New Approach can Control Large, Nonlinear Complex Networks
Nonlinearity is a hallmark of complex systems, but has generally been regarded as an obstacle to controlling their behavior. Our new Nature Communications paper shows how nonlinear dynamics can be harnessed to control a network and drive it to desired states. The new approach can be used to identify control interventions in a range of large complex networks, from cells to power grids. In a related publication in Nature's Protocol Exchange we present in detail our core algorithm for the control of complex networks and other nonlinear, high-dimensional dynamical systems. The algorithm is highly scalable, with the computational cost scaling as the number of dynamical variables to the power 2.5. This protocol includes ready-to-use software that can be applied to identify eligible control interventions in a general system described by coupled ordinary differential equations, whose specific form can be specified by the user.
- Movie: Animated step-by-step construction of control interventions in simple examples.
Network Frontier Workshop 2013
The Network Frontier Workshop 2013 is a three-day event highlighting leading-edge research on complex networks. The workshop will be held at Northwestern University from December 4th through 6th, 2013.
For more information, please visit the workshop website.
Synchronization and Observability in Power-Grid Networks
A key requirement for the functioning of a power-grid network is that its power generators remain synchronized. In our recent Nature Physics paper, we derive a condition under which the desired synchronous state of a power grid is stable, and use this condition to identify tunable parameters of the generators that can affect synchronization. A complementary problem concerns the comprehensive determination of the state of the system from limited measurements. In our most recent PRL paper, we show that this problem leads to a new type of percolation transition — a network observability transition. We also demonstrate a dual role of the network's community structure, which both facilitates optimal measurement placement and renders the networks substantially more sensitive to "observability attacks." These findings may be used to optimize stability and robustness and help devise new control schemes, contributing to the development of smart, self-healing power grids.
Visual Analytics Software to Resolve Network Structure
The visual pattern recognition ability of humans combined with the high processing speed of computers leads to a visual analytics approach for discovering network structure (including but not limited to network communities). The approach resolves the internal structure of complex networks by organizing the nodes into groups that share something in common, even if we do not know a priori what that thing is. At first this may sound a little like the Deep Thought's "answer to the ultimate question of life, the universe, and everything" in Douglas Adams' fiction comedy series, except that in this case we can actually identify the question itself. The core concept was introduced in our Scientific Reports paper and has been used to create a Matlab-based Software.
A first-generation version of the software is available here and a version with full functionality will be available soon.
This is of course only the very tip of the iceberg. We are currently engaged in developing similar exploratory approaches that can also systematically account for dynamical behavior.
For another interesting exploratory approach, we recommend the Newman & Leicht's 2007 PNAS paper.
Mechanical Networks and Negative Compressibility Materials
When tensioned, ordinary materials expand along the direction of the applied force. In our recent Nature Materials paper, we explore network concepts to design metamaterials exhibiting negative compressibility transitions, during which a material undergoes contraction when tensioned (or expansion when pressured). Continuous contraction of a material in the same direction of an applied tension is inherently unstable. The conceptually similar effect we demonstrate can be achieved, however, through destabilizations of (meta)stable equilibria of the constituents. These destabilizations give rise to a stress-induced solid-solid phase transition associated with a twisted hysteresis curve for the stress-strain relationship. We suggest that the proposed materials could be useful for the design of actuators, force amplifiers, micromechanical controls, and protective devices.
- Movie: Simulated response of the material to uniform, diagonal, pinched, and splayed stress profiles.
S.P. Cornelius, W.L. Kath, and A.E. Motter,
Realistic control of network dynamics,
Nature Communications 4, 1942 (2013).
arXiv:1307.0015v1 - doi:10.1038/ncomms2939 - PDF - Supplementary Information - Movie
Nontechnical Overview Article
Z.G. Nicolaou and A.E. Motter,
Mechanical metamaterials with negative compressibility transitions,
Nature Materials 11, 608 (2012).
arXiv:1207.2185 - doi:10.1038/nmat3331 - Supplementary Information - Movie
Nontechnical Overview Article
S.P. Cornelius, J.S. Lee, and A.E. Motter,
Dispensability of Escherichia coli's latent pathways,
Proc. Natl. Acad. Sci. USA 108, 3124 (2011).
arXiv:1103.5176v1 - doi:10.1073/pnas.1009772108 - Supplementary Information
B. Ravoori, A.B. Cohen, J. Sun, A.E. Motter, T.E. Murphy, and R. Roy,
Robustness of optimal synchronization in real networks,
Phys. Rev. Lett. 107, 034102 (2011).
arXiv:1106.3994v1 - doi:10.1103/PhysRevLett.107.034102 - Supplementary Information
S. Sahasrabudhe and A.E. Motter,
Rescuing ecosystems from extinction cascades through compensatory perturbations,
Nature Communications 2, 170 (2011).
arXiv:1103.1653v1 - doi:10.1038/ncomms1163 - PDF - Supplementary Information
Prof. Motter has postdoctoral positions open in the broad area of complex systems and networks. Applications for research faculty positions may also be considered. To apply, please send your CV, a brief statement of research interests, and the contact information of at least two references to Dr. Luciana Zanella. Applications received by November 1, 2013 will receive full consideration.
Featured projects on the control of complex systems and networks.
August 2013: Joo Sang Lee receives Baxter Young Investigator Award.
June 2013: Adilson E. Motter is awarded the Erdös-Rényi Prize in Network Science.
March 2013: Sascha Herrmann is awarded NSF Graduate Research Fellowship.
December 2012: Daniel Wells receives Chicago Biomedical Consortium (CBC) Scholar Award.
June 2012: Joo Sang Lee is awarded a PSOC Young Investigators Grant.
Tiny Trouble Spots can Fix Complex Networks
Futurity (July 9, 2013)
How Network Monitoring Could be Like Fishing
Slashdot (June 28, 2013)
Keeping Networks Under Control
NU Press Release (June 27, 2013)
Stabilizing the Electric Grid by
Keeping Generators in Sync
Ars Technica (March 13, 2013)
Niche as a Determinant of Word
Fate in Online Groups
Replicated Typo (October 3, 2012)
NU Press Release (May 23, 2012)
Model Could Help Predict and
Prevent Future Extinctions
NSF (January 25, 2011)