arXiv subjects

Andrei Smirnov

Publications and source records attributed to Andrei Smirnov.

4 recordsLinked to original sources

arXiv2018

Strategy of the Negative Sampling for Training Retrieval-Based Dialogue Systems

The article describes the new approach for quality improvement of automated dialogue systems for customer support service. Analysis produced in the paper demonstrates the dependency of the quality of the retrieval-based dialogue system quality on the choice of negative responses. The proposed approach implies choosing the negative samples according to the distribution of responses in the train set. In this implementation the negative samples are randomly chosen from the original response distribution and from the "artificial" distribution of negative responses, such as uniform distribution or the distribution obtained by transformation of the original one. The results obtained for the implemented systems and reported in this paper confirm the significant improvement of automated dialogue systems quality in case of using the negative responses from transformed distribution.

cs.CL↗

arXiv2015

On a particular form of a symmetric Pöschl-Teller potential

We show that solutions of the Schrödinger equation with a symmetric Pöschl-Teller potential of a particular form can be expressed in terms of a closed combination (not series) of trigonometric functions. Using some properties of the eigenfunctions of the Schrödinger equation and their inner product we determine a new exact representation of the hypergeometric function with certain values of parameters in terms of a closed combination of trigonometric functions. We also obtain new results in an explicit closed form for integrals with the hypergeometric function and with the specific combination of trigonometric functions.

math-ph↗

arXiv2014

Self-graviting Gas Spheres in Equilibrium State

In the paper we discuss equilibrium states of stars, using a simplified analytic model. A star is considered as self-graviting body of gas. We use a condition for the equilibrium state of the body in the form of a differential equation, which relates the pressure distribution and mass density in the body. The density distributions of constant, potential, gaussian, and exponential forms are discussed. Exact expressions for the distribution of mass and pressure along the radial direction, and the central pressure were obtained.

physics.gen-ph↗

arXiv2014

Green's function multiple-scattering theory with a truncated basis set: An Augmented-KKR formalism

Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient site-centered, electronic-structure technique for addressing an assembly of $N$ scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number $L_{max}=(l,m)_{max}$, while scattering matrices, which determine spectral properties, are truncated at $L_{tr}=(l,m)_{tr}$ where phase shifts $δ_{l>l_{tr}}$ are negligible. Historically, $L_{max}$ is set equal to $L_{tr}$; however, a more proper procedure retains free-electron and single-site contributions for $L_{max}>L_{tr}$ with $δ_{l>l_{tr}}$ set to zero [Zhang and Butler, Phys. Rev. B {\bf 46}, 7433]. We present a numerically efficient and accurate \emph{augmented}-KKR Green's function formalism that solves the KKR secular equations by matrix inversion [$\mathcal{R}^3$ process with rank $N(l_{tr}+1)^2$] and includes higher-order $L$ contributions via linear algebra [$\mathcal{R}^2$ process with rank $N(l_{max}+1)^2$]. Augmented-KKR yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. For fcc Cu, bcc Fe and L$1_0$ CoPt, we present the formalism and numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus $L_{max}$ for a given $L_{tr}$.

cond-mat.mtrl-sci↗