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)