Tootfinder

X changes its developer agreement to prevent third parties from using "the X API or X Content to fine-tune or train a foundation or frontier model" (Ivan Mehta/TechCrunch)
https://techcrunch.com/2025/06/05/x-changes-i…

X changes its terms to bar training of AI models using its content | TechCrunch
Social network X has changed its developer agreement to prevent third parties from using the platform's content to train large language models.

Wendelstein 7-X stellt neuen Fusionsrekord auf
In der Forschungsanlage Wendelstein 7-X ist ein Rekord gelungen. Die Forscher werten das als Fortschritt auf dem Weg zur kommerziellen Nutzung der Kernfusion.
https:/…

X-Ray Polarization of the Magnetar 1E 1841−045 / IXPE Detection of Highly Polarized X-Rays from the Magnetar 1E 1841-045: #Magnetar Outburst: https://www.nasa.gov/missions/ixpe/nasas-ixpe-obtains-first-x-ray-polarization-measurement-of-magnetar-outburst/

This https://arxiv.org/abs/2410.10884 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On evaluation of the lattice sum $\frac{1}{|x||y||x+y|}$
We study lattice sums $\sum 1/|x||y||x+y|$ and $\sum 1/|x|^2|y|^2|x+y|^2$ taken over the pairs $(x,y)$ of primitive lattice vectors in $\ZZ^2$ that span a parallelogram of area one. We prove convergence of these and similar sums, propose a new method to evaluate $\sum 1/|x|^2|y|^2|x+y|^2$, which, in turn, gives a new and simple proof of Zagier's formula for $D_{1,1,1}$.

Trump's proposed budget is a fiscal tightening relative to current policy.
And it doesn't even include the extra tightening from tariffs.
https://x.com/firstadopter/status/1930317264252793138/photo/1

tae kim (@firstadopter) on X
Great chart on the budget bill (Source: NYTimes)

Source: X is piloting a program to use Community Notes to highlight posts on which people of typically differing opinions agree (Sara Fischer/Axios)
https://www.axios.com/2025/06/05/x-elon-musk-community-notes

Exclusive: X piloting new program to elevate content users agree on
The goal is to build momentum around opinions that are widely shared.

https://x.com/yan_qing35527/status/1918913180463431881

This https://arxiv.org/abs/2501.16263 has been replaced.
link: https://scholar.google.com/scholar?q=a

Rotation number and dynamics of 3-interval piecewise $λ$-affine contractions
We consider a family of piecewise contractions admitting a rotation number and defined for every $x\in[0,1)$ by $f(x)=λx + δ+ d θ_a(x) \pmod 1$, where $λ\in(0,1)$, $d\in(0,1-λ)$, $δ\in[0,1]$, $a\in[0,1]$ and $θ_a(x)=1$ if $x\geq a$ and $θ_a(x)=0$ otherwise. In the special case where $a=1$, the family reduces to the well studied ``contracted rotations" $x\mapsto λx + δ\pmod 1$, which are 2-interval piecewise $λ$-affine contractions when $δ\in(1-λ,1)$. Considering $a\in(0,1)$ allows …

🇺🇦 Auf radioeins läuft...
The Black Keys:
🎵 Tighten Up
#NowPlaying #TheBlackKeys
https://goodrobotusses.bandcamp.com/track/tighten-up-bend-on-me-matchbox-twenty-bent-x-a-ha-take-on-me-x-the-black-keys-tighten-up
https://open.spotify.com/track/3C542UknrX76XSRXTyQ1Qg

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}…

Getting almost all the bits from a quantum random access code
Han-Hsuan Lin (National Tsing Hua University, Taiwan), Ronald de Wolf (QuSoft, CWI,University of Amsterdam)
https://arxiv.org/abs/2506.01903

Getting almost all the bits from a quantum random access code
A quantum random access code (QRAC) is a map $x\mapstoρ_x$ that encodes $n$-bit strings $x$ into $m$-qubit quantum states $ρ_x$, in a way that allows us to recover any one bit of $x$ with success probability $\geq p$. The measurement on $ρ_x$ that is used to recover, say, $x_1$ may destroy all the information about the other bits; this is in fact what happens in the well-known QRAC that encodes $n=2$ bits into $m=1$ qubits. Does this generalize to large $n$, i.e., could there exist QRACs tha…

X-ray spectroscopy method of white dwarf mass determination in intermediate polars. External systematic uncertainties
V. F. Suleimanov (IAAT, University of Tuebingen), L. Ducci (IAAT, University of Tuebingen), V. Doroshenko (IAAT, University of Tuebingen), K. Werner (IAAT, University of Tuebingen)
https://arxiv.org/abs/2506.0371…

X-ray spectroscopy method of white dwarf mass determination in intermediate polars. External systematic uncertainties
The masses of white dwarfs (WDs) in intermediate polars (IPs) can be determined from the shape of their hard X-ray spectra. Here we study the importance of all possible systematic uncertainties in this X-ray spectroscopy method, including finite radii and rotation of magnetospheres, finite accretion column height and accretion-flow inclination relative to the WD surface. We also investigate the importance of accretion-heated envelopes on WD surfaces in IPs which are increasing WD radii. Their p…

This https://arxiv.org/abs/2009.14324 has been replaced.
link: https://scholar.google.com/scholar?q=a

Characterizing Jacobians via the KP equation and via flexes and degenerate trisecants to the Kummer variety: an algebro-geometric approach
This paper is withdrawn since we found a flaw in the proof of Theorem 4, asserting that the base locus of the complete linear system of an ample line bundle on a complex abelian variety is reduced. The error is in page 7, line $ -14$, where we claim that the divisor "mathcal E" on the variety $X$ is linearly equivalent to zero. This is untrue. For instance, it would imply that, for a non-torsion point $x$ on an abelian surface $A$, letting $E_x$, $E_{-x}$, and $E_0$ the exceptional curves in th…

Wendelstein glüht! Nein, nicht der Berg in den Alpen, sondern der Fusionsreaktor! Ein wirklich interessanter Beitrag.
https://winfuture.de/news,151376.html

This https://arxiv.org/abs/2505.14806 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qbi…

Place Cells as Position Embeddings of Multi-Time Random Walk Transition Kernels for Path Planning
The hippocampus orchestrates spatial navigation through collective place cell encodings that form cognitive maps. We reconceptualize the population of place cells as position embeddings approximating multi-scale symmetric random walk transition kernels: the inner product $\langle h(x, t), h(y, t) \rangle = q(y|x, t)$ represents normalized transition probabilities, where $h(x, t)$ is the embedding at location $ x $, and $q(y|x, t)$ is the normalized symmetric transition probability ove…

