1,322 research outputs found
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 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 is sufficient to
destabilize the homogeneous regime for very large lattice sizes
Reinforced communication and social navigation generate groups in model networks
To investigate the role of information flow in group formation, we introduce
a model of communication and social navigation. We let agents gather
information in an idealized network society, and demonstrate that heterogeneous
groups can evolve without presuming that individuals have different interests.
In our scenario, individuals' access to global information is constrained by
local communication with the nearest neighbors on a dynamic network. The result
is reinforced interests among like-minded agents in modular networks; the flow
of information works as a glue that keeps individuals together. The model
explains group formation in terms of limited information access and highlights
global broadcasting of information as a way to counterbalance this
fragmentation. To illustrate how the information constraints imposed by the
communication structure affects future development of real-world systems, we
extrapolate dynamics from the topology of four social networks.Comment: 7 pages, 3 figure
Local syzygies of multiplier ideals
In recent years, multiplier ideals have found many applications in local and
global algebraic geometry. Because of their importance, there has been some
interest in the question of which ideals on a smooth complex variety can be
realized as multiplier ideals. Other than integral closure no local
obstructions have been known up to now, and in dimension two it was established
by Favre-Jonsson and Lipman-Watanabe that any integrally closed ideal is
locally a multiplier ideal. We prove the somewhat unexpected result that
multiplier ideals in fact satisfy some rather strong algebraic properties
involving higher syzygies. It follows that in dimensions three and higher,
multiplier ideals are very special among all integrally closed ideals.Comment: 8 page
Accelerating consensus on co-evolving networks: the effect of committed individuals
Social networks are not static but rather constantly evolve in time. One of
the elements thought to drive the evolution of social network structure is
homophily - the need for individuals to connect with others who are similar to
them. In this paper, we study how the spread of a new opinion, idea, or
behavior on such a homophily-driven social network is affected by the changing
network structure. In particular, using simulations, we study a variant of the
Axelrod model on a network with a homophilic rewiring rule imposed. First, we
find that the presence of homophilic rewiring within the network, in general,
impedes the reaching of consensus in opinion, as the time to reach consensus
diverges exponentially with network size . We then investigate whether the
introduction of committed individuals who are rigid in their opinion on a
particular issue, can speed up the convergence to consensus on that issue. We
demonstrate that as committed agents are added, beyond a critical value of the
committed fraction, the consensus time growth becomes logarithmic in network
size . Furthermore, we show that slight changes in the interaction rule can
produce strikingly different results in the scaling behavior of . However,
the benefit gained by introducing committed agents is qualitatively preserved
across all the interaction rules we consider
Bridgeness: A Local Index on Edge Significance in Maintaining Global Connectivity
Edges in a network can be divided into two kinds according to their different
roles: some enhance the locality like the ones inside a cluster while others
contribute to the global connectivity like the ones connecting two clusters. A
recent study by Onnela et al uncovered the weak ties effects in mobile
communication. In this article, we provide complementary results on document
networks, that is, the edges connecting less similar nodes in content are more
significant in maintaining the global connectivity. We propose an index named
bridgeness to quantify the edge significance in maintaining connectivity, which
only depends on local information of network topology. We compare the
bridgeness with content similarity and some other structural indices according
to an edge percolation process. Experimental results on document networks show
that the bridgeness outperforms content similarity in characterizing the edge
significance. Furthermore, extensive numerical results on disparate networks
indicate that the bridgeness is also better than some well-known indices on
edge significance, including the Jaccard coefficient, degree product and
betweenness centrality.Comment: 10 pages, 4 figures, 1 tabl
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
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
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
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
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