Precision shooting: Sampling long transition pathways

The kinetics of collective rearrangements in solution, such as protein folding and nanocrystal phase transitions, often involve free energy barriers that are both long and rough. Applying methods of transition path sampling to harvest simulated trajectories that exemplify such processes is typically made difficult by a very low acceptance rate for newly generated trajectories. We address this problem by introducing a new generation algorithm based on the linear short-time behavior of small disturbances in phase space. Using this ``precision shooting'' technique, arbitrarily small disturbances can be propagated in time, and any desired acceptance ratio of shooting moves can be obtained. We demonstrate the method for a simple but computationally problematic isomerization process in a dense liquid of soft spheres. We also discuss its applicability to barrier crossing events involving metastable intermediate states.Comment: 9 pages, 12 figures, submitted to J. Chem. Phy

Combining Adversarial Guarantees and Stochastic Fast Rates in Online Learning

We consider online learning algorithms that guarantee worst-case regret rates in adversarial environments (so they can be deployed safely and will perform robustly), yet adapt optimally to favorable stochastic environments (so they will perform well in a variety of settings of practical importance). We quantify the friendliness of stochastic environments by means of the well-known Bernstein (a.k.a. generalized Tsybakov margin) condition. For two recent algorithms (Squint for the Hedge setting and MetaGrad for online convex optimization) we show that the particular form of their data-dependent individual-sequence regret guarantees implies that they adapt automatically to the Bernstein parameters of the stochastic environment. We prove that these algorithms attain fast rates in their respective settings both in expectation and with high probability

Adaptive Hedge

Most methods for decision-theoretic online learning are based on the Hedge algorithm, which takes a parameter called the learning rate. In most previous analyses the learning rate was carefully tuned to obtain optimal worst-case performance, leading to suboptimal performance on easy instances, for example when there exists an action that is significantly better than all others. We propose a new way of setting the learning rate, which adapts to the difficulty of the learning problem: in the worst case our procedure still guarantees optimal performance, but on easy instances it achieves much smaller regret. In particular, our adaptive method achieves constant regret in a probabilistic setting, when there exists an action that on average obtains strictly smaller loss than all other actions. We also provide a simulation study comparing our approach to existing methods.Comment: This is the full version of the paper with the same name that will appear in Advances in Neural Information Processing Systems 24 (NIPS 2011), 2012. The two papers are identical, except that this version contains an extra section of Additional Materia

Metastability in pressure-induced structural transformations of CdSe/ZnS core/shell nanocrystals

The kinetics and thermodynamics of structural transformations under pressure depend strongly on particle size due to the influence of surface free energy. By suitable design of surface structure, composition, and passivation it is possible, in principle, to prepare nanocrystals in structures inaccessible to bulk materials. However, few realizations of such extreme size-dependent behavior exist. Here we show with molecular dynamics computer simulation that in a model of CdSe/ZnS core/shell nanocrystals the core high pressure structure can be made metastable under ambient conditions by tuning the thickness of the shell. In nanocrystals with thick shells, we furthermore observe a wurtzite to NiAs transformation, which does not occur in the pure bulk materials. These phenomena are linked to a fundamental change in the atomistic transformation mechanism from heterogenous nucleation at the surface to homogenous nucleation in the crystal core. Our results suggest a new route towards expanding the range of available nanoscale materials