Tootfinder

Barron Space Representations for Elliptic PDEs with Homogeneous Boundary Conditions
Ziang Chen, Liqiang Huang
https://arxiv.org/abs/2508.07559 https://arxi…

Barron Space Representations for Elliptic PDEs with Homogeneous Boundary Conditions
We study the approximation complexity of high-dimensional second-order elliptic PDEs with homogeneous boundary conditions on the unit hypercube, within the framework of Barron spaces. Under the assumption that the coefficients belong to suitably defined Barron spaces, we prove that the solution can be efficiently approximated by two-layer neural networks, circumventing the curse of dimensionality. Our results demonstrate the expressive power of shallow networks in capturing high-dimensional PDE…

Propagation Tree Is Not Deep: Adaptive Graph Contrastive Learning Approach for Rumor Detection
Chaoqun Cui, Caiyan Jia
https://arxiv.org/abs/2508.07201 https://

Propagation Tree Is Not Deep: Adaptive Graph Contrastive Learning Approach for Rumor Detection
Rumor detection on social media has become increasingly important. Most existing graph-based models presume rumor propagation trees (RPTs) have deep structures and learn sequential stance features along branches. However, through statistical analysis on real-world datasets, we find RPTs exhibit wide structures, with most nodes being shallow 1-level replies. To focus learning on intensive substructures, we propose Rumor Adaptive Graph Contrastive Learning (RAGCL) method with adaptive view augmen…

Second-order Optimally Stable IMEX (pseudo-)staggered Galerkin discretization: application to lava flow modeling
Federico Gatti, Giuseppe Orlando
https://arxiv.org/abs/2509.09460

Second-order Optimally Stable IMEX (pseudo-)staggered Galerkin discretization: application to lava flow modeling
We present second-order optimally stable Implicit-Explicit (IMEX) Runge-Kutta (RK) schemes with application to a modified set of shallow water equations that can be used to model the dynamics of lava flows. The schemes are optimally stable in the sense that they satisfy, at the space-time discretization level, a condition analogous to the \texttt{L}-stability of Runge-Kutta methods for ordinary differential equations. A novel (pseudo-)staggered Galerkin scheme is introduced, which can be interp…

PredNext: Explicit Cross-View Temporal Prediction for Unsupervised Learning in Spiking Neural Networks
Yiting Dong, Jianhao Ding, Zijie Xu, Tong Bu, Zhaofei Yu, Tiejun Huang
https://arxiv.org/abs/2509.24844

PredNext: Explicit Cross-View Temporal Prediction for Unsupervised Learning in Spiking Neural Networks
Spiking Neural Networks (SNNs), with their temporal processing capabilities and biologically plausible dynamics, offer a natural platform for unsupervised representation learning. However, current unsupervised SNNs predominantly employ shallow architectures or localized plasticity rules, limiting their ability to model long-range temporal dependencies and maintain temporal feature consistency. This results in semantically unstable representations, thereby impeding the development of deep unsupe…

Deep vs. Shallow: Benchmarking Physics-Informed Neural Architectures on the Biharmonic Equation
Akshay Govind Srinivasan, Vikas Dwivedi, Balaji Srinivasan
https://arxiv.org/abs/2510.04490

Deep vs. Shallow: Benchmarking Physics-Informed Neural Architectures on the Biharmonic Equation
Partial differential equation (PDE) solvers are fundamental to engineering simulation. Classical mesh-based approaches (finite difference/volume/element) are fast and accurate on high-quality meshes but struggle with higher-order operators and complex, hard-to-mesh geometries. Recently developed physics-informed neural networks (PINNs) and their variants are mesh-free and flexible, yet compute-intensive and often less accurate. This paper systematically benchmarks RBF-PIELM, a rapid PINN varian…

I have extended thoughts on a few nuances of burnout, resilience, and employment
Before taking time off for burnout, my skip manager reminded me to read the strongly positive 360 feedback from my reports. That's both a shallow and a deep reinforcement of resilience, first and foremost by rebuilding and grounding self-confidence. Reading positive feedback provides evidence that I'm capable and effective at my job.
Beyond self-confidence, I have other needs in a workplace, …

Reading Between the Lines: Scalable User Feedback via Implicit Sentiment in Developer Prompts
Daye Nam, Malgorzata Salawa, Satish Chandra
https://arxiv.org/abs/2509.18361 https:…

