Fragility Limits Performance in Complex Networks.
Journal
Scientific reports
ISSN: 2045-2322
Titre abrégé: Sci Rep
Pays: England
ID NLM: 101563288
Informations de publication
Date de publication:
04 02 2020
04 02 2020
Historique:
received:
21
05
2019
accepted:
15
01
2020
entrez:
6
2
2020
pubmed:
6
2
2020
medline:
6
2
2020
Statut:
epublish
Résumé
While numerous studies have suggested that large natural, biological, social, and technological networks are fragile, convincing theories are still lacking to explain why natural evolution and human design have failed to optimize networks and avoid fragility. In this paper we provide analytical and numerical evidence that a tradeoff exists in networks with linear dynamics, according to which general measures of robustness and performance are in fact competitive features that cannot be simultaneously optimized. Our findings show that large networks can either be robust to variations of their weights and parameters, or efficient in responding to external stimuli, processing noise, or transmitting information across long distances. As illustrated in our numerical studies, this performance tradeoff seems agnostic to the specific application domain, and in fact it applies to simplified models of ecological, neuronal, and traffic networks.
Identifiants
pubmed: 32019963
doi: 10.1038/s41598-020-58440-6
pii: 10.1038/s41598-020-58440-6
pmc: PMC7000764
doi:
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
1774Références
Bassett, D. S. & Bullmore, E. Small-world brain networks. The neuroscientist 12, 512–523 (2006).
doi: 10.1177/1073858406293182
Pilosof, S., Porter, M. A., Pascual, M. & Kéfi, S. The multilayer nature of ecological networks. Nature Ecology & Evolution 1, 0101 (2017).
doi: 10.1038/s41559-017-0101
Motter, A. E., Myers, S. A., Anghel, M. & Nishikawa, T. Spontaneous synchrony in power-grid networks. Nature Physics 9, 191 (2013).
doi: 10.1038/nphys2535
Allesina, S. & Tang, S. The stability-complexity relationship at age 40: a random matrix perspective. Population Ecology 57, 63–75 (2015).
doi: 10.1007/s10144-014-0471-0
Sritharan, D. & Sarma, S. V. Fragility in dynamic networks: application to neural networks in the epileptic cortex. Neural computation 26, 2294–2327 (2014).
doi: 10.1162/NECO_a_00644
McCulloch, M., Falter, J., Trotter, J. & Montagna, P. Coral resilience to ocean acidification and global warming through ph up-regulation. Nature Climate Change 2, 623–627 (2012).
doi: 10.1038/nclimate1473
Kinney, R., Crucitti, P., Albert, R. & Latora, V. Modeling cascading failures in the north american power grid. The European Physical Journal B-Condensed Matter and Complex Systems 46, 101–107 (2005).
doi: 10.1140/epjb/e2005-00237-9
Bando, M., Hasebe, K., Nakayama, A., Shibata, A. & Sugiyama, Y. Dynamical model of traffic congestion and numerical simulation. Physical Review E 51, 1035 (1995).
doi: 10.1103/PhysRevE.51.1035
Newman, M. E. J. Networks: An Introduction (Oxford University Press, 2010).
Watts, D. J. & Strogatz, S. H. Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998).
doi: 10.1038/30918
Barabási, A. L. & Albert, R. Emergence of scaling in random networks. Science 286, 509–512 (1999).
doi: 10.1126/science.286.5439.509
Fortunato, S. Community detection in graphs. Physics Reports 486, 75–174 (2010).
doi: 10.1016/j.physrep.2009.11.002
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M. & Hwang, D. U. Complex networks: Structure and dynamics. Physics Reports 424, 175–308 (2006).
doi: 10.1016/j.physrep.2005.10.009
Liu, Y. Y., Slotine, J. J. & Barabási, A. L. Controllability of complex networks. Nature 473, 167–173 (2011).
doi: 10.1038/nature10011
Pasqualetti, F., Zampieri, S. & Bullo, F. Controllability metrics, limitations and algorithms for complex networks. IEEE Transactions on Control of Network Systems 1, 40–52 (2014).
doi: 10.1109/TCNS.2014.2310254
Gu, S. et al. Controllability of structural brain networks. Nature Communications 6 (2015).
Yan, G. et al. Spectrum of controlling and observing complex networks. Nature Physics 11, 779–786 (2015).
doi: 10.1038/nphys3422
Skardal, P. S. & Arenas, A. Control of coupled oscillator networks with application to microgrid technologies. Science Advances 1, e1500339 (2015).
doi: 10.1126/sciadv.1500339
Hinrichsen, D. & Pritchard, A. J. Stability radii of linear systems. Systems & Control Letters 7, 1–10 (1986).
doi: 10.1016/0167-6911(86)90094-0
Qiu, L. et al. A formula for computation of the real stability radius. Automatica 31, 879–890 (1995).
doi: 10.1016/0005-1098(95)00024-Q
Kailath, T. Linear Systems (Prentice-Hall, 1980).
