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.

Electron and photon reconstruction and identification with the CMS experiment at the CERN LHC

Abstract: The performance is presented of the reconstruction and identification algorithms for electrons and photons with the CMS experiment at the LHC. The reported results are based on proton-proton collision data collected at a center-of-mass energy of 13 TeV and recorded in 2016-2018, corresponding to an integrated luminosity of 136 fb$^{-1}$. Results obtained from lead-lead collision data collected at $\sqrt{s_\mathrm{NN}}=$ 5.02 TeV are also presented. Innovative techniques are used to reconstruct the electron and photon signals in the detector and to optimize the energy resolution. Events with electrons and photons in the final state are used to measure the energy resolution and energy scale uncertainty in the recorded events. The measured energy resolution for electrons produced in Z boson decays in proton-proton collision data ranges from 2 to 5%, depending on electron pseudorapidity and energy loss through bremsstrahlung in the detector material. The energy scale in the same range of energies is measured with an uncertainty smaller than 0.1 (0.3)% in the barrel (endcap) region in proton-proton collisions and better than 1 (3)% in the barrel (endcap) region in heavy ion collisions. The timing resolution for electrons from Z boson decays with the full 2016-2018 proton-proton collision data set is measured to be 200 ps.

Generation of matrix models by Ŵ-operators

Abstract: We show that partition functions of various matrix models can be obtained by acting on elementary functions with exponents of operators. A number of illustrations is given, including the Gaussian Hermitian matrix model, Hermitian model in external field and the Hurwitz-Kontsevitch model, for which we suggest an elegant matrix-model representation. In all these examples, the relevant operators belong to the (3) algebra.