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

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(messages become corrupted as they are passed along) and add the novel feature of downweighting for age (messages go out of date).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

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

Highly erosive glaciers on Mars - the role of water

International audiencePolewards of 30 • in each hemisphere, the surface of Mars hosts a suite of landforms reminiscent of glacial landscapes on Earth. Amongst these landforms are: 1) Viscous Flow Features (VFF), which resemble glaciers on Earth and are thought to contain large volumes of water ice, 2) martian gullies which are km-scale features resembling water-eroded gullies on Earth and 3) arcuate ridges thought to be moraines from previous glaciations. Gullies have been long-associated with a surface unit originally called "pasted-on terrain" and now often called the "latitude dependant mantle". Arcuate ridges are often found at the base of hillslopes with gullies, but are also found on hillslopes with pasted-on terrain and no gullies. We have found a systematic lowering of the slope of the bedrock exposure located topographically above the pasted-on terrain whether that same slope hosts gullies or not. The lowered bedrock exposures display a different surface texture from bedrock exposed on other parts of the crater wall and from fresh crater walls-it appears fragmented and has reduced relief. Using 1-m-digital elevation models from the High Resolution Imaging Science Experiment (HiRISE) we compared the slopes of eight "eroded" craters and seven unmodified craters. We estimated their age using the crater size-frequency distribution of small craters on their ejecta blankets. From this information we calculated bedrock retreat rates for the eroded craters and found they were up to ∼103 m Myr-1-equivalent to erosion rates of wet-based glaciers on Earth. This is several orders of magnitude higher than previous estimates of erosion by VFF (10-2-101 m Myr-1), which themselves are roughly equivalent to cold-based glaciers on Earth. Such erosion rates are sufficient to erase previously existing landforms, such as martian gullies. We hypothesise, therefore, that the pasted-on terrain is a glacial deposit, overturning its previous interpretation as an airfall deposit of ice nucleated on dust. We maintain the interpretation of the arcuate ridges as moraines, but further conclude that they are likely the result of glaciotectonic deformation of sub-marginal and proglacial sediment in the presence of sediment pore-water. We do not support the generation of large quantities of glacial meltwater because it would have broken-up and degraded the arcuate ridges and pasted-on terrain an produced a suite of landforms (e.g., hummocky moraine, lacustrine forms, outwash plains, eskers) which are not observed

The deformed graph Laplacian and its applications to network centrality analysis

We introduce and study a new network centrality measure based on the concept of nonbacktracking walks; that is, walks not containing subsequences of the form uvu where u and v are any distinct connected vertices of the underlying graph . We argue that this feature can yield more meaningful rankings than traditional walk-based cent rality measures. We show that the resulting Katz-style centrality measure may be computed via the so -called deformed graph Laplacian?a quadratic matrix polynomial that can be associated with any graph. By proving a range of new results about this matrix polynomial, we gain insights into the behavior of the algorithm with respect to its Katz-like parameter. The results also inform implementation issues. In particular we show that, in an appropriate limit, the new measure coincide s with the nonbacktracking version of eigenvector centrality introduced by Martin, Zhang and New man in 2014. Rigorous analysis on star and star-like networks illustrates the benefits of the new approach, and further results are given on real networks

A model for dynamic communicators

We develop and test an intuitively simple dynamic network model to describe the type of time-varying connectivity structure present in many technological settings. The model assumes that nodes have an inherent hierarchy governing the emergence of new connections. This idea draws on newly established concepts in online human behaviour concerning the existence of discussion catalysts, who initiate long threads, and online leaders, who trigger feedback. We show that the model captures an important property found in e-mail and voice call data – ‘dynamic communicators’ with sufficient foresight or impact to generate effective links and having an influence that is grossly underestimated by static measures based on snaphots or aggregated data