the Plane with Four Tiles
Chao Yang, Zhujun Zhang
https://arxiv.org/abs/2506.19295 https://…

Undecidability of Translational Tiling of the Plane with Four Tiles
The translational tiling problem, dated back to Wang's domino problem in the 1960s, is one of the most representative undecidable problems in the field of discrete geometry and combinatorics. Ollinger initiated the study of the undecidability of translational tiling with a fixed number of tiles in 2009, and proved that translational tiling of the plane with a set of $11$ polyominoes is undecidable. The number of polyominoes needed to obtain undecidability was reduced from $11$ to $7$ by Yang an…

This https://arxiv.org/abs/2505.08992 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csAR_…

Dataflow & Tiling Strategies in Edge-AI FPGA Accelerators: A Comprehensive Literature Review
Edge-AI applications demand high-throughput, low-latency inference on FPGAs under tight resource and power constraints. This survey provides a comprehensive review of two key architectural decisions for FPGA-based neural network accelerators: (i) the dataflow (the order and manner in which data is moved and reused on chip), and (ii) the tiling/blocking strategy (how large tensors are partitioned to fit on-chip). We first present a broadened taxonomy of canonical dataflow styles: Weight-Stationa…

Geometric implications of weak tiling
Mihail N. Kolountzakis, Nir Lev, M\'at\'e Matolcsi
https://arxiv.org/abs/2506.23631 https://

Geometric implications of weak tiling
The notion of weak tiling played a key role in the proof of Fuglede's spectral set conjecture for convex domains, due to the fact that every spectral set must weakly tile its complement. In this paper, we revisit the notion of weak tiling and establish some geometric properties of sets that weakly tile their complement. If $A \subset \mathbb{R}^d$ is a convex polytope, we give a direct and self-contained proof that $A$ must be symmetric and have symmetric facets. If $A \subset \mathbb{R}$ is a …

Notes on the one-loop amplituhedron and its BCFW tiling
Ran J. Tessler
https://arxiv.org/abs/2506.22238 https://arxiv.org/pdf/2506.22…

Notes on the one-loop amplituhedron and its BCFW tiling
These notes are based on talks I gave in the seminar "Mathematical structures in scattering amplitudes in quantum field theories" I organized in Weizmann Institute on Fall 24'. They study amplituhedra, and extend the proof of \cite{even2021amplituhedron} of the BCFW conjecture for tree amplituhedra to one loop.

I'm having this wild idea of getting an SSD just for Linux, since I'm renewing the PC I only use for games (that I'm often too tired to play).
A friend keep saying that games just work on Linux now, but he's one of those tiling wm users so I'm not sure if I can trust him... 🧐

Undecidability of Translational Tiling of the Plane with Orthogonally Convex Polyominoes
Chao Yang, Zhujun Zhang
https://arxiv.org/abs/2506.12726 https://

Undecidability of Translational Tiling of the Plane with Orthogonally Convex Polyominoes
The first undecidability result on the tiling is the undecidability of translational tiling of the plane with Wang tiles, where there is an additional color matching requirement. Later, researchers obtained several undecidability results on translational tiling problems where the tilings are subject to the geometric shapes of the tiles only. However, all these results are proved by constructing tiles with extremely concave shapes. It is natural to ask: can we obtain undecidability results of tr…

Two Tiling is Undecidable
Jack Stade
https://arxiv.org/abs/2506.11628 https://arxiv.org/pdf/2506.11628…

Two Tiling is Undecidable
We show that the following problem is undecidable: given two polygonal prototiles, determine whether the plane can be tiled with rotated and translated copies of them. This improves a result of Demaine and Langerman [SoCG 2025], who showed undecidability for three tiles. Along the way, we show that tiling with one prototile is undecidable if there can be edge-to-edge matching rules. This is the first result to show undecidability for monotiling with only local matching constraints.

Everybody is crushing their challenges, but I'm ashamed to have lost my 0 post challenge for this year :) Here is the evidence: https://www-gem.codeberg.page/picom/.

