Synchronization,  Flow, and Opinion Dynamics in Complex Information and Social Networks


Recent Papers:
"Threshold-limited spreading in social networks with multiple initiators",
P. Singh, S. Sreenivasan, B.K. Szymanski, and G. Korniss, arXiv:1304.7034 (2013).

"Minimum Dominating Sets in Scale-Free Network Ensembles",
F. Molnar Jr., S. Sreenivasan, B.K. Szymanski, and G. Korniss, Scientific Reports 3, 1736 (2013).

"Extraordinary Sex Ratios: Cultural Effects on Ecological Consequences",
F. Molnar Jr., T. Caraco, and G. Korniss, PLoS One 7(8): e43364 (2012).

"Evolution of Opinions on Social Networks in the Presence of competing Committed Groups",
J. Xie, J. Emenheiser, M. Kirby, S. Sreenivasan, B.K. Szymanski, G. Korniss, PLoS One 7(3): e33215 (2012).

"Social consensus through the influence of committed minorities",
J. Xie, S. Sreenivasan, G. Korniss, W. Zhang, C. Lim, and B. K. Szymanski, Physical Review E 84, 011130 (2011).
            News:    Science News Focus, "The power of true believers", by Adrian Cho
                           RPI News, "Minority Rules: Scientists Discover Tipping Point for the Spread of Ideas", by Gabrielle DeMarco
                           Discovery News, "Minority Rules: Scientists Find the Tipping Point", by Emily Sohn    
                           Freakonomics, "Minority Rules: Why 10 Percent is All You Need", by Matthew Philips
                          
Communications of the ACM, "Researchers Find Tipping Point to Sway Public Opinion", by Paul Hyman

Current graduate students: Ferenc Molnar, Pramesh Singh, Panagiotis Karampourniotis
Current postdocs: Sameet Sreenivasan, Noemi Derzsy
Current undergraduate students: David Galehouse, Matthew Kirby
Former graduate students:
David Hunt, Qiming Lu, Hasan GucluBalazs Kozma
Former postdocs:
Andrea Asztalos
Former undergraduate students: Jefffrey Emenheiser, Adam Freese
Collaborators:
Boleslaw Szymanski (Rensselaer), Zoltan Toroczkai (Notre Dame), Chjan Lim (Rensselaer)


Optimizing Synchronization, Flow, and Robustness in Complex Networks

One of the major developments of the last two decades has been the ever-increasing interconnectivity of a broad class of information networks, including physical and data network types arising in telecommunication, transportation and energy infrastructures. This interconnectivity has led to immense temporal and spatial complexity in modern networks and a critical need for basic mathematical theory and statistical modeling of complex interacting networks.

As the number of nodes in the underlying these networks increases to hundreds of thousands, fundamental questions about the stability and vulnerability of these systems (ultimately governed by the fluctuations of the dynamic processes in the respective underlying networks) must be addressed. We address precisely these issues from a fundamental network science viewpoint. In this research project, we develop and employ a unified approach and framework connecting the concepts of flow and fluctuations in network dynamics, allowing us to investigate and analyze fundamental transport, load-balancing, and synchronization problems in complex networks on a common footing. Our research shall provide tools and methods to optimize the allocation of limited network resources in order to improve the quality of service and to minimize the possibility of global network failures in both piece-time and hostile environments.

Specifically, complex biological, social, and technological systems can be often modeled by weighted networks. The network topology, together with the distribution of available link or node capacity (represented by weights) and subject to cost constraints, strongly affect the dynamics or performance of the networks. In this project, we investigate optimization in fundamental synchronization and flow problems where the weights are proportional to the degrees of the nodes connected by the edge. In the context of synchronization, these weights represent the allocation of limited resources (coupling strength), while in the associated random walk and current flow problems, they control the extent of hub avoidance, relevant in routing and search.

This research has been supported in part by DTRA,  NSF-DMR, and ARL-NS-CTA
The views and conclusions contained in this material are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Department of the Defense, Defense Threat Reduction Agency, Army Research Laboratory, National Science Foundation, or the U.S. Government.

Related publications:

"Network Synchronization and Coordination in a Noisy Environment with Time Delays'',
D. Hunt, B.K. Szymanski, and G. Korniss, Physical Review E 86, 056114 (2012).

