Tootfinder

This https://arxiv.org/abs/2501.18569 has been replaced.
initial toot: https://mastoxiv.page/@…

Derivation of the free energy, entropy and specific heat for planar Ising models: Application to Archimedean lattices and their duals
The 2d ferromagnetic Ising model was solved by Onsager on the square lattice in 1944, and an explicit expression of the free energy density $f$ is presently available for some other planar lattices. But an exact derivation of the critical temperature $T_c$ only requires a partial derivation of $f$. It has been performed on many lattices, including the 11 Archimedean lattices. In this article, we give general expressions of the free energy, energy, entropy and specific heat for planar lattices w…

This https://arxiv.org/abs/2504.03393 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Effects of Interpolation Error and Bias on the Random Mesh Finite Element Method for Inverse Problems
Bayesian inverse problems are an important application for probabilistic solvers of partial differential equations: when fully resolving numerical error is computationally infeasible, probabilistic solvers can be used to consistently model the error and propagate it to the posterior. In this work, the performance of the random mesh finite element method (RM-FEM) is investigated in a Bayesian inverse setting. We show how interpolation error negatively affects the RM-FEM posterior, and how these …

This https://arxiv.org/abs/2105.05584 has been replaced.
link: https://scholar.google.com/scholar?q=a

Consistent approximate Q-conditional symmetries of PDEs: application to a hyperbolic reaction-diffusion-convection equation
Within the theoretical framework of a recently introduced approach to approximate Lie symmetries of differential equations containing small terms, which is consistent with the principles of perturbative analysis, we define accordingly approximate Q-conditional symmetries of partial differential equations. The approach is illustrated by considering the hyperbolic version of a reaction-diffusion-convection equation. By looking for its first order approximate Q-conditional symmetries, we are able …

An Efficient Class of Bayesian Generalized Quadratic Nonlinear Dynamic Models with Application to Birth Rate Monitoring
Madelyn Clinch, Jonathan R. Bradley
https://arxiv.org/abs/2506.22188

An Efficient Class of Bayesian Generalized Quadratic Nonlinear Dynamic Models with Application to Birth Rate Monitoring
Many real-world spatio-temporal processes exhibit nonlinear dynamics that can often be described through stochastic partial differential equations. These models are flexible and scientifically motivated, however, implementing them in a fully Bayesian framework can be computationally challenging. We are motivated by birth rate data, which has important implications for public health and are known to follow nonlinear dynamics. We propose a covariance calibration strategy that specifies the covari…

This https://arxiv.org/abs/2503.02041 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCE_…

Interpolating Neural Network-Tensor Decomposition (INN-TD): a scalable and interpretable approach for large-scale physics-based problems
Deep learning has been extensively employed as a powerful function approximator for modeling physics-based problems described by partial differential equations (PDEs). Despite their popularity, standard deep learning models often demand prohibitively large computational resources and yield limited accuracy when scaling to large-scale, high-dimensional physical problems. Their black-box nature further hinders the application in industrial problems where interpretability and high precision are cr…

An acyclic $d$-partition of the $r$-uniform complete hypergraph $K_{rd}^{(r)}$
Ayako Carter, Eric Montoya, Mihai D. Staic
https://arxiv.org/abs/2506.23238 …

An acyclic $d$-partition of the $r$-uniform complete hypergraph $K_{rd}^{(r)}$
In this paper we introduce a $d$-partition $\mathcal{E}_d^{(r)}=(Ω_1^{(r,d)}, Ω_2^{(r,d)},\dots, Ω_d^{(r,d)})$ of the $r$-uniform complete hypergraph $K_{rd}^{(r)}$. We prove that $\mathcal{E}_d^{(r)}$ is homogeneous and that each hypergraph $Ω_i^{(r,d)}$ is acyclic (i.e. has zero Betti numbers). As an application, we show that the map $det^{S^r}$ is nontrivial for every $r$, which gives a partial answer to a conjecture from [14].

