Abstract. The main theme of this paper is error analysis for approximations derived from two variants of dimensional decomposition of a multivariate function: the referential dimensional decomposition (RDD) and analysisof-variance dimensional decomposition (ADD). New formulae are presented for the lower and upper bounds of the expected errors committed by bivariately and arbitrarily truncated R...

Стохастическая оптимизация является актуальным направлением исследования в связи со значительными успехами области машинного обучения и их применениями для решения повседневных задач. В данной работе рассматриваются два принципиально различных метода задачи стохастической оптимизации — онлайн- офлайн-алгоритмы. Соответствующие алгоритмы имеют свои качественные преимущества перед друг другом. Та...

We derive a stochastic path integral representation of counting statistics in semiclassical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to find the propagator for charge distributions with an arbitrary number of counting fields and generalized charges. The counting statistics is given by the sad...

We propose an alternative formulation of many-body perturbation theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, which leads to excellent optical absorption and energy-loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for a...

Four multiphase flow models or correlations (Duns & Ros, Hagedorn & Brown, Orkiszewski, and Beggs & Brill) are currently available in Hydra for predicting the pressure profile in a well. The range of applicability of the multiphase flow models is dependent on several factors such as, tubing size or diameter, oil gravity, gas-liquid ratio, and, two-phase flow with or without water-cut. The effec...

We examine the problem of writing every sufficiently large even number as the sum of two primes and at most K powers of 2. We outline an approach that only just falls short of improving the current bounds on K. Finally, we improve the estimates in other Waring–Goldbach problems.