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

Effect of particle surface heating on the sedimentation rate

The Stokes and Hadamard-Rybchinsky formulas are generalized, making it possible to take into account the temperature dependence of viscosity in a wide range of temperatures and to calculate the force of resistance to motion and velocity of gravitational fall at arbitrary temperature differences between the particle surface and a remote regionye

Motion through a viscous liquid of a heated spheroidal solid particle under conditions of uniform internal heat release

An expression has been derived allowing the drag to be estimated on a spheroidal hydrosol particle moving in a liquid under conditions of an arbitrary temperature difference between the particle surface and a separate region, which takes into account the temperature dependence of the liquid viscosity presented in the form of an exponential power seriesyesBS

The effect of the medium on the thermocapillary force of a heated droplet drifting in a viscous liquid in the field of external temperature gradient

The Stokes approximation is used to theoretically investigate the effect of the medium on the thermocapillary drift of a heated droplet inside which nonuniformly distributed heat sources are operative. The droplet drift proceeds in a viscous incompressible liquid under conditions of arbitrary temperature differences between the particle surface and a region away from ityesBS

Features of the thermocapillary drift for a heated droplet in a viscous fluid placed into an electromagnetic field

Studies thermocapillary drift for a heated droplet in viscous fluid placed into an electromagnetic field. Causes of droplet motion in an electromagnetic field. Temperature dependence of the coefficient of dynamic viscosity. Direction of propagation of radiationyesBelgorod State Universit