Tootfinder

Here’s the real actual definition of “artificial intelligence,” the true technical meaning in research and engineering circles when it’s not being used as marketing hype.
Artificial intelligence is anything that
1. humans are generally good at, and
2. computers were recently bad at.
That’s it. That’s all it means. You’ll hear people refine it and dress it up, but that’s the heart of the definition. (Check Wikipedia!)
3/

The Agora Assistant got this one "wrong" about #2025 but I'm here for it

Here’s the real actual definition of “artificial intelligence,” the true technical meaning in research and engineering circles when it’s not being used as marketing hype.
Artificial intelligence is anything that
1. humans are generally good at, and
2. computers were recently bad at.
That’s it. That’s all it means. You’ll hear people refine it and dress it up, but that’s the heart of the definition. (Check Wikipedia!)
3/

This https://arxiv.org/abs/2404.02288 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Generalized saturation game
We study the following game version of the generalized graph Turán problem. For two fixed graphs F and H, two players, Max and Mini, alternately claim unclaimed edges of the complete graph Kn such that the graph G of the claimed edges must remain F-free throughout the game. The game ends when no further edges can be claimed, i.e. when G becomes F-saturated. The H-score of the game is the number of copies of H in G. Max aims to maximize the H-score, while Mini wants to minimize it. The H-score …

This https://arxiv.org/abs/2504.00804 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The prime number theorem over integers of power-free polynomial values
Let $f(x)\in \mathbb{Z}[x]$ be an irreducible polynomial of degree $d\ge 1$. Let $k\ge2$ be an integer. The number of integers $n$ such that $f(n)$ is $k$-free is widely studied in the literature. In principle, one expects that $f(n)$ is $k$-free infinitely often, if $f$ has no fixed $k$-th power divisor. In 2022, Bergelson and Richter established a new dynamical generalization of the prime number theorem (PNT). Inspired by their work, one may expect that this generalization of the PNT also hol…

This https://arxiv.org/abs/2402.06558 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

The Asymptotic Structure of Cosmological Integrals
We provide a general analysis of the asymptotic behaviour of perturbative contributions to observables in arbitrary power-law FRW cosmologies, indistinctly the Bunch-Davies wavefunction and cosmological correlators. We consider a large class of scalar toy models, including conformally-coupled and massless scalars in arbitrary dimensions, that admits a first principle definition in terms of (generalised/weighted) cosmological polytopes. The perturbative contributions to an observable can be expr…

This https://arxiv.org/abs/2406.00937 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Stochastic Variance-Reduced Forward-Reflected-Backward Splitting Methods for Nonmonotone Generalized Equations
We develop two novel stochastic variance-reduction methods to approximate solutions of a class of nonmonotone [generalized] equations. Our algorithms leverage a new combination of ideas from the forward-reflected-backward splitting method and a class of unbiased variance-reduced estimators. We construct two new stochastic estimators within this class, inspired by the well-known SVRG and SAGA estimators. These estimators significantly differ from existing approaches used in minimax and variation…

This https://arxiv.org/abs/2501.11437 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

More on the corner-vector construction for spherical designs
This paper explores a full generalization of the classical corner-vector method for constructing weighted spherical designs, which we call the {\it generalized corner-vector method}. First we establish a uniform upper bound for the degree of designs obtained from the proposed method. Our proof is a hybrid argument that employs techniques in analysis and combinatorics, especially a famous result by Xu(1998) on the interrelation between spherical designs and simplical designs, and the cross-ratio…

This https://arxiv.org/abs/2404.17061 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Gauge origami and quiver W-algebras II: Vertex function and beyond quantum $q$-Langlands correspondence
We continue the study of generalized gauge theory called gauge origami, based on the quantum algebraic approach initiated in [arXiv:2310.08545]. In this article, we in particular explore the D2 brane system realized by the screened vertex operators of the corresponding W-algebra. The partition function of this system given by the corresponding conformal block is identified with the vertex function associated with quasimaps to Nakajima quiver varieties and generalizations, that plays a central r…

This https://arxiv.org/abs/2505.19677 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Perfect codes in quartic Cayley graphs of generalized dihedral groups
For a graph $Γ=(VΓ,EΓ)$, a subset $D$ of $VΓ$ is a perfect code in $Γ$ if every vertex of $Γ$ is dominated by exactly one vertex in $D$. In this paper, we classify all connected quartic Cayley graphs on generalized dihedral groups admitting a perfect code, and determine all perfect codes in such graphs.