299,034 research outputs found
Community Detection from Location-Tagged Networks
Many real world systems or web services can be represented as a network such
as social networks and transportation networks. In the past decade, many
algorithms have been developed to detect the communities in a network using
connections between nodes. However in many real world networks, the locations
of nodes have great influence on the community structure. For example, in a
social network, more connections are established between geographically
proximate users. The impact of locations on community has not been fully
investigated by the research literature. In this paper, we propose a community
detection method which takes locations of nodes into consideration. The goal is
to detect communities with both geographic proximity and network closeness. We
analyze the distribution of the distances between connected and unconnected
nodes to measure the influence of location on the network structure on two real
location-tagged social networks. We propose a method to determine if a
location-based community detection method is suitable for a given network. We
propose a new community detection algorithm that pushes the location
information into the community detection. We test our proposed method on both
synthetic data and real world network datasets. The results show that the
communities detected by our method distribute in a smaller area compared with
the traditional methods and have the similar or higher tightness on network
connections
Convergence in and its exponential rate for a branching process in a random environment
We consider a supercritical branching process in a random environment
. Let be the limit of the normalized population size
. We first show a necessary and sufficient condition for
the quenched () convergence of , which completes the known
result for the annealed convergence. We then show that the convergence
rate is exponential, and we find the maximal value of such that
in , in both quenched and annealed sense.
Similar results are also shown for a branching process in a varying
environment
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