Active research areas
Epidemic modeling and control
Epidemics are one of the greatest public health challenges of the 21st century. We now have more data than ever before that we can leverage in designing dynamic interventions. This has required led to much interest in designing efficient scalable control algorithms that both solve mathematical problems and provide broad parameter-independent policy insights.
On the other hand, the engineering community has had much to learn from epidemiology and mathematical biology in recent years, e.g., epidemic models have been developed that neatly capture problems in cyber-security and data transfer.
My main contributions during my PhD were to provide a synthesis of ways information about heterogeneities within the affected population and the epidemic process could be used in new ways to design better
dynamic control policies that exploited. I used optimal control theory to design optimal containment and spreading policies for heterogeneous biological, malware, and data epidemics, and showed how derived structures can simplify difficult non-convex optimizations and provide easily implementible distributed policies.
Social influence maximization
Social influence can lead to changes in behavior, choices, and beliefs. Understanding the mechanisms of influence spread is important in effectively targetting interventions, such as public health messages, and designing incentives to aid the spread of desirable actions, such as ethical behavior in a company.
My main contribution has been in delineating the effects of information availability and timing on optimal influence policies.
I have examined optimal seeding strategies under partial network visibility, optimal budget allocation across time for an electoral campaign (including the development of a new centrality measure), the effect of incentives and whistleblowing policies on ethical behavior within a company, and the effect of social comparison and group norms on social group stability.
Optimal control and dynamic programming
I also have a methodological interest in deriving optimal control structures that simplify computations in difficult non-convex optimal control problems.
My main contributions here have been in showing that vectors of bang-bang policies with a limited number of switches are optimal for a wide variety of quadratic ODE differential equations (the mean-field regime), proving further timing structures to simplify direct methods, and integrating rigorous descent methods into practical solvers to speed up the computation of switching times.
Prior work
Information dissemination and monitoring in ad hoc networks
Efficient monitoring and routing of data in modern networks with no fixed infrastructure is complicated by their distributed nature and energy constraints. However, epidemic-like spreading processes can be used to facilitate communication in uncertain environments, while novel distributed algorithms have been developed to monitor such communications and to aggregate relevant information.
My main contribution in these fields has been to integrate the differing energy availability in these settings across network elements in the design of optimal routing and monitoring policies.
Battery control and charging of electric vehicles
The integration of renewables in the electrical grid at significant scale requires a simultaneous increase in the integration of batteries and electric vehicles to mitigate uncertainty in generation.
I studied how batteries and electric vehicles should be charged and discharged to meet goals and minimize operation costs, making the economic case for storage. My contributions included deriving patent-pending rigorous battery pricing methods for microgrids and developing a synthesis of offline electric vehicle charging methods and identifying major remaining challenges.