"Distributed flow optimization and cascading effects in weighted complex networks'',
A. Asztalos, S. Sreenivasan, B.K. Szymanski, and G. Korniss, European Physical Journal B 85, 288 (2012).

"The Impact of Competing Time Delays in Coupled Stochastic Systems”,
D. Hunt, G. Korniss, and B.K. Szymanski, Physics Letters A 375, 880—885 (2011).


"Network Synchronization in a Noisy Environment with Time Delays: Fundamental Limits and Trade-Offs”,
D. Hunt, G. Korniss, and B.K. Szymanski, Phys. Rev. Lett. 105, 068701 (2010) (Editors’ Suggestion).

     News:    Physics Synopsis, "Don’t micromanage when communication is delayed", by David Voss                      
                   Rensselaer News Release, by Gabrielle DeMarco
                   ScienceDaily
                   PhysOrg

"Optimizing Synchronization, Flow, and Robustness in Weighted Complex Networks",
G. Korniss, R. Huang, S. Sreenivasan, and B.K. Szymanski, iin Handbook of Optimization in Complex Networks, edited by M.T. Thai and P. Pardalos,
Springer Optimization and Its Applications Vol. 58, Part 1, (Springer, New York, 2012) pp. 61-96 [invited review/chapter to an edited compilation (peer-reviewed)];

"Interplay between Structural Randomness, Composite Disorder, and Electrical Response: Resonances and Transient Delays in Complex Impedance Networks",
R. Huang, G. Korniss, and S.K. Nayak, Physical Review E 80, 045101 (Rapid Communication) (2009).

"Synchronization in Weighted Uncorrelated Complex Networks in a Noisy Environment: Optimization and Connections with Transport Efficiency'',
G. Korniss, .Physical Review E 75, 051121  (2007).

"Extreme Fluctuations in Noisy Task-Completion Landscapes on Scale-Free Networks",
H. Guclu, G. Korniss, Z. Toroczkai, Chaos 17, 026104 (2007).

"Diffusion Processes on Small-World Networks with Distance-Dependent Random Links'',
B. Kozma, M.B. Hastings, and G. Korniss, Journal of Statistical Mechanics: Theory and Experiment, P08014 (2007).

"Threshold-Controlled Global Cascading in Wireless Sensor Networks'',
Q. Lu, G. Korniss, and B.K. Szymanski, in Proceedings of the Third International Conference of Networked Sensing Systems (INSS 2006) (Transducer Research Foundation, San Diego, 2006) pp.164-171.

"Scaling in Small-World Resistor Networks'',
G. Korniss, M.B. Hastings, K.E. Bassler, M.J. Berryman, B. Kozma, and D. Abbott, Phyiscs Letters A 350, 324 (2006).

"Synchronization Landscapes in Small-World-Connected Computer Networks'',
H. Guclu, G. Korniss, M.A. Novotny, Z. Toroczkai, and Z Racz, Physical Review E 73, 066115  (2006). 

"Diffusion Processes on Power-Law Small-World Networks'',
B. Kozma, M.B. Hastings, and G. Korniss, Physical Review Letters 95, 018701 (2005).

"Extreme Fluctuations in Small-World-Coupled Autonomous Systems with Relaxational Dynamics",
H. Guclu and G. Korniss,  Fluctuation and Noise Letters  5, L43 (2005).

"Extreme Fluctuations in Small-Worlds with Relaxational Dynamics'',
H. Guclu and G. Korniss,  Physycal Review E  69, 065104(R) (2004). 

"Suppressing Roughness of Virtual Times in Parallel Discrete-Event Simulations'',
G. Korniss, M.A. Novotny, H. Guclu, Z. Toroczkai, and P.A. Rikvold, Science299, 677 (2003).
     News:    Science Perspective, "Rough Times Ahead", by Scott Kirkpatrick,
                   The New York Times,
                   New Scientist,
                   Technology Research News

"Roughness Scaling for Edwards-Wilkinson Relaxation in Small-World Networks'',
B. Kozma, M.B. Hastings, and G. Korniss, Physical Review Letters 92, 108701 (2004). 

