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

Angular dependence of the coherent peak position in the polarization bremsstrahlung spectrum of relativistic electrons in polycrystalline targets

The spectra of the polarization bremsstrahlung (PB) in the X-ray range induced by 7-MeV electrons in polycrystalline Al, Cu, and Ni polycrystalline films have been measured and the angular dependences of the PB characteristics have been studiedyesBelgorod State Universit

Behavior of bulk high-temperature superconductors of finite thickness subjected to crossed magnetic fields

Crossed magnetic field effects on bulk high-temperature superconductors have been studied both experimentally and numerically. The sample geometry investigated involves finite-size effects along both (crossed) magnetic field directions. The experiments were carried out on bulk melt-processed Y-Ba-Cu-O (YBCO) single domains that had been pre-magnetized with the applied field parallel to their shortest direction (i.e. the c-axis) and then subjected to several cycles of the application of a transverse magnetic field parallel to the sample ab plane. The magnetic properties were measured using orthogonal pick-up coils, a Hall probe placed against the sample surface and Magneto-Optical Imaging (MOI). We show that all principal features of the experimental data can be reproduced qualitatively using a two-dimensional finite-element numerical model based on an E-J power law and in which the current density flows perpendicularly to the plane within which the two components of magnetic field are varied. The results of this study suggest that the suppression of the magnetic moment under the action of a transverse field can be predicted successfully by ignoring the existence of flux-free configurations or flux-cutting effects. These investigations show that the observed decay in magnetization results from the intricate modification of current distribution within the sample cross-section. It is also shown that the model does not predict any saturation of the magnetic induction, even after a large number (~ 100) of transverse field cycles. These features are shown to be consistent with the experimental data.Comment: 41 pages, 9 figures, accepted in Phys. Rev. B Changes : 8 references added, a few precisions added, some typos correcte

Magneto-optical studies of the uniform critical state in bulk MgB2

We present a detailed magneto-optical investigation of the magnetic flux penetration in polycrystalline MgB2 slabs made by direct reaction of B and Mg. Our results unambiguously indicate a uniform, Bean critical state magnetization behavior with almost no electromagnetic granularity. From the measured magnetic flux profiles we were able to extract the temperature dependence of the critical current density Jc(T). The Jc(T) value reaches 1.8x10^5 A/cm2 at 10K and 0.12T, in good agreement with global magnetization measurements