Tootfinder

On equivariant vector bundles on the Fargues--Fontaine curve over a finite extension
Rustam Steingart
https://arxiv.org/abs/2510.12533 https://arxiv.org/pd…

On equivariant vector bundles on the Fargues--Fontaine curve over a finite extension
Let $K/E/\mathbb{Q}_p$ be a tower of finite extensions with $E$ Galois. We relate the category of $G_K$-equivariant vector bundles on the Fargues--Fontaine curve with coefficients in $E$ with $E$-$G_K$-$B$-pairs and describe crystalline and de Rham objects in explicit terms. When $E$ is a proper extension, we give a new description of the category in terms of compatible tuples of $\mathbf{B}_e$-modules, which allows us to compute Galois cohomology in terms of an explicit Čech complex which can…

Bosses are still mandating RTO: workers are going but on their own terms
https://www.cnbc.com/2025/10/06/bosses-are-still-mandating-rto-workers-are-going-but-on-their-own-terms.html

Switzerland launches a preliminary investigation into whether Apple's terms for granting third-party access to NFC tech on iPhones violate its antitrust laws (Tim Hardwick/MacRumors)
https://www.macrumors.com/2025/12/12/apple-pay-swiss-antitrust-probe-nfc/

Apple Pay Faces Swiss Antitrust Investigation Over NFC Access
Switzerland's competition authority has launched a preliminary investigation into whether Apple's terms for granting third-party access to...

Formation of protostars and the launching of stellar core outflows with moving-mesh radiation non-ideal magnetohydrodynamics
Alexander C. Mayer, R\"udiger Pakmor, Thorsten Naab, Oliver Zier, Alexei V. Ivlev, Tommaso Grassi, Paola Caselli, Volker Springel
https://arxiv.org/abs/2510.12620

Formation of protostars and the launching of stellar core outflows with moving-mesh radiation non-ideal magnetohydrodynamics
We present an implementation of radiative transfer with flux-limited diffusion (FLD) for the moving-mesh code {\small AREPO} and use the method in a physical model for the formation of protostars with non-ideal radiation-magnetohydrodynamics (RMHD). We follow previous work in splitting the additional terms to the hydrodynamical equations arising from the inclusion of radiation into terms to be integrated explicitly and implicitly, as the diffusion and coupling terms would impose very restrictiv…

"simple" in terms of superficial appearance. There's some bloody good cinematography on show here. #TOTP

A universal approach to saddle-point methods in attosecond science
Anne Weber, Job Feldbrugge, Emilio Pisanty
https://arxiv.org/abs/2510.12545 https://arxi…

A universal approach to saddle-point methods in attosecond science
Light-matter interactions within the strong-field regime, where intense laser fields can ionise a target via tunnelling, give rise to fascinating phenomena such as the generation of high-order harmonic radiation (HHG). On the atomic scale, these strong-field processes are described in terms of highly-oscillatory time integrals which are often approximated using saddle-point methods. These methods simultaneously simplify the calculations and let us understand the physical processes in terms of s…

Sources: the MLS-Apple TV deal will end in 2029, three and a half years earlier than planned; compensation averages $250M for the three remaining full seasons (Sportico)
https://www.sportico.com/leagues/soccer/2025/apple-mls-streaming-contract-cha…

Apple TV MLS Streaming Deal Will End in 2029 Under Revised Terms
MLS and Apple's streaming rights agreement will now end three and half years early, letting the league explore new partners after the 2026 World Cup.

When even #Firefox ends up in my Mastodon filters. What a timeline. #FuckAI

Liouville results for $(p,q)$-Laplacian elliptic equations with source terms involving gradient nonlinearities
Mousomi Bhakta, Anup Biswas, Roberta Filippucci
https://arxiv.org/abs/2510.12486

Liouville results for $(p,q)$-Laplacian elliptic equations with source terms involving gradient nonlinearities
In this paper, we present a series of Liouville-type theorems for a class of nonhomogeneous quasilinear elliptic equations featuring reactions that depend on the solution and its gradient. Specifically, we investigate equations of the form $-Δ_p u - Δ_q u = f(u,\nabla u)$ with $p > q > 1$, where the nonlinearity $f$ takes forms such as $u^s|\nabla u|^m$ or $u^s + M|\nabla u|^m$ ($s, m\geq 0$). Our approach is twofold. For cases where the reaction term satisfies $|f(u,…

"Conventionally, the output of an AI is graded in a binary way, rewarding it when it gives a correct response and penalizing it when it gives an incorrect one.
In simple terms, in other words, guessing is rewarded — because it might be right — over an AI admitting it doesn't know the answer, which will be graded as incorrect no matter what.
As a result, through "natural statistical pressures," LLMs are far more prone to hallucinate an answer instead of "ac…

Had a great time presenting our paper “Domain-specific tensor languages” today at #ICFP2025 in Singapore 🇸🇬
The images attached are screenshots from the paper as teasers — diagrams for derivative rules, the Riemann curvature 4-tensor in Einstein’s index notation, and the same in diagram form.
📄 Slides:

Combined effects of particle geometry and applied vibrations on the mechanics and strength of entangled materials
Saeed Pezeshki, Francois Barthelat
https://arxiv.org/abs/2510.09933

Combined effects of particle geometry and applied vibrations on the mechanics and strength of entangled materials
Entangled materials offer attractive structural features including tensile strength and large deformations, combined with infinite assembly and disassembly capabilities. How the geometry of individual particles governs entanglement, and in turn translates into macroscopic structural properties, provides a rich landscape in terms of mechanics and offers intriguing possibilities in terms of structural design. Despite this potential, there are major knowledge gaps on the entanglement mechanisms an…

On the Formal Metatheory of the Pure Type Systems using One-sorted Variable Names and Multiple Substitutions
Sebasti\'an Urciuoli (Universidad ORT Uruguay)
https://arxiv.org/abs/2510.12300

On the Formal Metatheory of the Pure Type Systems using One-sorted Variable Names and Multiple Substitutions
We develop formal theories of conversion for Church-style lambda-terms with Pi-types in first-order syntax using one-sorted variables names and Stoughton's multiple substitutions. We then formalize the Pure Type Systems along some fundamental metatheoretic properties: weakening, syntactic validity, closure under alpha-conversion and substitution. Finally, we compare our formalization with others related. The whole development has been machine-checked using the Agda system. Our work demonstrate…

Color Me Correctly: Bridging Perceptual Color Spaces and Text Embeddings for Improved Diffusion Generation
Sung-Lin Tsai, Bo-Lun Huang, Yu Ting Shen, Cheng Yu Yeo, Chiang Tseng, Bo-Kai Ruan, Wen-Sheng Lien, Hong-Han Shuai
https://arxiv.org/abs/2509.10058

Color Me Correctly: Bridging Perceptual Color Spaces and Text Embeddings for Improved Diffusion Generation
Accurate color alignment in text-to-image (T2I) generation is critical for applications such as fashion, product visualization, and interior design, yet current diffusion models struggle with nuanced and compound color terms (e.g., Tiffany blue, lime green, hot pink), often producing images that are misaligned with human intent. Existing approaches rely on cross-attention manipulation, reference images, or fine-tuning but fail to systematically resolve ambiguous color descriptions. To precisely…

Tight Regret Upper and Lower Bounds for Optimistic Hedge in Two-Player Zero-Sum Games
Taira Tsuchiya
https://arxiv.org/abs/2510.11691 https://arxiv.org/pdf…

Tight Regret Upper and Lower Bounds for Optimistic Hedge in Two-Player Zero-Sum Games
In two-player zero-sum games, the learning dynamic based on optimistic Hedge achieves one of the best-known regret upper bounds among strongly-uncoupled learning dynamics. With an appropriately chosen learning rate, the social and individual regrets can be bounded by $O(\log(mn))$ in terms of the numbers of actions $m$ and $n$ of the two players. This study investigates the optimality of the dependence on $m$ and $n$ in the regret of optimistic Hedge. To this end, we begin by refining existing …

