9 citations · 9 across the 4 of their papers we have counts for
4 papers
Phase spaces of phase spaces: A method of constructing generalizable and topologically informed bases from time series demonstrated by reconstruction of the geometry of the macroeconomy
Maximilian Topel
Laws from physics to social science rest on a small, enumerable number of factors explaining variation in the systems they describe. While the orthodoxy of economics, physics and c…
Data-driven reconstruction of dynamical systems using Takens' Theorem, manifold learning, and universal function approximators
Maximilian Topel, Andrew L. Ferguson
Embedding theorems can be used to provide theoretical guarantees about the relation between low-dimensional observations of a system and its full-dimensional state and dynamics. Su…
Kolmogorov-Sinai entropies identify optimal observables for prediction and dynamics reconstruction in chaotic systems
Maximilian Topel
Choosing the optimal observable to model dynamical systems for which we do not know the driving equations is nearly always an ad hoc art. Takens' Delay Embedding Theorem guarantees…
Reconstruction of Protein Structures from Single-Molecule Time Series
Maximilian Topel, Andrew L. Ferguson
Single-molecule experimental techniques track the real-time dynamics of molecules by recording a small number of experimental observables. Following these observables provides a co…