Welcome to Vikram Krishnamurthy's lab in Statistical Signal Processing and Stochastic Optimization

Statistical signal processing and stochastic optimization are universal tools that have enormous impact in the way people, sensors and actuators communicate and process data. As you can see from the research projects below, we do state-of-the-art research in wireless communications, sensor networks, nanobiological systems and defense related systems (sensor fusion, sensor management for surveillance and tracking). The unifying theme that underlies our research are powerful tools in the mathematics of stochastic dynamical systems, dynamic stochatic optimization, game theory, and Bayesian inference.

The Statistical Signal Processing and Stochastic Optimization lab at UBC comprises of 10 graduate students, and typically 2 postdocs. Specific research areas within the lab include

PhD Alumni since 2007

Michael Maskery (2007)

Minh Ngo (2007)

Arsalan Farrokh (2007)

Laxminarayana Pillutla (2008)

Hassan Mansour (2009)

Alex Wang (2009)

Farhad Ghassemi (2009)

Jane Huang (2011)

Cognitive radio networks : Cognitive radio systems intelligently exploit vacant spectrum when primary users are inactive. We are working on several exciting aspects of cognitive radio including dynamic spectrum access using game theory; the effect of primary and secondary cognitive users on TCP/IP performance; scheduling over Markov modulated fading channels with partial observations.
PhD students: Lax Pillutla, Michael Maskery.
Postdoc: Dejan Djonin (currently working for Dyaptive Systems, Vancouver).
Wireless Sensor Networks : How can selfish agents behave in a socialistic way? This is a fundamental issue in energy management and information extraction in sensor networks.Each sensor wants to maximize its own utility function -- yet the entire network needs to perform in a way that is useful. Much of our recent research focuses on using state of the art results in economics and game theory for designing scalable large scale sensor networks. Our current research deals with sophisticated game theoretic and distributed algorithms for sensor activation, transmission control and energy management. Another important area we are working on is the use of Partially Observed Markov Decision Processes (POMDPs) in sensor scheduling. By using novel ideas such as supermodularity on simplices, we recently have some exiciting results in showing that in many cases the optimal policy has a simple threshold structure.
PhD students: Michael Maskery, Alex Wang, Farhad Ghassemi
Postdoc: I am looking for a postdoc in this area. If you are good in game theory (Bayesian games) please contact me. There is some cool stuff in the interface between economics (social games) and sensor networks.
Bayesian Signal Processing of multi-mode sensors such as multifunction radars. Some recent highlights of our research include constructing "syntactic" models for radars -- i.e. we view sophisticated radars as systems that speak a language. Our recent paper in the Proceedings of the IEEE, illustrate some of these new results.
PhD students: Alex Wang.
Permeation in Biological Ion channels : Biological ion channels are sub-nano-sized pores formed by large protein molecules in the cell membrane of all living cells. They are responsible for regulating all electrical activies of a cell. Many degenerative diseases such as cystic fibrosis, Parkinson's disease, etc are linked to faulty ion channels. Our recent research in this area uses large scale stochastic simulation models to model how drugs work at a molecular level. We are using Brownian dynamics and molecular dynamics simulation methods. Recent exciting results include modelling how molecules such as Tetra-ethyl-ammonium block ion channels.
PhD student: May Siksik.
Collaborator: Shin-Ho Chung, ANU.
Nanoscale Biosensors>: We are currenly working with a novel bionsensor that comprises of ion channels. These sensors can be used to detect target molecules such as explosives. Our recent work deals with how to model the stochastic dynamics of such biosensors and how to devise Bayseian algorithms for detecting the target molecules. Currently we are designing reconfigurable biosensors that can dynamically learn their environment and adapt their behaviour.
Master's students: Kai-Yuk Luk, Sahar Monfared.
Stochastic Calculus and Weak convergence Analysis We are also pursuing several projects in the applied mathematics area of convergence of adaptive estimators. A powerful method used to analyse the asymptotic behavior of multi-time scale systems is stochasstic averaging theory and weak convergence. We are work on continuous-time non-linear filtering and stochatic (Ito) calculus. Some applications include econometrics and mathematical finance.
Collaborators: George Yin (Wayne State Univ), Robert Elliott (U Alberta),

Projects in the lab are funded by:

National Science and Engineering Research Council (3 strategic research grants, discovery grant).
Bell Canada, MIMOW Technology, Dyaptive Systems, Telus.
Defense Research and Development Canada
Canada Foundation for Innovation
Canada Research Chairs Program

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