𝕐oδgδ в X: «Guardian angel..🐈🐾🐥🐥😍 https://t.co/lwXOjeHnMe» / X
https://x.com/Yoda4ever/status/1919031766066610642

This https://arxiv.org/abs/2106.02411 has been replaced.
link: https://scholar.google.com/scholar?q=a

Parametrized Kähler class and Zariski dense orbital 1-cohomology
Let $Γ$ be a finitely generated group and let $(X,μ_X)$ be an ergodic standard Borel probability $Γ$-space. Suppose that $G$ is the connected component of the identity of the isometry group of a Hermitian symmetric space. Given a Zariski dense measurable cocycle $σ:Γ\times X \rightarrow G$, we define the notion of parametrized Kähler class and we show that it completely determines the cocycle up to cohomology.x

This https://arxiv.org/abs/2502.06200 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

On the query complexity of sampling from non-log-concave distributions
We study the problem of sampling from a $d$-dimensional distribution with density $p(x)\propto e^{-f(x)}$, which does not necessarily satisfy good isoperimetric conditions. Specifically, we show that for any $L,M$ satisfying $LM\ge d\ge 5$, $ε\in \left(0,\frac{1}{32}\right)$, and any algorithm with query accesses to the value of $f(x)$ and $\nabla f(x)$, there exists an $L$-log-smooth distribution with second moment at most $M$ such that the algorithm requires $\left(\frac{LM}{dε}\right)^{�…

This https://arxiv.org/abs/2505.03447 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Asymptotic formula for the sum of a prime and a square-full number in intervals shorter than $X^{1/2}$
Let $R(N)$ be the number of representations of $N$ as a sum of a prime and a square-full number weighted with logarithmic function. In $2024$, the author and Y. Suzuki obtained an asymptotic formula for the sum of $R(N)$ over positive integers $N$ in a short interval ($X$, $X+H$] for $X^{\frac{1}{2}+\varepsilon} \le H < X^{1-\varepsilon}$. In this article, we improve the range of $H$, that is, we prove the same asymptotic formula for $X^{\frac{32-4\sqrt{15}}{49}+\varepsilon} \le H \le X^{1- \va…

This https://arxiv.org/abs/2406.10189 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Topological rigidity of small RCD(K,N) spaces with maximal rank
For a polycyclic group $Λ$, $\text{rank} ( Λ)$ is defined as the number of $\mathbb{Z}$ factors in a polycyclic decomposition of $Λ$. For a finitely generated group $G$, $\text{rank} (G)$ is defined as the infimum of $ \text{rank} (Λ)$ among finite index polycyclic subgroups $Λ\leq G$. For a compact $\text{RCD} (K,N)$ space $(X,\mathsf{d}, \mathfrak{m})$ with $\text{diam} (X) \leq \varepsilon (K,N)$, the rank of $π_1(X)$ is at most $N$. We show that in case of equality, $X$ is homeomorphi…

Steady state and relaxation dynamics of run and tumble particles in contact with a heat bath
R. K. Singh, Oded Farago
https://arxiv.org/abs/2506.02645 http…

Steady state and relaxation dynamics of run and tumble particles in contact with a heat bath
We study the relaxation dynamics of a run and tumble particle in a one-dimensional piecewise linear potential $U(x)=b|x|$, from delta-function initial conditions at $x=0$ to steady state. In addition to experiencing active telegraphic noise, the particle is in contact with a heat bath at temperature $T$ that applies white thermal noise. We find that the position distribution of the RTP is described by a sum of two distributions ("modes"), each of which of the form $P(x,t\to\infty)\sim…

Natura Urbana X - Perspectives 🏵️
城市自然 X - 角度 🏵️
📷 Nikon FE
🎞️Ilford FP4 Plus, expired 1995
buy me ☕️ ?/请我喝杯☕️？
#filmphotography

Yiding Cao Geld mit PayPal.Me senden
Folgen Sie dem Link PayPal.Me/dingsterdingster und geben Sie den Betrag ein. Es ist bequem und sicher. Sie haben noch kein PayPal-Konto? Kein Problem.

Gameplay enthüllt: Battlemarked bringt Dungeons & Dragons in die Virtual Reality
Mit Demeo x Dungeons & Dragons: Battlemarked erscheint ein Tabletop-RPG mit D&D-Lizenz für VR-Brillen, PC und Konsolen. Ein Trailer zeigt nun erstmals Gameplay.

This https://arxiv.org/abs/2501.04357 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Generators of top cohomology
Let $R$ be a commutative noetherian ring and $f: X \to \mathrm{Spec} R$ a proper smooth morphism, of relative dimension $n$. From Hartshorne, Residues and Duality, Springer, 1966, one knows that the trace map $\mathrm{Tr}_f : \mathrm{H}^n(X, ω_{X/R}) \to R$ is an isomorphism when $f$ has geometrically connected fibres. We construct an exact sequence that generates $\mathrm{Ext}_X^n(\mathcal{O}_X, ω_{X/R}) = \mathrm{H}^n(X, ω_{X/R})$ as an $R$-module in the following cases: (1) when $R$ is…

General Numerical Radius for Products of Sectorial Matrices
Mohammad Alakhrass
https://arxiv.org/abs/2506.02042 https://arxiv.org/pdf…

General Numerical Radius for Products of Sectorial Matrices
In this paper, we investigate the generalized numerical radius $ω_N$, associated with a matrix norm $N$ defined by $ω_N(X) = \sup_{θ\in \mathbb{R}} N(\operatorname{Re}(e^{iθ}X))$. We focus on matrices whose numerical ranges are contained in sectors of the complex plane (sectorial matrices) and derive upper bounds for $ω_N(XY)$ and $ω_N(X \circ Y)$ for such matrices $X$ and $Y$. Our results generalize and refine well known numerical radius inequalities. Several known inequalities for $ω(X…

Single-Shot, Single-Mask X-ray Dark-field and Phase Contrast Imaging
Jingcheng Yuan, Mini Das
https://arxiv.org/abs/2506.02427 https://

Single-Shot, Single-Mask X-ray Dark-field and Phase Contrast Imaging
X-ray imaging, traditionally relying on attenuation contrast, struggles to differentiate materials with similar attenuation coefficients like soft tissues. X-ray phase contrast imaging (XPCI) and dark-field (DF) imaging provide enhanced contrast by detecting phase shifts and ultra-small-angle X-ray scattering (USAXS). However, they typically require complex and costly setups, along with multiple exposures to retrieve various contrast features. In this study, we introduce a novel single-mask X-r…

