1,551 research outputs found
Dynamical Systems to Monitor Complex Networks in Continuous Time
In many settings it is appropriate to treat the evolution of pairwise
interactions over continuous time. We show that new Katz-style centrality
measures can be derived in this context via solutions to a nonautonomous ODE
driven by the network dynamics. This allows us to identify and track, at any
resolution, the most influential nodes in terms of broadcasting and receiving
information through time dependent links. In addition to the classical notion
of attenuation across edges used in the static Katz centrality measure, the ODE
also allows for attenuation over time, so that real time "running measures" can
be computed. With regard to computational efficiency, we explain why it is
cheaper to track good receivers of information than good broadcasters. We
illustrate the new measures on a large scale voice call network, where key
features are discovered that are not evident from snapshots or aggregates
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Bistability through triadic closure
We propose and analyse a class of evolving network models suitable for describing a dynamic topological structure. Applications include telecommunication, on-line social behaviour and information processing in neuroscience. We model the evolving network as a discrete time Markov chain, and study a very general framework where, conditioned on the current state, edges appear or disappear independently at the next timestep. We show how to exploit symmetries in the microscopic, localized rules in order to obtain conjugate classes of random graphs that simplify analysis and calibration of a model. Further, we develop a mean field theory for describing network evolution. For a simple but realistic scenario incorporating the triadic closure effect that has been empirically observed by social scientists (friends of friends tend to become friends), the mean field theory predicts bistable dynamics, and computational results confirm this prediction. We also discuss the calibration issue for a set of real cell phone data, and find support for a stratified model, where individuals are assigned to one of two distinct groups having different within-group and across-group dynamics
Twitter’s big hitters
We describe the results of a new computational experiment on Twitter data. By listening to Tweets on a selected topic, we generate a dynamic social interaction network. We then apply a recently proposed dynamic network analysis algorithm that ranks Tweeters according to their ability to broadcast information. In particular, we study the evolution of importance rankings over time. Our presentation will also describe the outcome of an experiment where results from automated ranking algorithms are compared with the views of social media experts
Minimal odd order automorphism groups
We show that 3^7 is the smallest order of a non-trivial odd order group which
occurs as the full automorphism group of a finite group.Comment: 11 pages, no figures. Manuscript accepted for publicatio
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A matrix iteration for dynamic network summaries
We propose a new algorithm for summarizing properties of large-scale time-evolving networks. This type of data, recording connections that come and go over time, is being generated in many modern applications, including telecommunications and on-line human social behavior. The
algorithm computes a dynamic measure of how well pairs of nodes can communicate by taking account of routes through the network that respect the arrow of time. We take the conventional approach of downweighting for length (messages become corrupted as they are passed along) and add the novel feature of downweighting for age (messages go out of date). This allows us to generalize widely used
Katz-style centrality measures that have proved popular in network science to the case of dynamic networks sampled at non-uniform points in time. We illustrate the new approach on synthetic and real data
DNA meets the SVD
This paper introduces an important area of computational cell biology where complex, publicly available genomic data is being examined by linear algebra methods, with the aim of revealing biological and medical insights
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