The bivariate gas-stellar mass distributions and the mass functions of early- and late-type galaxies at z∼0z\sim0

We report the bivariate HI- and H$_2$-stellar mass distributions of local galaxies in addition of an inventory of galaxy mass functions, MFs, for HI, H$_2$, cold gas, and baryonic mass, separately into early- and late-type galaxies. The MFs are determined using the HI and H$_2$ conditional distributions and the galaxy stellar mass function, GSMF. For the conditional distributions we use the compilation presented in Calette et al. 2018. For determining the GSMF from $M_{\ast}\sim3\times10^{7}$ to $3\times10^{12}$ $M_{\odot}$, we combine two spectroscopic samples from the SDSS at the redshift range $0.0033<z<0.2$. We find that the low-mass end slope of the GSMF, after correcting from surface brightness incompleteness, is $\alpha\approx-1.4$, consistent with previous determinations. The obtained HI MFs agree with radio blind surveys. Similarly, the H$_2$ MFs are consistent with CO follow-up optically-selected samples. We estimate the impact of systematics due to mass-to-light ratios and find that our MFs are robust against systematic errors. We deconvolve our MFs from random errors to obtain the intrinsic MFs. Using the MFs, we calculate cosmic density parameters of all the baryonic components. Baryons locked inside galaxies represent 5.4% of the universal baryon content, while $\sim96$% of the HI and H$_2$ mass inside galaxies reside in late-type morphologies. Our results imply cosmic depletion times of H$_2$ and total neutral H in late-type galaxies of $\sim 1.3$ and 7.2 Gyr, respectively, which shows that late type galaxies are on average inefficient in converting H$_2$ into stars and in transforming HI gas into H$_2$. Our results provide a fully self-consistent empirical description of galaxy demographics in terms of the bivariate gas--stellar mass distribution and their projections, the MFs. This description is ideal to compare and/or to constrain galaxy formation models.Comment: 37 pages, 17 figures. Accepted for publication in PASA. A code that displays tables and figures with all the relevant statistical distributions and correlations discussed in this paper is available here https://github.com/arcalette/Python-code-to-generate-Rodriguez-Puebla-2020-result

Stability of Influence Maximization

The present article serves as an erratum to our paper of the same title, which was presented and published in the KDD 2014 conference. In that article, we claimed falsely that the objective function defined in Section 1.4 is non-monotone submodular. We are deeply indebted to Debmalya Mandal, Jean Pouget-Abadie and Yaron Singer for bringing to our attention a counter-example to that claim. Subsequent to becoming aware of the counter-example, we have shown that the objective function is in fact NP-hard to approximate to within a factor of $O(n^{1-\epsilon})$ for any $\epsilon > 0$. In an attempt to fix the record, the present article combines the problem motivation, models, and experimental results sections from the original incorrect article with the new hardness result. We would like readers to only cite and use this version (which will remain an unpublished note) instead of the incorrect conference version.Comment: Erratum of Paper "Stability of Influence Maximization" which was presented and published in the KDD1

Collective resonances in plasmonic crystals: Size matters

Periodic arrays of metallic nanoparticles may sustain Surface Lattice Resonances (SLRs), which are collective resonances associated with the diffractive coupling of Localized Surface Plasmon Resonances (LSPRs). By investigating a series of arrays with varying number of particles, we traced the evolution of SLRs to its origins. Polarization resolved extinction spectra of arrays formed by a few nanoparticles were measured, and found to be in very good agreement with calculations based on a coupled dipole model. Finite size effects on the optical properties of the arrays are observed, and our results provide insight into the characteristic length scales for collective plasmonic effects: for arrays smaller than 5 x 5 particles, the Q-factors of SLRs are lower than those of LSPRs; for arrays larger than 20 x 20 particles, the Q-factors of SLRs saturate at a much larger value than those of LSPRs; in between, the Q-factors of SLRs are an increasing function of the number of particles in the array.Comment: 4 figure

Nekrasov-Shatashvili limit of the 5D superconformal index

C. P. is supported by the Royal Society through a University Research Fellowship. A. P. and D. R. G. are partly supported by the Spanish Government Grant No. MINECO-13-FPA2012-35043-C02-02. In addition, they acknowledge financial support from the Ramon y Cajal Grant No. RYC-2011-07593 as well as the EU CIG Grant No. UE-14-GT5LD2013-618459. The work of A. P. is funded by the Asturian Government SEVERO OCHOA Grant No. BP14-003