Reciprocity in Social Networks with Capacity Constraints

Directed links -- representing asymmetric social ties or interactions (e.g., "follower-followee") -- arise naturally in many social networks and other complex networks, giving rise to directed graphs (or digraphs) as basic topological models for these networks. Reciprocity, defined for a digraph as the percentage of edges with a reciprocal edge, is a key metric that has been used in the literature to compare different directed networks and provide "hints" about their structural properties: for example, are reciprocal edges generated randomly by chance or are there other processes driving their generation? In this paper we study the problem of maximizing achievable reciprocity for an ensemble of digraphs with the same prescribed in- and out-degree sequences. We show that the maximum reciprocity hinges crucially on the in- and out-degree sequences, which may be intuitively interpreted as constraints on some "social capacities" of nodes and impose fundamental limits on achievable reciprocity. We show that it is NP-complete to decide the achievability of a simple upper bound on maximum reciprocity, and provide conditions for achieving it. We demonstrate that many real networks exhibit reciprocities surprisingly close to the upper bound, which implies that users in these social networks are in a sense more "social" than suggested by the empirical reciprocity alone in that they are more willing to reciprocate, subject to their "social capacity" constraints. We find some surprising linear relationships between empirical reciprocity and the bound. We also show that a particular type of small network motifs that we call 3-paths are the major source of loss in reciprocity for real networks

High-precision U-Pb ages in the early Tithonian to early Berriasian and implications for the numerical age of the Jurassic-Cretaceous boundary

The numerical age of the Jurassic-Cretaceous boundary has been controversial and difficult to determine. In this study, we present high-precision U-Pb geochronological data around the Jurassic-Cretaceous boundary in two distinct sections from different sedimentary basins: the Las Loicas, Neuquén Basin, Argentina, and the Mazatepec, Sierra Madre Oriental, Mexico. These two sections contain primary and secondary fossiliferous markers for the boundary as well as interbedded volcanic ash horizons, allowing researchers to obtain new radioisotopic dates in the late Tithonian and early Berriasian. We also present the first age determinations in the early Tithonian and tentatively propose a minimum duration for the stage as a cross-check for our ages in the early Berriasian. Given our radioisotopic ages in the early Tithonian to early Berriasian, we discuss implications for the numerical age of the boundary.Fil: Lena, Luis. Universidad de Ginebra; SuizaFil: López Martínez, Rafael. Universidad Nacional Autónoma de México; MéxicoFil: Lescano, Marina Aurora. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Estudios Andinos "Don Pablo Groeber". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Estudios Andinos "Don Pablo Groeber"; ArgentinaFil: Aguirre-Urreta, Maria Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Estudios Andinos "Don Pablo Groeber". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Estudios Andinos "Don Pablo Groeber"; ArgentinaFil: Concheyro, Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Estudios Andinos "Don Pablo Groeber". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Estudios Andinos "Don Pablo Groeber"; ArgentinaFil: Vennari, Verónica Vanesa. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Estudios Andinos "Don Pablo Groeber". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Estudios Andinos "Don Pablo Groeber"; ArgentinaFil: Naipauer, Maximiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Estudios Andinos "Don Pablo Groeber". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Estudios Andinos "Don Pablo Groeber"; ArgentinaFil: Samankassou, Elias. Universidad de Ginebra; SuizaFil: Pimentel, Márcio. Universidade do Brasília; BrasilFil: Ramos, Victor Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Estudios Andinos "Don Pablo Groeber". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Estudios Andinos "Don Pablo Groeber"; ArgentinaFil: Schaltegger, Urs. Universidad de Ginebra; Suiz