On Multistage Learning a Hidden Hypergraph

Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph $H_{un}=H(V,E)$ by carrying out edge-detecting tests. In the given paper we focus our attention only on a specific family $F(t,s,\ell)$ of localized hypergraphs for which the total number of vertices $|V| = t$, the number of edges $|E|\le s$, $s\ll t$, and the cardinality of any edge $|e|\le\ell$, $\ell\ll t$. Our goal is to identify all edges of $H_{un}\in F(t,s,\ell)$ by using the minimal number of tests. We develop an adaptive algorithm that matches the information theory bound, i.e., the total number of tests of the algorithm in the worst case is at most $s\ell\log_2 t(1+o(1))$. We also discuss a probabilistic generalization of the problem.Comment: 5 pages, IEEE conferenc

On the thermophoresis of a spheroidal solid aerosol particle

The steady motion of a spheroidal aerosol particle with inner nonuniformly distributed heat sources (sinks) that is placed in an external temperature gradient is theoretically studied in the Stokes approximationyesBS

On the influence of motion of the medium on the photophoresis of a spheroidal solid aerosol particle

This paper considers the influence of motion of the medium (account of convective terms in the heat conduction equations) on the photophoresis of a large aerosol spheroidal particle at small relative temperature drops in its vicinity. It has been shown that at a fixed ratio of semiaxes with increasing intensity of the incident radiation the total contribution of the medium motion leads to a monotonic decrease in the rate of photophoresis, whose degree depends on the equatorial radius of the spheroidyesBelgorod State Universit

Investigation of boundary-value problem for stationary system of equations of viscous non-isothermal fluid

In the Stokes approximation at small Reynolds and Peclet numbers, we obtain a solution to the boundary-value problem of flow around of particles of spherical shape for stationary system of equations of a viscous non-isothermal fluid comprising a linearized by speed Navier-Stokes equation system and the equation of heat transfer given an exponential-power law of dependence of viscosity of fluid on temperatur

Effect of internal heat evolution on the motion of a solid particle in a viscous fluid

The problem of the effect of internal heat evolution on the motion of a heated solid spherical particle in a viscous fluid is analytically solved in the Stokes approximation at small Reynolds and Peclet numbers. The temperature drop between the surface of the particle and the area away from it is assumed to be arbitrary. In solving hydrodynamic equations, the thermal conductivity of the particle is set to be a power function of temperature and the viscosity of the fluid, an exponential-power function of temperature. The observability of this effect is discussedyesBelgorod State Universit