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Optimal Regularity for Two-Dimensional Pfaffian Systems and the Fundamental Theorem of Surface Theory

We prove that a Pfaffian system with coefficients in the critical space $L^2_\mathrm{loc}$ on a simply connected open subset of $\mathbb{R}^2$ has a non-trivial solution in $W^{1,2}_\mathrm{loc}$ if the coefficients are antisymmetric and satisfy a …

Rapid Calculation of Molecular Kinetics Using Compressed Sensing

Recent methods for the analysis of molecular kinetics from massive molecular dynamics (MD) data rely on the solution of very large eigenvalue problems. Here we build upon recent results from the field of compressed sensing and develop the spectral …