This https://arxiv.org/abs/2408.08689 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The splitting of the de Rham cohomology of soft function algebras is multiplicative
Let $A$ be a real soft function algebra. In arXiv:2208.11431 we have obtained a canonical splitting $\mathrm{H}^* (Ω^\bullet _{A|\mathrm{R}}) \cong \mathrm{H} ^* (X,\mathrm{R})\oplus \text{(something)}$ via the canonical maps $Λ_A:\mathrm{H} ^* (X,\mathrm{R})\to\mathrm{H} ^* (Ω^\bullet _{A|\mathrm{R}})$ and $Ψ_A:\mathrm{H} ^* (Ω^\bullet _{A|\mathrm{R}})\to\mathrm{H} ^* (X,\mathrm{R})$. In this paper we prove that these maps are multiplicative.

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…

Probing the semiconductor-to-dirac semimetal transition in Na-Sb-Bi alloys with x-ray Compton scattering
Aki Pulkkinen, Veenavee Nipunika Kothalawala, Kosuke Suzuki, Bernardo Barbiellini, Johannes Nokelainen, Wei-Chi Chiu, Bahadur Singh, Hsin Lin, Alok K. Pandey, Naoaki Yabuuchi, Naruki Tsuji, Yoshiharu Sakurai, Hiroshi Sakurai, J\'an Min\'ar, Arun Bansil

Probing the semiconductor-to-dirac semimetal transition in Na-Sb-Bi alloys with x-ray Compton scattering
We discuss electron redistribution during the Semiconductor-to-Dirac Semimetal transition in Na-Sb-Bi alloys using x-ray Compton scattering experiments combined with first-principles electronic structure modeling. A robust signature of the semiconductor-to-Dirac semimetal transition is identified in the spherically averaged Compton profile. We demonstrate how the number of electrons involved in this transition can be estimated to provide a novel descriptor for quantifying the strength of spin-o…

This https://arxiv.org/abs/2208.00676 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Pansiot-type subword complexity theorem for automorphisms of free groups
Inspired by Pansiot's work on substitutions, we prove a similar theorem for automorphisms of a free group F of finite rank: if a right-infinite word X represents an attracting fixed point of an automorphism of F, the subword complexity of X is equivalent to n, n log log n, n log n, or n^2. The proof uses combinatorial arguments analogue to Pansiot's as well as train tracks. We also define the recurrence complexity of X, and we apply it to laminations. In particular, we show that attracting lami…

Prediction of the SVOM MXT camera end of life spectral performance based onproton irradiation results
Clara Plasse, Diego G\"otz, Aline Meuris, Miguel Fernandez Moita, Philippe Ferrando, Leo Favier, Francesco Ceraudo
#toXiv_bot_toot

Jetzt wissen wir alle inzwischen, dass #ElonMusk mit dem, was früher mal #Wahrheit genannt wurde, eine sehr interessante und spannungsvolle Beziehung unterhält.
Anscheinend stehen ihm jedoch nicht alle

This https://arxiv.org/abs/2505.05098 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

X-Driver: Explainable Autonomous Driving with Vision-Language Models
End-to-end autonomous driving has advanced significantly, offering benefits such as system simplicity and stronger driving performance in both open-loop and closed-loop settings than conventional pipelines. However, existing frameworks still suffer from low success rates in closed-loop evaluations, highlighting their limitations in real-world deployment. In this paper, we introduce X-Driver, a unified multi-modal large language models(MLLMs) framework designed for closed-loop autonomous driving…

This https://arxiv.org/abs/2303.17191 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the continuity of Følner averages
It is known that if each point $x$ of a dynamical system is generic for some invariant measure $μ_x$, then there is a strong connection between certain ergodic and topological properties of that system. In particular, if the acting group is abelian and the map $x\mapsto μ_x$ is continuous, then every orbit closure is uniquely ergodic. In this note, we show that if the acting group is not abelian, orbit closures may well support more than one ergodic measure even if $x\mapsto μ_x$ is contin…

Holy cow!
Exclusive: Hackers Leak 86 Million AT&T Records with Decrypted SSNs
https://hackread.com/hackers-leak-86m-att-records-with-decrypted-ssns/

Exclusive: Hackers Leak 86 Million AT&T Records with Decrypted SSNs
Follow us on Bluesky, Twitter (X), Mastodon and Facebook at @Hackread

To Grok: "Why is Neuralink so vague about their Neuralink Blindsight brain implant, describing it as technology to "generate visual perception" - even unpatterned flashes of light qualify as such?" https://x.com/i/grok/share/vI84HuktzHHh093wRbd6YzHXl …

Atmosphärische Flüsse über der #Antarktis könnten sich bis 2100 verdoppeln, mit 2,5-mal mehr #Niederschlag als heute.
Der Grund ist steigende #Luftfeuchtigkeit durch die

Rising atmospheric moisture escalates the future impact of atmospheric rivers in the Antarctic climate system - Communications Earth & Environment
Antarctic atmospheric rivers are projected to double in frequency and cause 2.5 times more precipitation by 2066–2100 due to rising atmospheric moisture, according to large ensemble climate simulations that highlight the sensitivity of future atmospheric rivers to the detection threshold.

This https://arxiv.org/abs/2506.00689 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Mutual-visibility of the disjointness graph of segments in ${\mathbb R}^2$
Let $G=(V(G),E(G))$ be a simple graph, and let $U\subseteq V(G)$. Two distinct vertices $x,y\in U$ are $U$-mutually visible if $G$ contains a shortest $x$-$y$ path that is internally disjoint from $U$. $U$ is called a mutual-visibility set of $G$ if any two vertices of $U$ are $U$-mutually visible. The mutual-visibility number $μ(G)$ of $G$ is the size of a largest mutual-visibility set of $G$. Let $P$ be a set of $n\geq 3$ points in ${\mathbb R}^2$ in general position. The disjointness graph …

Even zwaaien naar de matties (m/v/x) in Basel voor #wceu
*zwaaahaaaait*

When my wife and I are watching things, we're always amused at how many characters in TV shows and movies are named Tommy or Billy. These are obviously fairly common names, but the amount of times we've noticed it in all kinds of different shows like X-Files, SVU etc is so often that it's comical-- it's bizarre. And sometimes in episodes right next to each other in a season. Just a ton of fictional guys out there with these two names across age groups, all over popular cultur…

