The DOI matches its Crossref record; 53 of the 53 references it cites were found in a registry or an index.
Spectrum of controlling and observing complex networks
Open accessAbstract
Recent studies have made important advances in identifying sensor or driver nodes, through which we can observe or control a complex system. But the observational uncertainty induced by measurement noise and the energy required for control continue to be significant challenges in practical applications. Here we show that the variability of control energy and observational uncertainty for different directions of the state space depend strongly on the number of driver nodes. In particular, we find that if all nodes are directly driven, control is energetically feasible, as the maximum energy increases sublinearly with the system size. If, however, we aim to control a system through a single node, control in some directions is energetically prohibitive, increasing exponentially with the system size. For the cases in between, the maximum energy decays exponentially when the number of driver nodes increases. We validate our findings in several model and real networks, arriving at a series of fundamental laws to describe the control energy that together deepen our understanding of complex systems. The complex interactions inherent in real-world networks grant us precise system control via manipulation of a subset of nodes. It turns out that the extent to which we can exercise this control depends sensitively on the number of nodes perturbed.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Collective dynamics of ‘small-world’ networks
Watts, D. J., & Strogatz, S. H. (1998) · Nature · doi:10.1038/30918 · Cited by 43,060
Statistical mechanics of complex networks
Albert, R., & Barabási, A.-L. (2002) · Reviews of Modern Physics · doi:10.1103/revmodphys.74.47 · Cited by 20,471
Self-citationSlotine, J.-J. E., & Li, W. (1991) · CERN Document Server (European Organization for Nuclear Research) · Cited by 18,975
Self-citationCommunity structure in social and biological networks
Girvan, M., & Newman, M. E. J. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.122653799 · Cited by 15,502
Complex networks: structure and dynamics
BOCCALETTI, S., LATORA, V, MORENO, Y., CHAVEZ, M., & HWANG, D. (2006) · Physics Reports · doi:10.1016/j.physrep.2005.10.009 · Cited by 11,010
Newman, M. (2010) · doi:10.1093/acprof:oso/9780199206650.001.0001 · Cited by 6,595
Stability and Complexity in Model Ecosystems
May, R. M. (2001) · Princeton University Press eBooks · doi:10.1515/9780691206912 · Cited by 5,183
Assortative Mixing in Networks
Newman, M. E. J. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.208701 · Cited by 4,988
Statistical physics of social dynamics
Castellano, C., Fortunato, S., & Loreto, V. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.591 · Cited by 4,119
STABILITY AND COMPLEXITY IN MODEL ECOSYSTEMS
Schoener, T. W. (1974) · Evolution · doi:10.1111/j.1558-5646.1974.tb00784.x · Cited by 3,928
Controllability of complex networks
Liu, Y.-Y., Slotine, J.-J., & Barabási, A.-L. (2011) · Nature · doi:10.1038/nature10011 · Cited by 3,215
Self-citationApproximation of Large-Scale Dynamical Systems
Antoulas, A. C. (2005) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898718713 · Cited by 3,088
Optimal feedback control as a theory of motor coordination
Todorov, E., & Jordan, M. I. (2002) · Nature Neuroscience · doi:10.1038/nn963 · Cited by 3,081
Dynamical Processes on Complex Networks
Barrat, A., Barthélemy, M., & Vespignani, A. (2008) · doi:10.1017/cbo9780511791383 · Cited by 2,704 · cited 7×
“Thus, if ND =N , p(Ê) is an exponential (one-peak) distribution for γ > 2 in (4); if ND= 1, as p(E)∼E−1 in (5), p(Ê) is a uniform distribution.”
