How do we study a system whose fundamental equations, like the equations of motion in mechanics, are not available, and how do we describe a system whose dynamics spread across a hierarchical spatiotemporal scales? Such systems can be found ubiquitously at the molecular and cellular levels. We are now developing the mathematical theory of data-driven science, in which the state-space networks, dynamics and energy landscapes are extracted directly from time series data of molecular and cellular systems. Our data-driven modeling techniques are built on the contemporary developments of information theory and discrete mathematics. On the other hand, by generalizing the notion of hyperbolic fixed points developed in dynamical systems we are now developing a new theory that enables us to analytically predict the outcome of chemical reactions. In both subjects we are expanding the collaborations with experimentalists from domestic and overseas.
- Hiroshi Teramoto, Mikito Toda, Masahiko Takahashi, Hirohiko Kono, and Tamiki Komatsuzaki, “Mechanism and Experimental Observability of Global Switching Between Reactive and Nonreactive Coordinates at High Total Energies”, Physical Review Letters 115, 093003 (5 pages) (2015)
- Hiroshi Teramoto, Mikito Toda, Tamiki Komatsuzaki, “Breakdown Mechanism of Normally Hyperbolic Invariant Manifold in terms of unstable periodic orbits and homoclinic/heteroclinic orbits in Hamiltonian Systems” Nonlinearity, 28, 2677–2698 (2015)
- N. Taylor, C.-B. Li, D. Cooper, C. F. Landes, T. Komatsuzaki, “Error-based Extraction of States and Energy Landscapes from Experimental Single-Molecule Time-Series” Scientific Reports 5, 9174 (9 pages) (2015)
- Hiroshi Teramoto, George Haller, Tamiki Komatsuzaki, “Detecting invariant manifolds as stationary Lagrangian coherent structures in autonomous dynamical systems” Chaos 23, 043107 (12 pages) (2013)
- Chun-Biu Li, Tamiki Komatsuzaki, “Aggregated Markov Model Using Time Series of Single Molecule Dwell Times with Minimum Excessive Information” Physical Review Letters 111, 58301 (5 pages) (2013)