This https://arxiv.org/abs/2503.22664 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Identities of relatively free algebras of Lie nilpotent associative algebras
In this paper, we consider the relatively free algebra of rank $n$, $F_n(\mathfrak{N}_p)$, in the variety of Lie nilpotent associative algebras of index $p$, denoted by $\mathfrak{N}_p$, over a field of characteristic zero. We describe an explicit minimal basis for the polynomial identities of $F_n(\mathfrak{N}_p)$ when $p=3$ and $p=4$, for all $n$, except for $F_3(\mathfrak{N}_4)$. In the general case, we exhibit a lower and an upper bound for the minimal $k$ such that $[x_1,x_2]\cdots[x_{2k-1…

Maybe it could even guess when you've been around someone, setting aside blocks where your hrv, etc. seem to be fairly uniform...and one could then identify that block as being x or y (could be a person, ones pet, watching a TV show) and then it could watch for similar patterns of measurements and ask if you were in xs proximity again, over time we might find unique signatures associated with specific people, activities, locations?

This https://arxiv.org/abs/2505.23240 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Joint estimation of smooth graph signals from partial linear measurements
Given an undirected and connected graph $G$ on $T$ vertices, suppose each vertex $t$ has a latent signal $x_t \in \mathbb{R}^n$ associated to it. Given partial linear measurements of the signals, for a potentially small subset of the vertices, our goal is to estimate $x_t$'s. Assuming that the signals are smooth w.r.t $G$, in the sense that the quadratic variation of the signals over the graph is small, we obtain non-asymptotic bounds on the mean squared error for jointly recovering $x_t$'s, fo…

AI?
”The staff was incredibly helpful and welcoming, just like I remembered. A special mention goes to X, the talented barman, who once again delivered drinks that were not only delicious but prepared with real dedication and professionalism. His attention to detail and friendly approach added so much to the overall experience.
Whether it's your first visit or your fifth, Y is a must-stop in Graz for anyone who appreciates quality drinks, great service, and a perfect city cent…

This https://arxiv.org/abs/2504.19616 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Exploring circumstellar chemistry in X-ray emitting AGB stars
Aims. Our goal is to characterize the chemistry and physical conditions of the circumstellar envelopes (CSEs) of Asymptotic Giant Branch (AGB) binary candidate stars with UV-excess and X-ray emission, in particular, to identify the effects of the internal X-ray emission in the abundance of certain key molecules. Methods. We observed the 86.0-94.0 and 260.0-272.5 GHz spectral ranges searching for rotational transitions of the X-ray sensitive molecule $HCO^{+}$ in four AGB stars, two of them dete…

TDCOSMO 2025 - cosmological constraints from strong lensing time delays: #H0 = 72-73, surprise, not) -> thread https://x.com/DScol/status/1930244844385120688

US-General Grynkewich wird neuer NATO-Militärchef
Der US-General Alexus Grynkewich wird neuer Oberbefehlshaber der NATO-Truppen in Europa. Der Nordatlantikrat stimmte seiner Nominierung in Brüssel zu, wie eine Sprecherin der Militärallianz auf der Online-Plattform X mitteilte. Grynkewich übernimmt die Militärführung der NATO im vierten Jahr des Ukraine-Krieges und zum Zeitpunkt massiver Aufrüstung in Europa.
Im Sommer soll G…
📑

Ukraine-Liveblog: ++ Satellitenbilder zeigen Schäden an Flugzeugen ++
Nach dem ukrainischen Angriff vom Sonntag auf russische Militärstützpunkte sind auf Satellitenbildern Schäden an einigen Maschinen zu sehen. Im Norden der Ukraine sind bei Angriffen laut Behörden mindestens fünf Menschen getötet worden. Der Liveblog vom Donnerstag zum Nachlesen.

📢 Niederlande: Rechtspopulist Wilders lässt Koalition platzen
Der Rechtspopulist Geert Wilders verlässt die niederländische Vier-Parteien-Koalition. Das teilte er auf der Plattform X mit. Hintergrund ist ein Streit über die Asylpolitik. Wilders sah seinen harten Kurs nicht erfüllt.
➡️ ht…

Niederlande: Rechtspopulist Wilders lässt Koalition platzen
Der Rechtspopulist Geert Wilders verlässt die niederländische Vier-Parteien-Koalition. Das teilte er auf der Plattform X mit. Hintergrund ist ein Streit über die Asylpolitik. Wilders sah seinen harten Kurs nicht erfüllt.

Good stuff for Mac Users. I’ve used it forever. Really handy, and it works well.
#Software #Mac #MacOS

St. Clair Software (@stclairsoft@mstdn.social)
Attached: 1 image Default Folder X 6.1.6 is out! It includes a Focus filter to automatically switch folder sets when you activate a macOS Focus. It's also faster in file dialogs and fixes issues with keyboard shortcuts, Finder-click, keyboard focus and making new folders. https://www.stclairsoft.com/blog/2025/05/13/default-folder-x-6-1-6-automatically-swap-favorites-and-default-folders-when-you-switch-macos-focus-modes

Die Bundesnetzagentur will das Vorgehen gegen verbotene Postings auf Social Media stärken: Die drei Organisationen HateAid, den Bundesverband Onlinehandel und die Verbraucherzentrale Bundesverband wurden als sogenannte »Trusted Flagger« zertifiziert. Sie sollen helfen, der Flut an Inhalten auf Facebook, X oder TikTok Herr zu werden. #Spiegel

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Mies
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Changing Look AGN: A study of Optical/UV and the Highly Ionized Fe K$\alpha$ X-ray Line Flux Variations Using Photo-Ionization Simulations
Tek P. Adhikari, Santanu Mondal, Zhicheng He, Agata Rozanska, Krzysztof Hryniewicz
https://arxiv.org/abs/2506.03540

Changing Look AGN: A study of Optical/UV and the Highly Ionized Fe K$α$ X-ray Line Flux Variations Using Photo-Ionization Simulations
Significant variability in broad emission line strengths of active galactic nuclei (AGN) over months to years has been observed, often accompanied by intrinsic continuum changes. Such spectral variability challenges the traditional AGN classification scheme, which attributes differences between Type 1 and Type 2 to geometrical effects, as transitions between these types occur on timescales shorter than viscous ones. In this work, using the {\sc cloudy} photo-ionization simulations, we investiga…

This https://arxiv.org/abs/2505.22813 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

