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Order in Partial Markov Categories
Elena Di Lavore, Mario Rom\'an, Pawe{\l} Soboci\'nski, M\'ark Sz\'eles
https://arxiv.org/abs/2507.19424 https://

Order in Partial Markov Categories
Partial Markov categories are a recent framework for categorical probability theory, providing an abstract account of partial probabilistic computation. In this article, we discuss two order relations on the morphisms of a partial Markov category. In particular, we prove that every partial Markov category is canonically enriched over the category of preordered sets and monotone maps. We show that our construction recovers several well-known order enrichments. We also demonstrate that the existe…

Kliamwandel: Prognosen zum Meeresspiegelanstieg überraschend präzise eingetreten
Seit etwas mehr als 30 Jahren vermessen Satelliten weltweit den Meeresspiegel. Ein Abgleich mit den Prognosen zu dessen Anstieg zeigt jetzt, wie gut die waren.

On $q$-deformed Markov numbers. Cohn matrices and perfect matchings with weighted edges
Sam Evans, Perrine Jouteur, Sophie Morier-Genoud, Valentin Ovsienko
https://arxiv.org/abs/2507.19080

On $q$-deformed Markov numbers. Cohn matrices and perfect matchings with weighted edges
We consider a natural $q$-deformation of the classical Markov numbers. This $q$-deformation is closely related to $q$-deformed rational numbers recently introduced by two of us. Both notions, those of $q$-rationals and $q$-Markov numbers, are based on invariance with respect to the action of the modular group $mathrm{PSL}(2,\mathbb{Z})$. We prove that every Markov number has a unique $q$-deformation, which is a monic unimodal palindromic Laurent polynomial with positive integer coefficients. Th…

Quantum Markovian master equation in the high-temperature limit
Ricardo C. Zamar, J. Agust\'in Taboada
https://arxiv.org/abs/2508.18385 https://arxiv.o…

Quantum Markovian master equation in the high-temperature limit
We present a critical derivation of the high-temperature quantum Markovian master equation (HTME), examining its foundational assumptions, their quantum-mechanical implications, and its range of validity. Starting from the Born-Markov master equation, and combining the spin Hamiltonian eigenoperator formalism with a linear expansion in statistical coefficients, as the only assumption, we obtain a quantum dissipator that generalizes the Abragam-Redfield-Hubbard inhomogeneous master equation (ARH…

Lower Bounds on the Size of Markov Equivalence Classes
Erik Jahn, Frederick Eberhardt, Leonard J. Schulman
https://arxiv.org/abs/2506.20933 https://…

Lower Bounds on the Size of Markov Equivalence Classes
Causal discovery algorithms typically recover causal graphs only up to their Markov equivalence classes unless additional parametric assumptions are made. The sizes of these equivalence classes reflect the limits of what can be learned about the underlying causal graph from purely observational data. Under the assumptions of acyclicity, causal sufficiency, and a uniform model prior, Markov equivalence classes are known to be small on average. In this paper, we show that this is no longer the ca…

Thread's "Repost" button actually has 4 options 😵‍💫:
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"Markup" takes a screenshot of the post, to be used as image for your post. Allows user to mark-up the image (draw arrows, circle things, etc).
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#vereinfachteSprache
Der Klimawandel lässt die Gletscher schmelzen. Dadurch gibt es weniger Wasser in Bächen und Flüssen. Die Gletscher verlieren weltweit viel Eis. In Grönland und der Antarktis schmilzt das Eis schneller als früher. Das führt zu steigendem Meeresspiegel. Was bedeutet das für Menschen in Küstenregionen?

Der Klimawandel schrumpft die Gletscher. Wassermangel in den Bächen und Flüssen. (vereinfachte Sprache)
Das Abschmelzen der Gletscher ist ein Kippelement des Klimasystems. Es führt zu einem Anstieg des Meeresspiegels und hat weitreichende Folgen für die Menschheit.

Übrigens: #Lübeck, ne? Wenn man einen Tag Zeit hat, eher länger schläft, #Marzipan mag (aber Niederegger eher nicht so), auch #Fisch sehr gern hat (aber der Mann nicht, sondern vegetarisch), und g…

Symbolic dynamics, shadowing and representation of real numbers with some countably piecewise linear Markov maps
Zolt\'an Kalocsai
https://arxiv.org/abs/2508.17159 https://

Symbolic dynamics, shadowing and representation of real numbers with some countably piecewise linear Markov maps
We study piecewise linear Markov maps, with countable Markov partitions, inspired by a problem of the Miklós Schweitzer competition of the János Bolyai Mathematical Society in 2022. We introduce $\ell$-Markov partitions and apply ideas of symbolic dynamics to our systems, relating them to Markov shifts. We prove the shadowing property for the system from the competition. We also investigate the possible orbits of rational numbers, for a class of piecewise linear Markov maps which generalize o…

Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games
Yann Kerzreho (ENS Paris Saclay)
https://arxiv.org/abs/2506.21079 https://

Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games
This paper introduces a new approach for approximating the learning dynamics of multiple reinforcement learning (RL) agents interacting in a finite-state Markov game. The idea is to rescale the learning process by simultaneously reducing the learning rate and increasing the update frequency, effectively treating the agent's parameters as a slow-evolving variable influenced by the fast-mixing game state. Under mild assumptions-ergodicity of the state process and continuity of the updates-we prov…