A network centrality method for the rating problem

We propose a new method for aggregating the information of multiple reviewers rating multiple products. Our approach is based on the network relations induced between products by the rating activity of the reviewers. We show that our method is algorithmically implementable even for large numbers of both products and consumers, as is the case for many online sites. Moreover, comparing it with the simple average, which is mostly used in practice, and with other methods previously proposed in the literature, it performs very well under various dimension, proving itself to be an optimal trade--off between computational efficiency, accordance with the reviewers original orderings, and robustness with respect to the inclusion of systematically biased reports.Comment: 25 pages, 8 figure

Fermionic phase transition induced by the effective impurity in holography

We investigate the holographic fermionic phase transition induced by the effective impurity in holography, which is introduced by massless scalar fields in Einstein-Maxwell-massless scalar gravity. We obtain a phase diagram in $(\alpha, T)$ plane separating the Fermi liquid phase and the non-Fermi liquid phase.Comment: 17 pages, 9 figure

The 3+1 holographic superconductor with Weyl corrections

In this paper we study $3+1$ holographic superconductors with Weyl corrections. We find that the critical temperature of a superconductor with Weyl corrections increases as we amplify the Weyl coupling parameter $\gamma$, indicating the condensation will be harder when the parameter $\gamma$ decreases. We also calculate the conductivity and the ratio of gap frequency over critical temperature $\omega_{g}/T_{c}$ numerically for various coupling parameters. We find that the ratio $\omega_g/T_c$ becomes larger when the Weyl coupling parameter $\gamma$ decreases. We also notice that when $\gamma< 0$ there is an extra spike that appears inside the gap.Comment: 16 pages, 7 figures and 1 table, typos corrected and reference added, appendix A added, version to be published in PL