A rose drying out naturally in a pot inside.
#wildlife #photography

A Radio-quiet AGN as a candidate counterpart to neutrino event IceCube-200615A
F. McBride, N. Schettino, J. D. O'Brien, W. Harwood, L. Perot, G. Temple, H. Ayalo Solares, A. Corsi, A. Coleiro, D. Cowen, D. B. Fox, Y. Li, K. Murase, A. Pellegrino, T. D. Russell, S. Wissel
https://arxiv.org/abs/2506.20064

A Radio-quiet AGN as a candidate counterpart to neutrino event IceCube-200615A
Follow-up observations of neutrino events have been a promising method for identifying sources of very-high-energy cosmic rays. Neutrinos are unambiguous tracers of hadronic interactions and cosmic rays. On June 15, 2020, IceCube detected a neutrino event with an 82.8% probability of being astrophysical in origin. To identify the astrophysical source of the neutrino, we used X-ray tiling observations to identify potential counterpart sources. We performed additional multiwavelength follow-up wi…

Non-spectrality of some piecewise smooth curves and unions of line segments
Mihail N. Kolountzakis, Chun-Kit Lai
https://arxiv.org/abs/2507.00581 https://

Non-spectrality of some piecewise smooth curves and unions of line segments
We develop a systematic study about the spectrality of measures supported on piecewise smooth curves by studying the support of the tempered distributions arising from the tiling equation of some singular spectral measures. In doing so, we show that the arc-length measures of all closed polygonal lines are not spectral. {In particular, the boundary of a square is not spectral. We also show that the ``plus space'' (two crossing line segments) is not spectral.} Furthermore, our theory also shows …

Kitaev model in regular hyperbolic tilings
Julien Vidal, R\'emy Mosseri
https://arxiv.org/abs/2506.17981 https://arxiv.org/pdf/25…

Kitaev model in regular hyperbolic tilings
We study the Kitaev model on regular hyperbolic trivalent tilings. Depending on the length $p$ of the elementary polygons, we examine two distinct tri-colorings of the tiling. Using a recent conjecture on the ground-state flux sector, we compute the phase diagram via exact diagonalizations and derive analytical expressions for the effective Hamiltonians in the isolated-dimer limit which are valid for all values of $p$. Our results interpolates between the Euclidean honeycomb lattice and the tri…

recap from my weekend distro hopping (that was severely limited by the good weather):
- tried Hyprland: cool but I still don't care about tiling window managers; terminals have tabs, emacs is its own window manager, the rest can be full screen or half screen.
- cool to learn about "new" things like Universal Kernel Image, a bit about UEFI, etc.
- I don't like the LEGO approach to build a Desktop; I care about this as much as 10 years ago: 0

A collection of results relating the geometry of plane domains and the exit time of planar Brownian motion, II
Greg Markowsky, Clayton McDonald
https://arxiv.org/abs/2506.09364

A collection of results relating the geometry of plane domains and the exit time of planar Brownian motion, II
This paper is the sequel to another with the same name (Buttigieg et al., Comput. Methods Funct. Theory, 2023), and is concerned with results of the same type. We deduce a result on the moments of the exit time of Brownian motion from domains whose boundary curve is replaced by a dashed line, and from domains arising from a periodic tiling of the plane. We also give a construction of a type of domain which is similar to a wedge domain, but the behaviour of whose exit time moments answer several…

This https://arxiv.org/abs/2501.07576 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The BCFW Tiling of the ABJM Amplituhedron
The orthogonal momentum amplituhedron O_k was introduced simultaneously in 2021 by Huang, Kojima, Wen, and Zhang, and by He, Kuo, and Zhang, in the study of scattering amplitudes of ABJM theory. It was conjectured that it admits a decomposition into BCFW cells. We prove this conjecture.

A Family of Non-Periodic Tilings, Describable Using Elementary Tools and Exhibiting a New Kind of Structural Regularity
Miki Imura
https://arxiv.org/abs/2506.07638

A Family of Non-Periodic Tilings, Describable Using Elementary Tools and Exhibiting a New Kind of Structural Regularity
We present a construction of a family of non-periodic tilings using elementary tools such as modular arithmetic and vector geometry. These tilings exhibit a distinct type of structural regularity, which we term modulo-staggered rotational symmetry. The construction is self-contained and does not rely on previous tiling theories or systems.