Tootfinder

Variational Learning Finds Flatter Solutions at the Edge of Stability
Avrajit Ghosh, Bai Cong, Rio Yokota, Saiprasad Ravishankar, Rongrong Wang, Molei Tao, Mohammad Emtiyaz Khan, Thomas M\"ollenhoff
https://arxiv.org/abs/2506.12903

Variational Learning Finds Flatter Solutions at the Edge of Stability
Variational Learning (VL) has recently gained popularity for training deep neural networks and is competitive to standard learning methods. Part of its empirical success can be explained by theories such as PAC-Bayes bounds, minimum description length and marginal likelihood, but there are few tools to unravel the implicit regularization in play. Here, we analyze the implicit regularization of VL through the Edge of Stability (EoS) framework. EoS has previously been used to show that gradient d…

Controlled manipulation of solitons in a recirculating fiber loop using external potentials
Fran\c{c}ois Copie, Pierre Suret, St\'ephane Randoux
https://arxiv.org/abs/2506.13544

Controlled manipulation of solitons in a recirculating fiber loop using external potentials
Optical solitons are self-sustained wave packets that propagate without distortion due to a balance between dispersion and nonlinearity. Their unique stability underpins key photonic applications while also playing a central role in nonlinear wave physics. However, real-time control over soliton dynamics in non-dissipative systems remains a major challenge, limiting their practical applications in photonic systems. Here, we introduce a fiber-based platform for soliton manipulation, by creating …

A solution to the tension of burning on neutron stars and nuclear physics
Y. Cavecchi, D. Galloway, A. Heger, P. Santill\'An-Ortega, M. Nava-Callejas, F. M. Vincentelli, L. Rivera Sandoval, A. Goodwin, Z. Johnston, S. Puente Mancilla, D. Page
https://arxiv.org/abs/2506.11966

A solution to the tension of burning on neutron stars and nuclear physics
When neutron stars accrete matter from a companion star, this matter forms a disc around them and eventually falls on their surface. Here, the fuel can ignite into bright flashes called Type I bursts. Theoretical calculations based on state-of-the-art nuclear reactions are able to explain many features of the bursts. However, models predict that the bursts should cease at high accretion rates, whereas in many sources they disappear at much lower rates. Moreover, their recurrence times also show…

Privacy-preserving and reward-based mechanisms of proof of engagement
Matteo Marco Montanari, Alessandro Aldini
https://arxiv.org/abs/2506.12523 https://…

Privacy-preserving and reward-based mechanisms of proof of engagement
Proof-of-Attendance (PoA) mechanisms are typically employed to demonstrate a specific user's participation in an event, whether virtual or in-person. The goal of this study is to extend such mechanisms to broader contexts where the user wishes to digitally demonstrate her involvement in a specific activity (Proof-of-Engagement, PoE). This work explores different solutions, including DLTs as well as established technologies based on centralized systems. The main aspects we consider include the l…

The evolution equation and the eigenvalue problem for the Laplacian in a regular tree
Leandro M. Del Pezzo, Nicolas Frevenza, Julio D. Rossi
https://arxiv.org/abs/2506.13728

The evolution equation and the eigenvalue problem for the Laplacian in a regular tree
In this paper our main goal is to study the evolution problem associated with the Laplacian operator with Dirichlet boundary conditions in a regular tree. First, we prove existence and uniqueness of solutions when the initial condition is compatible with the boundary condition. Next, we deal with the asymptotic behavior of the solutions and we prove that they decay to zero exponentially fast. This decay rate is governed by the associated first eigenvalue that we also study here.

Convergence of physics-informed neural networks modeling time-harmonic wave fields
Stefan Schoder, Aneta Furmanov\'a, Viktor Hru\v{s}ka
https://arxiv.org/abs/2506.11395

Convergence of physics-informed neural networks modeling time-harmonic wave fields
Studying physics-informed neural networks (PINNs) for modeling partial differential equations to solve the acoustic wave field has produced promising results for simple geometries in two-dimensional domains. One option is to compute the time-harmonic wave field using the Helmholtz equation. Compared to existing numerical models, the physics-informed neural networks forward problem has to overcome several topics related to the convergence of the optimization toward the "true" solution. The topic…

Impact of Buchdahl metric potential on thin-shell gravastar framework in de Rham-Gabadadze-Tolley like massive gravity
Meghanil Sinha, S. Surendra Singh
https://arxiv.org/abs/2506.11171

Impact of Buchdahl metric potential on thin-shell gravastar framework in de Rham-Gabadadze-Tolley like massive gravity
This paper presents a study on gravitational vacuum stars (gravastars) with an isotropic matter distribution in de Rham-Gabadadze-Tolley (dRGT) massive gravity incorporating Buchdahl metric function. Here we have conducted an analysis on thin-shell singularity-free gravastar configuration. The study demonstrates the viability of gravastars as alternatives to black holes (BHs) in this massive gravity. Our research yields singularity free analytical solutions for gravastar interior and without ev…

Partially rigid motions in the planar three-body problem
Richard Moeckel
https://arxiv.org/abs/2506.13570 https://arxiv.org/pdf/2506.…

Partially rigid motions in the planar three-body problem
A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid motions, where some but not all of the distances are constant. For the planar three-body problem with equal masses, we show that partially rigid motions are impossible -- if even one of the three mutual distances is constant, the motion must be a relative equilibr…

Characterizing the outer disk of eXtended-UV galaxies in the optical domain with deep surveys
E. Bernaud, S. Boissier, Junais, K. Malek, E. Hugot, G. Galaz
https://arxiv.org/abs/2506.11568

Characterizing the outer disk of eXtended-UV galaxies in the optical domain with deep surveys
Aims : Extended-UV (XUV) galaxies are galaxies presenting an extended outer ultraviolet disks. Although some Giant Low Surface Brightness (GLSB) galaxies are also XUV, their relation has been seldom studied. This work aims to determine whether a sample of nine XUV galaxies can be classified as GLSBs, by analyzing their photometric properties in deep optical images. Method : The method presented here uses optical data from the Dark Energy Survey (DES) to construct surface brightness (SB) profile…

Gradient regularity for widely degenerate elliptic partial differential equations
Michael Strunk
https://arxiv.org/abs/2506.11708 https://

Gradient regularity for widely degenerate elliptic partial differential equations
In this paper, we investigate the regularity of weak solutions $u\colonΩ\to\mathbb{R}$ to elliptic equations of the type \begin{equation*} \mathrm{div}\, \nabla \mathcal{F}(x,Du) = f\qquad\text{in $Ω$}, \end{equation*} whose ellipticity degenerates in a fixed bounded and convex set $E\subset\mathbb{R}^n$ with $0\in \mathrm{Int}\, E$. Here, $Ω\subset\mathbb{R}^n$ denotes a bounded domain, and $\mathcal{F} \colon Ω\times\mathbb{R}^n \to\mathbb{R}_{\geq 0}$ is a function with the properties:…