Nonlinear random walks
The finite-size-based description of the dynamical processes of networked systems captures structural features that are not possible to be detected otherwise. In this direction, I have formulated the nonlinear random walk diffusion process on a network when the nodes’ finite carrying capacities are taken into account.
Such nonlinear random walks allow the construction of inverse problems by reconstructing the degree distribution and the total number of nodes of the network based on a set of successive observations from a single (randomly chosen) node [1].
Furthermore, with V. Latora, we have proven that such nonlinear random walk processes contribute to optimal spatial support exploration, quantified by an entropy rate measure [2].
In the same direction, with J.P. Gleeson and E. Estrada, I have shown that the interplay of dynamics between the node-based and the global network makes impossible the full determination of the network structure [3].
In B.A. Siebert's Ph.D. thesis, we have introduced the ESIR epidemic model. Based on nonlinear random walks, such a model optimizes the trade-off between costs and prevention in epidemics lockdowns [4].
As part of J.-F. de Kemmeter's Ph.D. project, we show that a nonlinear diffusion process on a heterogeneous landscape can yield a self-segregation process and explain the emergence of vacant habitats (niches) [5].
References
[1] M. A., T. Carletti, F. Di Patti, D. Fanelli, F. Piazza “Hopping in the crowd to unveil network topology”, Physical Review Letters (IF: 9.161), 120, 158301 (2018)
[2] T. Carletti, M. A., D. Fanelli, V. Latora “Nonlinear walkers and efficient exploration of a crowded network”, Physical Review Research, 2 033012 (2020)
[3] M. A., B. R. da Cunha, E. Estrada, J. P. Gleeson “Dynamics imposes limits on detectability of network structures”, New Journal of Physics (IF: 3.729), 22 063037 (2020)
[4] B. A. Siebert, J. P. Gleeson, M. A., “Nonlinear random walks optimize the trade-off between cost and prevention in epidemics lockdown measures: the ESIR model", Chaos, Solitons & Fractals (IF: 9.922) 161, 112322 (2022)
[5] R. Muolo, T. Carletti, J. P. Gleeson, M. A.,“Synchronization dynamics in non-normal networks: the trade-off for optimality", Entropy (IF: 2.494) 23 36 (2021)
[6] J.-F. de Kemmeter, T. Carletti, M. A., “Self-segregation in heterogeneous metapopulation landscapes", Journal of Theoretical Biology (IF: 2.691) (Accepted) (2022)