X-Factor: Quality Is a Dataset-Intrinsic Property
In the universal quest to optimize machine-learning classifiers, three factors -- model architecture, dataset size, and class balance -- have been shown to influence test-time performance but do not fully account for it. Previously, evidence was presented for an additional factor that can be referred to as dataset quality, but it was unclear whether this was actually a joint property of the dataset and the model architecture, or an intrinsic property of the dataset itself. If quality is truly d…

auch sehr tückisch auf dem heutigen Weg durch die Stadt: hier geht es auf den benutzungspflichtigen Geh- und Radweg.
Keine 5m später, direkt in der Kurve, steht dann diese Absperrung für die andere Richtung voll im Weg. :-\
#Baustellenblockade #AmKochenhof

A Study on the MCP x A2A Framework for Enhancing Interoperability of LLM-based Autonomous Agents
Cheonsu Jeong
https://arxiv.org/abs/2506.01804 https://

A Study on the MCP x A2A Framework for Enhancing Interoperability of LLM-based Autonomous Agents
This paper provides an in-depth technical analysis and implementation methodology of the open-source Agent-to-Agent (A2A) protocol developed by Google and the Model Context Protocol (MCP) introduced by Anthropic. While the evolution of LLM-based autonomous agents is rapidly accelerating, efficient interactions among these agents and their integration with external systems remain significant challenges. In modern AI systems, collaboration between autonomous agents and integration with external t…

This https://arxiv.org/abs/2505.15915 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On spatial decay for coherent states of the Benjamin-Ono equation
We consider solutions to the Benjamin-Ono equation $$\partial_t u - H \partial_x^2 u = -\partial_x(u^2)$$ which are localized in a reference frame moving to the right with constant speed. We show that any such solution that decays at least like $\langle x\rangle^{-1-ε}$ for some $ε> 0$ in a comoving coordinate frame must in fact decay like $\langle x\rangle^{-2}$. In view of the explicit soliton solutions, this decay rate is sharp. Our proof has two main ingredients. The first is microloc…

Unramified Brauer groups of homogeneous spaces with finite stabilisers and the Grunwald Problem
Lucas Lagarde
https://arxiv.org/abs/2506.02600 https://

Unramified Brauer groups of homogeneous spaces with finite stabilisers and the Grunwald Problem
We provide an algorithm for calculating the unramified Brauer group of a homogeneous space $X$ of a semi-simple simply connected group $H$ with finite geometric stabiliser over any field of characteristic 0. When $k$ is a number field, we use the obtained description of the unramified Brauer group in order to study the Brauer-Manin obstruction to weak approximation on $X$. In particular, we provide an algorithm to compute the Brauer-Manin obstruction on $X$, which guarantees effectivity of the …

This https://arxiv.org/abs/2305.19415 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Euclidean nets under isometric embeddings
Suppose that there exists a discrete subset $X$ of a complete, connected, $n$-dimensional Riemannian manifold $M$ such that the Riemannian distances between points of $X$ correspond to the Euclidean distances of a net in $\mathbb{R}^{n}$. What can then be derived about the geometry of $M$? In arXiv:2004.08621 it was shown that if $n=2$ then $M$ is isometric to $\mathbb{R}^{2}$. In this paper we show two consequential geometric properties that the manifold $M$ shares with the Euclidean space in …

🇺🇦 #NowPlaying on KEXP's #VarietyMix
Jorja Smith:
🎵 The Way I Love You
#JorjaSmith
https://thedjedits.bandcamp.com/track/jorja-smith-x-wiley-skepta-jme-ms-d-can-you-hear-the-way-i-love-you-mashup-dirty
https://open.spotify.com/track/6u1xR1LKAiahXPrwjNCkky

This https://arxiv.org/abs/2502.15465 has been replaced.
link: https://scholar.google.com/scholar?q=a

Revisiting gluon density from the BK equation with kinematical constraint and large x terms
We perform analysis of the small x non-linear evolution equation formulated in momentum space supplemented by higher order terms. The equation is defined in wide range of transverse momentum and longitudinal momentum fraction extending previous studies performed in \cite{Kutak:2003bd,Kutak:2004ym}. The linear part of the equation is motivated by the renormalization group improved small x approach which accounts for resummation of higher orders, and includes collinear splitting function and kine…

This https://arxiv.org/abs/2005.10529 has been replaced.
link: https://scholar.google.com/scholar?q=a

Boundary maps and reducibility for cocycles into the isometries of CAT(0)-spaces
Let $Γ$ be a discrete countable group acting isometrically on a measurable field $\mathbf{X}$ of CAT(0)-spaces of finite telescopic dimension over some ergodic standard Borel probability $Γ$-space $(Ω,μ)$. If $\mathbf{X}$ does not admit any invariant Euclidean subfield, we prove that the measurable field $\widehat{\mathbf{X}}$ extended to a $Γ$-boundary admits an invariant section. In the case of constant fields this shows the existence of Furstenberg maps for measurable cocycles, extendin…

This https://arxiv.org/abs/2501.00671 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sylvester's problem for beta-type distributions
Consider $d+2$ i.i.d. random points $X_1,\ldots, X_{d+2}$ in $\mathbb R^d$. In this note, we compute the probability that their convex hull is a simplex focusing on three specific distributional settings: (i) the distribution of $X_1$ is multivariate standard normal; (ii) the density of $X_1$ is proportional to $(1-\|x\|^2)^β$ on the unit ball (the beta distribution); (iii) the density of $X_1$ is proportional to $(1+\|x\|^2)^{-β}$ (the beta prime distribution). In the Gau…

🇺🇦 Auf radioeins läuft...
Empire Of The Sun:
🎵 Standing On The Shore
#NowPlaying #EmpireOfTheSun
https://teambbc.bandcamp.com/track/empire-of-the-sun-x-standing-on-the-shore
https://open.spotify.com/track/5g7Qylrck8rh2lUgEWPQVS

Isotopisms of quadratic quasigroups
Jack Allsop
https://arxiv.org/abs/2506.02446 https://arxiv.org/pdf/2506.02446

Isotopisms of quadratic quasigroups
A quasigroup is a pair $(Q, \cdot)$ where $Q$ is a non-empty set and $\cdot$ is a binary operation on $Q$ such that for every $(u, v) \in Q^2$ there exists a unique $(x, y) \in Q^2$ such that $u \cdot x = v = y \cdot u$. Let $q$ be an odd prime power, let $\mathbb{F}_q$ denote the finite field of order $q$, and let $\mathcal{R}_q$ denote the set of non-zero squares in $\mathbb{F}_q$. Let $\{a, b\} \subseteq \mathbb{F}_q$ be such that $\{ab, (a-1)(b-1)\} \subseteq \mathcal{R}_q$. Let $\mathcal{Q…

