Applied Probability Group

The best mathematical description of many natural and engineered systems is a probabilistic one. This can be the case for a number of reasons:

• the system is stochastic by design, such as medium access control algorithms in wireless networks that can be analyzed using using queueing theory;
• the system operation depends on large amounts of heterogeneity in its components, such as in proliferating cell systems in biology that are studied in mathematical biology;
• the system has many unknowns about which complete knowledge is not available in any single specific instance, but whose distributional character can be identified, as is the case in the study of communication channels in information theory.

A sample of recent papers

Communication Networks

• On the validity of IEEE 802.11 MAC modeling hypotheses.
  K. D. Huang, K. R. Duffy and D. Malone.
  IEEE/ACM Transactions on Networking, 18 (6), 1935-1948, 2010.
• Mean field Markov models of wireless local area networks.
  K. R. Duffy.
  Markov Processes and Related Fields, 16 (2), 295-328, 2010.
• On a buffering hypothesis in 802.11 analytic models.
  K. D. Huang and K. R. Duffy
  IEEE Communications Letters, 13 (5), 312-314, 2009.
  
• Joint scheduling and resource allocation in Uplink OFDM systems.
  J. Huang, V. G. Subramanian, R. Agrawal and R. Berry.
  IEEE Journal on Selected Areas of Communications, 27 (2), 226--234, 2009.
• Downlink Scheduling and Resource Allocation for OFDMA Systems.
  J. Huang, V. G. Subramanian, R. Agrawal and R. Berry.
  IEEE Transactions on Wireless Communications, 8 (1), 288--296, 2009.
• Modeling the impact of buffering on 802.11.
  K. Duffy and A. J. Ganesh.
  IEEE Communications Letters, 11 (2), 219-221, 2007.
• Modeling the 802.11 distributed coordination function in non-saturated heterogeneous conditions.
  D. Malone, K. Duffy and D. J. Leith.
  IEEE/ACM Transactions on Networking, 15 (1), 159-172, 2007.

Immunology

• Intracellular competition for fates in the immune system.
  K. R. Duffy and P. D. Hodgkin. Trends in Cell Biology, 22 (9), 457-464, 2012.
• Activation-induced B cell fates are selected by intracellular stochastic competition.
  K. R. Duffy, C. J. Wellard, John F. Markham, J. H. S. Zhou, R. Holmberg, E. D. Hawkins, J. Hasbold, M. R. Dowling and P. D. Hodgkin.
  Science, 335 (6066), 338-341, 2012.
• On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics.
  K. R. Duffy and V. G. Subramanian
  Journal of Mathematical Biology, 59 (2), 255-285, 2009.
• Determining the expected variability of immune responses using the Cyton Model.
  V. G. Subramanian, K. R. Duffy and M. L. Turner and P. D. Hodgkin.
  Journal of Mathematical Biology, 56 (6), 861-892, 2008.

Stochastic processes

• Sample path large deviations of Poisson shot noise with heavy tail semi-exponential distributions.
  K. R. Duffy and G. L. Torrisi.
  Journal of Applied Probability, 48 (3), 688-698, 2011.
• Estimating Loynes' exponent.
  K. R. Duffy and Sean P. Meyn.
  Queueing Systems: Theory & Applications, 68 (3-4), 285-293, 2011.
• Sample path large deviations for order statistics.
  K. R. Duffy, C. Macci and G. L. Torrisi.
  Journal of Applied Probability, 48 (1), 238-257, 2011.
• LDP for Max-Weight scheduling over convex compact rate-regions.
  V. G. Subramanian.
  Mathematics of Operations Research, 35(4), 881-910, 2010.
• Most likely paths to error when estimating the mean of a reflected random walk.
  K. R. Duffy and S. P. Meyn.
  Performance Evaluation, 67 (12), 1290-1303, 2010.
• Complexity analysis of a decentralised graph colouring algorithm.
  K. R. Duffy, N. O'Connell and A. Sapozhnikov.
  Information Processing Letters, 107 (2), 60-63, 2008.
• The large deviation principle for the on/off Weibull sojourn process.
  K. R. Duffy and A. Sapozhnikov.
  Journal of Applied Probability, 45 (1), 107-117, 2008.
• Ambiguities in estimates of critical exponents for long-range dependent processes.
  K. Duffy, C. King and D. Malone.
  Physica A, 377 (1), 43-52, 2007.

Econophysics

• Loss aversion, large deviation preferences and optimal portfolio weights for some classes of return processes.
  K. Duffy, O. Lobunets and Y. Suhov.
  Physica A, 378 (2), 408-422, 2007.