Tootfinder

Long strings of composite values of polynomials and a basis of order 2
Artyom Radomskii
https://arxiv.org/abs/2506.15641 https://arxi…

Long strings of composite values of polynomials and a basis of order 2
We show that for any polynomial $f: \mathbb{Z}\to \mathbb{Z}$ with positive leading coefficient and irreducible over $\mathbb{Q}$, if $N$ is large enough then there are two strings of consecutive positive integers $I_{1}=\{n_1-m,\ldots, n_1+m\}$ and $I_{2}=\{n_2-m, \ldots, n_2+m\}$, where $m = [(\log N) (\log \log N)^{1/325525}]$, such that $I_{1}\cup I_{2} \subset [1, N]$, $N = n_1 + n_2$, and $f(n)$ is composite for any $n\in I_{1}\cup I_{2}$. This extends the result in [5] which showed the s…

Reminder: public protest is about visibility, not hiding. The power comes from people being willing to be visible, put their time on the line, and if needed, their bodies.
If you're going to start shit, maybe just ... don't. Direct action of the illegal sort requires careful planning and a tactical and strategic plan for why it will win. It happens sometimes, but it's not the mode, it's not the mode of the No Kings protests. This is a popular, public demonstration of outrage. It's legal (for now, and I hope, ever).
Yes, the police may try to kettle protesters and then trap them into curfew violations in places that have curfews. Masks won't save us from that where it happens. Just running the system with competent representation (and enough bodies to make it A Problem for the system) will.
We don't all need to be masked vigilantes at protests, and in a lot of cases, we need to be worried about the people masking up and starting shit. Remember that this is our opponents current tactic: masked, violent attacks. Don't look like them.

Seeking a quadratic refinement of Sendov's conjecture
Michael J. Miller
https://arxiv.org/abs/2506.12951 https://arxiv.org/pdf/25…

Seeking a quadratic refinement of Sendov's conjecture
A conjecture of Sendov states that if a polynomial has all its roots in the unit disk and if $β$ is one of those roots, then within one unit of $β$ lies a root of the polynomial's derivative. If we define $r(β)$ to be the greatest possible distance between $β$ and the closest root of the derivative, then Sendov's conjecture claims that $r(β) \le 1$. In this paper, we conjecture that there is a constant $c>0$ so that $r(β) \le 1-cβ(1-β)$ for all $β\in [0,1]$. We find such constants fo…

Counting homomorphisms in antiferromagnetic graphs via Lorentzian polynomials
Joonkyung Lee, Jaeseong Oh, Jaehyeon Seo
https://arxiv.org/abs/2506.13659 htt…

Counting homomorphisms in antiferromagnetic graphs via Lorentzian polynomials
An edge-weighted graph $G$, possibly with loops, is said to be antiferromagnetic if it has nonnegative weights and at most one positive eigenvalue, counting multiplicities. The number of graph homomorphisms from a graph $H$ to an antiferromagnetic graph $G$ generalises various important parameters in graph theory, including the number of independent sets and proper vertex-colourings, as well as their relaxations in statistical physics. We obtain homomorphism inequalities for various graphs $H…

Minneapolis and Saint Paul are finally launching this BRT line that was already in the planning phase when I last visited in ... 2019.
Good, but if it's gonna take that long, maybe agencies should just incrementally upgrade the buses that exist instead of these big fancy unicorn "BRT" projects?
https://

Creating Buzz for the B Line
The Twin Cities’ newest BRT line is an attractive option that could turn more people into transit users — if they know about it!

If you feel comfortable doing so, please register for this event at https://www.mobilize.us/nokings/event/788033/.
It helps us with our planning to have an idea how many people to expect. Thanks!

NO KINGS Santa Barbara · No Kings
**In America, we don’t put up with would-be kings.** NO KINGS is a national day of action and mass mobilization in response to increasing authoritarian excesses and corruption from Trump and his allies. We’ve watched as they’ve cracked down on free speech, detained people for their political views, threatened to deport American citizens, and defied the courts. They’ve done this all while continuing to serve and enrich their billionaire allies. 🚨**On Saturday, June 14, we’re takin…

Attention-based Learning for 3D Informative Path Planning
Rui Zhao, Xingjian Zhang, Yuhong Cao, Yizhuo Wang, Guillaume Sartoretti
https://arxiv.org/abs/2506.08434

Attention-based Learning for 3D Informative Path Planning
In this work, we propose an attention-based deep reinforcement learning approach to address the adaptive informative path planning (IPP) problem in 3D space, where an aerial robot equipped with a downward-facing sensor must dynamically adjust its 3D position to balance sensing footprint and accuracy, and finally obtain a high-quality belief of an underlying field of interest over a given domain (e.g., presence of specific plants, hazardous gas, geological structures, etc.). In adaptive IPP task…

Niners LT Trent Williams on goal of playing till he’s 40: ‘Not going to retire with something left on the table’ https://www.nfl.com/news/niners-lt-trent-williams-on-goal-of-playing-till-he-s-40-not-g…

Replaced article(s) found for eess.IV. https://arxiv.org/list/eess.IV/new/
[1/1]:
Towards Clinical Practice in CT-Based Pulmonary Disease Screening: An Efficient and Reliable Fram...

The Urban Model Platform: A Public Backbone for Modeling and Simulation in Urban Digital Twins
Rico H Herzog, Till Degkwitz, Trivik Verma
https://arxiv.org/abs/2506.10964

The Urban Model Platform: A Public Backbone for Modeling and Simulation in Urban Digital Twins
Urban digital twins are increasingly perceived as a way to pool the growing digital resources of cities for the purpose of a more sustainable and integrated urban planning. Models and simulations are central to this undertaking: They enable "what if?" scenarios, create insights and describe relationships between the vast data that is being collected. However, the process of integrating and subsequently using models in urban digital twins is an inherently complex undertaking. It raises questions…