Properties of complex systems: recent research has shown that, at a gross level, all complex systems have a topology that can be described using a graphical representation called a real-world graph, examples of which are scale-free and small-world graphs. However, we have shown that real-world graphs are too simple to model the details of actual complex systems, and one has to define the topological model for a complex system in terms of an optimization problem, in which we optimize the system’s structure with respect to a particular functionality. In particular, we have explored the optimization problem underlying designing circuits that are easily diagnosable, and are exploring the optimization problem underlying biological systems and various biological functions.

Models for complex systems: many different

Inference algorithms for complex systems: we are developing techniques for performing inference efficiently on large, complex systems using compilation techniques and approximation methods. Compilation refers to pre-computing the complex system to generate a compiled representation such that embedded inference is at worst linear in the size of the embedded representation. For many interesting tasks, such as control, diagnosis and estimation, the size of the embedded representation is exponential in the size of the original system parameters, so we focus on generating compact compiled representations or compact approximate compiled representations. We are also studying a variety of other approximation methods, such as local search and Monte-Carlo sampling approaches.

Modeling Complex Systems; Automated Model Generators