# MoN16: Sixteenth Mathematics of Networks meeting

## Antoine Messager (University of Sussex) – Inferring the functional topology of a computer network and its temporal evolution from sparse alert time series emitted by its nodes

We consider the problem of inferring functional links in a computer network using sparse time series of alerts emitted by its nodes. Based on the idea that the probability of two nodes being functionally coupled correlates with the mean delay between their respective alerts, we develop a method whose output is an undirected weighted network where the weight of an edge between two nodes denotes the probability of these nodes being functionally coupled. The method attempts to deal with three challenges, namely: the non-stationarity induced by temporal changes in the topology, the sparsity of the time-series of alerts that limits the effectiveness of classical statistical analysis, and the lack of an explicit model explaining even partly the dynamics of the nodes. Using a combination of windowing and convolution to calculate at each time window a score that quantifies the likelihood of a pair of nodes emitting alerts in quick succession, we develop a dynamic model of the temporal relationship between score and edge probability whose parameters are optimised through maximising the modelâ€™s predictive power from one time window to the other. We apply our method to both synthetic data and a real computer network.

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Contact:
Keith Briggs
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or
Richard G. Clegg (richard@richardclegg.org)