Tootfinder

Generating Sizing Fields for Mesh Generation via GCN-based Simplification of Adaptive Background Grids
Xunyang Zhu, Hongfei Ye, Yifei Wang, Taoran Liu, Jianjun Chen
https://arxiv.org/abs/2510.08645

Generating Sizing Fields for Mesh Generation via GCN-based Simplification of Adaptive Background Grids
The sizing field defined on a triangular background grid is pivotal for controlling the quality and efficiency of unstructured mesh generation. However, creating an optimal background grid that is geometrically conforming, computationally lightweight, and free from artifacts like banding is a significant challenge. This paper introduces a novel, adaptive background grid simplification (ABGS) framework based on a Graph Convolutional Network (GCN). We reformulate the grid simplification task as a…

The chanciness of time
John M. Myers, Hadi Madjid
https://arxiv.org/abs/2511.08611 https://arxiv.org/pdf/2511.08611 https://arxiv.org/html/2511.08611
arXiv:2511.08611v1 Announce Type: new
Abstract: Digital network failures stemming from instabilities in measurements of temporal order motivate attention to concurrent events. A century of attempts to resolve the instabilities have never eliminated them. Do concurrent events occur at indeterminate times, or are they better seen as events to which the very concept of temporal order cannot apply? Logical dependencies of messages propagating through digital networks can be represented by marked graphs on which tokens are moved in formal token games. However, available mathematical formulations of these token games invoke "markings"-- global snapshots of the locations of tokens on the graph. The formulation in terms of global snapshots is misleading, because distributed networks are never still: they exhibit concurrent events inexpressible by global snapshots. We reformulate token games used to represent digital networks so as to express concurrency. The trick is to replace global snapshots with "local snapshots." Detached from any central clock, a local snapshot records an action at a node during a play of a token game. Assemblages of local records define acyclic directed graphs that we call history graphs. We show how history graphs represent plays of token games with concurrent motions, and, importantly, how history graphs can represent the history of a network operating while undergoing unpredictable changes.
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A Practical Guide to Rigorously Locate Periodic Orbits in Discrete Dynamics
Luc\'ia Alonso Mozo, Olivier H\'enot, Phillipo Lappicy
https://arxiv.org/abs/2510.06373 https…

A Practical Guide to Rigorously Locate Periodic Orbits in Discrete Dynamics
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the aid of the computer. The method consists in three main steps. First, we reformulate the problem of identifying a $p$-periodic orbit as a root-finding problem. Second, we find a numerical approximation of the root (i.e. a periodic orbit candidate). Third, we ve…

Eigenvalues of a coupled system of thermostat-type via a Birkhoff--Kellogg type Theorem
Sajid Ullah
https://arxiv.org/abs/2510.08516 https://arxiv.org/pdf/…

Eigenvalues of a coupled system of thermostat-type via a Birkhoff--Kellogg type Theorem
In this paper, by means of Birkhoff--Kellogg type Theorem in cones we address the existence of eigenvalues and the corresponding eigenvectors to a family of coupled system of thermostat type. The system is characterized by the presence of a real parameter that influences not only the differential equations but also the boundary conditions. Motivated by models of temperature regulation and feedback-controlled systems, we reformulate the original boundary value problems into systems of Hammerstei…

Agent P: Guiding UI Agents via Symbolic Planning
Shang Ma, Xusheng Xiao, Yanfang Ye
https://arxiv.org/abs/2510.06042 https://arxiv.org/pdf/2510.06042

Agent+P: Guiding UI Agents via Symbolic Planning
Large Language Model (LLM)-based UI agents show great promise for UI automation but often hallucinate in long-horizon tasks due to their lack of understanding of the global UI transition structure. To address this, we introduce AGENT+P, a novel framework that leverages symbolic planning to guide LLM-based UI agents. Specifically, we model an app's UI transition structure as a UI Transition Graph (UTG), which allows us to reformulate the UI automation task as a pathfinding problem on the UTG. Th…

The Narasimhan-Seshadri Theorem revisited
Nitin Nitsure
https://arxiv.org/abs/2509.24617 https://arxiv.org/pdf/2509.24617

The Narasimhan-Seshadri Theorem revisited
Let $X$ be a compact Riemann surface. The famous Narasimhan-Seshadri theorem [13] of 1965 uses the Grothendieck construction [4] of 1956 that associates vector bundles $E(σ)$ on $X$ to representations $σ$ of a certain Fuchsian group $π$. Narasimhan and Seshadri show that by taking the representations $σ$ to be irreducible unitary of a certain kind, this exactly gives all stable vector bundles on $X$ of a given rank and degree. In this note we reformulate the correspondence from representa…

PALQO: Physics-informed Model for Accelerating Large-scale Quantum Optimization
Yiming Huang, Yajie Hao, Jing Zhou, Xiao Yuan, Xiaoting Wang, Yuxuan Du
https://arxiv.org/abs/2509.20733

PALQO: Physics-informed Model for Accelerating Large-scale Quantum Optimization
Variational quantum algorithms (VQAs) are leading strategies to reach practical utilities of near-term quantum devices. However, the no-cloning theorem in quantum mechanics precludes standard backpropagation, leading to prohibitive quantum resource costs when applying VQAs to large-scale tasks. To address this challenge, we reformulate the training dynamics of VQAs as a nonlinear partial differential equation and propose a novel protocol that leverages physics-informed neural networks (PINNs) t…

