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

Dependence of vestibular reactions on frequency of action of sign-variable accelerations

It was revealed that during the tests with continuous action of sign variable Coriolis acceleration the development of kinetosis was proportionate to the time of head inclinations in the range of 1 to 4 seconds while illusions of rocking in sagittal plane was more expressed in fast inclinations. The obtained data provided the evidence of sufficient dependence of vestibulovegetative and vestibulosensory reactions on the period of repetition of sign variable Coriolis acceleration

Numerical analysis of electromagnetic cascades in emulsion chambers

A new calculational scheme of the Monte Carlo method assigned for the investigation of the development of high and extremely high energy electromagnetic cascades (EMC) in the matter was elaborated. The scheme was applied to the analysis of angular and radial distributions of EMC electrons in the atmosphere. By means of this scheme the EMC development in dense medium is investigated and some preliminary data are presented on the behavior of EMC in emulsion chambers. The results of more detailed theoretical analysis of the EMC development in emulsion chambers are discussed

A Modified Version of the Waxman Algorithm

The iterative algorithm recently proposed by Waxman for solving eigenvalue problems, which relies on the method of moments, has been modified to improve its convergence considerably without sacrificing its benefits or elegance. The suggested modification is based on methods to calculate low-lying eigenpairs of large bounded hermitian operators or matrices