At some point, DOPs should stop going for even shallower depth of field or even weirder anamorphic lens distortion. I'm feeling like an old guy complaining about how "you can't see anything on the screen! It's too dark". Only I'm like "nothing is in focus anymore you doofuses!"
Yes, this is a subtoot about #Brick on

Vision-Free Retrieval: Rethinking Multimodal Search with Textual Scene Descriptions
Ioanna Ntinou, Alexandros Xenos, Yassine Ouali, Adrian Bulat, Georgios Tzimiropoulos
https://arxiv.org/abs/2509.19203

Vision-Free Retrieval: Rethinking Multimodal Search with Textual Scene Descriptions
Contrastively-trained Vision-Language Models (VLMs), such as CLIP, have become the standard approach for learning discriminative vision-language representations. However, these models often exhibit shallow language understanding, manifesting bag-of-words behaviour. These limitations are reinforced by their dual-encoder design, which induces a modality gap. Additionally, the reliance on vast web-collected data corpora for training makes the process computationally expensive and introduces signif…

Confidence-gated training for efficient early-exit neural networks
Saad Mokssit, Ouassim Karrakchou, Alejandro Mousist, Mounir Ghogho
https://arxiv.org/abs/2509.17885 https://…

Confidence-gated training for efficient early-exit neural networks
Early-exit neural networks reduce inference cost by enabling confident predictions at intermediate layers. However, joint training often leads to gradient interference, with deeper classifiers dominating optimization. We propose Confidence-Gated Training (CGT), a paradigm that conditionally propagates gradients from deeper exits only when preceding exits fail. This encourages shallow classifiers to act as primary decision points while reserving deeper layers for harder inputs. By aligning train…

A practical route to donor binding energies: The DFT-1/2 method for shallow defects
Joshua Claes, Bart Partoens, Dirk Lamoen, Marcelo Marques, Lara K. Teles
https://arxiv.org/abs/2508.14738

A practical route to donor binding energies: The DFT-1/2 method for shallow defects
Accurately calculating the binding energies of shallow defects requires large supercells to capture the extended nature of their wavefunctions. This makes many beyond-DFT methods, such as hybrid functionals, impractical for direct calculations, often requiring indirect or approximate approaches. However, standard DFT alone fails to provide reliable results due to the well-known band gap underestimation and delocalization errors. In this work, we employ the DFT-1/2 method to address these defici…

Probing the Ground State of the Antiferromagnetic Heisenberg Model on the Kagome Lattice using Geometrically Informed Variational Quantum Eigensolver
Abdellah Tounsi, Nacer Eddine Belaloui, Abdelmouheymen Rabah Khamadja, Takei Eddine Fadi Lalaoui, Mohamed Messaoud Louamri, David E. Bernal Neira, Mohamed Taha Rouabah
https://arxiv.org/abs/2…

Probing the Ground State of the Antiferromagnetic Heisenberg Model on the Kagome Lattice using Geometrically Informed Variational Quantum Eigensolver
This work investigates the nature of the ground state of the antiferromagnetic Heisenberg model on minimal kagome cells -- a triangle and a star -- using the variational quantum eigensolver (VQE) algorithm on real quantum hardware. We demonstrate that the ground state preparation is achievable using a shallow hardware-efficient quantum circuit with a naturally Euclidean parameter space. Our custom ansatz is capable of accurately recovering essential properties such as the spin correlation terms…

Effective theories for incompressible magnetoelastic shallow shells
Emanuele Tasso, Tobias Unterberger
https://arxiv.org/abs/2508.13916 https://arxiv.org/p…

Effective theories for incompressible magnetoelastic shallow shells
We characterize the asymptotic behaviour, in the sense of $Γ$-convergence, of a thin magnetoelastic shallow shell. The compactness is achieved up to rigid motions. For deformations, it relies on an approximation by rigid movements, whereas for magnetizations it is based on a careful consideration of the geometry of the deformed domain. The result is obtained by a combination of variational methods ($Γ$-convergence) with degree theory, fixed-point and geometrical arguments. The proof strategy …

Tsunami modeling with dynamic seafloors: a high-order solver validated with shallow water benchmarks
Thomas Melkior (LMPS, LGENS), Harsha S Bhat (LGENS), Faisal Amlani (LMPS)
https://arxiv.org/abs/2508.20596