BackgroundInfluentialMaster Stability Functions for Synchronized Coupled Systems
Pecora, L. M., & Carroll, T. L. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.2109 · Cited by 2,643
Resilience of the Internet to Random Breakdowns
Cohen, R., Erez, K., ben-Avraham, D., & Havlin, S. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.4626 · Cited by 2,391
Anticipating Critical Transitions
Scheffer, M., Carpenter, S. R., Lenton, T. M., Bascompte, J., Brock, W., Dakos, V., van de Koppel, J., van de Leemput, I. A., Levin, S. A., van Nes, E. H., et al. (2012) · Science · doi:10.1126/science.1225244 · Cited by 2,208
Rugh, W. J. (1992) · Cited by 1,395
Sontag, E. D. (1998) · Texts in Applied Mathematics · doi:10.1007/978-1-4612-0577-7 · Cited by 1,226
Inferring Cellular Networks Using Probabilistic Graphical Models
Friedman, N. (2004) · Science · doi:10.1126/science.1094068 · Cited by 1,202
On pinning synchronization of complex dynamical networks
Yu, W., Chen, G., & Lü, J. (2009) · Automatica · doi:10.1016/j.automatica.2008.07.016 · Cited by 1,016
Coron, J. (2009) · Mathematical surveys and monographs · doi:10.1090/surv/136 · Cited by 854
Controllability of Multi-Agent Systems from a Graph-Theoretic Perspective
Rahmani, A., Ji, M., Mesbahi, M., & Egerstedt, M. (2009) · SIAM Journal on Control and Optimization · doi:10.1137/060674909 · Cited by 767
Complex Networks: Structure, Robustness and Function
(2010) · Cited by 729
Global organization of metabolic fluxes in the bacterium Escherichia coli
Almaas, E., Kovács, B., Vicsek, T., Oltvai, Z. N., & Barabási, A.-L. (2004) · Nature · doi:10.1038/nature02289 · Cited by 709
Self-citationComplex Networks: Structure, Robustness and Function
Cohen, R., & Havlin, S. (2010) · Cambridge University Press eBooks · doi:10.1017/cbo9780511780356 · Cited by 696
How basin stability complements the linear-stability paradigm
Menck, P. J., Heitzig, J., Marwan, N., & Kurths, J. (2013) · Nature Physics · doi:10.1038/nphys2516 · Cited by 617
Controllability Metrics, Limitations and Algorithms for Complex Networks
Pasqualetti, F., Zampieri, S., & Bullo, F. (2014) · IEEE Transactions on Control of Network Systems · doi:10.1109/tcns.2014.2310254 · Cited by 594
Exact controllability of complex networks
Yuan, Z., Zhao, C., Di, Z., Wang, W.-X., & Lai, Y.-C. (2013) · Nature Communications · doi:10.1038/ncomms3447 · Cited by 565
Observability of complex systems
Liu, Y.-Y., Slotine, J.-J., & Barabási, A.-L. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1215508110 · Cited by 516
Self-citationSpectra of random graphs with given expected degrees
Chung, F., Lu, L., & Vu, V. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0937490100 · Cited by 492
On Submodularity and Controllability in Complex Dynamical Networks
Summers, T. H., Cortesi, F. L., & Lygeros, J. (2016) · IEEE Transactions on Control of Network Systems · doi:10.1109/tcns.2015.2453711 · Cited by 482
Spread of (mis)information in social networks
Acemoglu, D., Ozdaglar, A., & ParandehGheibi, A. (2010) · Games and Economic Behavior · doi:10.1016/j.geb.2010.01.005 · Cited by 444
Controllability of complex networks via pinning
Sorrentino, F., di Bernardo, M., Garofalo, F., & Chen, G. (2007) · Physical Review E · doi:10.1103/physreve.75.046103 · Cited by 439
How dead ends undermine power grid stability
Menck, P. J., Heitzig, J., Kurths, J., & Joachim Schellnhuber, H. (2014) · Nature Communications · doi:10.1038/ncomms4969 · Cited by 430
Controlling edge dynamics in complex networks
Nepusz, T., & Vicsek, T. (2012) · Nature Physics · doi:10.1038/nphys2327 · Cited by 430
Controlling Complex Networks: How Much Energy Is Needed?