PAC-Bayesian Bounds on Constrained f-Entropic Risk Measures
Hind Atbir, Farah Cherfaoui, Guillaume Metzler, Emilie Morvant, Paul Viallard
https://arxiv.org/abs/2510.11169 https:…

PAC-Bayesian Bounds on Constrained f-Entropic Risk Measures
PAC generalization bounds on the risk, when expressed in terms of the expected loss, are often insufficient to capture imbalances between subgroups in the data. To overcome this limitation, we introduce a new family of risk measures, called constrained f-entropic risk measures, which enable finer control over distributional shifts and subgroup imbalances via f-divergences, and include the Conditional Value at Risk (CVaR), a well-known risk measure. We derive both classical and disintegrated PAC…

Revisiting Trust in the Era of Generative AI: Factorial Structure and Latent Profiles
Haocan Sun, Weizi Liu, Di Wu, Guoming Yu, Mike Yao
https://arxiv.org/abs/2510.10199 https:/…

Revisiting Trust in the Era of Generative AI: Factorial Structure and Latent Profiles
Trust is one of the most important factors shaping whether and how people adopt and rely on artificial intelligence (AI). Yet most existing studies measure trust in terms of functionality, focusing on whether a system is reliable, accurate, or easy to use, while giving less attention to the social and emotional dimensions that are increasingly relevant for today's generative AI (GenAI) systems. These systems do not just process information; they converse, respond, and collaborate with users, bl…

More birational involutions
Pietro Beri, Laurent Manivel
https://arxiv.org/abs/2509.10130 https://arxiv.org/pdf/2509.10130…

More birational involutions
For $S$ a very general polarized K3 surface of degree $8n-6$, we describe in geometrical terms a birational involution of the Hilbert scheme $S^{[n]}$ of $n$ points on the surface, whose existence was established from lattice theoretical considerations. In a previous work we studied this involution for $n=3$, with the help of the exceptional Lie group $G_2$, since the Mukai model of $S$ is embedded in its projectivized Lie algebra. Here we use different, more general arguments to show that some…

When Openness Fails: Lessons from System Safety for Assessing Openness in AI
Tamara Paris, Shalaleh Rismani
https://arxiv.org/abs/2510.10732 https://arxiv.…

When Openness Fails: Lessons from System Safety for Assessing Openness in AI
Most frameworks for assessing the openness of AI systems use narrow criteria such as availability of data, model, code, documentation, and licensing terms. However, to evaluate whether the intended effects of openness - such as democratization and autonomy - are realized, we need a more holistic approach that considers the context of release: who will reuse the system, for what purposes, and under what conditions. To this end, we adapt five lessons from system safety that offer guidance on how …

Counting conjugacy classes of elements of finite order in p-compact groups
Jos\'e Cantarero, Bernardo Villarreal
https://arxiv.org/abs/2510.11069 https://

Counting conjugacy classes of elements of finite order in p-compact groups
We express the set of representations from a cyclic $p$-group to a connected $p$-compact group in terms of the associated reflection group and compute its cardinality for each exotic $p$-compact group.

Mordell--Tornheim zeta function: Kronecker limit type formulas and Special values
Sumukha Sathyanarayana, N. Guru Sharan
https://arxiv.org/abs/2510.10093 https://

Mordell--Tornheim zeta function: Kronecker limit type formulas and Special values
In this paper, we establish Kronecker limit type formulas for the generalized Mordell--Tornheim zeta function $Θ(r,s,t,x)$ as a function of the third variable, in terms of Riemann-zeta and Gamma values. We also give series evaluations of $Θ(r,s,t,x)$ in terms of Herglotz-Zagier type functions, and their derivatives. As applications of this, we derive Kronecker limit type formula in the second variable and a new infinite family of modular relations called mixed functional equations. We also st…

Glossary of Technical and Green Terms - Understand key words, abbreviations and other terms used on Earth Notes. #tech #glossary #energy -

Glossary of Technical and Green Terms
Understand key words, abbreviations and other terms used on Earth Notes. #tech #glossary #energy

Discrete Curvatures and Convex Polytopes
Jes\'us A. De Loera, Jillian Eddy, Sawyer Jack Robertson, Jos\'e Alejandro Samper
https://arxiv.org/abs/2510.11894 https://

Discrete Curvatures and Convex Polytopes
We study Forman--Ricci and effective resistance curvatures on the skeleta of convex polytopes. Our guiding questions are: how frequently do polytopal graphs exhibit everywhere positive curvature, and what structural constraints does positivity impose? For Forman--Ricci curvature we derive an exact identity for the average edge curvature in terms of flag $f$-numbers and establish the existence of infinite families of Forman--Ricci-positive polytopes in every fixed dimension $d\ge 6$. We prove fi…

QM2-branes and the Swampland Distance Conjecture in nine dimensions
Mar\'ia Pilar Garc\'ia del Moral, Camilo las Heras, Alvaro Restuccia
https://arxiv.org/abs/2509.09967

QM2-branes and the Swampland Distance Conjecture in nine dimensions
We discuss the relationship between the Swampland program and QM2-branes, which are supersymmetric M2-branes with discrete spectrum. The worldvolume description of these M2-branes is well-known. The global description is given in terms of twisted torus bundles with monodromy in $\mathrm{SL}(2,\mathbb{Z})$. In particular, we show that the towers of states that ensure the Swampland Distance Conjecture for type II maximal supergravity in nine dimensions are directly related to QM2-branes with triv…

Little Caesars Pizza!Pizza! Pregame Show | Week 15 vs. Raiders https://www.philadelphiaeagles.com/video/little-caesars-pizza-pizza-pregame-show-week-15-vs-raiders-2025-nfl-season

Carleman Estimates and Controllability of Forward Stochastic Parabolic Equations with General Dynamic Boundary Conditions
Said Boulite, Abdellatif Elgrou, Lahcen Maniar, Abdelaziz Rhandi
https://arxiv.org/abs/2510.12345

Carleman Estimates and Controllability of Forward Stochastic Parabolic Equations with General Dynamic Boundary Conditions
We derive a new Carleman estimate for a general backward stochastic parabolic equation with dynamic boundary conditions, incorporating weak divergence source terms in both the bulk and surface equations. This estimate is obtained through two main steps: first, by refining a known Carleman estimate for backward stochastic parabolic equations to explicitly account for the dependence of the parameters on the final control time \(T\); second, by applying a duality technique to address weak divergen…

An information theorist's tour of differential privacy
Anand D. Sarwate, Flavio P. Calmon, Oliver Kosut, Lalitha Sankar
https://arxiv.org/abs/2510.10316 https://

An information theorist's tour of differential privacy
Since being proposed in 2006, differential privacy has become a standard method for quantifying certain risks in publishing or sharing analyses of sensitive data. At its heart, differential privacy measures risk in terms of the differences between probability distributions, which is a central topic in information theory. A differentially private algorithm is a channel between the underlying data and the output of the analysis. Seen in this way, the guarantees made by differential privacy can be…

Google and Disney's agreement gives YouTube TV users access to ESPN's full lineup of sports, including ESPN Unlimited, at no additional cost by the end of 2026 (Todd Spangler/Variety)
https://variety.com/2025/tv/news/youtube-tv-disney-bla…

YouTube TV and Disney Reach Deal Ending Two-Week Blackout of ESPN, ABC
ESPN, ABC and other Disney TV networks are coming back to YouTube TV, after the media conglomerate and Google reached a deal on pricing and terms for a renewed carriage deal.

Braise, stew, soup... is a spectrum to some.
Here is the fix: Just call it a #brewp.
No need to fighter over terms.

Local regularity of spacetimes under Ricci curvature and Lie derivative conditions
Bing-Long Chen
https://arxiv.org/abs/2510.09946 https://arxiv.org/pdf/25…

Local regularity of spacetimes under Ricci curvature and Lie derivative conditions
In this paper, we derive a general regularity estimate for any 4-d spacetime, in terms of a priori bounds of the Ricci curvature and Lie derivative of the Lorentzian metric with respect to an arbitrary timelike vector field.