As the Senate weighs possible changes to the state and local tax (SALT) deduction cap as part of the tax portion of the "big, beautiful bill,"
House Republicans from blue states are already threatening to derail the bill's prospects.
"Let's be clear — no SALT, no deal," New York Republican Mike Lawler said Wednesday in a post on X

Trump admin live updates: Trump signs proclamation banning travel from 12 countries
The president cited national security concerns for enacting the ban.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem
Masaya Kitajima
https://arxiv.org/abs/2506.03331 https://

Generalized Hardy's identity for the astroid-type p-circle lattice point problem
Let $r$ be a positive real number and $p$ satisfy $(2/p)\in\mathbb{N}$. Then, we consider the lattice point problem of the closed curves astroid-type $p$-circle $\{x\in\mathbb{R}^{2}|\ |x_{1}|^{p}+|x_{2}|^{p}=r^{p}\}$ which generalize the circle. In investigating the asymptotic behavior of the error term in the area approximation of the circle, G.H. Hardy conjectured an infimum for the evaluation in 1917. One of the grounds for this conjecture is the Hardy's identity, w…

Verbandsklage: Tiktok soll Verbrauchern Schadenersatz zahlen
Die gemeinnützige Stiftung Somi hat sich auf Datenschutz-Sammelklagen von Verbrauchern gegen Techriesen spezialisiert. Nach der Plattform X ist nun Tiktok dran.

On the Inversion Modulo a Power of an Integer
Guangwu Xu, Yunxiao Tian, Bingxin Yang
https://arxiv.org/abs/2506.02491 https://arxiv.o…

On the Inversion Modulo a Power of an Integer
Recently, Koc proposed a neat and efficient algorithm for computing $x = a^{-1} \pmod {p^k}$ for a prime $p$ based on the exact solution of linear equations using $p$-adic expansions. The algorithm requires only addition and right shift per step. In this paper, we design an algorithm that computes $x = a^{-1} \pmod {n^k}$ for any integer $n>1$. The algorithm has a motivation from the schoolbook multiplication and achieves both efficiency and generality. The greater flexibility of our algorithm …

Huawei Pura X review: the ~$1,050, China-only clamshell is Huawei's first flagship running HarmonyOS 5, with novel ergonomics and an incomplete app ecosystem (Bloomberg)
https://www.bloomberg.com/news/features/20

Tunable direct bandgap and optical response in \ch{Mo_{1-x}W_xS2} monolayer alloys: A first-principles investigation
Kevin Ndang Amassa, Jean-Pierre Tchapet Njafa, Anne Justine Etindele, Chetty Nithaya, Serge Guy Nana Engo
https://arxiv.org/abs/2506.01464

Tunable direct bandgap and optical response in \ch{Mo_{1-x}W_xS2} monolayer alloys: A first-principles investigation
This study presents a comprehensive first-principles investigation of the structural, electronic and optical properties of monolayer \ch{Mo_{1-x}W_xS2} alloys, systematically exploring the full compositional range ($x=0$ to $1$) using density functional theory (DFT). We establish that these alloys are thermodynamically stable and maintain the characteristic 2H crystal structure with minimal structural perturbation upon alloying. A key finding is the preservation of a direct bandgap at the $K$-p…

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 …

Pinched Arnol'd tongues for Families of circle maps
Philip Boyland
https://arxiv.org/abs/2506.02988 https://arxiv.org/pdf/2506.02…

Pinched Arnol'd tongues for Families of circle maps
The family of circle maps \begin{equation*} f_{b, ω} (x) = x + ω+ b\, ϕ(x) \end{equation*} is used as a simple model for a periodically forced oscillator. The parameter $ω$ represents the unforced frequency, $b$ the coupling, and $ϕ$ the forcing. When $ϕ= \frac{1}{2 π} \sin(2 πx)$ this is the classical Arnol'd standard family. Such families are often studied in the $(ω,b)$-plane via the so-called tongues $T_β$ consisting of all $(ω,b)$ such that $f_{b, ω}$ has rotation number $β$. …

🇺🇦 Auf radioeins läuft...
NEIKED feat. Portugal. The Man:
🎵 Glide
#NowPlaying #NEIKED #PortugalTheMan
https://mikizaradj.bandcamp.com/track/neiked-x-portugal-the-man-glide-miki-zara-rework

PSZ2 G181.06 48.47 - X-Ray Exploration of / Radio Analysis of / Weak-lensing Analysis and Merging Scenario Reconstruction of a Low-mass Cluster with Exceptionally Distant Radio Relics: #GalaxyClusters on Course to Crash Again, NASA's Chandra Finds: https://chandra.si.edu/photo/2025/g181/ / https://www.nasa.gov/image-article/galaxy-clusters-on-course-to-crash-again-nasas-chandra-finds/

This https://arxiv.org/abs/2504.18632 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Backward stochastic differential equations with nonlinear Young driver
We study backward stochastic differential equations (BSDEs) involving a nonlinear Young integral of the form $\int_{t}^{T}g(Y_{r})η(dr,X_{r})$, where the driver $η(t,x)$ is a space-time Hölder continuous function and $X$ is a diffusion process. Solutions to such equations provide a probabilistic interpretation of the solutions to stochastic partial differential equations (SPDEs) driven by space-time noise. We first obtain the existence and uniqueness of the solutions to these BSDEs under the…

This https://arxiv.org/abs/2310.19597 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Automorphism groups of $\mathbb{P}^1$-bundles over ruled surfaces
We classify the pairs $(X,π)$, where $π\colon X\to S$ is a $\mathbb{P}^1$-bundle over a non-rational ruled surface $S$ and $\mathrm{Aut}^\circ(X)$ is relatively maximal, i.e., maximal with respect to the inclusion in the group $\mathrm{Bir}(X/S)$. The results hold over any algebraically closed field of characteristic zero.

