A new modularity measure for Fuzzy Community detection problems based on overlap and grouping functions

One of the main challenges of fuzzy community detection problems is to be able to measure the quality of a fuzzy partition. In this paper, we present an alternative way of measuring the quality of a fuzzy community detection output based on n-dimensional grouping and overlap functions. Moreover, the proposed modularity measure generalizes the classical Girvan–Newman (GN) modularity for crisp community detection problems and also for crisp overlapping community detection problems. Therefore, it can be used to compare partitions of different nature (i.e. those composed of classical, overlapping and fuzzy communities). Particularly, as is usually done with the GN modularity, the proposed measure may be used to identify the optimal number of communities to be obtained by any network clustering algorithm in a given network. We illustrate this usage by adapting in this way a well-known algorithm for fuzzy community detection problems, extending it to also deal with overlapping community detection problems and produce a ranking of the overlapping nodes. Some computational experiments show the feasibility of the proposed approach to modularity measures through n-dimensional overlap and grouping functions.

Large-scale clustering measurements with photometric redshifts: comparing the dark matter haloes of X-ray AGN, star-forming and passive galaxies at z ≈ 1

We combine multi-wavelength data in the AEGIS-XD and C-COSMOS surveys to measure the typical dark matter halo mass of X-ray selected active galactic nuclei (AGN) [L_X(2–10 keV) > 10^42 erg s^− 1] in comparison with far-infrared selected star-forming galaxies detected in the Herschel/PEP survey (PACS Evolutionary Probe; L_IR > 10^11 L_⊙) and quiescent systems at z ≈ 1. We develop a novel method to measure the clustering of extragalactic populations that uses photometric redshift probability distribution functions in addition to any spectroscopy. This is advantageous in that all sources in the sample are used in the clustering analysis, not just the subset with secure spectroscopy. The method works best for large samples. The loss of accuracy because of the lack of spectroscopy is balanced by increasing the number of sources used to measure the clustering. We find that X-ray AGN, far-infrared selected star-forming galaxies and passive systems in the redshift interval 0.6 < z < 1.4 are found in haloes of similar mass, log M_DMH/(M_⊙ h^−1) ≈ 13.0. We argue that this is because the galaxies in all three samples (AGN, star-forming, passive) have similar stellar mass distributions, approximated by the J-band luminosity. Therefore, all galaxies that can potentially host X-ray AGN, because they have stellar masses in the appropriate range, live in dark matter haloes of log M_DMH/(M_⊙ h^−1) ≈ 13.0 independent of their star formation rates. This suggests that the stellar mass of X-ray AGN hosts is driving the observed clustering properties of this population. We also speculate that trends between AGN properties (e.g. luminosity, level of obscuration) and large-scale environment may be related to differences in the stellar mass of the host galaxies.

La lengua de las inscripciones métricas del Peloponeso (siglos VII- IV a.C.)

Many works deal with the study of Greek epigrams. These texts gather precious historical, religious and epigraphic content whose analysis has been addressed from a literary point of view. The degree of dependence of Hellenistic epigrams of earlier period epigrams are of great interest, as shown by recent and numerous papers on this matter (Harder et al . 1998; 2002; 2006; 2012; Bing and Bruss 2007; Baumbach et al. 2010). Another major line of research is focused on the origin of epigrams and their relation to elegy (Gentilli 1968; Passa 1998b) or to hexametric poetry and the oral-formulaic language inherited from Homeric tradition (di Tillio 1969; Moranti 1971, 1972; Gentili and Giannini 1977). Furthermore, other authors, such as Day (2010), have pointed out the significance of the performative and ritual nature of epigrams. Likewise, this field of study has undergone a renewal because of new papyrological findings enriching the existing epigram collection corpora. Compared to all these works, monographs and studies dedicated to the analysis of the language of the verse inscriptions are fewer. Many of them explore the linguistic differences between literary epigrams and those epigrams preserved by epigraphic means, as well as the degree of intervention of later tradition on such texts (Tiberi 1996, del Barrio Vega 2008; Kaczko 2009). The first exclusively linguistic reviews were published by the end of the 19th century (Wagner 1883; Fengler 1892), however, they are descriptive analyses lacking from an independent methodology. Kock(1910) was the first researcher who systematized and suggested a linguistic hypothesis and upheld the use of epichoric dialects by poets. His theory was supported by adepts such as Kretschmer (1913; 1915) although some discordant voices appeared soon, such as Buck (1923) who denied the existence of a linguistic standard and endorsed the importance of the Ionic model over the epichoric one. Traditionally, Greek language manuals point out the significance of the Ionic model and accept the adaptation of Homeric language to epichoric dialect. The study of verse inscription language was not systematically resumed until Mickey's publications (1981a; 1981b). According to this researcher, epigraphic poetry consists of a tempered version of the epichoric dialect where the dialect-characteristic features are avoided. Following the same line but with some differences, Alonso Déniz and Nieto Izquierdo (2009) conclude that the most distinctive features of Argolic are not avoided, at least at the metrical inscriptions from Argolid...