OK, let's be clear about #Autism:
A majority of engineers, including software engineers, are #ActuallyAutistic; I suspect a majority of architects and people who invent new stuff generally are; many people in the creative arts are.
Without

Independent review into mental health conditions, ADHD and autism: terms of reference

Towards a category-theoretic foundation of Classical and Quantum Information Geometry
Florio M. Ciaglia, Fabio Di Cosmo, Laura Gonz\'alez-Bravo
https://arxiv.org/abs/2509.10262

Towards a category-theoretic foundation of Classical and Quantum Information Geometry
We introduce the category $\mathsf{NCP}$, whose objects are pairs of W$^\ast$-algebras and normal states and whose morphisms are state-preserving unital completely positive (CPU) maps, as a common stage for classical and quantum information geometry, and we formulate two results that will appear in forthcoming works. First, we recast the problem of classifying admissible Riemannian geometries on classical and quantum statistical models in terms of functors $\mathfrak{C}:\mathsf{NCP}\to\mathsf…

Proof of the exact diffusion constant via first passage time in quasi-periodic potentials
Ming Gong
https://arxiv.org/abs/2510.10435 https://arxiv.org/pdf/…

Proof of the exact diffusion constant via first passage time in quasi-periodic potentials
Brownian motion in terms of Lifson and Jackson (LJ) formula has been widely explored in periodic systems and it has been believed for a long time that the LJ formula only applies to periodic potentials. Recently we show that for the following Brownian motion $γ\dot{x} = -U'(x) + ξ$, where $U(x)$ is the quasi-periodic potential, the effective diffusion constant can still be described by the LJ formula $D^* = D/(\langle \exp(βU)\rangle \langle \exp(-βU)\rangle)$, where the average is redefine…

Limit cycles and invariant algebraic curves
Armengol Gasull, Paulo Santana
https://arxiv.org/abs/2510.11705 https://arxiv.org/pdf/2510.11705

Limit cycles and invariant algebraic curves
We give lower bounds in terms of~$n,$ for the number of limit cycles of polynomial vector fields of degree~$n,$ having any prescribed invariant algebraic curve. By applying them when the ovals of this curve are also algebraic limit cycles we obtain a new recurrent property for the Hilbert numbers. Finally, we apply our results to two important families of models: Kolmogorov systems and a general family of systems appearing in Game Theory.

DIPLODOCUS II: Implementation of transport equations and test cases relevant to micro-scale physics of jetted astrophysical sources
Christopher N. Everett, Marc Klinger-Plaisier, Garret Cotter
https://arxiv.org/abs/2510.12505

DIPLODOCUS II: Implementation of transport equations and test cases relevant to micro-scale physics of jetted astrophysical sources
DIPLODOCUS (Distribution-In-PLateaux methODOlogy for the CompUtation of transport equationS) is a novel framework being developed for the general transport of particle distribution functions through the seven dimensions of phase space, including forcing terms and interactions between particles. Following Paper I, which details the background analytic framework, this second paper provides an overview of the numerical implementation in the form of the code package Diplodocus.jl, written in Julia,…

Gradient-flowed operator product expansion without IR renormalons
Martin Beneke (TU Munich), Hiromasa Takaura (Kyoto University)
https://arxiv.org/abs/2510.12193 https://…

Gradient-flowed operator product expansion without IR renormalons
A long-standing problem concerns the question how to consistently combine perturbative expansions in QCD with power corrections in the context of the operator product expansion (OPE), since the former exhibit ambiguities due to infrared renormalons, which are of the same order as the power corrections. We propose to use the gradient flow time $1/\sqrt{t}$ as a factorization scale and to express the OPE in terms of IR renormalon-free subtracted perturbative expansions and unambiguous matrix elem…

On the integral simplicial volume of cyclic covers of mapping tori
Federica Bertolotti, Ervin Hadziosmanovic
https://arxiv.org/abs/2510.11651 https://arxiv…

On the integral simplicial volume of cyclic covers of mapping tori
In this paper, we investigate the asymptotic behavior of the integral simplicial volume of cyclic covers of manifolds that fiber over the circle with fiber given by an $n$-dimensional torus. By studying the integral filling volume -- an invariant introduced by Frigerio and the first author -- for the monodromy, we establish both lower and upper bounds for the limit of the integral simplicial volume of these covers, normalized by the degree of the covering. These bounds are expressed in terms of…

The Doppler boosted LISA response to gravitational waves
Tom van der Steen, Henri Inchausp\'e, Thomas Hertog, Aur\'elien Hees
https://arxiv.org/abs/2509.10038 https://…

The Doppler boosted LISA response to gravitational waves
The future space-based gravitational wave observatory LISA is expected to detect massive black hole binaries (MBHBs) with high signal-to-noise ratios (SNRs), ranging up to thousands. Such high-precision observations require accurate modeling of the detector response. However, current derivations of the response function neglect the motion of the spacecraft during light travel time, omitting velocity-dependent terms of order $β= v/c \sim 10^{-4}$. In this work, we derive the velocity-dependent …

HypoGeneAgent: A Hypothesis Language Agent for Gene-Set Cluster Resolution Selection Using Perturb-seq Datasets
Ying Yuan, Xing-Yue Monica Ge, Aaron Archer Waterman, Tommaso Biancalani, David Richmond, Yogesh Pandit, Avtar Singh, Russell Littman, Jin Liu, Jan-Christian Huetter, Vladimir Ermakov
https://arxiv.org/abs/2509.09740

HypoGeneAgent: A Hypothesis Language Agent for Gene-Set Cluster Resolution Selection Using Perturb-seq Datasets
Large-scale single-cell and Perturb-seq investigations routinely involve clustering cells and subsequently annotating each cluster with Gene-Ontology (GO) terms to elucidate the underlying biological programs. However, both stages, resolution selection and functional annotation, are inherently subjective, relying on heuristics and expert curation. We present HYPOGENEAGENT, a large language model (LLM)-driven framework, transforming cluster annotation into a quantitatively optimizable task. Init…

Staggered time discretization in finitely-strained heterogeneous visco-elastodynamics with damage or diffusion in the Eulerian frame
Tom\'a\v{s} Roub\'i\v{c}ek
https://arxiv.org/abs/2510.10355 …

Staggered time discretization in finitely-strained heterogeneous visco-elastodynamics with damage or diffusion in the Eulerian frame
The semi-implicit (partly decoupled, also called staggered or fraction-step) time discretization is applied to compressible nonlinear dynamical models of viscoelastic solids in the Eulerian description, i.e.\ in the actual deforming configuration, formulated fully in terms of rates. The Kelvin-Voigt rheology and also, in the deviatoric part, the Jeffreys rheology are considered. The numerical stability and, considering the Stokes-type viscosity multipolar of the 2nd-grade, also convergence towa…

For a few years now I have the impression that Big Tech companies resemble more and more something like ecosystem states but without any functional judicial system. And that horrifies me. Their terms of service which should be their constitutions seem more like a dictatorial permission slip with the ability to denaturalize and disown people.
https:…

Castelnuovo-Mumford Regularity and Combinatorial Invariants of Trees
Ahtsham Ul Haq, Muhammad Usman Rashid, Muhammad Ishaq
https://arxiv.org/abs/2510.11265 https://

Castelnuovo-Mumford Regularity and Combinatorial Invariants of Trees
This work establishes combinatorial bounds on the Castelnuovo-Mumford regularity of edge ideals for trees and their multi-whiskered variants. For a tree \( T \), we give bounds for the Castelnuovo-Mumford regularity of \( I(T) \) in terms of the order, diameter, and number of pendant vertices. Furthermore, we present an upper bound for multi-whiskered trees \( T_{\mathbf{a}} \), demonstrating that the Castelnuovo-Mumford regularity of \( I(T_{\mathbf{a}}) \) is bounded by the same invariants of…

foldoc: FOLDOC entries (2002)
A network of hyperlinks among entries in the Free On-line Dictionary of Computing (FOLDOC, www.foldoc.org), an online dictionary of acronyms and technical terms for computers. An edge points from i to j if the term j is referred to in the entry for term i. Edge weight denotes number of uses of the same term.
This network has 13356 nodes and 120238 edges.
Tags: Informational, Web graph, Weighted

