Tootfinder

A recursive approach for the determination of the nice sections of width three having a 4-crown stack as retract
Frank a Campo
https://arxiv.org/abs/2510.05640 https://

A recursive approach for the determination of the nice sections of width three having a 4-crown stack as retract
The characterization of the finite minimal automorphic posets of width three is still an open problem. Niederle has shown that this task can be reduced to the characterization of the nice sections of width three having a non-trivial tower of nice sections as retract. In our article, we characterize those of them which have a 4-crown stack as retract and we develop a recursive approach for their determination. We apply the approach on a sub-class $\mathfrak{N}_2$ of nice sections of width three …

An approach using geometric diagrams to generic Bell inequalities with multiple observables
Junghee Ryu, Jinhyoung Lee, Hoon Ryu
https://arxiv.org/abs/2510.05622 https://…

An approach using geometric diagrams to generic Bell inequalities with multiple observables
We extend the generic Bell inequalities suggested by Son, Lee, and Kim [Phys. Rev. Lett. 96, 060406 (2006)] to incorporate multiple observables for tripartite systems and introduce a geometric methodology for calculating classical upper bounds of the inequalities. Our method transforms the problem of finding the classical upper bounds into identifying constraints in linear congruence relations. Using this approach, we derive the upper bounds for scenarios with three and four observables per par…

ReasonEmbed: Enhanced Text Embeddings for Reasoning-Intensive Document Retrieval
Jianlyu Chen, Junwei Lan, Chaofan Li, Defu Lian, Zheng Liu
https://arxiv.org/abs/2510.08252 http…

ReasonEmbed: Enhanced Text Embeddings for Reasoning-Intensive Document Retrieval
In this paper, we introduce ReasonEmbed, a novel text embedding model developed for reasoning-intensive document retrieval. Our work includes three key technical contributions. First, we propose ReMixer, a new data synthesis method that overcomes the triviality problem prevalent in previous synthetic datasets, enabling large-scale production of 82K high-quality training samples. Second, we design Redapter, a self-adaptive learning algorithm that dynamically adjusts training each sample's weight…

Series C, Episode 04 - Dawn of the Gods
DAYNA: Orac with delusions of grandeur, Zen unable to control the ship. I'd say we've a lot of little problems on our hands.
AVON: Course deflection is zero zero five. Speed Standard by five and increasing. I'd say we have one large problem on our hands.
https://blake.torpidit…

ECHO: Ego-Centric modeling of Human-Object interactions
Ilya A. Petrov, Vladimir Guzov, Riccardo Marin, Emre Aksan, Xu Chen, Daniel Cremers, Thabo Beeler, Gerard Pons-Moll
https://arxiv.org/abs/2508.21556

ECHO: Ego-Centric modeling of Human-Object interactions
Modeling human-object interactions (HOI) from an egocentric perspective is a largely unexplored yet important problem due to the increasing adoption of wearable devices, such as smart glasses and watches. We investigate how much information about interaction can be recovered from only head and wrists tracking. Our answer is ECHO (Ego-Centric modeling of Human-Object interactions), which, for the first time, proposes a unified framework to recover three modalities: human pose, object motion, and…

Autoencoder-based non-intrusive model order reduction in continuum mechanics
Jannick Kehls, Ellen Kuhl, Tim Brepols, Kevin Linka, Hagen Holthusen
https://arxiv.org/abs/2509.02237

Autoencoder-based non-intrusive model order reduction in continuum mechanics
We propose a non-intrusive, Autoencoder-based framework for reduced-order modeling in continuum mechanics. Our method integrates three stages: (i) an unsupervised Autoencoder compresses high-dimensional finite element solutions into a compact latent space, (ii) a supervised regression network maps problem parameters to latent codes, and (iii) an end-to-end surrogate reconstructs full-field solutions directly from input parameters. To overcome limitations of existing approaches, we propose two…

Limits to the Hall effect and other nonreciprocal effects in three-dimensional metamaterials
Christian Kern, Graeme W. Milton
https://arxiv.org/abs/2509.01593 https://

Limits to the Hall effect and other nonreciprocal effects in three-dimensional metamaterials
Metamaterials can exhibit exotic nonreciprocal properties, yet corresponding fundamental limits and design blueprints achieving them are largely unexplored. Here, we derive comprehensive bounds on the effective nonreciprocal properties of three-dimensional metamaterials and identify microstructures achieving or approaching these bounds. We assume that the underlying equations are equivalent to the conductivity problem in a weak applied magnetic field. While we focus on the Hall effect, our resu…

