
Euler Characteristic Surfaces
We study the use of the Euler characteristic for multiparameter topologi...
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Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images
We present an efficient algorithm to compute Euler characteristic curves...
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Bootstrapping Persistent Betti Numbers and Other Stabilizing Statistics
The present contribution investigates multivariate bootstrap procedures ...
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Computing oscillatory solutions of the Euler system via Kconvergence
We develop a method to compute effectively the Young measures associated...
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Dances between continuous and discrete: Euler's summation formula
Leonhard Euler likely developed his summation formula in 1732, and soon ...
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Estimation of Expected Euler Characteristic Curves of Nonstationary Smooth Gaussian Random Fields
The expected Euler characteristic (EEC) curve of excursion sets of a Gau...
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Perturbation of the expected Minkowski functional for weakly nonGaussian isotropic fields on a bounded domain
The Minkowski functionals (MF) including the Euler characteristic (EC) s...
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On approximation theorems for the Euler characteristic with applications to the bootstrap
We study approximation theorems for the Euler characteristic of the VietorisRips and Čech filtration. The filtration is obtained from a Poisson or binomial sampling scheme in the critical regime. We apply our results to the smooth bootstrap of the Euler characteristic and determine its rate of convergence in the KantorovichWasserstein distance and in the Kolmogorov distance.
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