Cyclic and alternating $U$-statistics
Svante Janson
https://arxiv.org/abs/2510.12480 https://arxiv.org/pdf/2510.12480…

Cyclic and alternating $U$-statistics
We define cyclic $U$-statistics as a variant of $U$-statistics based on variables $X_1,\dots,X_n$ that are assumed to be cyclically ordered. We also define alternating $U$-statistics where in the definition terms are summed with alternating sings (in three different ways). Only $U$-statistics of order 2 are considered. The definitions are inspired by special cases studied by Chebikin (2008) and Even-Zohar (2017) for random permutations. We show limit theorems similar to well-known results for…

Origin of pressure-flow non-linearity in two-phase intermittent flow in porous media
Paolo Botticini, Davide Picchi, Santanu Sinha, Alex Hansen
https://arxiv.org/abs/2510.12588 …

Origin of pressure-flow non-linearity in two-phase intermittent flow in porous media
This study presents a first-principles model to predict the two-phase pressure drop in gas-liquid intermittent flow through round capillaries, which serve as the simplest analogous of a porous medium. Building upon the classical capillary flow theory, we derive a model for a train of elongated bubbles, and rigorously quantify its validity in terms of the dimensionless parameters of the problem (capillary number, number of bubbles, gas volume fraction, and channel length-to-diameter ratio). The …

Derivation over twisted group ring and its applications
Alvaro Otero Sanchez
https://arxiv.org/abs/2510.09623 https://arxiv.org/pdf/2510.09623

Derivation over twisted group ring and its applications
This paper classifies the derivations of twisted group algebras in terms of the generators and defining relations of the group. In particular, we generalize some know results over group algebras to the case of twisted group algebras. We will give necessary and sufficient condition for a map defined over the generators to be extended to a derivation over a twisted group ring. We present how this results can be use in case of an abelian group or dihedral group. We also present how this results ca…

Triangulated Categories Admitting Linear Generators
Marina Godinho, Dave Murphy
https://arxiv.org/abs/2510.12433 https://arxiv.org/pdf/2510.12433

Triangulated Categories Admitting Linear Generators
The main result of this paper is that there is an additive equivalence between $\overline{\mathcal{C}}_n$, the Paquette-Yildirim completion of the discrete cluster categories of Dynkin type $A_{\infty}$, and the perfect derived category of a certain DG algebra. This additive equivalence preserves some of the triangulated structure: it commutes with the suspension functor and preserves triangles with at least two indecomposable terms. In the process, we introduce the notion of a linear generator…

What do the fundamental constants of physics tell us about life?
Pankaj Mehta, Jane Kondev
https://arxiv.org/abs/2509.09892 https://arxiv.org/pdf/2509.0989…

What do the fundamental constants of physics tell us about life?
In the 1970s, the renowned physicist Victor Weisskopf famously developed a research program to qualitatively explain properties of matter in terms of the fundamental constants of physics. But there was one type of matter prominently missing from Weisskopf's analysis: life. Here, we develop Weisskopf-style arguments demonstrating how the fundamental constants of physics can be used to understand the properties of living systems. By combining biophysical arguments and dimensional analysis, we sho…

A Class of Functionals on the Sequence Space $s$ Satisfying the Palais-Smale Condition
Kaveh Eftekharinasab
https://arxiv.org/abs/2510.10146 https://arxiv.…

A Class of Functionals on the Sequence Space $s$ Satisfying the Palais-Smale Condition
We introduce a class of functionals on the space of rapidly decreasing sequences $s$, called $\mathcal{F}_s$-functionals, defined as decomposable sums of quadratic and convex terms with quadratic growth. We prove that such functionals satisfy the Palais-Smale condition and admit a unique global minimum. Furthermore, we show that the Palais-Smale condition is preserved under linear homeomorphisms. This allows us to construct corresponding functionals satisfying the Palais-Smale condition on Fré…

Tiny-R1V: Lightweight Multimodal Unified Reasoning Model via Model Merging
Qixiang Yin, Huanjin Yao, Jianghao Chen, Jiaxing Huang, Zhicheng Zhao, Fei Su
https://arxiv.org/abs/2510.08987

Tiny-R1V: Lightweight Multimodal Unified Reasoning Model via Model Merging
Although Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities across diverse tasks, they encounter numerous challenges in terms of reasoning efficiency, such as large model size, overthinking, and compromised accuracy in lightweight scenarios. However, research on the reasoning capabilities of lightweight MLLMs is quite lacking. To this end, we propose Tiny-R1V, a novel lightweight 3B model that achieves faster inference and higher accuracy via a two-stage optimiza…

Centralizers of discrete Temperley-Lieb-Jones subfactors
Corey Jones, Emily McGovern
https://arxiv.org/abs/2510.12675 https://arxiv.org/pdf/2510.12675

Centralizers of discrete Temperley-Lieb-Jones subfactors
Discrete, unimodular inclusions of factors $(N\subseteq M, E)$ with $N$ of type $\rm{II}_{1}$ have a natural notion of standard invariant, generalizing the finite index case. When the unitary tensor category of $N$-$N$ bimodules generated by $_{N}L^{2}(M, τ\circ E)_{N}$ is equivalent to the Temperley-Lieb-Jones category $\text{TLJ}(δ)$, the associated discrete standard invariants are classified in terms of fair and balanced $δ$-graphs. Many examples of these subfactors naturally arise in the…

"Digital Sovereignty" as a term always has the implicit danger of fueling nationalist narratives. We should be finding better terms, I like @… 's "resilient infrastructure" framing.

Just finished "Beasts Made of Night" by Tochi Onyebuchi...
Indirect CW for fantasy police state violence.
So I very much enjoyed Onyebuchi's "Riot Baby," and when I grabbed this at the library, I was certain it would be excellent. But having finished it, I'm not sure I like it that much overall?
The first maybe third is excellent, including the world-building, which is fascinating. I feel like Onyebuchi must have played "Shadow of the Colossus" at some point. Onyebuchi certainly does know how to make me care for his characters.
Some spoilers from here on out...
.
.
.
I felt like it stumbles towards the middle, with Bo's reactions neither making sense in the immediate context, nor in retrospect by the end when we've learned more. Things are a bit floaty in the middle with an unclear picture of what exactly is going on politics-wise and what the motivations are. Here I think there were some nuances that didn't make it to the page, or perhaps I'm just a bit thick and not getting stuff I should be? More is of course revealed by the end, but I still wasn't satisfied with the explanations of things. For example, (spoilers) I don't feel I understand clearly what kind of power the army of aki was supposed to represent within the city? Perhaps necessary to wield the threat of offensive inisisia use? In that case, a single scene somewhere of Izu's faction deploying that tactic would have been helpful I think.
Then towards the end, for me things really started to jumble, with unclear motivations, revelations that didn't feel well-paced or -structured, and a finale where both the action & collapsing concerns felt stilted and disjointed. Particularly the mechanics/ethics of the most important death that set the finale in motion bothered me, and the unexplained mechanism by which that led to what came next? I can read a couple of possible interesting morals into the whole denouement, but didn't feel that any of them were sufficiently explored. Especially if we're supposed to see some personal failing in the protagonist's actions, I don't think it's made clear enough what that is, since I feel his reasons to reject each faction are pretty solid, and if we're meant to either pity or abjure his indecision, I don't think the message lands clearly enough.
There *is* a sequel, which honestly I wasn't sure of after the last page, and which I now very interested in. Beasts is Onyebuchi's debut, which maybe makes sense of me feeling that Riot Baby didn't have the same plotting issues. It also maybe means that Onyebuchi couldn't be sure a sequel would make it to publication in terms of setting up the ending.
Overall I really enjoyed at least 80% of this, but was expecting even better (especially politically) given Onyebuchi's other work, and I didn't feel like I found it.
#AmReading

