Tootfinder

An interview with Gaia Marcus, director of the UK-based think tank Ada Lovelace Institute, on AI regulation in the UK and Europe, AI safety, bias, and more (Melissa Heikkilä/Financial Times)

Ada Lovelace Institute’s Gaia Marcus: regulation would increase people’s comfort with AI
The head of the UK-based think-tank talks about her hopes and fears for future oversight of AI

Regularity and pointwise convergence for dispersive equations with asymptotically concave phase on Damek-Ricci spaces
Utsav Dewan
https://arxiv.org/abs/2506.00881

Regularity and pointwise convergence for dispersive equations with asymptotically concave phase on Damek-Ricci spaces
We study the Carleson's problem on Damek-Ricci spaces $S$ for dispersive equations: \begin{equation*} \begin{cases} i\frac{\partial u}{\partial t} +Ψ(\sqrt{-\mathcal{L}} )u=0\:,\: (x,t) \in S \times \mathbb{R} \:, \\ u(0,\cdot)=f\:,\: \text{ on } S \:, \end{cases} \end{equation*} where $\mathcal{L}= Δ$, the Laplace-Beltrami operator or $\tildeΔ$, the shifted Laplace-Beltrami operator, so that the corresponding phase function $ψ$ satisfies for some $a \in (0,1)$, the large frequency as…

On the rate of convergence in the CLT for LSS of large-dimensional sample covariance matrices
Jiang Cui, Jiang Hu, Zhidong Bai, Guorong Hu
https://arxiv.org/abs/2506.02880

On the rate of convergence in the CLT for LSS of large-dimensional sample covariance matrices
This paper investigates the rate of convergence for the central limit theorem of linear spectral statistic (LSS) associated with large-dimensional sample covariance matrices. We consider matrices of the form ${\mathbf B}_n=\frac{1}{n}{\mathbf T}_p^{1/2}{\mathbf X}_n{\mathbf X}_n^*{\mathbf T}_p^{1/2},$ where ${\mathbf X}_n= (x_{i j} ) $ is a $p \times n$ matrix whose entries are independent and identically distributed (i.i.d.) real or complex variables, and ${\mathbf T} _p$ is a $p\times p$ nonr…

A look at Walmart's use of automation to grow sales without adding staff, as analysts say its efforts raise questions about the future of US retail labor (Gregory Meyer/Financial Times)
https://www.ft.com/content/5be70b28-018d-42d7-af8d-ea5a4bed4d44

Walmart is supercharging revenue — but with fewer workers
Growth in ecommerce and automation sparks questions about future of retail sector’s labour force

This https://arxiv.org/abs/2405.05727 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Chen's theorem, Goldbach's conjecture and almost prime twins II
Let $N$ denote a sufficiently large even integer and $x$ denote a sufficiently large integer, we define $D_{1,2}(N)$ as the number of primes $p$ that such that $N - p$ has at most 2 prime factors. In this paper, we show that $D_{1,2}(N) \geqslant 1.9728 \frac{C(N) N}{(\log N)^2}$, which is rather near to the asymptotic constant $2$ in Hardy--Littlewood conjecture for Goldbach's conjecture. We also get similar results on twin prime problem and additive representations of integers. The proof comb…

❝Think! Think! What do people love? The warmth of sunshine on their skin? Fresh fruit? The smell of the top of a baby’s head? Doritos? Laughter? Joy? The feeling of being seen? No, no! These answers are all wrong. It needs to be something that you can access after the Event!❞ https://

Hey you, hold onto your humanity. You’ll thank me later.
Columnist and alum Alexandra Petri offers a little advice for the graduates — or, at least, for one of them (you know who you are).

Enormous early-season wildfireshave erupted across the prairie provinces of Canada this week,
taxing local emergency response and threatening a long stretch of dangerous air quality across eastern North America.
The country’s largest fires
– the Bird River fire and the Border fire
– remain completely uncontained in northern Manitoba.
In Manitoba alone, wildfires have burned about 200,000 hectares already this year – already about three times the recent full-year …

H\"{o}lder continuous weak solutions of the 3D Boussinesq equation with thermal diffusion
Zipeng Chen, Zhaoyang Yin
https://arxiv.org/abs/2506.02927 h…

Hölder continuous weak solutions of the 3D Boussinesq equation with thermal diffusion
In this paper, we show the existence of Hölder continuous periodic weak solutions of the 3D Boussinesq equation with thermal diffusion, which apprroximate the Onsager's critical spatial regularity and satisfy the prescribed kinetic energy. More precisely, for any smooth $e(t):[0,T]\rightarrow \mathbb{R}_+$ and $β\in (0, \frac{1}{3})$, there exist $v\in C^β([0,T]\times {\mathbb{T} }^3)$ and $ θ\in C_t^{1,\fracβ{2}}C_x^{2,β}([0,T]\times {\mathbb{T} }^3)$ which solve (\ref{e:boussinesq equat…

This https://arxiv.org/abs/2306.15210 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finite time blow-up of non-radial solutions for some inhomogeneous Schrödinger equations
This work studies the inhomogeneous Schrödinger equation $$ i\partial_t u-\mathcal{K}_{s,λ}u +F(x,u)=0 , \quad u(t,x):\mathbb{R}\times\mathbb{R}^N\to\mathbb{C}. $$ Here, $s\in\{1,2\}$, $N>2s$ and $λ>-\frac{(N-2)^2}{4}$. The linear Schrödinger operator reads $\mathcal{K}_{s,λ}:= (-Δ)^s +(2-s)\fracλ{|x|^2}$ and the focusing source term is local or non-local $$F(x,u)\in\{|x|^{-2τ}|u|^{2(q-1)}u,|x|^{-τ}|u|^{p-2}(J_α*|\cdot|^{-τ}…

The New York Times reports that President Trump has enlisted the firm Palantir, founded by far-right billionaire Peter Thiel,
to carry out his March executive order
instructing government agencies to share data with each other.
The order has increased fears that the government is putting together a database to wield surveillance powers over the American public.

Trump Taps Palantir to Create Master Database on Every American
Trump’s dystopian plan is already underway.