This paper is devoted to the asymptotic behavior of solutions to a non-autonomous stochastic wave equation with nonlinear damping and multiplicative white noise defined on an unbounded domain. By showing the pullback asymptotic compactness of the cocycle in a certain parameter region, we prove the existence of a random attractor when the intensity of noise is sufficiently small. For the stochastic wave equation with rapidly oscillating external force we prove that the Hausdorff distance between the random attractor A of the original equation and the random attractor A 0 of the averaged equation is in the order of O( ).
With the popularization of Topological Data Analysis, the Reeb graph has found new applications as a summarization technique in the analysis and visualization of large and complex data, whose usefulness extends beyond just the graph itself. Pairing critical points enables forming topological fingerprints, known as persistence diagrams, that provides insights into the structure and noise in data. Although the body of work addressing the efficient calculation of Reeb graphs is large, the literature on pairing is limited. In this paper, we discuss two algorithmic approaches for pairing critical points in Reeb graphs, first a multipass approach, followed by a new single-pass algorithm, called Propagate and Pair.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.