One-dimensional topological superconductors with nonsymmorphic symmetries
Max Tymczyszyn, Edward McCann
https://arxiv.org/abs/2510.11342 https://arxiv.org/…

One-dimensional topological superconductors with nonsymmorphic symmetries
We present example four-band Hermitian tight-binding Bogoliubov-de-Gennes (BdG) Hamiltonians and Kramer's degenerate Hamiltonians in one dimension. Starting from a generalized Rice-Mele model, we incorporate superconducting terms to obtain a four-band BdG Hamiltonian with intrinsic charge-conjugation symmetry, and constrain it using symmorphic or nonsymmorphic time-reversal symmetries. In position space we find that each form of time-reversal symmetry, when applied to random BdG matrices, resul…

P3D: Scalable Neural Surrogates for High-Resolution 3D Physics Simulations with Global Context
Benjamin Holzschuh, Georg Kohl, Florian Redinger, Nils Thuerey
https://arxiv.org/abs/2509.10186

P3D: Scalable Neural Surrogates for High-Resolution 3D Physics Simulations with Global Context
We present a scalable framework for learning deterministic and probabilistic neural surrogates for high-resolution 3D physics simulations. We introduce a hybrid CNN-Transformer backbone architecture targeted for 3D physics simulations, which significantly outperforms existing architectures in terms of speed and accuracy. Our proposed network can be pretrained on small patches of the simulation domain, which can be fused to obtain a global solution, optionally guided via a fast and scalable sequ…

Marcus Theory and The Condon Approximation Revisited I: E-SHAKE and Seam Sampling
D. Vale Cofer-Shabica, Jennifer R. DeRosa, Joseph E. Subotnik
https://arxiv.org/abs/2510.11810 …

Marcus Theory and The Condon Approximation Revisited I: E-SHAKE and Seam Sampling
Marcus theory is the workhorse of theoretical chemistry for predicting the rates of charge and energy transfer. Marcus theory overwhelmingly agrees with experiment -- both in terms of electron transfer and triplet energy transfer -- for the famous set of naphthalene-bridge-biphenyl and naphthalene-bridge-benzophenone systems studied by Piotrowiak, Miller, and Closs. That being said, the agreement is not perfect, and in this manuscript, we revisit one key point of disagreement: the molecule C-13…

A minimal and universal representation of fermionic wavefunctions (fermions = bosons one)
Liang Fu
https://arxiv.org/abs/2510.11431 https://arxiv.org/pdf…

A minimal and universal representation of fermionic wavefunctions (fermions = bosons + one)
Representing fermionic wavefunctions efficiently is a central problem in quantum physics, chemistry and materials science. In this work, we introduce a universal and exact representation of continuous antisymmetric functions by lifting them to continuous symmetric functions defined on an enlarged space. Building on this lifting, we obtain a \emph{parity-graded representation} of fermionic wavefunctions, expressed in terms of symmetric feature variables that encode particle configuration and ant…

The Strength of Local Structures in Decentralized Network Formation
Jose M. Betancourt
https://arxiv.org/abs/2510.10997 https://arxiv.org/pdf/2510.10997

The Strength of Local Structures in Decentralized Network Formation
I study dynamic network formation games in which agents assign arbitrary values to network structures. Any such game admits an equivalent representation in terms of the values agents assign to its sub-structures, linking local valuations to equilibrium behavior. The game is a potential game precisely when all participants in a structure value it equally, yielding a closed-form stationary distribution. When valuations are restricted to a finite set of repeated sub-structures, or motifs, the mode…

Linear fractional relative risk aversion
Kristian Behrens, Yasusada Murata
https://arxiv.org/abs/2509.09865 https://arxiv.org/pdf/2509.09865

Linear fractional relative risk aversion
We characterize the family of utility functions satisfying linear fractional relative risk aversion (LFRRA) in terms of the Gauss hypergeometric functions. We apply this family, which nests various utility functions used in different strands of literature, to monopolistic competition and obtain a closed-form solution for the profit-maximizing price by generalizing the Lambert W function. We let firm-level data decide whether the RRA in each sector or in the aggregate economy is increasing, decr…

We're eating good tonight! >:3

Fluctuation-guided adaptive random compiler for Hamiltonian simulation
Yu-Xia Wu, Yun-Zhuo Fan, Dan-Bo Zhang
https://arxiv.org/abs/2509.10158 https://arxiv…

Fluctuation-guided adaptive random compiler for Hamiltonian simulation
Stochastic methods offer an effective way to suppress coherent errors in quantum simulation. In particular, the randomized compilation protocol may reduce circuit depth by randomly sampling Hamiltonian terms rather than following the deterministic Trotter-Suzuki sequence. However, its fixed sampling distribution does not adapt to the dynamics of the system, limiting its accuracy. In this work, we propose a fluctuation-guided adaptive algorithm that adaptively updates sampling probabilities base…

Oh. Parece que morreu o John Varley.
Um autor de FC americano de segunda linha com alguns livros publicados em Portugal. Toda a série Gaea (uma trilogia que a Europa-América publicou em 6 volumes) é muito boa.
https://fed.brid.gy/r/https://bsky.app

Jesse Sheidlower (@jessesword.com)
RIP John Varley. We have a lot of quotations from him in the Historical #Dictionary of #ScienceFiction, and he is credited as being the originator of four terms: cryosuspension, cyborg (v.), cyborged, and nearside (n.): https://sfdictionary.com/author/59/john-varley?firstquotes=1 [contains quote post or other embedded content]

Bertrand's Representation of the Optimal Detector
Vladimir Lenok
https://arxiv.org/abs/2509.10198 https://arxiv.org/pdf/2509.10198

Bertrand's Representation of the Optimal Detector
It is shown how the optimal detector of Gaussian signals can be represented in terms of Bertrand's class of time-frequency distributions. In this representation, the detector is a correlation between the corresponding time-frequency distributions. Since Bertrand's class is related to the power-law chirp signals, the new representation can be useful for their detection. The new approach is shown to be more effective then other time-frequency methods for the case of phase-insensitive detection. T…

The Motivic Picard--Lefschetz Formula
Ran Azouri, Emil Jacobsen
https://arxiv.org/abs/2510.12762 https://arxiv.org/pdf/2510.12762

The Motivic Picard--Lefschetz Formula
We prove a motivic enhancement of the classical Picard--Lefschetz formula. Our proof is completely motivic, and yields a description of the motivic nearby cycles at a quasi-homogeneous singularity, as well as its monodromy, in terms of an embedding of projective hypersurfaces.

On the quadratic complexity of subsets of $\mathbb{F}_p^n$ of bounded $\mathrm{VC_{2}}$-dimension
C. Terry, J. Wolf
https://arxiv.org/abs/2510.12767 https://

On the quadratic complexity of subsets of $\mathbb{F}_p^n$ of bounded $\mathrm{VC_{2}}$-dimension
In prior work, we showed that subsets of $\mathbb{F}_{p}^{n}$ of $\mathrm{VC_{2}}$-dimension at most $k$ are well approximated by a union of atoms of a quadratic factor of complexity $(\ell,q)$, where the complexity $\ell$ of the linear part and the complexity $q$ of the quadratic part are both bounded in terms of $k$, $p$, and the desired level of approximation $μ$. A key tool in the proof of this result was an arithmetic regularity lemma for the Gowers $U^3$-norm by Green and Tao, which resu…

Only one paper telling the truth... is that funny?
https://theonion.com/israel-agrees-to-go-back-to-killing-palestinians-on-less-frequent-basis/

Israel Agrees To Go Back To Killing Palestinians On Less Frequent Basis
CAIRO—As part of a historic ceasefire agreement with Hamas following two years of war, the Israeli government reportedly agreed Thursday to go back to killing Palestinians on a less frequent basis. “In line with the terms of the deal, Hamas will release all remaining Israeli hostages, and Israel will still murder innocent Palestinian civilians on […]

Bleh. Just saw a friend who found out they couldn’t be followed by one of their friends because (unbeknownst to both parties) the moderators of their friend’s instance had defederated from their own instance. All of this, for people who barely know what any of these terms mean. What they experience is, “Two people you’ve never met have a beef you’ve never heard about over an issue you don’t know about, so your friend can’t see you. And there’s no fix.” It’s just terrible all around.

