My primary research interest is the modeling, analysis, and control of dynamical processes and strategic interactions in complex interconnected systems, with applications in complex large socio-technical networks, such as social, biological and robotic networks
. Since critical societal functions are increasingly dependent on these complex networks, it is important to acquire a deeper understanding of the relationship between the structure and the dynamics of these systems.



Data-Driven Analysis and Control of Complex Networks

During the last decade, the complex structure of many large- scale networked systems has attracted the attention of the scientific community. The availability of massive databases describing these networks allows researchers to explore their structural properties with great detail. Statistical analysis of empirical data has unveiled the existence of multiple common patterns in a large variety of network properties, such as power-law degree distributions, or the small-world phenomenon. 

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Spectral Analysis of Complex Socio-Technical Systems

The main aim of our work is to develop a framework, based on spectral and algebraic graph theory and convex optimization, to compute with low computational overhead global spectral properties of a network from its local structural properties. In particular, we derive optimal bounds and estimators of spectral properties of interest from structural information. Our results are useful to unveil the set of structural properties that have the highest impact in the eigenvalue spectrum of a network. In particular, in the case of online social networks, we find that the correlation between the distribution of degrees and triangles in the network plays a key role in the spectral radius.


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Optimal Resource Allocation for Epidemic Control

Understanding spreading processes in complex networks and designing control strategies to contain them are relevant problems in many different settings, such as epidemiology and public health. The aim of our research is to control spreading processes in networks by distributing protection resources throughout the nodes. In our study, we consider two types of containment resources: (iPreventive resources able to protect (or ‘immunize’) nodes against the spreading (such as vaccines in a viral infection process), and (iicorrective resources able to neutralize the spreading after it has reached a node, such as antidotes in a viral infection. In our framework, we associate a cost to these resources and study the problem of finding the cost-optimal distribution of resources throughout the network to contain the spreading.

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Resilience of Critical Networked Infrastructure


Multi-agent networked systems are used to model a wide variety of systems, from robotic networks, to power systems, to biological networks. The emergent dynamics of a network of dynamic agents can be strongly affected by the presence of network failures. The main of our research in this direction is to find computationally efficient methods to study the effects of link or node failures on networked infrastructure. We have provided several methods for detection and isolation of failures in network of dynamic agents, based on the presence of discontinuities in the derivatives of the output responses of a subset of nodes.


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Network Identification from Dynamic Behavior

The reconstruction of networks of dynamical systems is an important task in many realms of science and engineering, including biology, physics and finance. The aim of our research is to propose several algorithms to reconstruct the structure of a directed dynamic networks. We have proposed an algorithm to find the Boolean structure of the unknown topology based on the analysis of power spectral properties of the network response when the inputs are wide-sense stationary (WSS) processes of unknown power spectral density (PSD). Apart from recovering the Boolean structure of the network, we have also proposed an algorithm to recover the exact structure of the network (including edge weights) when an eigenvalue-eigenvector pair of the connectivity matrix is known.


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CURRENT GROUP MEMBERS:

Graduate Students:
  • Cassiano Becker (Ph.D. candidate 2013-)
  • Ximing Chen (Ph.D. candidate 2013-)
  • Mahyar Fazlyab (Ph.D. candidate 2013-)
  • Zhen Xiang (Ph.D. candidate 2014-)
Postdoctoral Researcher:
  • Masaki Ogura
Undergraduate Student:
  • Ishaan Nerurkar


PAST MEMBERS:

Graduate Students:
  • Zhengwei Wu (M.Sc. 2012-2013). Thesis: "Spectral Analysis of Spreading Processes in Networks"
  • David Sun (M.Sc. 2012-2015). Thesis: "Predicting Mean-Field Theory Accuracy on Real-World Networks"