This https://arxiv.org/abs/2502.12423 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Local well-posedness for a system of modified KdV equations in modulation spaces
In this work, we consider the initial value problem (IVP) for a system of modified Korteweg-de Vries (mKdV) equations \begin{equation*} \begin{cases} \partial_t v + \partial_x^3 v+ \partial_x (v w^2) = 0, \hspace{0.98 cm} v(x,0)=ψ(x),\\ \partial_t w + α\partial_x^3 w+\partial_x (v^2 w) = 0,\hspace{0.5 cm} w(x,0)=ϕ(x). \end{cases} \end{equation*} The main interest is in addressing the well-posedness issues of the IVP when the initial data are considered in the modulation space $M_s^{2,p}(…

Google pauses the rollout of Photos' AI-powered Ask Photos feature due to issues with latency, quality, and user experience, per a Google product manager on X (Hayden Field/The Verge)
https://www.theverge.com/news/678858/google-photos-ask-…

Google quietly paused the rollout of its AI-powered ‘Ask Photos’ search feature
Google paused the rollout of “Ask Photos,” its Gemini AI-powered natural language search feature in Google Photos, citing problems with speed and quality.

This https://arxiv.org/abs/2412.18457 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Patterns of Geodesics, Shearing, and Anosov Representations of the Modular Group
Let $X=SL_3(\R)/SO(3)$. Let $\cal DFR$ be the space of discrete faithful representations of the modular group into ${\rm Isom\/}(X)$ which map the order $2$ generator to an isometry with a unique fixed point. I prove many things about the component $\cal B$ of $\cal DFR$ known as the Barbot component: It is homeomorphic to $\R^2 \times [0,\infty)$. The boundary parametrizes the Pappus representations from [{\bf S0\/}]. The interior parametrizes the complete extension of the family of Anosov rep…

On the number of exceptional intervals to the prime number theorem in short intervals
Ayla Gafni, Terence Tao
https://arxiv.org/abs/2505.24017 https://

On the number of exceptional intervals to the prime number theorem in short intervals
For a fixed exponent $0 < θ\leq 1$, it is expected that we have the prime number theorem in short intervals $\sum_{x \leq n < x+x^θ} Λ(n) \sim x^θ$ as $x \to \infty$. From the recent zero density estimates of Guth and Maynard, this result is known for all $x$ for $θ> \frac{17}{30}$ and for almost all $x$ for $θ> \frac{2}{15}$. Prior to this work, Bazzanella and Perelli obtained some upper bounds on the size of the exceptional set where the prime number theorem in short intervals fails. We…

This https://arxiv.org/abs/2408.14648 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Induced Saturation of the Poset 2C_2
Given a set $X$, the power set $\mathbb{P}(X)$, and a finite poset $P$, a family $F\subset \mathbb{P}(X)$ is said to be induced-$P$-free if there is no injection $ϕ: P\rightarrow \mathbb{F}$ such that $ϕ(p)\subseteqϕ(q)$ if and only if $p\leq_{P} q$, for all $p, q \in P$. The family $F$ is induced-$P$-saturated if it is maximal with respect to being induced-$P$-free. If $n=|X|$, then the size of the smallest induced-$P$-saturated family in $\mathbb{P}(X)$ is denoted $sat(n,P)$. T…

CGCS 6306, another X-ray-emitting asymptotic giant branch star confirmed to be a symbiotic binary
Jaroslav Merc, Mart\'in A. Guerrero, Jes\'us A. Toal\'a, Roberto Ortiz
https://arxiv.org/abs/2505.24660

CGCS 6306, another X-ray-emitting asymptotic giant branch star confirmed to be a symbiotic binary
A number of asymptotic giant branch (AGB) stars are known to exhibit UV excess and/or X-ray emission. These have been considered signposts of a hot white dwarf (WD) companion in a symbiotic system (SySt), but AGB stars are so bright that they easily outshine these companions hampering their detection at optical wavelengths. A recent multi-wavelength investigation on the X-ray-emitting AGB (X-AGB) star Y Gem has confirmed the presence of a WD companion and, thus, its SySt nature. Our goal is to …

This https://arxiv.org/abs/2412.17457 has been replaced.
initial toot: https://mastoxiv.page/@a…

Optical Properties and Spin States of Inter-layer Carbon Defect Pairs in Hexagonal Boron Nitride: A First-Principles Study
Substitutional carbon defects in hexagonal boron nitride (hBN) are prominent single photon emitters (SPEs), and their potential for spin activity ($S\geq1$) is particularly intriguing. While studies have largely focused on intra-layer defects, we employ density functional theory (DFT) to investigate inter-layer dimers of identical carbon species (C$_X$C$_X$). We demonstrate that these C$_X$C$_X$ pairs can exhibit a stable triplet spin state at room temperature when closely spaced (e.g., within …

Slicing Correspondences with High Degree Hypersurfaces
Ishan Banerjee
https://arxiv.org/abs/2506.02977 https://arxiv.org/pdf/2506.029…

Slicing Correspondences with High Degree Hypersurfaces
We approximately compute the correspondence degree (as defined by Lazarsfeld and Martin) between two unbalanced complete intersections. This is accomplished by showing that the procedure of taking a subvariety of a product $Y \times Y'$ and intersecting it with $X \times Y'$ (for $X$ a sufficiently ample smooth divisor in $Y$) induces a bijection between two sets of varieties. This may be of independent interest.

Trump says Elon Musk "went CRAZY" and that canceling his government contracts is "the easiest way to save money", as their One Big Beautiful bill feud escalates (Kevin Breuninger/CNBC)
https://www.cnbc.com/2025/06/05/trump-musk-crazy-…

Trump says Musk went 'CRAZY,' suggests cutting government contracts for his companies
Musk is the CEO of Tesla and SpaceX and founded The Boring Company, xAI and Neuralink. He also owns the social media platform X.

Simplicial volume via foliated simplices and duality
Filippo Sarti
https://arxiv.org/abs/2506.02962 https://arxiv.org/pdf/2506.02962

Simplicial volume via foliated simplices and duality
Let $M$ be an aspherical oriented closed connected manifold with universal cover $\widetilde{M}\to M$ and let $Γ=π_1(M)\curvearrowright (X,μ)$ be a measure preserving action on a standard Borel probability space. We consider singular foliated simplices on the measured foliation $Γ\backslash(\widetilde{M}\times X)$ defined by Sauer and we compare the \emph{real singular foliated homology} with classic singular homology. We introduce a notion of \emph{foliated fundamental class} and we prove …

Symmetrization for high dimensional dependent random variables
Jonathan B. Hill
https://arxiv.org/abs/2506.00547 https://arxiv.org/pd…