"Small-World Synchronized Computing Networks for Scalable Parallel Discrete-Event Simulations'',
H. Guclu, G. Korniss, Z.  Toroczkai, and  M.A. Novotny, in Complex Networks, edited by E. Ben-Naim, H. Frauenfelder, and Z. Toroczkai, Lecture Notes in Physics Vol. 650 (Springer-Verlag, Berlin, 2004) 255--275. 

"Stochastic Growth in a Small World'',
B. Kozma and G. Korniss, in Computer Simulation Studies in Condensed Matter Physics XVI,  edited by D.P. Landau, S.P. Lewis, and H.-B. Schüttler, Springer Proceedings in Physics Vol. 95 (Springer-Verlag, Berlin, 2004), pp. 29-33. 

"From Massively Parallel Algorithms and Fluctuating Time Horizons to Non-equilibrium Surface Growth'',
G. Korniss, Z. Toroczkai, M.A. Novotny,  and P.A. Rikvold, Phys. Rev. Lett. 84, 1351 (2000).





Social Dynamics, Opinion Spreading, and Influencing in Social  Networks

The current state of knowledge about the interdependency between structure, dynamics, and behaviors of large infrastructure, communication, and social networks is only at the preliminary stage. In this project, we investigate real data projected out from empirical social networks, to develop methodologies and techniques for extracting relevant information and behavioral patterns from the underlying social network. With the availability and accessibility of vast amount of data in recent years, our project will not only gain fundamental knowledge, from a network science viewpoint, but also will create methodologies and techniques that could be applied to address strategic and urgent needs aligned with national priorities for network research.

For example, fighting irregular warfare (IW) is a complex and ambiguous inherently social phenomenon: “insurgency and counterinsurgency operations focusing on the control or influence of populations, not on the control of an adversary’s forces or territory” (IW, Joint Operating Concept, 2007). To help operations in such an environment, we will develop and employ individual-based models to investigate social influencing and associated strategies in social networks. Our methods and models for community detection, community stability, and social influencing will be applicable to data sets of different types and spanning all scales, including those collected by the military.

Mainstream ideology does not freely spread into an “ideological vacuum” as standard models for social influencing assume, but instead, is severely inhibited by existing adversary or extremist opinion clusters, strengthened by the collective identity of the individuals forming these extremist clusters. Therefore we develop and employ models for social dynamics with multiple (potentially coexisting) opinions.

Investigating social dynamics and diffusion of opinions on empirical social graphs on graphs with multiple co-existing opinion clusters/communities, we will develop both heuristic and rigorous algorithmic methods to find influential nodes and to disintegrate or control adversary clusters in ideological warfare. We will systematically investigate the “influential hypothesis” in military-relevant scenarios.

Over the past few years, we and the other network science-researchers have been shifting the focus of network research from structure to dynamics (or function) in real-life networks. To accelerate this transition, in this research we study social dynamics on large-scale empirical social networks from a fundamental viewpoint. Our investigations will focus on the emergence and stability of communities in social graphs and the elimination of such communities by introducing agents committed to stabilizing society or by exerting external/media influence. 


This research has been supported in part by ONR, ARL NS-CTA, and ARO

The views and conclusions contained in this material are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Office of Naval Research, Army Research Laboratory or the U.S. Government.


Related publications:

"Threshold-limited spreading in social networks with multiple initiators",
P. Singh, S. Sreenivasan, B.K. Szymanski, and G. Korniss, arXiv:1304.7034 (2013).

"Minimum Dominating Sets in Scale-Free Network Ensembles",
F. Molnar Jr., S. Sreenivasan, B.K. Szymanski, and G. Korniss, Scientific Reports 3, 1736 (2013).

"Evolution of opinions on social networks in the presence of competing committed groups'',
J. Xie, J. Emenheiser, M. Kirby, S. Sreenivasan, B.K. Szymanski, G. Korniss, PLoS One 7(3): e33215 (2012).

