| Project Detail |
The ability to infer information about hidden degrees of freedom from time series would revolutionize experiments on single molecules, mesoscale assemblies, and tissues, as well as financial and climate systems. Hidden dynamics are often essential, as they reflect the approaching of a critical transition or describe its mechanism, e.g. the folding of a protein or RNA, or an abrupt shift in climate. With the project proposed here I plan to push our quantitative understanding of experiments, ranging from single-molecule spectroscopy to observations of migrating cells and developing tissues, to a new level, by exploiting how the properties of a high-dimensional landscape and current imprint onto the time ordering of projected states along individual trajectories. I will introduce functionals of projected paths that are easily inferred from data, and analyze their statistics and measure concentration by combining the theory of functionals of stochastic paths, concentration inequalities, and semiclassical analysis, and apply these to single-molecule force spectroscopy and plasmon ruler experiments, cell tracking, and Molecular Dynamics simulations. A distinctive characteristic of the project is the focus on non-asymptotic measure concentration, i.e. on “occurs with high probability” results that will be addressed for the first time in the context of non-equilibrium physics. Providing a new framework for interpreting experiments—using the information readily encoded in the data but inaccessible to existing approaches—the project will generate new knowledge that will resolve the long-standing debate about intermediates in DNA, RNA and protein folding, controversies about non converging dynamics of folded proteins, and shed new light on the operation of nanomachines and self-assembly far from equilibrium, as well as cell movements during tissue regeneration. It will lead to a paradigm-shift in soft matter and biophysics and may reshape actuarial and climate science. |