Tsunami modeling with dynamic seafloors: a high-order solver validated with shallow water benchmarks
Recent scientific studies have suggested that, in certain physical configurations, the time-dependent behavior of earthquake rupture and seafloor (bathymetry) motion can leave observable near-field signatures in tsunami wave generation and propagation. However, dynamic ground movement is often neglected in conventional tsunami models, which commonly assume instantaneous ground displacement (sourcing). This work introduces a pseudo-spectral algorithm for the solution of the nonlinear shallow wat…

From shallow to full wrapping: geometry and deformability dictate lipid vesicle internalization
Stijn van der Ham, Alexander Brown, Halim Kusumaatmaja, Hanumantha Rao Vutukuri
https://arxiv.org/abs/2507.17434

From shallow to full wrapping: geometry and deformability dictate lipid vesicle internalization
The deformability of vesicles critically influences their engulfment by lipid membranes, a process central to endocytosis, viral entry, drug delivery, and intercellular transport. While theoretical models have long predicted this influence, direct experimental validation has remained elusive. Here, we combine experiments with continuum simulations to quantify how vesicle deformability affects the engulfment of small giant unilamellar vesicles (GUVs) by larger GUVs under depletion-induced adhesi…

A Practical Flake Segmentation and Indexing Pipeline for Automated 2D Material Stacking
Yutao Li, Logan Sherlock, Ryan Benderson, Daniel Ostrom, Huandong Chen, Kazuhiro Fujita, Abhay Pasupathy
https://arxiv.org/abs/2509.01826

A Practical Flake Segmentation and Indexing Pipeline for Automated 2D Material Stacking
A cost-effective and robust image-processing pipeline is presented for the detection and characterization of exfoliated two-dimensional (2D) material flakes in optical microscope images, designed to facilitate automation in van der Waals heterostructure assembly. The system combines shallow machine learning (ML)-based material classification with a precision-first flake detection algorithm driven by edge morphology and color discontinuity. Step edges are resolved when supported by optical contr…

Collapsi is strongly solved
Michael Young
https://arxiv.org/abs/2507.16823 https://arxiv.org/pdf/2507.16823

Collapsi is strongly solved
Collapsi is a two-player game of complete information released in June 2025 by Mark S. Ball of Riffle Shuffle & Roll. Played with two pawns on a toroidal board of 16 randomly mixed playing cards, players take it in turns to move based on the value of the card they sit on, with the game ending when a player has no legal moves. The number of possible deals after symmetry breaking is low enough, and the game tree shallow enough, to make an exhaustive analysis of the game feasible. A solver was wri…

A well-balanced gas-kinetic scheme with adaptive mesh refinement for shallow water equations
Gaocheng Liu, Fengxiang Zhao, Jianping Gan, Kun Xu
https://arxiv.org/abs/2508.14216 …

A well-balanced gas-kinetic scheme with adaptive mesh refinement for shallow water equations
This paper is about the construction of a well-balanced gas-kinetic scheme (GKS) with space-time adaptive mesh refinement (STAMR) for the shallow water equations (SWE). While the well-balanced GKS has been established on Cartesian and triangular meshes, the present STAMR framework employs arbitrary quadrilateral meshes with hanging nodes, posing additional challenges for constructing well-balanced schemes. Complementing spatial adaptivity, temporal adaptivity is achieved by selecting adaptive t…

Fully implicit timestepping methods for the rotating shallow water equations
Werner Bauer, Colin J. Cotter
https://arxiv.org/abs/2508.02358 https://arxiv.o…

Fully implicit timestepping methods for the rotating shallow water equations
Fully implicit timestepping methods have several potential advantages for atmosphere/ocean simulation. First, being unconditionally stable, they degrade more gracefully as the Courant number increases, typically requiring more solver iterations rather than suddenly blowing up. Second, particular choices of implicit timestepping methods can extend energy conservation properties of spatial discretisations to the fully discrete method. Third, these methods avoid issues related to splitting errors …

Entropic approximations of the semigeostrophic shallow water equations
Jean-David Benamou, Colin J. Cotter, Jacob J. M. Francis, Hugo Malamut
https://arxiv.org/abs/2507.16415 ht…

Entropic approximations of the semigeostrophic shallow water equations
We develop a discretisation of the semigeostrophic rotating shallow water equations, based upon their optimal transport formulation. This takes the form of a Moreau-Yoshida regularisation of the Wasserstein metric. Solutions of the optimal transport formulation provide the shallow water layer depth represented as a measure, which is itself the push forward of an evolving measure under the semigeostrophic coordinate transformation. First, we propose and study an entropy regularised version of th…