Surfaces and Hypersurfaces with Prescribed Radial Mean Curvature
Marcelo Lopes Ferro, Armando M. V. Corro
https://arxiv.org/abs/2510.11669 https://arxiv.or…

Surfaces and Hypersurfaces with Prescribed Radial Mean Curvature
In this work, we provide a local classification of certain special classes of surfaces determined by the prescription of the radial mean curvature in terms of the height and angle functions. Moreover, we introduce a special class of hypersurfaces, and we also provide a local classification of these three-dimensional hypersurfaces whose second mean curvature vanishes. Finally, we present a recursive method for constructing such hypersurfaces, extending the same curvature prescription approach to…

Want a used car that works?
You’d be wise to not get an older Tesla.
In Consumer Reports’ latest ranking for used cars,
the Elon Musk-run automaker came dead last in terms of reliability,
trailing by over forty points from the top spot on a scale between 0 and 100
https://futurism.co…

Old Teslas Are Falling Apart
On Consumer Reports' latest ranking of used car reliability, Tesla came in dead last with a rating not even half of the top placed brand.

Local Lipschitz continuity for energy integrals with fast growth and lower order terms
Andrea Torricelli
https://arxiv.org/abs/2510.09142 https://arxiv.org…

Local Lipschitz continuity for energy integrals with fast growth and lower order terms
We consider integral functionals with fast growth and the lagrangian explicitly depending on $u$. We prove that the local minimizers are locally Lipschitz continuous.

Outer length billiards on polygons
Lael Edwards-Costa
https://arxiv.org/abs/2510.11869 https://arxiv.org/pdf/2510.11869

Outer length billiards on polygons
The classical inner and outer billiards can be formulated in variational terms, with length and area as the respective generating functions. The other two combinations, ``inner with area'' and ``outer with length,'' are more recently described. Here, we consider the latter system in the special case of polygonal tables. We describe the behavior of orbits far away from the table and pose conjectures regarding an escaping orbit when the table is a square. This paper is meant to complement arXiv:2…

A streamline upwind/Petrov-Galerkin method for the magnetic advection-diffusion problem
Haochen Li, Yangfan Luo, Jindong Wang, Shuonan Wu
https://arxiv.org/abs/2509.09913 https:…

A streamline upwind/Petrov-Galerkin method for the magnetic advection-diffusion problem
This paper presents the development and analysis of a streamline upwind/Petrov-Galerkin (SUPG) method for the magnetic advection-diffusion problem. A key feature of the method is an SUPG-type stabilization term based on the residuals and weighted advection terms of the test function. By introducing a lifting operator to characterize the jumps of finite element functions across element interfaces, we define a discrete magnetic advection operator, which subsequently enables the formulation of the…

"Labour has also won every time the Senedd has been contested, as it will be again in May. Yet, if the most recent Wales-wide poll holds good, that is set to change. Plaid will instead be the largest party, just ahead of Reform UK, with Labour third. Though still a minority, Plaid would be in government. In Welsh terms, that would be a political earthquake. Perhaps in Britain-wide terms too"
#UKPol

Interacting point processes
Fabrizio Cinque, Enzo Orsingher
https://arxiv.org/abs/2510.12531 https://arxiv.org/pdf/2510.12531

Interacting point processes
We study two different types of vector point processes with interacting components, introducing a migration-type effect. The first case concerns two groups which modify their states with rate functions depending on time only. This yields a representation of the vector process in terms of independent non-homogeneous Skellam processes. In the general case, the decomposition involves independent Poisson processes. The second model is a birth-death-migration vector process. In the case of the linea…

Evolution of moments in atmospheric scintillation
Filippus S. Roux
https://arxiv.org/abs/2509.10171 https://arxiv.org/pdf/2509.10171

Evolution of moments in atmospheric scintillation
Evolution equations for the moments of a photonic quantum state propagating through atmospheric turbulence are derived. These evolution equations are obtain from an evolution equation for the characteristic functional of the state, incorporating all spatiotemporal degrees of freedom. The measured quantities, such as the intensity or photon distribution, of the evolving state can be expressed in terms of such moments without having to know the exact final state. The case of an initial coherent s…

Arithmetic Hirzebruch-Zagier divisors and central derivative values of Rankin-Selberg $L$-functions
Jeanine Van Order
https://arxiv.org/abs/2510.10303 https://

Arithmetic Hirzebruch-Zagier divisors and central derivative values of Rankin-Selberg $L$-functions
We give two distinct proofs of the Gross-Zagier formula in terms of sums of automorphic Green's functions realized as regularized theta lifts, including one involving arithmetic Hirzebruch-Zagier divisors on the Hilbert modular surface $X_0(N) \times X_0(N)$. We then describe applications to the refined conjecture of Birch and Swinnerton-Dyer. Through these calculations, we also describe known and conjectural relations of the central derivative values of Rankin-Selberg $L$-functions that appear…

The Age-Structured Chemostat with Substrate Dynamics as a Control System
Iasson Karafyllis, Dionysis Theodosis, Miroslav Krstic
https://arxiv.org/abs/2511.09963 https://arxiv.org/pdf/2511.09963 https://arxiv.org/html/2511.09963
arXiv:2511.09963v1 Announce Type: new
Abstract: In this work we study an age-structured chemostat model with a renewal boundary condition and a coupled substrate equation. The model is nonlinear and consists of a hyperbolic partial differential equation and an ordinary differential equation with nonlinear, nonlocal terms appearing both in the ordinary differential equation and the boundary condition. Both differential equations contain a non-negative control input, while the states of the model are required to be positive. Under an appropriate weak solution framework, we determine the state space and the input space for this model. We prove global existence and uniqueness of solutions for all admissible initial conditions and all allowable control inputs. To this purpose we employ a combination of Banach's fixed-point theorem with implicit solution formulas and useful solution estimates. Finally, we show that the age-structured chemostat model gives a well-defined control system on a metric space.
toXiv_bot_toot

H-harmonic reproducing kernels on the ball
Mat\v{e}j Morav\'ik
https://arxiv.org/abs/2510.11821 https://arxiv.org/pdf/2510.11821

H-harmonic reproducing kernels on the ball
We consider the Szegő reproducing kernel associated with the space of $H$-harmonic functions on the unit ball in n-dimensional space, i.e. functions that are characterized by being annihilated by the hyperbolic Laplacian. This paper derives an explicit series expansion for the reproducing kernel in terms of a triple hypergeometric function introduced of Exton. Moreover, we demonstrate that the Szegő kernel admits a representation as a finite sum of hypergeometric functions. We further show th…

Equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids
Alice L. L. Gao, Yun Li, Matthew H. Y. Xie
https://arxiv.org/abs/2510.11322 https://

Equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids
In this paper, we focus on the equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids, a natural family of graphic matroids associated with the complete tripartite graphs $K_{1,1,n}$. These polynomials were introduced by Proudfoot as an extension of the Kazhdan--Lusztig theory for matroids. We derive closed-form expressions for the $\mathfrak{S}_n$-equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids and present them explicitly in terms of the irreducible rep…

Topological weak containment
Riley Thornton
https://arxiv.org/abs/2510.10882 https://arxiv.org/pdf/2510.10882

Topological weak containment
We build on work of Elek and Zucker and develop a topological analogue of the theory of weak containment. We show that definitions in terms of local patterns, containment in ultra(co)products, and continuous model theory are all equivalent, just as in ergodic theory. And, for actions on Cantor space, we show these are all equivalent to approximate conjugacy. Restricting our attention to Cantor space, we connect this theory to questions about generic actions. We show how the shape of the space…

Counting Homogeneous Einstein Metrics
Renato G. Bettiol, Hannah Friedman
https://arxiv.org/abs/2509.09830 https://arxiv.org/pdf/2509.09830