This https://arxiv.org/abs/2402.01593 has been replaced.
link: https://scholar.google.com/scholar?q=a

Statistical Accuracy of Approximate Filtering Methods
Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including problems such as probabilistic weather forecasting and prediction of epidemics. Particle filters provide a well-founded approach to the problem, leading to provably accurate approximations of the statistics. However these methods perform poorly in high dimensions…

Failure of Bott vanishing for (co)adjoint partial flag varieties
Pieter Belmans
https://arxiv.org/abs/2506.09811 https://arxiv.org/pd…

Failure of Bott vanishing for (co)adjoint partial flag varieties
Bott vanishing is a strong vanishing result for the cohomology of exterior powers of the cotangent bundle twisted by ample line bundles. Buch-Thomsen-Lauritzen-Mehta conjectured that partial flag varieties (which are not products of projective spaces) do not satisfy Bott vanishing, despite all their other nice properties. The cominuscule case is an easy application of the Borel-Weil-Bott theorem, following results of Snow. We show that the (co)adjoint partial flag varieties of all classical and…

Annihilating and breaking Lorentz cone entanglement
Francesca La Piana, Alexander M\"uller-Hermes
https://arxiv.org/abs/2506.14480 https://

Annihilating and breaking Lorentz cone entanglement
Linear maps between finite-dimensional ordered vector spaces with orders induced by proper cones $C_A$ and $C_B$ are called entanglement breaking if their partial application sends the maximal tensor product $K\otimes_{\max} C_A$ into the minimal tensor product $K\otimes_{\min} C_B$ for any proper cone $K$. We study the larger class of Lorentz-entanglement breaking maps where $K$ is restricted to be a Lorentz cone of any dimension, i.e., any cone over a Euclidean ball. This class of maps appear…

An approximate Riemann Solver Approach in Physics-Informed Neural Networks for hyperbolic conservation laws
Jorge F. Urb\'an, Jos\'e A. Pons
https://arxiv.org/abs/2506.11959

An approximate Riemann Solver Approach in Physics-Informed Neural Networks for hyperbolic conservation laws
This study enhances the application of Physics-Informed Neural Networks (PINNs) for modeling discontinuous solutions in both hydrodynamics and relativistic hydrodynamics. Conventional PINNs, trained with partial differential equation residuals, frequently face convergence issues and lower accuracy near discontinuities. To address these issues, we build on the recently proposed Locally-Linearized PINNs, which improve shock detection by modifying the Jacobian matrix resulting from the linearizati…

Global hypoellipticity on time-periodic Gelfand-Shilov spaces via non-discrete Fourier analysis
Andr\'e Pedroso Kowacs, Pedro Meyer Tokoro
https://arxiv.org/abs/2506.13475

Global hypoellipticity on time-periodic Gelfand-Shilov spaces via non-discrete Fourier analysis
In this paper, we provide a characterization of the time-periodic Gelfand-Shilov spaces, as introduced by F. de Ávila Silva and M. Cappiello [J. Funct. Anal., 282(9):29, 2022], through the asymptotic behaviour of both the Euclidean and periodic partial Fourier transforms of their elements. As an application, we establish necessary and sufficient conditions for global regularity -- within this framework -- for a broad class of constant-coefficient differential operators, as well as for first-or…

Multiple mixing and fractional cohomological equation
Zhenqi Jenny Wang
https://arxiv.org/abs/2506.08392 https://arxiv.org/pdf/2506.0…

Multiple mixing and fractional cohomological equation
We introduce the notion of the (multiple) fractional cohomological equation and, by studying its solutions, develop a novel framework to obtain the decay of matrix coefficients for partially hyperbolic algebraic actions. In particular, we show that mere partial Hölder regularity of \(L^2\) vectors is sufficient for exponential decay of matrix coefficients. As an application, under the assumption of ergodicity, we obtain explicit and sharp exponential mixing rates of all orders for a large cl…

Random Batch Methods for Discretized PDEs on Graphs
Mart\'in Hern\'andez, Enrique Zuazua
https://arxiv.org/abs/2506.11809 https://

Random Batch Methods for Discretized PDEs on Graphs
Gas transport and other complex real-world challenges often require solving and controlling partial differential equations (PDEs) defined on graph structures, which typically demand substantial memory and computational resources. The Random Batch Method (RBM) offers significant relief from these demands by enabling the simulation of large-scale systems with reduced computational cost. In this paper, we analyze the application of RBM for solving PDEs on one-dimensional graphs, specifically con…