Sign refinement for combinatorial link Floer homology

Link Floer homology is an invariant for links which has recently been described entirely in a combinatorial way. Originally constructed with mod 2 coefficients, it was generalized to integer coefficients thanks to a sign refinement. In this paper, thanks to the spin extension of the permutation group we give an alternative construction of the combinatorial link Floer chain complex associated to a grid diagram with integer coefficients. We prove that the filtered homology of this complex is an invariant for the link and that it gives the previous sign refinement by means of a 2-cohomological class corresponding to the spin extension of the permutation group.Comment: 17 pages, 10 figures. correction of the Alexander grading and of the formula of lemma 5.2 of the sign refinemen

Resonant Raman scattering in mercurate single crystals

We report resonant electronic Raman scattering in optimally doped single layer HgBa$_2$CuO$_{4+\delta}$ (Hg-1201) and trilayer HgBa$_2$Ca$_2$Cu$_3$O$_{8+\delta}$ (Hg-1223) single crystals. Analysis of the $B_{1g}$ and B$_{2g}$ channels in the superconducting state of Hg-1201 advocates for a gap having d-wave symmetry. In addition a resonant study $B_{1g}$ pair-breaking peak and the $A_{1g}$ peak suggests that the $A_{1g}$ peak is not directly related to the d-wave superconducting gap amplitude. Comparison with trilayer Hg-1223 demonstrates the universal behavior of this two energy scales in optimally doped cuprates.Comment: 4 pages, 4 figures, M2S-Rio (invited paper). to appear in Physica

Nematic resonance in the Raman response of iron-based superconductors

In a fully-gapped superconductor the electronic Raman response has a pair-breaking peak at twice the superconducting gap $\Delta$, if the Bogoliubov excitations are uncorrelated. Motivated by the iron based superconductors, we study how this peak is modified if the superconducting phase hosts a nematic-structural quantum critical point. We show that, upon approaching this point by tuning, e.g., doping, the growth of nematic correlations between the quasiparticles transforms the pair-breaking peak into a nematic resonance. The mode energy is below 2$\Delta$, and stays finite at the quantum critical point, where its spectral weight is sharply enhanced. The latter is consistent with recent experiments on electron-doped iron based superconductors and provides direct evidence of nematic correlations in their superconducting phases.Comment: Phys. Rev. Lett. 116, 017001 (2016

The necessity to correct hedge fund returns: empirical evidence and correction method

We study two principal mechanisms suggested in the literature to correct the serial correlationin hedge fund returns and the impact of this correction on financial characteristics of their returnsas well as on their risk level and on their performances. The methods of Geltner (1993), its extensionby Okunev & White (2003) and of Getmansky, Lo & Makarov (2004) are realized on a sampleof 54 hedge fund indexes. The results show that the unsmoothing leaves the mean unchangedbut increases significantly the risk level of hedge funds, whether the risk is measured in terms ofthe return standard-deviation or the modified Value-At-Risk. Funds' performances, measured bytraditional Sharpe ratio and Omega index decline considerably. By contrast, funds' rankings afterthe unsmoothing unexpectedly change slightly. However, some notable modifications in ranks ofseveral funds are observed. The necessary transparency of the management practice requires thatsuch a correction must be systematically done.hedge funds; smoothed returns; performance evaluation; Sharpe ratio; Omega index