Network structure of phonographic market with characteristic similarities between musicians

We investigate relations between best selling artists in last decade on phonographic market and from perspective of listeners by using the Social Network Analyzes. Starting network is obtained from the matrix of correlations between the world's best selling artists by considering the synchronous time evolution of weekly record sales. This method reveals the structure of phonographic market, but we claim that it has no impact on people who see relationship between artists and music genres. We compare 'sale' (based on correlation of record sales) or 'popularity' (based on data mining of the record charts) networks with 'similarity' (obtained mainly from survey within music experts opinion) and find no significant relations. We postulate that non-laminar phenomena on this specific market introduce turbulence to how people view relations of artists.Comment: 15

Monochromatic loose paths in multicolored kk-uniform cliques

For integers $k\ge 2$ and $\ell\ge 0$, a $k$-uniform hypergraph is called a loose path of length $\ell$, and denoted by $P_\ell^{(k)}$, if it consists of $\ell$ edges $e_1,\dots,e_\ell$ such that $|e_i\cap e_j|=1$ if $|i-j|=1$ and $e_i\cap e_j=\emptyset$ if $|i-j|\ge2$. In other words, each pair of consecutive edges intersects on a single vertex, while all other pairs are disjoint. Let $R(P_\ell^{(k)};r)$ be the minimum integer $n$ such that every $r$-edge-coloring of the complete $k$-uniform hypergraph $K_n^{(k)}$ yields a monochromatic copy of $P_\ell^{(k)}$. In this paper we are mostly interested in constructive upper bounds on $R(P_\ell^{(k)};r)$, meaning that on the cost of possibly enlarging the order of the complete hypergraph, we would like to efficiently find a monochromatic copy of $P_\ell^{(k)}$ in every coloring. In particular, we show that there is a constant $c>0$ such that for all $k\ge 2$, $\ell\ge3$, $2\le r\le k-1$, and $n\ge k(\ell+1)r(1+\ln(r))$, there is an algorithm such that for every $r$-edge-coloring of the edges of $K_n^{(k)}$, it finds a monochromatic copy of $P_\ell^{(k)}$ in time at most $cn^k$. We also prove a non-constructive upper bound $R(P_\ell^{(k)};r)\le(k-1)\ell r$

Bulk motion Comptonization in black-hole accretion flows

We study spectra generated by Comptonization of soft photons by cold electrons radially free-falling onto a black hole. We use a Monte Carlo method involving a fully relativistic description of Comptonization in the Kerr space-time. In agreement with previous studies, we find that Comptonization on the bulk motion of free fall gives rise to power-law spectra with the photon index of Gamma >~ 3. In contrast to some previous studies, we find that these power-law spectra extend only to energies << 511 keV. We indicate several effects resulting in generic cutoffs of such spectra at several tens of keV, regardless of any specific values of physical parameters in the model. This inefficiency of producing photons with energies > 100 keV rules out bulk motion Comptonization as a main radiative process in soft spectral states of black-hole binaries. The normalization of the power law (below the cutoff) with respect to the peak of the blackbody emission of the surrounding disc is typically very low, except for models with an overlap between the disc and the plasma, in which case the spectra are very soft, Gamma >~ 4.Comment: 10 pages, 4 figures, revised version, accepted for publication in MNRA

Metallization of solid molecular hydrogen in two dimensions: Mott-Hubbard-type transition

We analyze the pressure-induced metal-insulator transition in a two-dimensional vertical stack of $H_2$ molecules in x-y plane, and show that it represents a striking example of the Mott-Hubbard-type transition. Our combined exact diagonalization approach, formulated and solved in the second quantization formalism, includes also simultaneous ab initio readjustment of the single-particle wave functions, contained in the model microscopic parameters. The system is studied as a function of applied side force (generalized pressure), both in the $H_2$-molecular and $H$-quasiatomic states. Extended Hubbard model is taken at the start, together with longer-range electron-electron interactions incorporated into the scheme. The stacked molecular plane transforms discontinuously into a (quasi)atomic state under the applied force via a two-step transition: the first between molecular insulating phases and the second from the molecular to the quasiatomic metallic phase. No quasiatomic insulating phase occurs. All the transitions are accompanied by an abrupt changes of the bond length and the intermolecular distance (lattice parameter), as well as by discontinuous changes of the principal electronic properties, which are characteristic of the Mott-Hubbard transition here associated with the jumps of the predetermined equilibrium lattice parameter and the effective bond length. The phase transition can be interpreted in terms of the solid hydrogen metallization under pressure exerted by e.g., the substrate covered with a monomolecular $H_2$ film of the vertically stacked molecules. Both the Mott and Hubbard criteria at the insulator to metal transition are discussed