Yan, G., Ren, J., Lai, Y.-C., Lai, C.-H., & Li, B. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.218703 · Cited by 413
Self-citationLocating the Source of Diffusion in Large-Scale Networks
Pinto, P. C., Thiran, P., & Vetterli, M. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.068702 · Cited by 409
Universality in network dynamics
Barzel, B., & Barabási, A.-L. (2013) · Nature Physics · doi:10.1038/nphys2741 · Cited by 396
Self-citationControl Profiles of Complex Networks
Ruths, J., & Ruths, D. (2014) · Science · doi:10.1126/science.1242063 · Cited by 391
Realistic control of network dynamics
Cornelius, S. P., Kath, W. L., & Motter, A. E. (2013) · Nature Communications · doi:10.1038/ncomms2939 · Cited by 352
Cowan, N. J., Chastain, E. J., Vilhena, D. A., Freudenberg, J. S., & Bergstrom, C. T. (2012) · PLoS ONE · doi:10.1371/journal.pone.0038398 · Cited by 273
Reshuffling scale-free networks: From random to assortative
Xulvi-Brunet, R., & Sokolov, I. M. (2004) · Physical Review E · doi:10.1103/physreve.70.066102 · Cited by 243
Emergence of bimodality in controlling complex networks
Jia, T., Liu, Y.-Y., Csóka, E., Pósfai, M., Slotine, J.-J., & Barabási, A.-L. (2013) · Nature Communications · doi:10.1038/ncomms3002 · Cited by 220
Self-citationControllability Transition and Nonlocality in Network Control
Sun, J., & Motter, A. E. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.208701 · Cited by 192
Observability and Controllability of Nonlinear Networks: The Role of Symmetry
Whalen, A. J., Brennan, S., SAUER, T. D., & Schiff, S. J. (2015) · Physical Review X · doi:10.1103/physrevx.5.011005 · Cited by 171
Network Controllability Is Determined by the Density of Low In-Degree and Out-Degree Nodes
Menichetti, G., Dall’Asta, L., & Bianconi, G. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.078701 · Cited by 160
All Scale-Free Networks Are Sparse
del Genio, C. I., Groß, T., & Bassler, K. E. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.178701 · Cited by 156
In-Vivo Real-Time Control of Protein Expression from Endogenous and Synthetic Gene Networks
Menolascina, F., Fiore, G., Orabona, E., Stefano, L. D., Ferry, M., Hasty, J., di Bernardo, M., & di Bernardo, D. (2014) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1003625 · Cited by 118
Few inputs can reprogram biological networks
Müller, F.-J., & Schuppert, A. (2011) · Nature · doi:10.1038/nature10543 · Cited by 109
Dynamics and control of state-dependent networks for probing genomic organization
Rajapakse, I., Groudine, M. T., & Mesbahi, M. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1113249108 · Cited by 63
Spectral densities of scale-free networks
Kim, D., & Kahng, B. (2007) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2735019 · Cited by 30
Minimal actuator placement with optimal control constraints
Tzoumas, V., Rahimian, M. A., Pappas, G. J., & Jadbabaie, A. (2015) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2015.7171040 · Cited by 29
Cited by
Data based identification and prediction of nonlinear and complex dynamical systems
Wang, W.-X., Lai, Y.-C., & Grebogi, C. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.06.004 · Cited by 299
Metadata
- Authors
- Yan, G., Tsekenis, G., Barzel, B., Slotine, J.-J., Liu, Y.-Y., & Barabási, A.-L.
- Venue
- Nature Physics
- Published
- 2015-08-10
- Volume
- 11
- Issue
- 9
- Pages
- 779-786
- ISSN
- 1745-2473 (ISSN-L)
- 1745-2481
- OpenAlex
- W1791725676
- Cited by
- 279
- References
- 53
- FWCI
- 28.44
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
