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

Collapse of the critical state in superconducting niobium

Giant abrupt changes in the magnetic flux distribution in niobium foils were studied by using magneto-optical visualization, thermal and magnetic measurements. Uniform flux jumps and sometimes almost total catastrophic collapse of the critical state are reported. Results are discussed in terms of thermomagnetic instability mechanism with different development scenarios.Comment: arXiv.org produced artifacts in color images (three versions were attempts to make better images). Download clean PDF and watch video-figures at: "http://cmp.ameslab.gov/supermaglab/video/Nb.html

Roles of intrinsic anisotropy and pi-band pairbreaking effects on critical currents in tilted c-axis MgB2 films probed by magneto-optical and transport measurements

Investigations of MgB2 and Fe-based superconductors in recent years have revealed many unusual effects of multiband superconductivity but manifestations of anisotropic multiband effects in the critical current density Jc have not been addressed experimentally, mostly because of the difficulties to measure Jc along the c-axis. To investigate the effect of very different intrinsic anisotropies of sigma and pi electron bands in MgB2 on current transport, we grew epitaxial films with tilted c-axis (THETA ~ 19.5{\deg}), which enabled us to measure the components of Jc both along the ab-plane and the c-axis using magneto-optical and transport techniques. These measurements were combined with scanning and transmission electron microscopy, which revealed terraced steps on the surface of the c-axis tilted films. The measured field and temperature dependencies of the anisotropic Jc(H) show that Jc,L parallel to the terraced steps is higher than Jc,T perpendicular to the terraced steps, and Jc of thinner films (50 nm) obtained from transport experiments at 0.1 T reaches ~10% of the depairing current density Jd in the ab plane, while magneto-optical imaging revealed much higher Jc at lower fields. To analyze the experimental data we developed a model of anisotropic vortex pinning which accounts for the observed behavior of Jc in the c-axis tilted films and suggests that the apparent anisotropy of Jc is affected by current pairbreaking effects in the weaker {\pi} band. Our results indicate that the out-of-plane current transport mediated by the {\pi} band could set the ultimate limit of Jc in MgB2 polycrystals.Comment: 21 pges, 13 figure

Real time magneto-optical imaging of vortices in superconductors

We demonstrate here real-time imaging of individual vortices in a NbSe2 single crystal using polarized light microscopy. A new high-sensitivity magneto-optical (MO) imaging system enables observation of the static vortex lattice as well as single vortex motion at low flux densities.Comment: 3 pages, 1 figur