A Computationally Efficient Finite Element Method for Shape Reconstruction of Inverse Conductivity Problems
Lefu Cai, Zhixin Liu, Minghui Song, Xianchao Wang
https://arxiv.org/abs/2510.00597

A Computationally Efficient Finite Element Method for Shape Reconstruction of Inverse Conductivity Problems
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE constraints have been widely used to deal with this problem. However, such approaches typically require repeated iterations and solving the forward problem at each iteration, which leads to a heavy computational cost. To address this issue, we first reformulate …

Excursion Set Approach to Primordial Black Holes: Cloud-in-Cloud and Mass Function Revisited
Ashu Kushwaha, Teruaki Suyama
https://arxiv.org/abs/2509.25871 https://

Excursion Set Approach to Primordial Black Holes: Cloud-in-Cloud and Mass Function Revisited
The abundance and mass function of primordial black holes (PBHs) are often estimated using the Press-Schechter (PS) formalism. In the case of halo formation, the PS formalism suffers from the miscounting of regions collapsing into halos, known as the cloud-in-cloud problem, which is usually corrected by introducing a multiplicative `fudge factor 2'. By analogy, this factor has sometimes been applied to PBH calculations, although its validity has remained unsettled. We reformulate the PS approac…

Can Audio Large Language Models Verify Speaker Identity?
Yiming Ren, Xuenan Xu, Baoxiang Li, Shuai Wang, Chao Zhang
https://arxiv.org/abs/2509.19755 https://

Can Audio Large Language Models Verify Speaker Identity?
This paper investigates adapting Audio Large Language Models (ALLMs) for speaker verification (SV). We reformulate SV as an audio question-answering task and conduct comprehensive zero-shot evaluations on public benchmarks, showing that current ALLMs have limited zero-shot SV capability and often struggle in diverse acoustic conditions. To address this challenge, we perform supervised fine-tuning on speaker verification data. A rule-based hard pair sampling strategy is proposed to construct mor…

Entropy Regularization in Mean-Field Games of Optimal Stopping
Jodi Dianetti, Roxana Dumitrescu, Giorgio Ferrari, Renyuan Xu
https://arxiv.org/abs/2509.18821 https://

Entropy Regularization in Mean-Field Games of Optimal Stopping
We study mean-field games of optimal stopping (OS-MFGs) and introduce an entropy-regularized framework to enable learning-based solution methods. By utilizing randomized stopping times, we reformulate the OS-MFG as a mean-field game of singular stochastic controls (SC-MFG) with entropy regularization. We establish the existence of equilibria and prove their stability as the entropy parameter vanishes. Fictitious play algorithms tailored for the regularized setting are introduced, and we show th…

An inverse problem for linear system of dispersive equations
Deissy Marcela Pizo, Juan Carlos Mu\~noz Grajales
https://arxiv.org/abs/2509.21524 https://arx…

An inverse problem for linear system of dispersive equations
This paper addresses the inverse problem of identifying the linear velocity coefficient in a linear system governed by two Benjamin-Bona-Mahony-type equations, which model the displacement of water waves propagating along the surface of a shallow channel, incorporating effects of dispersion and topography. To solve this, we reformulate the inverse problem as a restricted minimization problem (RMP), aimed at optimizing a suitably regularized objective functional. We use numerical techniques, spe…

A note on the Maxwell's eigenvalues on thin sets
Francesco Ferraresso, Luigi Provenzano
https://arxiv.org/abs/2510.01846 https://arxiv.org/pdf/2510.018…

A note on the Maxwell's eigenvalues on thin sets
We analyse the Maxwell's spectrum on thin tubular neighborhoods of embedded surfaces of $\mathbb R^3$. We show that the Maxwell eigenvalues converge to the Laplacian eigenvalues of the surface as the thin parameter tends to zero. To achieve this, we reformulate the problem in terms of the spectrum of the Hodge Laplacian with relative conditions acting on co-closed differential $1$-forms. The result leads to new examples of domains where the Faber-Krahn inequality for Maxwell's eigenvalues fails…

Persuasion in Lemons Markets
Andrea Di Giovan Paolo, Jose Higueras
https://arxiv.org/abs/2510.01413 https://arxiv.org/pdf/2510.01413

Persuasion in Lemons Markets
We study information disclosure in competitive markets with adverse selection. Sellers privately observe product quality, with higher quality entailing higher production costs, while buyers trade at the market-clearing price after observing a public signal. Because sellers' participation in trade conveys information about quality, the designer faces endogenous constraints in the set of posteriors that she can induce. We reformulate the designer's problem as a martingale optimal transport exerci…

Computing Resilience Measures in Dynamical Systems
Andreas Morr, Christian Kuehn, George Datseris
https://arxiv.org/abs/2509.19609 https://arxiv.org/pdf/25…

Computing Resilience Measures in Dynamical Systems
Resilience broadly describes a quality of withstanding perturbations. Measures of system resilience have gathered increasing attention across applied disciplines, yet existing metrics often lack computational accessibility and generalizability. In this work, we review the literature on resilience measures through the lens of dynamical systems theory and numerical methods. In this context, we reformulate pertinent measures into a general form and introduce a resource-efficient algorithm designed…