Who Contributes to the Knowledge Sharing Economy?

Information sharing dynamics of social networks rely on a small set of influencers to effectively reach a large audience. Our recent results and observations demonstrate that the shape and identity of this elite, especially those contributing \emph{original} content, is difficult to predict. Information acquisition is often cited as an example of a public good. However, this emerging and powerful theory has yet to provably offer qualitative insights on how specialization of users into active and passive participants occurs. This paper bridges, for the first time, the theory of public goods and the analysis of diffusion in social media. We introduce a non-linear model of \emph{perishable} public goods, leveraging new observations about sharing of media sources. The primary contribution of this work is to show that \emph{shelf time}, which characterizes the rate at which content get renewed, is a critical factor in audience participation. Our model proves a fundamental \emph{dichotomy} in information diffusion: While short-lived content has simple and predictable diffusion, long-lived content has complex specialization. This occurs even when all information seekers are \emph{ex ante} identical and could be a contributing factor to the difficulty of predicting social network participation and evolution.Comment: 15 pages in ACM Conference on Online Social Networks 201

Mass media destabilizes the cultural homogeneous regime in Axelrod's model

An important feature of Axelrod's model for culture dissemination or social influence is the emergence of many multicultural absorbing states, despite the fact that the local rules that specify the agents interactions are explicitly designed to decrease the cultural differences between agents. Here we re-examine the problem of introducing an external, global interaction -- the mass media -- in the rules of Axelrod's model: in addition to their nearest-neighbors, each agent has a certain probability $p$ to interact with a virtual neighbor whose cultural features are fixed from the outset. Most surprisingly, this apparently homogenizing effect actually increases the cultural diversity of the population. We show that, contrary to previous claims in the literature, even a vanishingly small value of $p$ is sufficient to destabilize the homogeneous regime for very large lattice sizes

Network dynamics with a nested node set: sociability in seven villages in Senegal

We propose two complementary ways to deal with a nesting structure in the node set of a network—such a structure may be called a multilevel network, with a node set consisting of several groups. First, within‐group ties are distinguished from between‐group ties by considering them as two distinct but interrelated networks. Second, effects of nodal variables are differentiated according to the levels of the nesting structure, to prevent ecological fallacies. This is elaborated in a study of two repeated observations of a sociability network in seven villages in Senegal, analyzed using the Stochastic Actor‐oriented Model

The media effect in Axelrod's model explained

We revisit the problem of introducing an external global field -- the mass media -- in Axelrod's model of social dynamics, where in addition to their nearest neighbors, the agents can interact with a virtual neighbor whose cultural features are fixed from the outset. The finding that this apparently homogenizing field actually increases the cultural diversity has been considered a puzzle since the phenomenon was first reported more than a decade ago. Here we offer a simple explanation for it, which is based on the pedestrian observation that Axelrod's model exhibits more cultural diversity, i.e., more distinct cultural domains, when the agents are allowed to interact solely with the media field than when they can interact with their neighbors as well. In this perspective, it is the local homogenizing interactions that work towards making the absorbing configurations less fragmented as compared with the extreme situation in which the agents interact with the media only

On the classification of OADP varieties

The main purpose of this paper is to show that OADP varieties stand at an important crossroad of various main streets in different disciplines like projective geometry, birational geometry and algebra. This is a good reason for studying and classifying them. Main specific results are: (a) the classification of all OADP surfaces (regardless to their smoothness); (b) the classification of a relevant class of normal OADP varieties of any dimension, which includes interesting examples like lagrangian grassmannians. Following [PR], the equivalence of the classification in (b) with the one of quadro-quadric Cremona transformations and of complex, unitary, cubic Jordan algebras are explained.Comment: 13 pages. Dedicated to Fabrizio Catanese on the occasion of his 60th birthday. To appear in a special issue of Science in China Series A: Mathematic

Big Line Bundles over Arithmetic Varieties

We prove a Hilbert-Samuel type result of arithmetic big line bundles in Arakelov geometry, which is an analogue of a classical theorem of Siu. An application of this result gives equidistribution of small points over algebraic dynamical systems, following the work of Szpiro-Ullmo-Zhang. We also generalize Chambert-Loir's non-archimedean equidistribution

Triangulations and Severi varieties

We consider the problem of constructing triangulations of projective planes over Hurwitz algebras with minimal numbers of vertices. We observe that the numbers of faces of each dimension must be equal to the dimensions of certain representations of the automorphism groups of the corresponding Severi varieties. We construct a complex involving these representations, which should be considered as a geometric version of the (putative) triangulations

Longitudinal Peer Network Data in Higher Education

This chapter employs a longitudinal social network approach to research small group teaching in higher education. Longitudinal social network analyses can provide in-depth understanding of the social dynamics in small groups. Specifically, it is possible to investigate and disentangle the processes by which students make or break social connections with peers and are influenced by them, as well as how those processes relate to group compositions and personal attributes, such as achievement level. With advanced methods for modelling longitudinal social networks, researchers can identify social processes affecting small group teaching and learning

Three embeddings of the Klein simple group into the Cremona group of rank three

We study the action of the Klein simple group G consisting of 168 elements on two rational threefolds: the three-dimensional projective space and a smooth Fano threefold X of anticanonical degree 22 and index 1. We show that the Cremona group of rank three has at least three non-conjugate subgroups isomorphic to G. As a by-product, we prove that X admits a Kahler-Einstein metric, and we construct a smooth polarized K3 surface of degree 22 with an action of the group G.Comment: 43 page

Critical Values for Yen’s Q3: Identification of Local Dependence in the Rasch model using Residual Correlations

The assumption of local independence is central to all IRT models. Violations can lead to inflated estimates of reliability and problems with construct validity. For the most widely used fit statistic Q3 there are currently no well-documented suggestions of the critical values which should be used to indicate local dependence, and for this reason a variety of arbitrary rules of thumb are used. In this study, we used an empirical data example and Monte Carlo simulation to investigate the different factors that can influence the null distribution of residual correlations, with the objective of proposing guidelines that researchers and practitioners can follow when making decisions about local dependence during scale development and validation. We propose that a parametric bootstrapping procedure should be implemented in each separate situation in order to obtain the critical value of local dependence applicable to the data set, and provide example critical values for a number of data structure situations. The results show that for the Q3 fit statistic no single critical value is appropriate for all situations, as the percentiles in the empirical null distribution are influenced by the number of items, the sample size, and the number of response categories. Furthermore, our results show that local dependence should be considered relative to the average observed residual correlation, rather than to a uniform value, as this results in more stable percentiles for the null distribution of an adjusted fit statistic