In a broad sense my research is on the application of Signal Processing to the study of Networks. We are currently witnessing the emergence of a field of research devoted to developing a mathematical understanding of networks, in what has come to be regarded as Network Science. My vision is that tools and methods of Signal Processing can be used in this effort that I foresee taking up the best part of the next decade.
At this moment I am working on two research projects
- Theoretical foundations of wireless communication networks In their classical work on limit distributions Gnedenko and Kolmogorov wrote that the "epistemological value of the theory of probability is based on this: that large-scale random phenomena in their collective action create strict, nonrandom regularity." As the less enlightened of us would put it, randomness generates structure. It is often possible to infer properties of large-scale stochastic systems even if analogous deterministic counterparts are intractable. In light of the former comments, it should not come as a surprise if stochastic networks exhibit more regular structure than deterministic networks. My research aims at exploiting randomness in discovering fundamental properties of networks...read more
- Statistical inference in wireless sensor networks The goal of this project is to develop a generic approach to statistical inference in wireless sensor networks (WSN). The common challenge in different inference problems is that observations are distributed through the WSN. The statistical inference task at hand, therefore, necessitates percolation of observations through the network. At the moment, parameter estimation, hypothesis testing, Kalman filtering and field estimation among others are investigated with different approaches. However, a common characteristic of all of them is that the entity to be inferred can be found as the maximazing argument of a function defined by the observations. Exploiting this commonality, is the starting point of this project...read more