Tootfinder

Howe duality for the dual pair $\left(\mathfrak{spo}(2n|1)\,, \mathfrak{osp}(2|2)\right)$
Roman Lavicka, Allan Merino
https://arxiv.org/abs/2506.04075 http…

Howe duality for the dual pair $\left(\mathfrak{spo}(2n|1)\,, \mathfrak{osp}(2|2)\right)$
The goal of our work is to study the decomposition of the joint action of $\mathfrak{g} = \mathfrak{spo}(2n|1)$ and $\mathfrak{g}' = \mathfrak{osp}(2|2)$ on the supersymmetric algebra S = S($\mathbb{C}^{2n|1} \otimes \mathbb{C}^{1|1}$). As proved by Merino and Salmasian, we have a one-to-one correspondence between irreducible representations of $\mathfrak{g}$ and $\mathfrak{g}'$ appearing as subrepresentations of S. In this paper, we obtained an explicit description of the h…

Maximizing the Promptness of Metaverse Systems using Edge Computing by Deep Reinforcement Learning
Tam Ninh Thi-Thanh, Trinh Van Chien, Hung Tran, Nguyen Hoai Son, Van Nhan Vo
https://arxiv.org/abs/2506.02657

Maximizing the Promptness of Metaverse Systems using Edge Computing by Deep Reinforcement Learning
Metaverse and Digital Twin (DT) have attracted much academic and industrial attraction to approach the future digital world. This paper introduces the advantages of deep reinforcement learning (DRL) in assisting Metaverse system-based Digital Twin. In this system, we assume that it includes several Metaverse User devices collecting data from the real world to transfer it into the virtual world, a Metaverse Virtual Access Point (MVAP) undertaking the processing of data, and an edge computing ser…

🇺🇦 Auf radioeins läuft...
Matt Berninger:
🎵 Bonnet Of Pins (Radio-Edit)
#NowPlaying #MattBerninger
https://mattberninger.bandcamp.com/track/bonnet-of-pins
https://open.spotify.com/track/0hLFRJetaM0qj09lyyJ9a5

The metaverse is going great!

Studie: Apple kassiert nur bei 10 Prozent der App-Umsätze mit
Mit einer Studie tritt Apple dem Eindruck dagegen, dass beim iPhone überall mitverdient wird. Zugleich wird der Wirtschaftsfaktor App-Ökosystem aufgezeigt.

The $\mu-$invariant of fine Selmer groups associated to general Drinfeld modules
Hang Chen
https://arxiv.org/abs/2507.02688 https://a…

The $μ-$invariant of fine Selmer groups associated to general Drinfeld modules
Let $F$ be a global function field over the finite field $\mathbb{F}_q$ where $q$ is a prime power and $A$ be the ring of elements in $F$ regular outside $\infty$. Let $ϕ$ be an arbitrary Drinfeld module over $F$ For a fixed non-zero prime ideal $\mathfrak{p}$ of $A$, we show that on the constant $\mathbb{Z}_{\textit{p}}-$extension $\mathfrak{F}$ of $F$, the Pontryagin dual of the fine Selmer group associated to the $\mathfrak{p}-$primary torsion of $ϕ$ over $\mathfrak{F}$ is a finitely gener…

This https://arxiv.org/abs/2504.21760 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Bounded powers of edge ideals: Gorenstein toric rings
Let $S=K[x_1, \ldots,x_n]$ denote the polynomial ring in $n$ variables over a field $K$ and $I \subset S$ a monomial ideal. Given a vector $\mathfrak{c}\in\mathbb{N}^n$, the ideal $I_{\mathfrak{c}}$ is the ideal generated by those monomials belonging to $I$ whose exponent vectors are componentwise bounded above by $\mathfrak{c}$. Let $δ_{\mathfrak{c}}(I)$ be the largest integer $q$ for which $(I^q)_{\mathfrak{c}}\neq 0$. For a finite graph $G$, its edge ideal is denoted by $I(G)$. Let $\mathca…

Zum ersten Mal hat ein US-Geschworenengericht den E-Autobauer im Zusammenhang mit seinem Autopilot-System für einen tödlichen Unfall mitverantwortlich gemacht.
Zum Artikel: https://heise.de/-10507879?wt_mc=sm.red.ho.mastodon.mas…

C'est bien de pouvoir mettre un nom sur ces campagnes.
https://www.mediapart.fr/journal/france/030725/une-agence-pro-orban-mene-une-campagne-numerique-occulte-pour-le-rn-en-france

Une agence pro-Orbán a mené une campagne numérique occulte pour le RN en France
Des contenus ont été diffusés sur le réseau social X en ciblant les internautes sur la base de critères politiques, ce qui est interdit par les réglementations françaises et européennes.

Bounded powers of edge ideals: The strong exchange property
Takayuki Hibi, Seyed Amin Seyed Fakhari
https://arxiv.org/abs/2506.03480 https://

Bounded powers of edge ideals: The strong exchange property
Let $S=K[x_1, \ldots,x_n]$ denote the polynomial ring in $n$ variables over a field $K$ and $I \subset S$ a monomial ideal. Given a vector $\mathfrak{c}\in\mathbb{Z}_{>0}^n$, the ideal $I_{\mathfrak{c}}$ is the ideal generated by those monomials belonging to $I$ whose exponent vectors are componentwise bounded above by $\mathfrak{c}$. Let $δ_{\mathfrak{c}}(I)$ be the largest integer $q$ for which $(I^q)_{\mathfrak{c}}\neq 0$. Let $I(G) \subset S$ denote the edge ideal of a finite graph $G$ on …