Symmetrization for high dimensional dependent random variables
We establish a generic symmetrization property for dependent random variables $\{x_{t}\}_{t=1}^{n}$ on $\mathbb{R}^{p}$, where $p$ $>>$ $n$ is allowed. We link $\mathbb{E}ψ(\max_{1\leq i\leq p}|1/n\sum_{t=1}^{n}(x_{i,t}$ $-$ $\mathbb{E}x_{i,t})|)$ to $\mathbb{E}ψ(\max_{1\leq i\leq p}|1/n$ $\sum_{t=1}^{n}η_{t}(x_{i,t}$ $-$ $\mathbb{E}% x_{i,t})|)$ for non-decreasing convex $ψ$ $:$ $[0,\infty )$ $\rightarrow $ $\mathbb{R}$, where $\{η_{t}\}_{t=1}^{n}$ are block-wise indep…

This https://arxiv.org/abs/2404.04747 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The $L^1$ mean of the exponential sum of the divisor function
We give a relatively simple proof that \[ \int _0^1\left |\sum _{n\leq x}d(n)e(nα)\right |dα\asymp \sqrt x.\]

This https://arxiv.org/abs/2401.04391 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Kawamata-Miyaoka type inequality for canonical $\mathbb Q$-Fano varieties II: Terminal $\mathbb Q$-Fano threefolds
We prove an optimal Kawamata-Miyaoka type inequality for terminal $\mathbb Q$-Fano threefolds with Fano index at least $3$. As an application, we obtain that any terminal $\mathbb Q$-Fano threefold $X$ satisfies the following Kawamata-Miyaoka type inequality \[ c_1(X)^3 < 3c_2(X)c_1(X). \]

This https://arxiv.org/abs/2505.11172 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the holomorphic foliations admitting a common invariant algebraic curve
In this paper, we prove the following result using an entirely elementary method: for any algebraic curve $C$ given by $f(x,y)=0$, where $f(x,y)$ is a weakly tame polynomial in $ \mathbb{K}[x,y]$, the $\mathbb{K}[x,y]$-module of polynomial 1-forms admitting $C$ as an invariant curve is generated by two polynomail 1-forms, one of which is $\mathrm{d}f$, if and only if, $f$ belongs to the Jacobian ideal $\langle f_x, f_y\rangle$ in $\mathbb{K}[x,y]$, where $\mathbb{K}\subseteq\mathbb{C}$ is an ar…

Share of news influencers on Bluesky has doubled after the 2024 US election to 43%, but X remains popular, with 82% of news influencers maintaining an account (Pew Research Center)
https://www.pewresearch.org/short-reads/20

Bluesky has caught on with many news influencers, but X remains popular
The share of news influencers in our sample with a Bluesky account roughly doubled in the four months after Election Day 2024, from 21% beforehand to 43% by March.

The number of primes not in a numerical semigroup
Yong-Gao Chen, Hui Zhu
https://arxiv.org/abs/2506.03625 https://arxiv.org/pdf/2506.…

The number of primes not in a numerical semigroup
For two coprime positive integers $a,b$, let $π^* (a, b)$ be the number of primes that cannot be represented as $au+bv$, where $u,v$ are nonnegative integers. In this paper, we prove that $π^* (a, b)\ge 0.014 π(ab-a-b)$ and pose following conjecture: $π^* (a, b)\ge \frac 12 π(ab-a-b)$, where $π(x)$ denotes the number of primes not exceeding $x$. This conjecture is confirmed for $1\le a\le 8$.

This https://arxiv.org/abs/2009.14324 has been replaced.
link: https://scholar.google.com/scholar?q=a

Characterizing Jacobians via the KP equation and via flexes and degenerate trisecants to the Kummer variety: an algebro-geometric approach
This paper is withdrawn since we found a flaw in the proof of Theorem 4, asserting that the base locus of the complete linear system of an ample line bundle on a complex abelian variety is reduced. The error is in page 7, line $ -14$, where we claim that the divisor "mathcal E" on the variety $X$ is linearly equivalent to zero. This is untrue. For instance, it would imply that, for a non-torsion point $x$ on an abelian surface $A$, letting $E_x$, $E_{-x}$, and $E_0$ the exceptional curves in th…

Markovian projections for functionals of It\^o semimartingales with jumps
Martin Larsson, Shukun Long
https://arxiv.org/abs/2506.00762 https://

Markovian projections for functionals of Itô semimartingales with jumps
Given an Itô semimartingale $X$, its Markovian projection is an Itô semimartingale $\widehat{X}$, with Markovian differential characteristics, that matches the one-dimensional marginal laws of $X$. One may even require certain functionals of the two processes to have the same fixed-time marginals, at the cost of enhancing the differential characteristics of $\widehat{X}$ but still in a Markovian sense. In the continuous case, the definitive result on existence of Markovian projections was obt…

X aims to roll out an "XChat" messaging feature "with encryption, vanishing messages and the ability to send any kind of file" to all users this week (Sarah Perez/TechCrunch)
https://techcrunch.com/2025/06/02/elon

Elon Musk says XChat is rolling out to all, but questions remain about its alleged security | TechCrunch
Elon Musk on Sunday announced that a new version of X's Direct Messaging (DM) feature, XChat, was rolling out with support for features like vanishing

This https://arxiv.org/abs/2406.07575 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the largest prime factor of quadratic polynomials
Let $x$ denote a sufficiently large integer. We show that the recent result of Grimmelt and Merikoski actually yields the largest prime factor of $n^2 +1$ is greater than $x^{1.317}$ infinitely often. As an application, we give a new upper bound for the number of integers $n \leqslant x$ which $n^2 +1$ has a primitive divisor.

This https://arxiv.org/abs/2311.01835 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Surjective rational maps and del Pezzo surfaces
We study surjective (not necessarily regular) rational endomorphisms $f$ of smooth del Pezzo surfaces $X$. We prove that under certain natural non\,-\,degeneracy condition $f$ can have degree bigger than $1$ only when $(-K_X^2) > 5$. Some structural properties of $f$ in the case $X = \p^2$ are also established.

This https://arxiv.org/abs/2505.23488 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Moduli spaces of twisted equivariant G-bundles over a curve
Let $X$ be a compact Riemann surface, $Γ$ a finite group of automorphisms of $X$ and $G$ a connected reductive complex Lie group with center $Z$. If we equip this data with a homomorphism $θ:Γ\to\text{Aut}(G)$ and a 2-cocycle $c:Γ\timesΓ\to Z$, there is a notion of $(θ,c)$-twisted $Γ$-equivariant $G$-bundle over $X$. The aim of this paper is to construct a coarse moduli space of isomorphism classes of polystable $(θ,c)$-twisted equivariant $G$-bundles over $X$, according to the definiti…