Pricing storage operation in the real-time market under demand and generation stochasticities is considered. A scenario-based stochastic rolling-window dispatch model formulated for market, consisting of conventional generators, utility-scale storage, distributed energy resource aggregators. We show that uniform pricing mechanisms require discriminative out-of-the-market uplifts, making settlem...

The time evolution of quantum fields is shown to be equivalent a time-symmetric Fokker-Planck equation. Results are obtained using Q-function representation, including fermion-fermion, boson-boson, and fermion-boson interactions with linear, quadratic, cubic, quartic Hamiltonians, typical QED many other cases. For local boson-boson coupling, the resulting probability distribution proved have po...

We propose a generic method for iteratively approximating various second-order gradient steps - Newton, Gauss-Newton, Levenberg-Marquardt, and natural gradient - in linear time per iteration, using special curvature matrix-vector products that can be computed in O(n). Two recent acceleration techniques for on-line learning, matrix momentum and stochastic meta-descent (SMD), implement this appro...

It has great significance to research the dynamical reliability probability of rolling mill rolls system for improving its stochastic dynamical reliability and products quality rolled. The fifth-octave vertical vibration stochastic dynamical model of rolls system was established, and the pseudo-excitation method was used to obtain the power spectral density and the variance variation characteri...