Oof, fuck microsoft.
But also, there's no reason to use permissive licenses any more. "Open source" has taken over the world. We no longer have to work with billion-dollar companies in order to get our stuff used. Now we need to protect ourselves from being taken advantage of by them.
https://

The hereditariness problem for the \v{C}ern\'y conjecture
Emanuele Rodaro, Riccardo Venturi
https://arxiv.org/abs/2509.17992 https://arxiv.org/pdf/2509…

The hereditariness problem for the Černý conjecture
This paper addresses the lifting problem for the Černý conjecture: namely, whether the validity of the conjecture for a quotient automaton can always be transferred (or "lifted") to the original automaton. Although a complete solution remains open, we show that it is sufficient to verify the Černý conjecture for three specific subclasses of reset automata: radical, simple, and quasi-simple. Our approach relies on establishing a Galois connection between the lattices of congruences and ideal…

Two out of three night trains on this trip has had our sleeper carriage cancelled or replaced last minute (causing 1hr delay).. I wonder if there's a bed bug problem in Europe at the moment

Risk Comparisons in Linear Regression: Implicit Regularization Dominates Explicit Regularization
Jingfeng Wu, Peter L. Bartlett, Jason D. Lee, Sham M. Kakade, Bin Yu
https://arxiv.org/abs/2509.17251

Risk Comparisons in Linear Regression: Implicit Regularization Dominates Explicit Regularization
Existing theory suggests that for linear regression problems categorized by capacity and source conditions, gradient descent (GD) is always minimax optimal, while both ridge regression and online stochastic gradient descent (SGD) are polynomially suboptimal for certain categories of such problems. Moving beyond minimax theory, this work provides instance-wise comparisons of the finite-sample risks for these algorithms on any well-specified linear regression problem. Our analysis yields three …

Non-invertible Symmetry as a Solution to the Strong CP Problem in a GUT-inspired Standard Model
Tatsuo Kobayashi, Hajime Otsuka, Tsutomu T. Yanagida
https://arxiv.org/abs/2508.12287

Non-invertible Symmetry as a Solution to the Strong CP Problem in a GUT-inspired Standard Model
We propose a three-zero texture for the down-quark mass matrix within a $SU(5)$ GUT-inspired Standard Model, enforced by a non-invertible selection rule originating from $\mathbb{Z}_2$ gauging of $\mathbb{Z}_N$ symmetries. Assuming CP invariance at the high-energy scale, our framework solves the strong CP problem while reproducing a realistic quark mass matrix. The CP symmetry is spontaneously broken down at an intermediate scale via complex vacuum expectation values of new scalar fields $η_i$…

Goldman-Turaev formality from the Kontsevitch integral
Dror Bar-Natan, Zsuzsanna Dancso, Tamara Hogan, Jessica Liu, Nancy Scherich
https://arxiv.org/abs/2509.20983 https://

Goldman-Turaev formality from the Kontsevitch integral
We present a new solution to the formality problem for the framed Goldman--Turaev Lie bialgebra, constructing Goldman-Turaev homomorphic expansions (formality isomorphisms) from the Kontsevich integral. Our proof uses a three dimensional derivation of the Goldman-Turaev Lie biaglebra arising from a low-degree Vassiliev quotient -- the {\em emergent} quotient -- of tangles in a thickened punctured disk, modulo a Conway skein relation. This is in contrast to Massuyeau's 2018 proof using braids. A…

Three-Dimensional Numerical Simulations of Magnetar Crust Quakes
Yuanhong Qu, Ashley Bransgrove
https://arxiv.org/abs/2508.12567 https://arxiv.org/pdf/2508…

Three-Dimensional Numerical Simulations of Magnetar Crust Quakes
Crust quakes are frequently invoked as a mechanism to trigger sudden transients in the magnetospheres of magnetars. In this picture, a mechanical failure of the crust excites seismic motions of the magnetar surface that launch force-free waves into the magnetosphere. We first investigate this problem analytically and then perform three-dimensional numerical simulations. Our simulations follow the propagation of high-frequency magneto-elastic waves in the entire crust, and include magnetic coupl…

