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In this paper, we use machine learning to show that the Cheeger constant of a connected regular graph has a predominant linear dependence on the largest two eigenvalues of the graph spectrum. We also show that a trained deep neural network on graphs of smaller sizes can be used as an effective estimator in estimating the Cheeger constant of larger graphs.
We review the theory of Cheeger constants for graphs and quantum graphs and their present and envisaged applications.
Estimating health benefits of reducing fossil fuel use from improved air quality provides important rationales for carbon emissions abatement. Simulating pollution concentration is a crucial step of the estimation, but traditional approaches often re
We compute the Cheeger constant of spherical shells and tubular neighbourhoods of complete curves in an arbitrary dimensional Euclidean space.
In this article we study the top of the spectrum of the normalized Laplace operator on infinite graphs. We introduce the dual Cheeger constant and show that it controls the top of the spectrum from above and below in a similar way as the Cheeger cons
Lattice constants such as unit cell edge lengths and plane angles are important parameters of the periodic structures of crystal materials. Predicting crystal lattice constants has wide applications in crystal structure prediction and materials prope