"Social Consensus through the Influence of Commited Minorities",
J. Xie, S. Sreenivasan, G. Korniss, W. Zhang, C. Lim, B. K. Szymanski, Physical Review E 84, 011130 (2011).
     News:    Science News Focus, "The power of true believers", by Adrian Cho
                   RPI News, "Minority Rules: Scientists Discover Tipping Point for the Spread of Ideas", by Gabrielle DeMarco
                   Discovery News, "Minority Rules: Scientists Find the Tipping Point", by Emily Sohn    
                   Freakonomics, "Minority Rules: Why 10 Percent is All You Need", by Matthew Philips
                  
Communications of the ACM, "Researchers Find Tipping Point to Sway Public Opinion", by Paul Hyman    

"Social Influencing and Associated Random Walk Models: Asymptotic Consensus Times on the Complete Graph",
W. Zhang, C. Lim, S. Sreenivasan, J. Xie, B.K. Szymanski, G. Korniss, Chaos  21, 025115 (2011).

"The Naming Game in Social Networks: Community Formation and Consensus Engineering",
Q. Lu, G. Korniss, and B.K. Szymanski, Journal of Economic Interaction and Coordination, 4, 221—235 (2009).

"Naming Games in Two-Dimensional and Small-World-Connected Random Geometric Networks",
Qiming Lu, G. Korniss, and B.K. Szymanski, Physical Review E 77, 016111 (2008).

"Naming Games in Spatially-Embedded Random Networks'',
Qiming Lu, B.K. Szymanski, and G. Korniss, in Proceedings of the 2006 American Association for Artificial Intelligence Fall Symposium Series, Interaction and Emergent Phenomena in Societies of Agents (AAAI Press, Menlo Park, CA, 2006) pp. 148—155.

"Threshold-Controlled Global Cascading in Wireless Sensor Networks'',
Q. Lu, G. Korniss, and B.K. Szymanski, in Proceedings of the Third International Conference of Networked Sensing Systems (INSS 2006) (Transducer Research

"Competition-Driven Network Dynamics: Emergence of a scale-free Leadership Structure and Collective Efficiency'',
M. Anghel, Z. Toroczkai, K.E. Bassler, and G. Korniss, Physical Review Letters 92, 058701 (2004).  
     News:     Technology Research News





Biological Invasion in Multi-Species Population Dynamics

Current graduate students: Ferenc Molnar
Current undergraduate students: Christina Caragine
Former graduate students: Lauren O'Malley, Balazs Kozma
Former undergraduate students: Joseph Yasi, James Basham, Matt Nagy
Collaborators: Thomas Caraco (SUNY Albany), Andy Allstadt (University of Virginia),  Zoltan Racz (Eotvos University, Budapest)


Spatial Ecologies under Temporal Variation

Better understanding the processes that allow one species to invade the habitat of another will help answer fundamental questions in ecology. Just as importantly, understanding the processes of biological invasion to the point of prediction should enhance our capacity to respond effectively to invading species that impose economic problems on agriculture and threaten native biodiversity across North America.

Spatially structured biotic interactions generate demographic variation at the level of individuals; this variation can govern ecological invasion and competitive coexistence.  Temporal abiotic variation can directly modulate demographic rates, exerting further effects on competitors’ dynamics. Theory for individual-based spatial processes has remained distinct from theory for population dynamics in temporally variable environments. In this project, we study the interplay between discrete, stochastic spatial interactions and temporally varying environmental forces, with a focus on competitive invasion. To advance understanding of the multi-scale ecological complexity predicted by the theory, and to identify novel predictions, we apply concepts of statistical physics.

When a superior competitor’s invades an inferior resident species in a constant environment, and introduction occurs only rarely, spatial competition will be driven by local dispersal and mortality, so that we can apply the physical theory for nucleation of spatial systems. Low introduction rates and small environments may permit only single-cluster invasion by the superior competitor. Increasing the introduction rate or system size allows multi-cluster invasive growth. In both regimes, the invasion dynamics exhibits strong spatial correlation and stochasticity. Consequently, standard deterministic approaches fail to predict the behavior of the invasion process. However, for multi-cluster invasion, the time to competitive exclusion is approximated accurately by Avrami’s law, an analytical framework of nucleation theory. The Avrami result links individual-level propagation and mortality rates to community-level features of spatial invasion, a major research objective in ecology. We are developing an integrative theory of stochastic spatial growth; judicious parameter choice should let the theory address data on invasive fronts ranging from the within-habitat to the biogeographic scale. To study invasion in two-dimensional environments, we analyze stochastic “roughening” of advancing fronts; several results apply to a broad class of spatial-growth models. Analysis has yielded novel predictions; habitat size (length of the front) should affect both invasion velocity and the expected location of the maximal invasive incursion beyond the front’s mean position.

