An imperative condition for the functioning of a power-grid network is that its power generators remain synchronized. Disturbances can prompt desynchronization, which is a process that has been involved in large power outages. Here we derive a condit
ion under which the desired synchronous state of a power grid is stable, and use this condition to identify tunable parameters of the generators that are determinants of spontaneous synchronization. Our analysis gives rise to an approach to specify parameter assignments that can enhance synchronization of any given network, which we demonstrate for a selection of both test systems and real power grids. Because our results concern spontaneous synchronization, they are relevant both for reducing dependence on conventional control devices, thus offering an additional layer of protection given that most power outages involve equipment or operational errors, and for contributing to the development of smart grids that can recover from failures in real time.
We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamical system from a noisy observation of the present state. Our main result shows, for example, that support vector machines (SVMs) using Gaussian RBF kernel
s can learn the best forecaster from a sequence of noisy observations if (a) the unknown observational noise process is bounded and has a summable $alpha$-mixing rate and (b) the unknown ergodic dynamical system is defined by a Lipschitz continuous function on some compact subset of $mathbb{R}^d$ and has a summable decay of correlations for Lipschitz continuous functions. In order to prove this result we first establish a general consistency result for SVMs and all stochastic processes that satisfy a mixing notion that is substantially weaker than $alpha$-mixing.
Inherent structure theory is used to discover strong connections between simple characteristics of protein structure and the energy landscape of a Go model. The potential energies and vibrational free energies of inherent structures are highly correl
ated, and both reflect simple measures of networks of native contacts. These connections have important consequences for models of protein dynamics and thermodynamics.
