Related papers: Numerical Analysis of Target Enumeration via Euler…

This paper proposes a method to reduce noise in acyclic sensor networks enumerating targets using the integral theory with respect to Euler characteristic. For an acyclic network (a partially ordered set) equipped with sensors detecting…

For dynamical systems evolving on a manifold and admitting first integrals, standard one-step numerical methods generally cause the discrete trajectory to drift off the manifold and the numerical values of the first integrals to deviate…

Euler integrals of deterministic functions have recently been shown to have a wide variety of possible applications, including in signal processing, data aggregation and network sensing. Adding random noise to these scenarios, as is natural…

In this article, we study Euler characteristic techniques in topological data analysis. Pointwise computing the Euler characteristic of a family of simplicial complexes built from data gives rise to the so-called Euler characteristic…

The Euler scheme is up to date the most important numerical method for ordinary differential inclusions, because the use of the available higher-order methods is prohibited by their enormous complexity after spatial discretization.…

This paper considers the implicit Euler discretization of Levant's arbitrary order robust exact differentiator in presence of sampled measurements. Existing implicit discretizations of that differentiator are shown to exhibit either…

We study the convergence of a discrete Luenberger observer for the barotropic Euler equations in one dimension, for measurements of the velocity only. We use a mixed finite element method in space and implicit Euler integration in time. We…

We study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, including in the context of…

This article surveys the Euler calculus - an integral calculus based on Euler characteristic - and its applications to data, sensing, networks, and imaging.

This paper introduces a multiple-input discrete Urysohn operator for modelling non-linear control systems and a technique of its identification by processing the observed input and output signals. It is shown that, due to the nature of the…

High-index saddle dynamics provides an effective means to compute the any-index saddle points and construct the solution landscape. In this paper we prove error estimates for Euler discretization of high-index saddle dynamics with respect…

Methodologies for incorporating the uncertainties characteristic of data-driven object detectors into object tracking algorithms are explored. Object tracking methods rely on measurement error models, typically in the form of measurement…

We address the problem of attack detection and isolation for a class of discrete-time nonlinear systems under (potentially unbounded) sensor attacks and measurement noise. We consider the case when a subset of sensors is subject to additive…

We implement methods from the geometry of numbers to give explicit estimates for the number of integral ideals in a number field. We pay particular attention to minimising the effect of the degree $n$ of the number field on the error term…

We analyze the behavior of the Euler method for delay differential equations under nonstandard assumptions on the right-hand-side function f, when evaluations of f are corrupted by informational noise. We provide theoretical upper bounds on…

We study two sensor assignment problems for multi-target tracking with the goal of improving the observability of the underlying estimator. We consider various measures of the observability matrix as the assignment value function. We first…

Reachable sets of nonlinear control systems can in general only be approximated numerically, and these approximations are typically very expensive to compute. In this paper, we explore a strategy for choosing the temporal and spatial…

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…

Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional…

The issue of single-grid discretization error estimator, operating in the postprocessor mode, is addressed in the paper. An ensemble of numerical solutions, obtained using solvers of different accuracy, is shown to provide an upper estimate…