Moscow Institute of Physics and Technology

About: Moscow Institute of Physics and Technology is a education organization based out in Dolgoprudnyy, Russia. It is known for research contribution in the topics: Laser & Plasma. The organization has 8594 authors who have published 16968 publications receiving 246551 citations. The organization is also known as: MIPT & Moscow Institute of Physics and Technology (State University).

SGD: General Analysis and Improved Rates

Abstract: We propose a general yet simple theorem describing the convergence of SGD under the arbitrary sampling paradigm. Our theorem describes the convergence of an infinite array of variants of SGD, each of which is associated with a specific probability law governing the data selection rule used to form mini-batches. This is the first time such an analysis is performed, and most of our variants of SGD were never explicitly considered in the literature before. Our analysis relies on the recently introduced notion of expected smoothness and does not rely on a uniform bound on the variance of the stochastic gradients. By specializing our theorem to different mini-batching strategies, such as sampling with replacement and independent sampling, we derive exact expressions for the stepsize as a function of the mini-batch size. With this we can also determine the mini-batch size that optimizes the total complexity, and show explicitly that as the variance of the stochastic gradient evaluated at the minimum grows, so does the optimal mini-batch size. For zero variance, the optimal mini-batch size is one. Moreover, we prove insightful stepsize-switching rules which describe when one should switch from a constant to a decreasing stepsize regime.

Quantum phenomena in nonstationary media

Abstract: The problem of electromagnetic-field quantization in time-dependent nonuniform linear nondispersive media is investigated. The explicit formulas for the number of photons generated from the initial vacuum state due to the change in time of dielectric permeability of the medium are obtained in the case when the spatial and temporal dependences are factorized. The concrete time dependences include adiabatic and sudden changes of permeability, the parametric resonance at twice the eigenfrequency of the mode, Epstein's symmetric and transition profiles, «temporal Fabry-Perot resonator,» and some others

Deterministic microscopic three-phase traffic flow models

Abstract: Two different deterministic microscopic traffic flow models, which are in the context of the Kerner's there-phase traffic theory, are introduced. In an acceleration time delay model (ATD model), different time delays in driver acceleration associated with driver behaviour in various local driving situations are explicitly incorporated into the model. Vehicle acceleration depends on local traffic situation, i.e., whether a driver is within the free flow or synchronized flow or else wide moving jam traffic phase. In a speed adaptation model (SA model), vehicle speed adaptation occurs in synchronized flow depending on driving conditions. It is found that the ATD and SA models show spatiotemporal congested traffic patterns that are adequate with empirical results. In the ATD and SA models, the onset of congestion in free flow at a freeway bottleneck is associated with a first-order phase transition from free flow to synchronized flow; moving jams emerge spontaneously in synchronized flow only. Differences between the ATD and SA models are studied. A comparison of the ATD and SA models with stochastic models in the context of three-phase traffic theory is made. A critical discussion of earlier traffic flow theories and models based on the fundamental diagram approach is presented.