Luc Berthouze | Dynamical processes on structured networks

Key collaborators: Prof. Istvan Z Kiss, Prof. Peter L Simon

Graduate students: Dr Francesco Di Lauro (PhD, 2018-2021), Dr Peter Overbury (PhD, 2015-2020), Dr Rosanna Barnard (PhD, 2014-2018), Dr Martin Ritchie (PhD, 2012-2015)

Topics of interest here are:

Dynamics on structured networks

Di Lauro, F., Berthouze, L., Dorey, M. D., Miller, J. C., & Kiss, I. Z. (2020). The impact of network properties and mixing on control measures and disease-induced herd immunity in epidemic models: a mean-field model perspective. ArXiv:2007.06975 [Physics, q-Bio]. http://arxiv.org/abs/2007.06975

Barnard, R. C., Berthouze, L., Simon, P. L., & Kiss, I. Z. (2019). Epidemic threshold in pairwise models for clustered networks: closures and fast correlations. Journal of Mathematical Biology. https://doi.org/10.1007/s00285-019-01380-1

Barnard, R. C., Kiss, I. Z., Berthouze, L., & Miller, J. C. (2018). Edge-Based Compartmental Modelling of an SIR Epidemic on a Dual-Layer Static–Dynamic Multiplex Network with Tunable Clustering. Bulletin of Mathematical Biology, 80(10), 2698–2733. https://doi.org/10.1007/s11538-018-0484-5

Kiss, I. Z., Berthouze, L., Miller, J. C., & Simon, P. L. (2017). Mapping Out Emerging Network Structures in Dynamic Network Models Coupled with Epidemics. In N. Masuda & P. Holme (Eds.), Temporal Network Epidemiology (pp. 267–289). Springer Singapore. https://doi.org/10.1007/978-981-10-5287-3_12

Szabó-Solticzky, A., Berthouze, L., Kiss, I. Z., & Simon, P. L. (2016). Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis. Journal of Mathematical Biology, 72(5), 1153–1176. https://doi.org/10.1007/s00285-015-0902-3

Rattana, P., Berthouze, L., & Kiss, I. Z. (2014). Impact of constrained rewiring on network structure and node dynamics. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 90(5-1), 052806. https://doi.org/10.1103/PhysRevE.90.052806

Kiss, I. Z., Berthouze, L., Taylor, T. J., & Simon, P. L. (2012). Modelling approaches for simple dynamic networks and applications to disease transmission models. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468(2141), 1332–1355. https://doi.org/10.1098/rspa.2011.0349

Impact of higher-order structure on dynamics

Ritchie, M., Berthouze, L., & Kiss, I. Z. (2016). Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition. Journal of Mathematical Biology, 72(1-2), 255–281. https://doi.org/10.1007/s00285-015-0884-1

Ritchie, M., Berthouze, L., House, T., & Kiss, I. Z. (2014). Higher-order structure and epidemic dynamics in clustered networks. Journal of Theoretical Biology, 348, 21–32. https://doi.org/10.1016/j.jtbi.2014.01.025

Exploration of diversity in networks satisfying constraints

Overbury, P., Kiss, I. Z., & Berthouze, L. (2019). Mapping Structural Diversity in Networks Sharing a Given Degree Distribution and Global Clustering: Adaptive Resolution Grid Search Evolution with Diophantine Equation-Based Mutations. In L. M. Aiello, C. Cherifi, H. Cherifi, R. Lambiotte, P. Lió, & L. M. Rocha (Eds.), Complex Networks and Their Applications VII (Vol. 812, pp. 718–730). Springer International Publishing. https://doi.org/10.1007/978-3-030-05411-3_57

Overbury, P., Kiss, I. Z., & Berthouze, L. (2017). A genetic algorithm-based approach to mapping the diversity of networks sharing a given degree distribution and global clustering. In H. Cherifi, S. Gaito, W. Quattrociocchi, & A. Sala (Eds.), Complex Networks & Their Applications V (Vol. 693, pp. 223–233). Springer International Publishing. https://doi.org/10.1007/978-3-319-50901-3_18

Ritchie, M., Berthouze, L., & Kiss, I. Z. (2016). Generation and analysis of networks with a prescribed degree sequence and subgraph family: higher-order structure matters. Journal of Complex Networks, cnw011. https://doi.org/10.1093/comnet/cnw011

Overbury, P., & Berthouze, L. (2015). Using Novelty-Biased GA to Sample Diversity in Graphs Satisfying Constraints. Proceedings of the Companion Publication of the 2015 on Genetic and Evolutionary Computation Conference - GECCO Companion ’15, 1445–1446. https://doi.org/10.1145/2739482.2764637

Confronting high-dimensional network models with data description

Funded by the Leverhulme Trust

Other collaborators: Dr Masoumeh Dashti (co-I), Dr Jean-Charles Croix (PDRA, until April 2020)

The use of networks to model complex systems has revolutionised the way in which brains, epidemics, social interactions and more generally the flow of information are modelled. However, many of the resulting mathematical models suffer from high model dimensionality and therefore limited analytical tractability, sensitivity to incomplete information about the network, and inaccuracies due to simplifying assumptions or approximations. The aim of this research is to develop a new modelling paradigm that will tackle these challenges as well as offer several other major benefits. This paradigm relies on the specification of a new class of parametric models that are flexible enough to handle networks currently out of reach of state-of-the-art models. The inference of the parameters is formulated as Bayesian inverse problems, which in turn makes it possible to rigorously quantify the uncertainty introduced by simplifying assumptions and incomplete network data. This research harnesses a novel combination of techniques from stochastic analysis, partial differential equations (PDEs) and uncertainty quantification and could prove a step change in the ability of network science to deal with real-world applications.

Publications to date:

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Di Lauro, F., Croix, J.-C., Dashti, M., Berthouze, L., & Kiss, I. Z. (2019). Network Inference from Population-Level Observation of Epidemics. ArXiv:1906.10966 [Physics, q-Bio]. http://arxiv.org/abs/1906.10966