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On the dynamical Mordell-Lang conjecture in positive characteristic
Junyi Xie, She Yang
https://arxiv.org/abs/2403.09181 https://arxi…

On the dynamical Mordell-Lang conjecture in positive characteristic
We prove that the dynamical Mordell-Lang conjecture in positive characteristic holds for bounded-degree self-maps of projective varieties. The key ingredient of the proof is a Mordell-Lang-type result for arbitrary algebraic groups over algebraically closed fields of positive characteristic, which is also interesting on its own. Moreover, we propose a geometric version of dynamical Mordell-Lang conjecture in positive characteristic.

Skin Test Accurately Detects Neurodegenerative Disorders
https://www.medscape.com/viewarticle/skin-test-accurately-detects-parkinsons-other-2024a10…

Skin Test Accurately Detects Parkinson's, Other Neurodegenerative Disorders
A skin biopsy that can detect an abnormal protein in cutaneous nerve fibers holds promise for early detection of Parkinson's and other neurodegenerative disorders.

"Hallitus ei halua hillitä velkaantumista lainkaan veronkorotuksilla, vaikka veroasteen pitäminen Marinin hallituksen tasolla hillitsisi merkittävästi velkaantumista tai poistaisi leikkaustarpeen lähes kokonaan."
#velka #verotus

Orpolle ja Purralle velka ei ole periaate vaan keino luokkapolitiikan toteuttamiseksi - Vallan mahotonta!
Riikka Purran budjetin 10 miljardin alijäämä osoittaa, ettei Orpon hallitus poikkea merkittävästi Marinin hallituksesta suhtautumisessa velkaan. Hallitukselle naljailtaessa ”velkarallin” jatkamisesta tulee huomata, että Orpo ja Purra…

Matchings in multipartite hypergraphs
Candida Bowtell, Richard Mycroft
https://arxiv.org/abs/2403.05219 https://arxiv.org/pdf/2403.05…

Matchings in multipartite hypergraphs
A folklore result on matchings in graphs states that if $G$ is a bipartite graph whose vertex classes $A$ and $B$ each have size $n$, with $\mathrm{deg}(u) \geq a$ for every $u \in A$ and $\mathrm{deg}(v) \geq b$ for every $v \in B$, then $G$ admits a matching of size $\min\{n, a+b\}$. In this paper we establish the analogous result for large $k$-partite $k$-uniform hypergraphs, answering a question of Han, Zang and Zhao, who previously demonstrated that this result holds under the additional c…

This https://arxiv.org/abs/2303.04786 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Quotients of abelian varieties by reflection groups
We prove (by a case-by-case analysis) a conjecture of Bernstein/Schwarzman to the effect that quotients of abelian varieties by suitable actions of (complex) reflection groups are weighted projective spaces, and show that this remains true after reduction to finite characteristic (including characteristics dividing the order of the group!). We also show that an analogous statement holds (with five explicitly enumerated exceptions) for actions of quaternionic reflection groups on supersingular a…

A conditional lower bound for the Tur\'an number of spheres
Andrew Newman, Marta Pavelka
https://arxiv.org/abs/2403.05364 https://

A conditional lower bound for the Turán number of spheres
We consider the hypergraph Turán problem of determining $\mathrm{ex}(n, S^d)$, the maximum number of facets in a $d$-dimensional simplicial complex on $n$ vertices that does not contain a simplicial $d$-sphere (a homeomorph of $S^d$) as a subcomplex. We show that if there is an affirmative answer to a question of Gromov about sphere enumeration in high dimensions, then $\mathrm{ex}(n, S^d) \geq Ω(n^{d + 1 - (d + 1)/(2^{d + 1} - 2)})$. Furthermore, this lower bound holds unconditionally for 2-…

”Tämä hallitus käy nyt todella rajusti kansalaisyhteiskunnan kimppuun leikaten kaikelta siltä, mikä tukee moniäänistä demokraattista yhteiskuntaa. Ihmisten ja rauhantyötä tekevien suut halutaan tukkia. Tähän asti suomalaisessa rauhanliikkeessä on yritetty tukea sodanvastustajia ja rauhanliikettä Venäjällä, Turkissa ja muissa autoritäärisissä maissa. Nyt on varmaan pyydettävä sieltä vertaistukea meille”, Lodenius toteaa.

Rauhan­järjestöjen rahoitus leikattiin yllättäen nollaan
Perjantaina iltapäivällä lähetetyn tiedotteen mukaan lakkautuspäätöksestä kerrottiin aikaisemmin päivällä epävirallisessa tilaisuudessa.

Variety of general position problems in graphs
Jing Tian, Sandi Klav\v{z}ar
https://arxiv.org/abs/2402.17338 https://arxiv.org/pdf/24…

Variety of general position problems in graphs
Let $X$ be a vertex subset of a graph $G$. Then $u, v\in V(G)$ are $X$-positionable if $V(P)\cap X \subseteq \{u,v\}$ holds for any shortest $u,v$-path $P$. If each two vertices from $X$ are $X$-positionable, then $X$ is a general position set. The general position number of $G$ is the cardinality of a largest general position set of $G$ and has been already well investigated. In this paper a variety of general position problems is introduced based on which natural pairs of vertices are require…

Variety of general position problems in graphs
Jing Tian, Sandi Klav\v{z}ar
https://arxiv.org/abs/2402.17338 https://arxiv.org/pdf/24…

Variety of general position problems in graphs
Let $X$ be a vertex subset of a graph $G$. Then $u, v\in V(G)$ are $X$-positionable if $V(P)\cap X \subseteq \{u,v\}$ holds for any shortest $u,v$-path $P$. If each two vertices from $X$ are $X$-positionable, then $X$ is a general position set. The general position number of $G$ is the cardinality of a largest general position set of $G$ and has been already well investigated. In this paper a variety of general position problems is introduced based on which natural pairs of vertices are require…