Most importantly, we are developing a new theory for spatial competition in a time-varying environment. If each species is alternately favored, single-cluster invasion may admit competitive coexistence via stochastic resonance, indicating a matching of the (stochastic) spatial-dynamic and (periodic) environmental time scales. The multi-cluster mode may exhibit different limit cycles and long-term coexistence through large-scale clustering of each species, depending on comparison of the population dynamics’ characteristic time scale and the period-length of environmental variation.

This research develops new approaches to understanding stochastic, nonlinear effects in ecological systems and will lead to insights concerning the way individual-based ecological interactions may amplify or attenuate environmental variability.


This research has been supported in part by NSF-DEB (QEIB)
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Related publications:

"Extraordinary Sex Ratios: Cultural Effects on Ecological Consequences'',
F. Molnar Jr., T. Caraco, and G. Korniss, PLoS One 7(8): e43364 (2012).

"Interference Competition and Invasion: Spatial Structure, Novel Weapons and Resistance Zones'',
A. Allstadt, Thomas Caraco, F. Molnár Jr., G. Korniss, Journal of Theoretical Biology 306, 46 (2012).

"Spatial Competition and the Dynamics of Rarity in a Temporally Varying Environment",
L. O’Malley, G. Korniss, S.S. Praveen Mungara, and T.Caraco, Evolutionary Ecology Research 12, 279-305 (2010).

"Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models",
L. O’Malley, G. Korniss, and T. Caraco, Bulletin of Mathematical Biology 71, 1160-1188 (2009).

"Preemptive Spatial Competition Under a Reproduction-Mortality Constraint",
Andrew Allstadt, Thomas Caraco, and G. Korniss, Journal of Theoretical Biology, 258, 537—549 (2009).

"Ecological Invasion: Spatial Clustering and the Critical Radius",
A. Allstadt, T. Caraco, and G. Korniss, Evolutionary Ecology Research 9, 375 (2007).

"Fisher Waves and Front Roughening in a Two-Species Invasion Model with Preemptive Competition",
L. O'Malley, B. Kozma, G. Korniss, Z. Racz, T. Caraco, Physical Review E 74, 041116 (2006).

"Fisher Waves and the Velocity of Front Propagation in a Two-Species Invasion Model with Preemptive Competition",
L. O'Malley, B. Kozma, G. Korniss, Z. Racz, T. Caraco, in Computer Simulation Studies in Condensed Matter Physics XIX,  edited by D.P. Landau, S.P. Lewis, and H.-B. Schüttler, Springer Proceedings in Physics Vol. 123 (Springer, Berlin, 2009), pp. 73-78.

"Invasive advance of an advantageous mutation: nucleation theory",
Lauren O'Malley, James Basham, Joseph A. Yasi, G. Korniss, Andrew Allstadt, Tom Caraco, Theoretical Population Biology 70, 464-478 (2006).

"Spatial Dynamics of Invasion: The Geometry of Introduced Species'' ,
G. Korniss and T. Caraco, Journal of Theoretical Biology 233, 137--150 (2005).

"Nucleation and Global Time Scales in Ecological Invasion under Preemptive Competition'',
L. O'Malley, A. Allstadt, G. Korniss, T. Caraco, in Fluctuations and Noise in Biological, Biophysical, and Biomedical Systems III, edited by N.G. Stocks, D. Abbott, and R.P. Morse, Proceedings of SPIE Vol. 5841 (SPIE, Bellingham, WA, 2005), pp. 117-124.

"Invasive Allele Spread under Preemptive Competititon" ,
J.A. Yasi, G. Korniss and T. Caraco, in Computer Simulation Studies in Condensed Matter Physics XVIII,  edited by D.P. Landau, S.P. Lewis, and H.-B. Schüttler, Springer Proceedings in Physics Vol. 105 (Springer, Berlin, 2006), pp. 165-169.