Related papers: Long-time relative error analysis for linear ordin…
This paper proposes local exponential observers for systems on linear Lie groups. We study two different classes of systems. In the first class, the full state of the system evolves on a linear Lie group and is available for measurement. In…
This paper introduces, up to the author's knowledge, for the first time the generalized initial value problem. In this problem, given an ordinary differential equation defined in some set, the initial conditions are mapped to a subset of…
In this paper a special type of difference equations is investigated. The impulses start abruptly at some points and their action continue on given finite intervals. This type of equations is used to model a real process. An algorithm,…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
Environmental epidemiologists are often interested in estimating the effect of time-varying functions of the exposure history on health outcomes. However, the individual exposure measurements that constitute the history upon which an…
We study the set of $T$-periodic solutions of a class of $T$-periodically perturbed Differential-Algebraic Equations, allowing the perturbation to contain a distributed and possibly infinite delay. Under suitable assumptions, the perturbed…
In the propositional setting, the marginal problem is to find a (maximum-entropy) distribution that has some given marginals. We study this problem in a relational setting and make the following contributions. First, we compare two…
Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…
This paper studies the error metric selection for long-term memory learning in sequence modelling. We examine the bias towards short-term memory in commonly used errors, including mean absolute/squared error. Our findings show that all…
Linear discriminant analysis is a widely used method for classification. However, the high dimensionality of predictors combined with small sample sizes often results in large classification errors. To address this challenge, it is crucial…
This article provides a brief introduction to the a posteriori error analysis of parabolic partial differential equations, with an emphasis on challenges distinct from those of steady-state problems. Using the heat equation as a model…
The goal of this paper is to establish relative perturbation bounds, tailored for empirical covariance operators. Our main results are expansions for empirical eigenvalues and spectral projectors, leading to concentration inequalities and…
The paper considers mediation analysis with longitudinal data under latent growth curve models within a counterfactual framework. Estimators and their standard errors are derived for natural direct and indirect effects when the mediator,…
Conformal defects -- extended objects in conformal field theories -- carry localised excitations inherited from symmetry currents, known as the displacements and tilts. They capture the linear response of the defect to deformations of its…
In this paper we propose a new lifetime model, called the odd generalized exponential linear failure rate distribution. Some statistical properties of the proposed distribution such as the moments, the quantiles, the median, and the mode…
We consider an initial value problem for a nonlocal differential equation with a bistable nonlinearity in several space dimensions. The equation is an ordinary differential equation with respect to the time variable t, while the nonlocal…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
In this paper, we consider the initial boundary value problem of a doubly nonlinear parabolic equation with nonlinear perturbation. We impose the homogeneous Dirichlet condition on this problem. We aim to reduce the growth condition of the…
This article deals with the weak errors for averaging principle for a stochastic wave equation in a bounded interval $[0,L]$, perturbed by a oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving with…
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…