Lynn, C. W. & Bassett, D. S. The physics of brain network structure, function and control. Nature Reviews Physics 1, 318 (2019).
doi: 10.1038/s42254-019-0040-8
Stacey, W. et al. Emerging roles of network analysis for epilepsy. Epilepsy Research 106255 (2019).
Liu, J. et al. Analysis and control of a continuous-time bi-virus model. IEEE Transactions on Automatic Control, In press (2019).
Betzel, R. F., Gu, S., Medaglia, J. D., Pasqualetti, F. & Bassett, D. S. Optimally controlling the human connectome: the role of network topology. Scientific Reports 6, 30770 (2016).
doi: 10.1038/srep30770
Trefethen, L. N. & Embree, M. Spectra and Pseudospectra: the Behavior of Nonnormal Matrices and Operators (Princeton University Press, 2005).
Pasqualetti, F. & Zampieri, S. On the controllability of isotropic and anisotropic networks. In IEEE Conf. on Decision and Control, 607–612 (Los Angeles, CA, USA, 2014).
Zhao, S. & Pasqualetti, F. Networks with diagonal controllability gramians: Analysis, graphical conditions, and design algorithms. Automatica 102, 10–18 (2019).
doi: 10.1016/j.automatica.2018.12.038
Baggio, G. & Zampieri, S. On the relation between non-normality and diameter in linear dynamical networks. In European Control Conference, 1839–1844 (Limassol, Cyprus, 2018).
Olshevsky, A. Eigenvalue clustering, control energy, and logarithmic capacity. Systems & Control Letters 96, 45–50 (2016).
doi: 10.1016/j.sysconle.2016.06.013
Meyer, C. D. Matrix Analysis and Applied Linear Algebra (SIAM, 2001).
Hespanha, J. P. Linear Systems Theory (Princeton University Press, 2009).
Suweis, S., Simini, F., Banavar, J. R. & Maritan, A. Emergence of structural and dynamical properties of ecological mutualistic networks. Nature 500, 449–452 (2013).
doi: 10.1038/nature12438
Hennequin, G., Vogels, T. P. & Gerstner, W. Optimal control of transient dynamics in balanced networks supports generation of complex movements. Neuron 82, 1394–1406 (2014).
doi: 10.1016/j.neuron.2014.04.045
Caines, P. E. Linear stochastic systems 11 (Wiley, New York, 1988).
Acemoglu, D., Carvalho, V. M., Ozdaglar, A. & Tahbaz-Salehi, A. The network origins of aggregate fluctuations. Econometrica 80, 1977–2016 (2012).
doi: 10.3982/ECTA9623
Huang, Q., Yuan, Y., Goncalves, J. & Dahleh, M. A. h
Hoogendoorn, S. P. & Bovy, P. H. State-of-the-art of vehicular traffic flow modelling. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 215, 283–303 (2001).
doi: 10.1243/0954405011515316
Spall, J. C. Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control (John Wiley & Sons, 2003).
Powell, W. B. Approximate Dynamic Programming: Solving the Curses of Dimensionality (John Wiley and Sons, 2007).
Kauffman, S. A. The Origins of Order: Self-Organization and Selection in Evolution (Oxford University Press, 1993).
Svensson, E. & Calsbeek, R. The Adaptive Landscape in Evolutionary Biology (Oxford University Press, 2012).
Hennequin, G., Vogels, T. P. & Gerstner, W. Non-normal amplification in random balanced neuronal networks. Phys. Rev. E 86, 011909 (2012).
doi: 10.1103/PhysRevE.86.011909
Ganguli, S., Huh, D. & Sompolinsky, H. Memory traces in dynamical systems. Proceedings of the National Academy of Sciences 105, 18970–18975 (2008).
doi: 10.1073/pnas.0804451105
Ganguli, S. & Latham, P. Feedforward to the past: The relation between neuronal connectivity, amplification, and short-term memory. Neuron 61, 499–501 (2009).
doi: 10.1016/j.neuron.2009.02.006
Goldman, M. S. Memory without feedback in a neural network. Neuron 61, 621–634 (2009).
doi: 10.1016/j.neuron.2008.12.012
Bascompte, J., Jordano, P. & Olesen, J. M. Asymmetric coevolutionary networks facilitate biodiversity maintenance. Science 312, 431–433 (2006).
doi: 10.1126/science.1123412