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To impart directionality to the motions of a molecular mechanism, one must overcome the random thermal forces that are ubiquitous on such small scales and in liquid solution at ambient temperature. In equilibrium without energy supply, directional motion cannot be sustained without violating the laws of thermodynamics. Under conditions away from thermodynamic equilibrium, directional motion may be achieved within the framework of Brownian ratchets, which are diffusive mechanisms that have broken inversion symmetry1–5. Ratcheting is thought to underpin the function of many natural biological motors, such as the F1F0-ATPase6–8, and it has been demonstrated experimentally in synthetic microscale systems (for example, to our knowledge, first in ref. 3) and also in artificial molecular motors created by organic chemical synthesis9–12. DNA nanotechnology13 has yielded a variety of nanoscale mechanisms, including pivots, hinges, crank sliders and rotary systems14–17, which can adopt different configurations, for example, triggered by strand-displacement reactions18,19 or by changing environmental parameters such as pH, ionic strength, temperature, external fields and by coupling their motions to those of natural motor proteins20–26. This previous work and considering low-Reynolds-number dynamics and inherent stochasticity27,28 led us to develop a nanoscale rotary motor built from DNA origami that is driven by ratcheting and whose mechanical capabilities approach those of biological motors such as F1F0-ATPase.A nanoscale rotary motor made of DNA origami, driven by ratcheting and powered by an external electric field, shows the ability to wind up a spring and has mechanical capabilities approaching those of biological motors. [ABSTRACT FROM AUTHOR]

We present a method for both cross-estimation and iterated time series prediction of spatio-temporal dynamics based on local modelling and dimension reduction techniques. Assuming homogeneity of the underlying dynamics, we construct delay coordinates of local states and then further reduce their dimensionality through Principle Component Analysis. The prediction uses nearest neighbour methods in the space of dimension reduced states to either cross-estimate or iteratively predict the future of a given frame. The effectiveness of this approach is shown for (noisy) data from a (cubic) Barkley model, the Bueno-Orovio–Cherry–Fenton model, and the Kuramoto–Sivashinsky model. [ABSTRACT FROM AUTHOR]