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. Network Image 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

Net Frontier 2013 Image

The Network Frontier Workshop 2013 is a three-day event highlighting leading-edge research on complex networks. The workshop was held at Northwestern University from December 4th through 6th, 2013.

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Selected presentation slides of the workshop.

Synchronization and Observability in Power-Grid Networks

Power Grid Image

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.

P&A Complex Systems Seminars

Seminars are held at the last Thursday of each month at 2:00 PM in Tech F160, unless otherwise noted.

Visual Analytics Software to Resolve Network Structure

Grouping Network Nodes Image

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 bit 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.

Mechanical Networks and Negative Compressibility Materials

Illustration of negative compressibility cube

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.

Recent Publications

A.E. Motter, M. Gruiz, G. Károlyi, and T. Tél,
Doubly transient chaos: Generic form of chaos in autonomous dissipative systems,
Phys. Rev. Lett. 111, 194101 (2013).
arXiv:1310.4209 - doi:10.1103/PhysRevLett.111.194101 - Synopsis

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

S.P. Cornelius and A.E. Motter,
NECO - A scalable algorithm for NEtwork COntrol,
Protocol Exchange (2013), doi:10.1038/protex.2013.063.
arXiv:1307.2582 - doi:10.1038/protex.2013.063 - Source Codes

J. Sun and A.E. Motter,
Controllability transition and nonlocality in network control,
Phys. Rev. Lett. 110, 208701 (2013).
arXiv:1305.5848 - doi:10.1103/PhysRevLett.110.208701

A.E. Motter, S.A. Myers, M. Anghel, and T. Nishikawa,
Spontaneous synchrony in power-grid networks,
Nature Physics 9, 191 (2013).
arXiv:1302.1914 - doi:10.1038/nphys2535 - Supplementary Information

Y. Yang, J. Wang, and A. E. Motter,
Network observability transitions,
Phys. Rev. Lett. 109, 258701 (2012).
arXiv:1301.5916 - doi:10.1103/PhysRevLett.109.258701 - Supplementary Information

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

Positions Available

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.

Network Control

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Featured projects on the control of complex systems and networks.

Group News

November 2013: Motter and Campbell's article Chaos at Fifty is translated into French by Pour la Science.

September 2013: Adilson E. Motter is elected APS Fellow.

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: Motter and Albert's paper was the most read subscription-only Physics Today item in 2012.

December 2012: Daniel Wells receives Chicago Biomedical Consortium (CBC) Scholar Award.

Selected Press

New Scientist cover

When not to Tackle Problems Head-on
New Scientist (January 18, 2014) - cover story
http://..Preview http://..Full Article

Chaos Reigns in Unexpected Places
Physics World (November 20, 2013)
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Upgrading the US Grid - Building a Smart Self-Healing Grid
Power Technology (September 23, 2013)
http://...

Tiny Trouble Spots can Fix Complex Networks
Futurity (July 9, 2013)
http://...

How Network Monitoring Could be Like Fishing
Slashdot (June 28, 2013)
http://...

Keeping Networks Under Control
NU Press Release (June 27, 2013)
http://...

Stabilizing the Electric Grid by
Keeping Generators in Sync
Ars Technica (March 13, 2013)
http://...

Mystifying Materials
NU Press Release (May 23, 2012)
http://...

 
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