6 papers
Denoising 3D images: robustness of persistent homology measures
Ebru Dagdelen, Aakash Karlekar, Manav Arora +4
When computing sub/super-level-set persistent homology (PH), the effect of noise may introduce millions of (short-lived) topological generators, presenting an obstacle to both the…
Topological Data Analysis combined with Machine Learning for Predicting Permeability of Porous Media
Ebru Dagdelen, Catherin Neena Lalu, Aakash Karlekar +5
Flow in porous media is difficult to address using standard analytical or numerical methods due to its complexity. However, since synthetic representations of porous media are easy…
Resonant vector bundles, conjugate points, and the stability of pulse solutions to the {S}wift-{H}ohenberg equation using validated numerics: Part I
Margaret Beck, Jonathan Jaquette, Hannah Pieper
In this paper, we develop new theory connected with resonant vector bundles that will allow for the use of validated numerics to rigorously determine the stability of pulse solutio…
The Maslov index, degenerate crossings and the stability of pulse solutions to the Swift-Hohenberg equation
Margaret Beck, Jonathan Jaquette, Hannah Pieper
In the scalar Swift-Hohenberg equation with quadratic-cubic nonlinearity, it is known that symmetric pulse solutions exist for certain parameter regions. In this paper we develop a…
Validated matrix multiplication transform for orthogonal polynomials with applications to computer-assisted proofs for PDEs
Matthieu Cadiot, Jonathan Jaquette, Jean-Philippe Lessard +1
In this paper, we achieve three primary objectives related to the rigorous computational analysis of nonlinear PDEs posed on complex geometries such as disks and cylinders. First,…
Mechanisms of unstable blowup in a quadratic nonlinear Schrödinger equation
Jonathan Jaquette
In the work Cho et al. [Jpn. J. Ind. Appl. Math. 33 (2016): 145-166] the authors conjecture that the quadratic nonlinear Schrödinger equation (NLS) for $ x…