16 research outputs found

    Impact of Temporal Features of Cattle Exchanges on the Size and Speed of Epidemic Outbreaks

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    International audienceDatabases recording cattle exchanges offer unique opportunities for a better understanding and fighting of disease spreading. Most studies model contacts with (sequences of) networks, but this approach neglects important dynamical features of exchanges, that are known to play a key role in spreading. We use here a fully dynamic modeling of contacts and empirically compare the spreading outbreaks obtained with it to the ones obtained with network approaches. We show that neglecting time information leads to significant overestimates of actual sizes of spreading cascades, and that these sizes are much more heterogeneous than generally assumed. Our approach also makes it possible to study the speed of spreading, and we show that the observed speeds vary greatly, even for a same cascade size

    Exploring concurrency and reachability in the presence of high temporal resolution

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    Network properties govern the rate and extent of spreading processes on networks, from simple contagions to complex cascades. Recent advances have extended the study of spreading processes from static networks to temporal networks, where nodes and links appear and disappear. We review previous studies on the effects of temporal connectivity for understanding the spreading rate and outbreak size of model infection processes. We focus on the effects of "accessibility", whether there is a temporally consistent path from one node to another, and "reachability", the density of the corresponding "accessibility graph" representation of the temporal network. We study reachability in terms of the overall level of temporal concurrency between edges, quantifying the overlap of edges in time. We explore the role of temporal resolution of contacts by calculating reachability with the full temporal information as well as with a simplified interval representation approximation that demands less computation. We demonstrate the extent to which the computed reachability changes due to this simplified interval representation.Comment: To appear in Holme and Saramaki (Editors). "Temporal Network Theory". Springer- Nature, New York. 201

    Sparse matrix computations for dynamic network centrality

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    Time sliced networks describing human-human digital interactions are typically large and sparse. This is the case, for example, with pairwise connectivity describing social media, voice call or physical proximity, when measured over seconds, minutes or hours. However, if we wish to quantify and compare the overall time-dependent centrality of the network nodes, then we should account for the global flow of information through time. Because the time-dependent edge structure typically allows information to diffuse widely around the network, a natural summary of sparse but dynamic pairwise interactions will generally take the form of a large dense matrix. For this reason, computing nodal centralities for a timedependent network can be extremely expensive in terms of both computation and storage; much more so than for a single, static network. In this work, we focus on the case of dynamic communicability, which leads to broadcast and receive centrality measures. We derive a new algorithm for computing time-dependent centrality that works with a sparsified version of the dynamic communicability matrix. In this way, the computation and storage requirements are reduced to those of a sparse, static network at each time point. The new algorithm is justified from first principles and then tested on a large scale data set. We find that even with very stringent sparsity requirements (retaining no more than ten times the number of nonzeros in the individual time slices), the algorithm accurately reproduces the list of highly central nodes given by the underlying full system. This allows us to capture centrality over time with a minimal level of storage and with a cost that scales only linearly with the number of time points. We also describe and test three variants of the proposed algorithm that require fewer parameters and achieve a further reduction in the computational cost