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math.DS2019★ 2 cited
Rigorous numerics for nonlinear heat equations in the complex plane of time
Akitoshi Takayasu, Jean-Philippe Lessard, Jonathan Jaquette +1
In this paper, we introduce a method for computing rigorous local inclusions of solutions of Cauchy problems for nonlinear heat equations for complex time values. Using a solution…
math.DS2019
Fractal Dimension Estimation with Persistent Homology: A Comparative Study
Jonathan Jaquette, Benjamin Schweinhart
We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate th…