Mathematical Computation and Reasoning Errors by Large Language Models
Liang Zhang, Edith Aurora Graf
https://arxiv.org/abs/2508.09932 https://arxiv.org/pd…

Mathematical Computation and Reasoning Errors by Large Language Models
Large Language Models (LLMs) are increasingly utilized in AI-driven educational instruction and assessment, particularly within mathematics education. The capability of LLMs to generate accurate answers and detailed solutions for math problem-solving tasks is foundational for ensuring reliable and precise feedback and assessment in math education practices. Our study focuses on evaluating the accuracy of four LLMs (OpenAI GPT-4o and o1, DeepSeek-V3 and DeepSeek-R1) solving three categories of m…

Fast and Compact Sketch-Based Dynamic Connectivity
Quinten De Man, Qamber Jafri, Daniel Delayo, Evan T. West, Michael A. Bender, David Tench
https://arxiv.org/abs/2509.14433 htt…

Fast and Compact Sketch-Based Dynamic Connectivity
We study the dynamic connectivity problem for massive, dense graphs. Our goal is to build a system for dense graphs that simultaneously answers connectivity queries quickly, maintains a fast update throughput, and a uses a small amount of memory. Existing systems at best achieve two of these three performance goals at once. We present a parallel dynamic connectivity algorithm using graph sketching techniques that has space complexity $O(V \log^3 V)$ and query complexity $O(\log V/\log\log V)$…

Efficient Enumeration of At Most $k$-Out Polygons
Waseem Akram, Katsuhisa Yamanaka
https://arxiv.org/abs/2509.12696 https://arxiv.org/pdf/2509.12696…

Efficient Enumeration of At Most $k$-Out Polygons
Let $S$ be a set of $n$ points in the Euclidean plane and general position i.e., no three points are collinear. An \emph{at most $k$-out polygon of $S$} is a simple polygon such that each vertex is a point in $S$ and there are at most $k$ points outside the polygon. In this paper, we consider the problem of enumerating all the at most $k$-out polygon of $S$. We propose a new enumeration algorithm for the at most $k$-out polygons of a point set. Our algorithm enumerates all the at most $k$-out p…

Requirements for Early Quantum Advantage and Quantum Utility in the Capacitated Vehicle Routing Problem
Chinonso Onah, Kristel Michielsen
https://arxiv.org/abs/2509.11469 https:…

Requirements for Early Quantum Advantage and Quantum Utility in the Capacitated Vehicle Routing Problem
We introduce a transparent, encoding-agnostic framework for determining when the Capacitated Vehicle Routing Problem (CVRP) can achieve early quantum advantage. Our analysis shows this is unlikely on noisy intermediate scale quantum (NISQ) hardware even in best case scenarios that use the most qubit-efficient direct encodings. Closed-form resource counts, combined with recent device benchmarks, yield three decisive go/no-go figures of merit: the quantum feasibility point and the qubit- and gate…

Long-Time Dynamics of the 3D Vlasov-Maxwell System with Boundaries
Jin Woo Jang, Chanwoo Kim
https://arxiv.org/abs/2509.11064 https://arxiv.org/pdf/2509.11…

Long-Time Dynamics of the 3D Vlasov-Maxwell System with Boundaries
We construct global-in-time classical solutions to the nonlinear Vlasov-Maxwell system in a three-dimensional half-space beyond the vacuum scattering regime. Our approach combines the construction of stationary solutions to the associated boundary-value problem with a proof of their asymptotic dynamical stability in $L^\infty$ under small perturbations, providing a new framework for understanding long-time wave-particle interactions in the presence of boundaries and interacting magnetic fields.…

Fast adaptive tubal rank-revealing algorithm for t-product based tensor approximation
Qiaohua Liu, Jiehui Gu
https://arxiv.org/abs/2508.08557 https://arxiv…

Fast adaptive tubal rank-revealing algorithm for t-product based tensor approximation
Color images and video sequences can be modeled as three-way tensors, which admit low tubal-rank approximations via convex surrogate minimization. This optimization problem is efficiently addressed by tensor singular value thresholding (t-SVT). To mitigate the computational burden of tensor singular value decomposition (t-SVD) in each iteration, this paper introduces an adaptive randomized algorithm for tubal rank revelation in data tensors \(\mathcal{A}\). Our method selectively captures the p…