Counting Homogeneous Einstein Metrics
We present an explicit upper bound on the number of isolated homogeneous Einstein metrics on compact homogeneous spaces whose isotropy representations consist of pairwise inequivalent irreducibles. This is the BKK bound of the corresponding system of Laurent polynomials and is found combinatorially by computing the volume of a polytope. Inspired by a connection with algebraic statistics, we describe this system's BKK discriminant in terms of the principal $A$-determinant of scalar curvature. As…

Rethinking How We Discuss the Guidance of Student Researchers in Computing
Shomir Wilson
https://arxiv.org/abs/2510.08885 https://arxiv.org/pdf/2510.08885

Rethinking How We Discuss the Guidance of Student Researchers in Computing
Computing faculty at research universities are often expected to guide the work of undergraduate and graduate student researchers. This guidance is typically called advising or mentoring, but these terms belie the complexity of the relationship, which includes several related but distinct roles. I examine the guidance of student researchers in computing (abbreviated to research guidance or guidance throughout) within a facet framework, creating an inventory of roles that faculty members can hol…

$L$-functions of elliptic curves in ring class extensions of real quadratic fields via regularized theta liftings
Jeanine Van Order
https://arxiv.org/abs/2510.10277 https://

$L$-functions of elliptic curves in ring class extensions of real quadratic fields via regularized theta liftings
We derive new integral presentations for central derivative values of $L$-functions of elliptic curves defined over the rationals, basechanged to a real quadratic field $K$, twisted by ring class characters of $K$ in terms of sums along ``geodesics" corresponding to the class group of $K$ of automorphic Green's functions for certain Hirzebruch-Zagier-like arithmetic divisors on Hilbert modular surfaces. We also relate these sums to Birch-Swinnerton-Dyer constants and periods.

Stability Estimates for Commutativity Properties of the Dirichlet-to-Neumann Operator
Romain Speciel
https://arxiv.org/abs/2510.08822 https://arxiv.org/pdf…

Stability Estimates for Commutativity Properties of the Dirichlet-to-Neumann Operator
The Laplacian $Δ_{\mathbb{S}^{n-1}}$ on the unit sphere $\mathbb{S}^{n-1}\subset \mathbb{R}^n$ has the property that it can explicitly be expressed in terms of $Λ$, the Dirichlet-to-Neumann map of the unit ball, as $Δ_{\mathbb{S}^{n-1}}=Λ^2+(n-2)Λ$. In this paper, we seek to characterize those manifolds for which such an exact relationship holds, and more generally measure the discrepancy of such a relationship holding in terms of geometric data. To this end, we obtain a stability estimate…

On the fully analytical cumulative distribution of product of correlated Gaussian random Variables with zero means
Erdinc Akyildirim, Alper Hekimoglu
https://arxiv.org/abs/2509.09866

On the fully analytical cumulative distribution of product of correlated Gaussian random Variables with zero means
We derive a fully analytical, one-line closed-form expression for the cumulative distribution function (CDF) of the product of two correlated zero-mean normal random variables, avoiding any series representation. This result complements the well-known compact density formula with an equally compact and computationally practical CDF representation. Our main formula expresses the CDF in terms of Humbert's confluent hypergeometric function $Φ_1$ and modified Bessel functions $K_ν$, offering both…

Riccati-ZORO: An efficient algorithm for heuristic online optimization of internal feedback laws in robust and stochastic model predictive control
Florian Messerer, Yunfan Gao, Jonathan Frey, Moritz Diehl
https://arxiv.org/abs/2511.10473 https://arxiv.org/pdf/2511.10473 https://arxiv.org/html/2511.10473
arXiv:2511.10473v1 Announce Type: new
Abstract: We present Riccati-ZORO, an algorithm for tube-based optimal control problems (OCP). Tube OCPs predict a tube of trajectories in order to capture predictive uncertainty. The tube induces a constraint tightening via additional backoff terms. This backoff can significantly affect the performance, and thus implicitly defines a cost of uncertainty. Optimizing the feedback law used to predict the tube can significantly reduce the backoffs, but its online computation is challenging.
Riccati-ZORO jointly optimizes the nominal trajectory and uncertainty tube based on a heuristic uncertainty cost design. The algorithm alternates between two subproblems: (i) a nominal OCP with fixed backoffs, (ii) an unconstrained tube OCP, which optimizes the feedback gains for a fixed nominal trajectory. For the tube optimization, we propose a cost function informed by the proximity of the nominal trajectory to constraints, prioritizing reduction of the corresponding backoffs. These ideas are developed in detail for ellipsoidal tubes under linear state feedback. In this case, the decomposition into the two subproblems yields a substantial reduction of the computational complexity with respect to the state dimension from $\mathcal{O}(n_x^6)$ to $\mathcal{O}(n_x^3)$, i.e., the complexity of a nominal OCP.
We investigate the algorithm in numerical experiments, and provide two open-source implementations: a prototyping version in CasADi and a high-performance implementation integrated into the acados OCP solver.
toXiv_bot_toot

Random Nonlinear Fusion Frames from Averaged Operator Iterations
James Tian
https://arxiv.org/abs/2509.09927 https://arxiv.org/pdf/2509.09927

Random Nonlinear Fusion Frames from Averaged Operator Iterations
We study random iterations of averaged operators in Hilbert spaces and prove that the associated residuals converge exponentially fast, both in expectation and almost surely. Our results provide quantitative bounds in terms of a single geometric parameter, giving sharp control of convergence rates under minimal assumptions. As an application, we introduce the concept of random nonlinear fusion frames. Here the atoms are generated dynamically from the residuals of the iteration and yield exact s…

An alternative proof of the asymptotic formula for the Fourier coefficients of the elliptic modular $j$-function
Karin Ikeda
https://arxiv.org/abs/2510.10598 https://

An alternative proof of the asymptotic formula for the Fourier coefficients of the elliptic modular $j$-function
In 1997, Báez-Duarte gave a probabilistic proof of the asymptotic formula for the partition function, which had originally been proved by Hardy-Ramanujan. Based on the probabilistic approach, this paper proves an asymptotic formula for the coefficients of the elliptic modular $j$-function using various expressions in terms of modular functions having simple infinite products.

Extreme events and impact statistics for unipotent actions on the space of lattices
Jens Marklof, Andreas Str\"ombergsson, Shucheng Yu
https://arxiv.org/abs/2510.11371 http…

Extreme events and impact statistics for unipotent actions on the space of lattices
This paper extends a recent extreme value law for horocycle flows on the space of two-dimensional lattices, due to Kirsebom and Mallahi-Karai, to the simplest examples of rank-$k$ unipotent actions on the space of $n$-dimensional lattices. We analyse the problem in terms of the hitting time and impact statistics for the unipotent action with respect to a shrinking surface of section, following the strategy of Pollicott and the first named author in the case of hyperbolic surfaces. If $k=n-1$, t…

Asymptotics of the solution of the Cauchy problem for a singularly perturbed system of hyperbolic equations. Part 2. Initial conditions
Andrey Nesterov
https://arxiv.org/abs/2510.12550

Asymptotics of the solution of the Cauchy problem for a singularly perturbed system of hyperbolic equations. Part 2. Initial conditions
An asymptotic small parameter expansion of a single Cauchy problem is constructed for a singularly perturbed system of hyperbolic equations describing vibrations of two rigidly connected strings. Equations (such as generalized Korteweg-de Vriesequations) and initial conditions for the terms of the asymptotic expansion of the solution are determined, and under certain assumptions, the residual term is estimated from the residual.

Cohomology theories in the moduli of ring stacks
Dhilan Lahoti, Deven Manam
https://arxiv.org/abs/2510.09582 https://arxiv.org/pdf/2510.09582

Cohomology theories in the moduli of ring stacks
We show that the natural map from the syntomification of a ring $R$ to the stack of $R$-algebra stacks is fully faithful, answering a question of Drinfeld, and we describe its essential image in terms of underlying monoid stacks. We also give similar statements in the characteristic 0 filtered de Rham, $\ell = p$ étale, and Betti settings.

