@misc{OatesCockaynePrangleetal.2020, author = {Oates, Chris and Cockayne, Jon and Prangle, Dennis and Sullivan, T. J. and Girolami, Mark}, title = {Optimality criteria for probabilistic numerical methods}, volume = {27}, journal = {Multivariate Algorithms and Information-Based Complexity}, editor = {Hickernell, F. J. and Kritzer, P.}, publisher = {De Gruyter}, arxiv = {http://arxiv.org/abs/1901.04326}, doi = {10.1515/9783110635461-005}, pages = {65 -- 88}, year = {2020}, abstract = {It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that the decision-theoretic framework is neither appropriate nor sufficient. To this end, we consider an alternative optimality criterion from Bayesian experimental design and study its implied optimal information in the numerical context. This information is demonstrated to differ, in general, from the information that would be used in an average-case-optimal numerical method. The explicit connection to Bayesian experimental design suggests several distinct regimes in which optimal probabilistic numerical methods can be developed.}, language = {en} } @article{KerstingSullivanHennig2020, author = {Kersting, Hans and Sullivan, T. J. and Hennig, Philipp}, title = {Convergence rates of Gaussian ODE filters}, volume = {30}, journal = {Statistics and Computing}, publisher = {Springer}, address = {Statistics and Computing}, arxiv = {http://arxiv.org/abs/1807.09737}, doi = {10.1007/s11222-020-09972-4}, pages = {1791 -- 1816}, year = {2020}, language = {en} } @article{StoopStraubeJohansenetal.2020, author = {Stoop, Ralph L. and Straube, Arthur and Johansen, Tom H. and Tierno, Pietro}, title = {Collective directional locking of colloidal monolayers on a periodic substrate}, volume = {124}, journal = {Phys. Rev. Lett.}, doi = {10.1103/PhysRevLett.124.058002}, pages = {058002}, year = {2020}, abstract = {We investigate the directional locking effects that arise when a monolayer of paramagnetic colloidal particles is driven across a triangular lattice of magnetic bubbles. We use an external rotating magnetic field to generate a two-dimensional traveling wave ratchet forcing the transport of particles along a direction that intersects two crystallographic axes of the lattice. We find that, while single particles show no preferred direction, collective effects induce transversal current and directional locking at high density via a spontaneous symmetry breaking. The colloidal current may be polarized via an additional bias field that makes one transport direction energetically preferred.}, language = {en} }