Postdoctoral researcher
Carolina Center for Interdisciplinary Applied Mathematics
Department of Mathematics
University of North Carolina-Chapel Hill

 email:   sshai@live.unc.edu
 twitter:  @sarayshai
 web:  http://sshai.web.unc.edu
 office:  Chapman Hall, room 444
 address  1
20 E. Cameron Ave. 
 Chapel Hill
 NC 27599

About me

Hi, welcome to my webpage! I am a postdoc in the Mathematics Department at the University of North Carolina at Chapel Hill
My area of expertise is the cross-disciplinary field known as "network science", which aims at analyzing complex systems, such as human cells in the body and individuals in our society, by describing which components interact with one another. I work with Peter J. Mucha to develop mathematical and computational tools and apply them to data analysis problems arising in a variety of contexts.

I did my undergrad in Mathematics and Computer Science at the Israel Institute of Technology (Technion) and then worked in an Israeli startup called Diligent (which is now part of IBM) offering data "de-duplication" technology (basically, a smart way to identity repeated blocks of data in a huge storage system). Looking for a new challenge, I went back to university to do a PhD in Computer Science. I completed my PhD at the University of St Andrews under the supervision of Simon Dobson. Simon and I discovered our passion for networks together, and it is now a main part of the research of both of us.

Research Interests 

1. Data analysis and visualization using networks
A main part of my research focuses on the analysis of complex network data like arising in the social, biological and physical sciences. I believe that looking at data through a “network lens” provides us with useful perspectives on diverse problems, and I am constantly looking for new datasets on which I can apply my “network machinery” to solve real-world problems and to inspire the development of new methodologies.
    • Network science applications in cancer care researchwe have recently submitted a manuscript to the Journal of Clinical Oncology on the analysis of care-coordination networks between physicians that provided care to patients diagnosed with colorectal cancer.
    • Network Science applications in urban planning and engineering: check out our recent work on the analysis of the coupling between the street network and the subway in the two large metropolitan areas of London and New York City.
2. Analytical and computational frameworks for modeling complex systems
One of the ultimate goals of network science is to understand the implications of emerging non-trivial structures to the behavior and functionality of networked dynamical systems, and how these in turn affect the structural evolution of the network. This was the main line of research that I pursued during my graduate work in Computer Science and is still an active direction that I am very interested in.
    • Epidemic spreading in adaptive networks: I developed an analytical framework (based on numerical analysis of nonlinear ODEs) supported by numerical simulation (which is a C++ implementation of the Gillespie algorithm) to study SIS model in adaptive networks.
3. Network robustness using percolation theory
I am interested in "realistic percolation models" to study the response of networks (e.g. critical infrastructures) to failures and attacks. 
  • Percolation of modular and interdependent networks: we developed the analytical framework to study the resilience of modular organization of interconnected and interdependent systems showing that interdependent infrastructures can be susceptible to failure or attacks causing the system to break into separate modules.
  • Modular networks under localized attacks: I am currently working with Gaogao Dong and Shlomo Havlin to extend this work to localized attacks, where a group of neighboring nodes are attacked and fail.
4. Community (cluster) detection and other structures 
Community structure is thought to be one of the main organizing principles in most complex networks. A quantitative description of the grouping patterns of entities in a system, such as social communities, is often very hard to find and requires powerful mathematical tools  and large-scale data manipulation techniques.
  • Inferring stochastic block models in multilayer networks: check out our new generative model for community structure in multilayer networks demonstrated microbial interaction networks extracted from the Human Microbiome Project.
  • Detectability of community structure in multilayer networks: check out our new theory based on random matrices (RMT) to find a phase transition in the detectability of structures in multilayer network.
5. Multilayer networks
Multilayer networks is a mathematical framework that incorporates "multilayer features" (e.g. multiple subsystems and layers of connectivity) into traditional network theory. I am interesting in extending exiting network methods to support time-dependence among interactions, consider interactions among arbitrary numbers of entities, and multiple modes of interactions that take place simultaneously. I would like to better understand the challenges that practitioners face when coming to analyze different types of time-varying, multi-relational and multi-scale datasets.

6. Phase transitions and finite size scaling
I am interested in network formation processes such as road expansion and its relationship with land use. In a recent work, we used finite-size scaling analysis to show that road length distributions within croplands are the same as urban roads up to a proper rescaling, suggesting simple and universal mechanisms that regulate urban and cropland road expansion at global scale.

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