Related papers: Random Fixed Points, Limits and Systemic risk

This paper investigates the controllability of finite-dimensional linear fractional systems involving an uncertain parameter. We establish new results on the simultaneous and average controllability. In particular, we show that average…

This paper studies the stability of velocity-pressure mixed approximations of the Stokes problem when different finite element (FE) spaces for each component of the velocity field are considered. We consider some new combinations of…

We propose and analyze an unfitted finite element method for solving elliptic problems on domains with curved boundaries and interfaces. The approximation space on the whole domain is obtained by the direct extension of the finite element…

Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding…

We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a…

We compare the fixed-phase approximation with the better known, but closely related fixed-node approximation on several testing examples. We found that both approximations behave very similarly with the fixed-phase results being very close…

This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…

In this paper, we study some new fixed point results for self maps defined on partial metric type spaces. In particular, we give common fixed point theorems in the same setting. Some examples are given which illustrate the results.

Recent empirical studies have identified fixed point iteration phenomena in deep neural networks, where the hidden state tends to stabilize after several layers, showing minimal change in subsequent layers. This observation has spurred the…

In this paper, we prove some random fixed point theorems for Hardy-Rogers self-random operators in separable Banach spaces and, as some applications, we show the existence of a solution for random nonlinear integral equations in Banach…

We present a detailed study of roundoff errors in probabilistic floating-point computations. We derive closed-form expressions for the distribution of roundoff errors associated with a random variable, and we prove that roundoff errors are…

A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this…

Consider a random geometric graph over a random point process in $\mathbb{R}^d$. Two points are connected by an edge if and only if their distance is bounded by a prescribed distance parameter. We show that projecting the graph onto a two…

This paper addresses the problem of localization, which is inherently non-convex and non-smooth in a federated setting where the data is distributed across a multitude of devices. Due to the decentralized nature of federated environments,…

We provide conditions for the existence of measurable solutions to the equation $\xi(T\omega)=f(\omega,\xi(\omega))$, where $T:\Omega \rightarrow\Omega$ is an automorphism of the probability space $\Omega$ and $f(\omega,\cdot)$ is a…

Interface problems have long been a major focus of scientific computing, leading to the development of various numerical methods. Traditional mesh-based methods often employ time-consuming body-fitted meshes with standard discretization…

We consider systems of stochastic fixed-point equations that arise in the asymptotic analysis of random recursive structures and algorithms such as Quicksort, generalized P\'olya urn processes and path lengths of random recursive trees and…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

Let a graph be observed through a finite random sampling mechanism. Spectral methods are routinely applied to such graphs, yet their outputs are treated as deterministic objects. This paper develops finite-sample inference for spectral…

The stationary points (SPs) of the potential energy landscapes (PELs) of multivariate random potentials (RPs) have found many applications in many areas of Physics, Chemistry and Mathematical Biology. However, there are few reliable methods…