Recent results

  Some Recent Papers (this is a list of submitted papers with abstracts -- for published papers please check my list of journal papers):

  • new Shin-Ho Chung, Olaf S. Andersen and Vikram Krishnamurthy, Biological Ion Channels: Structure, Dynamics and Applications , Springer Verlag 2007, ISBN10: 0-387-33323-1 (a 658 page book on ion channels comprising of 20 chapters written by experts in the field.) The book is in the Springer Biological/Medical Physics and Biomedical Engineering Series. new

  • new M. Hoyles, V. Krishnamurthy, M Siksik, S.H Chung, Brownian Dynamics Theory for Predicting Internal and External Blockages of Tetraethylamonium in the KcsA Potassium Channel ,Biophysical Journal, accepted 2007.

  • new T.Vora, V. Krishnamurthy, S.H Chung, Estimating the dielectric constant of the channel protein and pore , European Biophysics Journal, accepted 2007.

  • new V. Krishnamurthy, K. Luk, B. Cornell, D. Martin, Gramicidin Ion Channel based Nano-Biosensors: Construction, Stochastic Dynamical Models and Statistical Detection Algorithms , IEEE Sensors Journal, Vol.7, No.9, September 2007.

  • new V. Krishnamurthy, D. Djonin, Structured  Threshold Policies for Dynamic Sensor Scheduling--A Partially Observed Markov Decision Process Approach
    • (to appear IEEE transactions Signal Processing 2007) -- you can download the first 15 pages as a sampler!

    The above paper proves that under several cases, the optimal scheduling policy for a POMDP with large number of states has a simple threshold structure. We use supermodularity with respect to the monotone likelihood ratio ordering. In our current work, we have generalized the results to multi-variate POMDPs.

  • new D. Djonin, V.Krishnamurthy, Monotone Optimal Policies for Constrained Markov Decision Processes. (to appear in IEEE transactions Signal Processing 2007)
    The paper shows how by using a Lagrangian formulation for dynamic programming for constrained MDPs one can prove that the optimal policy is a randomized mixture of threshold policies. A novel aspect is the use of supermodularity for constrained MDPs to show monotonicity of the optimal policy. Another novel feature is the use of multimodularity to prove convexity of the value function.
  • new V. Krishnamurthy and S.H. Chung, Large-scale Dynamical Models and Estimation for Permeation in Biological Membrane Ion Channels, Proceedings of the IEEE, Special Issue on Estimation and Control of Large Scale Systems, April 2007, 23 pages, to appear.

  • new N. Visnevski, V Krishnamurthy, A. Wang and S. Haykin, Syntactic Model\ ing ad Signal Processing of Multifunction Radars: A Stochastic Context Free Grammar Approach , Proceedings of the IEEE, Special Issue on Estimation and Control of Large Scale Systems, April 2007, 21 pages, to appear.

    With zillions of papers on state estimation of state space models (the occult of particle filters -- I am currently working on a particle smasher that will annihilate all particle filters), the above paper deals with a completely different problem: How to do meta-level state estimation of stochastic context free grammars. Context free grammars are a generalization of stochastic automata that allow for large scale dependencies. For example suppose you had a C-program corrupted in noise. How would you reconstruct it? Note a C-program is a context free grammar -- a "begin if" always has an "end if" however far away it may be -- this cannot be modeled by a finite state automata (e.g. Markov chain). We are currently looking at distributed estimation and detection of context free grammars in metalevel sensor management.

  • new M. Maskery, V. Krishnamurthy, Q. Zhao, Game Theoretic Learning and Pricing for Dynamic +Spectrum Access in Cognitive Radio, in Cognitive Wireless Communications Networks, Springer Verlag, Editors: V. Bhargava and E. Hossain, 2007. {\bf (invited)}.
  • new S Ali, V. Krishnamurthy, V. Leung, Mobility Assisted Opportunistic Scheduling in Cellular Data Networks , Featured Article in IEEE Transactions Mobile Computing, June 2007 ). (We use the Mcdiarmid Freize inequality to say what constitutes a good mobility pattern for a user in opportunistic scheduling).

    •     Papers in Biological Ion Channels (for already published papers on ion channel permeation via brownian dynamics, see publication list).

        Papers in Game theory, structural results in stochastic control, re-inforcement learning and sensor networks:


     

    My main research contributions are in the areas listed below -- if you click on any of these you can view my recent papers in these areas. -- otherwise email me.


  • Biological Nanotubes: Control of Ion Channels both at a macroscopic and molecular level. Currently, we are developing stochastic gradient based learning controllers for determining the molecular structure of an ion chqnnel. From a math point of view this involves a novel use of re-informcement learning to control the evolution of a multi-particle Brownian dynamics simulation. (this work is joint with Prof Shin Ho Chung, Australian National University).
  • Adaptive learning, Reinforcement learning, Discrete Stochastic Optimization -- with applications in neurobiology and wireless communications.

  • Nonlinear filtering and stochastic calculus

  • Sensor Networks, Weapons allocation, Sensor Scheduling, Target Tracking, Bayesian Networks.

  • Hidden Markov Models -- Online (Recursive) Estimation and bounds, Scheduling and Management of HMM sensors.

  • CDMA Wireless Networks -- multiuser detection, interaction of physical and network layers, admission control