Halpern Acceleration of the Inexact Proximal Point Method of Rockafellar
Liwei Zhang, Fanli Zhuang, Ning Zhang
https://arxiv.org/abs/2511.10372 https://arxiv.org/pdf/2511.10372 https://arxiv.org/html/2511.10372
arXiv:2511.10372v1 Announce Type: new
Abstract: This paper investigates a Halpern acceleration of the inexact proximal point method for solving maximal monotone inclusion problems in Hilbert spaces. The proposed Halpern inexact proximal point method (HiPPM) is shown to be globally convergent, and a unified framework is developed to analyze its worst-case convergence rate. Under mild summability conditions on the inexactness tolerances, HiPPM achieves an $\mathcal{O}(1/k^{2})$ rate in terms of the squared fixed-point residual. Furthermore, under additional mild condition, the method retains a fast linear convergence rate. Building upon this framework, we further extend the acceleration technique to constrained convex optimization through the augmented Lagrangian formulation. In analogy to Rockafellar's classical results, the resulting accelerated inexact augmented Lagrangian method inherits the convergence rate and complexity guarantees of HiPPM. The analysis thus provides a unified theoretical foundation for accelerated inexact proximal algorithms and their augmented Lagrangian extensions.
toXiv_bot_toot

Kronecker second limit formula for real quadratic fields
YoungJu Choie, Rahul Kumar
https://arxiv.org/abs/2510.10554 https://arxiv.org/pdf/2510.10554

Kronecker second limit formula for real quadratic fields
In this paper, the second Kronecker ``limit" formula for a real quadratic field is established for the first time. More precisely, we obtain the second Kronecker limit formula of Zagier's zeta function. Using the reduction theory of Zagier, which connects Zagier's zeta function to the zeta function of real quadratic fields, we express the values of the zeta function of narrow ideal classes in real quadratic fields at natural arguments in terms of an analytic function which we call the \emph{hig…

On the cohomology of homshifts
Nishant Chandgotia, Silv\`ere Gangloff, Benjamin Hellouin de Menibus, Piotr Oprocha
https://arxiv.org/abs/2510.11969 https://

On the cohomology of homshifts
We study the cohomology of symbolic dynamical systems called homshifts: they are the nearest-neighbour $\mathbb{Z}^d$ shifts of finite type whose adjacency rules are the same in every direction. Building on the work of Klaus Schmidt (Pacific J. Math. 170 (1995), no.1, 237-269) we give a necessary and sufficient condition for their cohomological triviality. This condition is expressed in terms of the topology of a natural simplicial complex arising from the shift space which can be analyzed in m…

A classification algorithm for reflexive simplices
Marco Ghirlanda
https://arxiv.org/abs/2510.09131 https://arxiv.org/pdf/2510.09131

A classification algorithm for reflexive simplices
We present a general classification algorithm for reflexive simplices, which allows us to determine all reflexive simplices in dimensions five and six. In terms of algebraic geometry this means that we classify the Gorenstein fake weighted projective spaces in dimensions five and six. As a byproduct of our methods, we obtain explicit formulae for the Picard group and the Gorenstein index of any fake weighted projective space.

dHPR: A Distributed Halpern Peaceman--Rachford Method for Non-smooth Distributed Optimization Problems
Zhangcheng Feng, Defeng Sun, Yancheng Yuan, Guojun Zhang
https://arxiv.org/abs/2511.10069 https://arxiv.org/pdf/2511.10069 https://arxiv.org/html/2511.10069
arXiv:2511.10069v1 Announce Type: new
Abstract: This paper introduces the distributed Halpern Peaceman--Rachford (dHPR) method, an efficient algorithm for solving distributed convex composite optimization problems with non-smooth objectives, which achieves a non-ergodic $O(1/k)$ iteration complexity regarding Karush--Kuhn--Tucker residual. By leveraging the symmetric Gauss--Seidel decomposition, the dHPR effectively decouples the linear operators in the objective functions and consensus constraints while maintaining parallelizability and avoiding additional large proximal terms, leading to a decentralized implementation with provably fast convergence. The superior performance of dHPR is demonstrated through comprehensive numerical experiments on distributed LASSO, group LASSO, and $L_1$-regularized logistic regression problems.
toXiv_bot_toot

Iterated sumset expansion in $\mathbb{F}_p^n$
Manik Dhar, Sammy Luo
https://arxiv.org/abs/2510.08857 https://arxiv.org/pdf/2510.08857

Iterated sumset expansion in $\mathbb{F}_p^n$
Given a set $A \subseteq \mathbb{F}_p^n$, what conditions does one need to guarantee that iterated sumsets of the form $A+\cdots+A$ expand quickly (say, within $O(p)$ terms) to the whole space? When only the size of $A$ is known, such expansion results are only possible when $|A|>\frac{1}{p}|\mathbb{F}_p^n|$. However, heuristic considerations suggest that expansion should begin with much smaller sets under just mild ``nondegeneracy'' conditions. In this paper, we confirm thi…

S-D-RSM: Stochastic Distributed Regularized Splitting Method for Large-Scale Convex Optimization Problems
Maoran Wang, Xingju Cai, Yongxin Chen
https://arxiv.org/abs/2511.10133 https://arxiv.org/pdf/2511.10133 https://arxiv.org/html/2511.10133
arXiv:2511.10133v1 Announce Type: new
Abstract: This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks, compressed sensing, and so on. Stochastic gradient descent (SGD) and its variants are commonly employed to solve such problems. However, existing algorithms often rely on vanishing step sizes, strong convexity assumptions, or entail substantial computational overhead to ensure convergence or obtain favorable complexity. To bridge the gap between theory and practice, we integrate consensus optimization and operator splitting techniques (see Problem Reformulation) to develop a novel stochastic splitting algorithm, termed the \emph{stochastic distributed regularized splitting method} (S-D-RSM). In practice, S-D-RSM performs parallel updates of proximal mappings and gradient information for only a randomly selected subset of agents at each iteration. By introducing regularization terms, it effectively mitigates consensus discrepancies among distributed nodes. In contrast to conventional stochastic methods, our theoretical analysis establishes that S-D-RSM achieves global convergence without requiring diminishing step sizes or strong convexity assumptions. Furthermore, it achieves an iteration complexity of $\mathcal{O}(1/\epsilon)$ with respect to both the objective function value and the consensus error. Numerical experiments show that S-D-RSM achieves up to 2--3$\times$ speedup compared to state-of-the-art baselines, while maintaining comparable or better accuracy. These results not only validate the algorithm's theoretical guarantees but also demonstrate its effectiveness in practical tasks such as compressed sensing and empirical risk minimization.
toXiv_bot_toot

Sums of Exponential Terms, Conserved Quantities, and the Real Wave Numbers
Terence R. Smith
https://arxiv.org/abs/2510.07803 https://arxiv.org/pdf/2510.078…

Sums of Exponential Terms, Conserved Quantities, and the Real Wave Numbers
There is consensus that sums $S_n={ {Σ}_{k=1}^n R_{0k} e^{i θ_k}}$ of complex exponential terms, despite their mathematical significance, only possess closed-form representations for specific values of n and special values of their parameters and that there are no generally-accepted recursive formulae for their computation. This note is focused on recursive formulae that: (1) provide closed-form analytic representations of $S_n$ for any finite n; (2) include generalizations of the usual formu…

Joint distributions of error terms for primes in arithmetic progressions modulo 11
K\"ubra Benl\.i, Greg Martin, Paul P\'eringuey
https://arxiv.org/abs/2510.05427 https…

Joint distributions of error terms for primes in arithmetic progressions modulo 11
We provide a formula for the logarithmic density of the set of positive real numbers on which two prime counting functions $ψ(x;q,a)$ and $ψ(x;q,b)$ are simultaneously larger than their asymptotic main terms, as well as a method for calculating the numerical values of such densities with rigorously bounded errors. We apply these formulas to the pairwise races in the case $q=11$, determining which pairs of residues $a$ and $b$ are more or less correlated in this way. The outcomes when $q=11$ p…