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

Additional spectroscopic redshift measurements for galaxy clusters from the First Planck Catalogue

We present the results of spectroscopic redshift measurements for the galaxy clusters from the first all-sky Planck catalogue of the Sunyaev-Zeldovich sources, that have been mostly identified by means of the optical observations performed previously by our team (Planck Collaboration, 2015a). The data on 13 galaxy clusters at redshifts from z=~0.2 to z=~0.8, including the improved identification and redshift measurement for the cluster PSZ1 G141.73+14.22 at z=0.828, are provided. The measurements were done using the data from Russian-Turkish 1.5-m telescope (RTT-150), 2.2-m Calar Alto Observatory telescope, and 6-m SAO RAS telescope (Bolshoy Teleskop Azimutalnyi, BTA).Comment: published in Astronomy Letter

Lactamomethylation of alkylphenols: synthesis and quantum-chemical study of the reaction pathway

Six novel lactamomethyl derivatives of 2,5-dimethylphenol and 2,3,5-trimethylphenol were prepared with moderate yields by the reaction of corresponding phenols with 1-(hydroxymethyl)lactams in the presence of an acid catalyst. In all cases, the substitution occurred at position 4 to the phenolic hydroxyl group. The structures of all synthesized compounds were confirmed by FT-IR, 1H and 13C NMR, 2D NMR and elemental analysis. The selectivity and possible pathways of the lactamomethylation reaction were studied by quantum-chemical methods. In silico calculations showed that the substitution at para-position to the hydroxyl group of the corresponding phenols was more preferable due to the higher stability of forming intermediates

Influence of the Rigid Connection Between Discs in the Tetrahedral Prisms on Equivalent Stresses When Cutting Work Faces

This paper presents the results of modeling of the stressed state of structural elements of the paired fastening points of the two disc tools to the tetrahedral prisms of the working bodies of the roadheaders of selective action when cutting work faces of heterogeneous structure. The advantages of cooperative mode rotation to separate two disc tools on each of the tetrahedral prisms placed between the axial cutting crowns