Related papers: Observability for heat equations with time-depende…
In this paper, we first give a direct proof for two recurrence relations of the heat kernels for hyperbolic spaces in \cite{DM}. Then, by similar computation, we give two similar recurrence relations of the heat kernels for spheres.…
Studying extreme events and how they evolve in a changing climate is one of the most important current scientific challenges. Starting from complex climate models, a key difficulty is to be able to run long enough simulations in order to…
We discuss differential-- versus integral--equation based methods describing out--of thermal equilibrium systems and emphasize the importance of a well defined reduction to statistical observables. Applying the projection operator approach,…
We present a space-time virtual element method for the discretization of the heat equation, which is defined on general prismatic meshes and variable degrees of accuracy. Strategies to handle efficiently the space-time mesh structure are…
It is shown that the heat kernel operator for the Laplace operator on any covariantly constant curved background, i.e. in symmetric spaces, may be presented in form of an averaging over the Lie group of isometries with some nontrivial…
In this work, we investigate the solvability of a heat equation involving the Grushin operator. The equation is perturbed by two nonlinear reaction terms, one of which includes a memory component, introducing nonlocal effects in time. We…
Attributions are a common local explanation technique for deep learning models on single samples as they are easily extractable and demonstrate the relevance of input values. In many cases, heatmaps visualize such attributions for samples,…
In this paper we consider the heat equation with memory in a bounded region $\Omega \subset\mathbb{R}^d$, $d\geq 1$, in the case that the propagation speed of the signal is infinite (i.e. the Colemann-Gurtin model). The memory kernel is of…
We derive a Bell-type inequality for observables with arbitrary spectra. For the case of continuous variable systems we propose a possible experimental violation of this inequality, by using squeezed light and homodyne detection together…
Numerous complex systems, such as those arisen in ecological networks, genomic contact networks, and social networks, exhibit higher-order and time-varying characteristics, which can be effectively modeled using temporal hypergraphs.…
Leveraging data collected from smart meters in buildings can aid in developing policies towards energy conservation. Significant energy savings could be realised if deviations in the building operating conditions are detected early, and…
In this paper, we show that efficient separated sum-of-exponentials approximations can be constructed for the heat kernel in any dimension. In one space dimension, the heat kernel admits an approximation involving a number of terms that is…
Network theory and inverse modeling are two standard tools of applied physics, whose combination is needed when studying the dynamical organization of spatially distributed systems from indirect measurements. However, the associated…
Theorists are often told to express things in the "observational plane". One can do this for space-time geometry, considering "visual" observations of matter in our universe by a single observer over time, with no assumptions about…
In this paper, the asymptotic behavior of a semilinear heat equation with long time memory and non-local diffusion is analyzed in the usual set-up for dynamical systems generated by differential equations with delay terms. This approach is…
Irreversible thermodynamics of simple fluids have been connected recently to the theory of dynamical systems and some interesting assumptions have been made about the nature of the associated invariant measures. We show that the tests of…
In this paper, we present a novel framework for enhancing model interpretability by integrating heatmaps produced separately by ResNet and a restructured 2D Transformer with globally weighted input saliency. We address the critical problem…
The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients…
We study the memory-type null controllability property for wave equations involving memory terms. The goal is not only to drive the displacement and the velocity (of the considered wave) to rest at some time-instant but also to require the…
We characterize the observability property (and, by duality, the controllability and the stabilization) of the wave equation on a Riemannian manifold $\Omega,$ with or without boundary, where the observation (or control) domain is…