Pouria Ramazi

Professor, Mathematics & Statistics

Ph.D. (the University of Groningen, the Netherlands),
Postdoc (University of Alberta, Canada),
Office: Mackenzie Chown J-Block
pramazi@brocku.ca

My research interests are in two main categories: Evolutionary game theory and Machine learning.
Networks of decision-making individuals may exhibit complicated and seemingly unpredictable behaviors, e.g., unsettlement in stock markets, spread of fake news in social media, and initiation and growth of tumors in organisms. While some networks eventually reach a state of equilibrium, others undergo perpetual chaotic fluctuations. Characterizing these possible asymptotic outcomes and finding the convergence conditions shed light on the collective behaviors. They also open the door to investigating possibilities for controlling the population dynamics, a fascinating yet open field of study. Evolutionary game theory provides a promising framework to study these problems: a network of individuals playing strategies in `games’ matched with their neighbors, earning payoffs, and correspondingly update their strategies over time. I am interested in studying the discrete nature of structured population dynamics with heterogeneous individuals and design control protocols to derive the dynamics to the desired outcomes. I am currently working on

  • Characterization and stability analysis of equilibrium states and fluctuation sets
  • Convergence analysis
  • Efficient control
  • Reinforcement learning
  • Experimental studies

Although mathematical analysis provides valuable intuitions on population dynamics, they often stay behind machine-learning algorithms when it comes to prediction making. I am interested in exploiting (and if necessary, developing) basic and advanced machine-learning models to both better understand (hypothesis testing) and accurately predict different processes. For example, we have developed machine-learning algorithms that predict future 1-year mountain pine beetle infestations in the Cypress Hills Park in Canada with an AUC score of 92%. I am currently working on the following topics:

  • Forecasting COVID-19 mortalities
  • Forecasting the spread of diseases and infestations
  • Time-series prediction making
  • Probabilistic graphical models

Recent Publications

JOURNALS

[15] Ramazi, P., Kunegel-Lion, M., Greiner, R. and Lewis, M. A. “Exploiting the full potential of Bayesian networks in predictive ecology.” Methods in Ecology and Evolution, 2020.

[14] Le, H., and Ramazi, P. “Heterogeneous mixed populations of best-responders and imitators: equilibrium convergence and stability.” IEEE Transactions on Automatic Control, (accepted 2020) to appear Aug 2021.

[13] Ramazi, P., Kunegel-Lion, M., Greiner, R. and Lewis, M. A. “Predicting infestations using machine-learning: A mountain pine beetle case study.” Ecology and Evolution, (accepted 2020).

[12] Ramazi, P. and Cao, M. “Convergence of linear threshold decision-making dynamics in finite heterogeneous populations.” Automatica, 2020.

[11] Ramazi, P. and Cao, M.  “Global convergence for replicator dynamics of repeated snowdrift games.” IEEE Transactions on Automatic Control, (accepted 2020) to appear Jan 2021.

[10] Riehl, J., Ramazi, P. and Cao, M. “Incentive-Based control of asynchronous best-response dynamics on binary decision networks.” IEEE Transactions on Control of Network Systems, 2018.

[9] Riehl, J., Ramazi, P. and Cao, M. “A survey on the analysis and control of evolutionary matrix games.” Annual Reviews in Control, 2018.

[8] Ramazi, P. Riehl, J. and Cao, M. “Homophily, heterophily and the diversity of messages in decision-making social networks.” Royal Society Open Science, 2018.

[7] Ramazi, P. and Cao, M. “Asynchronous decision-making dynamics under best-response update rule in finite heterogeneous populations.” IEEE Transactions on Automatic Control, 2017.

[6] Ramazi, P., Jardon, H. and Cao, M. “Limit sets within curves where trajectories converge to.” Applied Mathematics Letters, 2017.

[5] Ramazi, P., Riehl, J. and Cao, M. “Networks of conforming and non-conforming individuals tend to reach satisfactory decisions.” Proceedings of National Academy of Sciences (PNAS), 2016.

[4] Ramazi, P., Cao, M. and Weissing F.J. “Evolutionary dynamics of homophily and heterophily.” Scientific Reports, 2016.

[3] Ramazi, P., Hessel, J. and Cao, M. “How feeling betrayed affects cooperation.” PLoS ONE, 2015.

[2] Ramazi, P., Hjalmarsson, H. and Martensson, J. “Variance analysis of identified linear MISO models having spatially correlated inputs, with application to parallel Hammerstein models.” Automatica, 2014.

[1] Ramazi, P., Shoeiby, B. and Abbasian, T.  “The extension of Sarrus’ Rule for finding the determinant of a 4×4 matrix.” The American Mathematical Monthly, 2012.

CONFERENCES

[7] Le, H. and Ramazi, P. “Heterogeneous mixed populations of best-responders and imitators: Equilibrium convergence.” In Proc. of the 58th Conference on Decision and Control (CDC19), Nice, France, Dec. 2019.

[6] Fu, Y. and Ramazi, P. “Asynchronous decision-making dynamics under imitation update rule in heterogeneous populations.” In Proc. of the 58th Conference on Decision and Control (CDC19), Nice, France, Dec. 2019.

[5] Govaert, A., Ramazi, P. and Cao, M. “Convergence of imitation dynamics for public goods games on networks.” In Proc. of the 56th Conference on Decision and Control (CDC17), Melbourne, Australia, Dec. 2017.

[4] Riehl, J., Ramazi, P. and Cao, M. “Controlling networks of imitative agents.” In Proc. of the 56th Conference on Decision and Control (CDC17), Melbourne, Australia, Dec. 2017.

[3] Ramazi, P. and Cao, M. “Analysis and control of strategic interactions in finite heterogeneous populations under best-response update rule.” In Proc. of the 54th Conference on Decision and Control (CDC15), Osaka, Japan, Dec. 2015.

[2] Ramazi, P. and Cao, M. “Stability analysis for replicator dynamics of evolutionary snowdrift games.” In Proc. of the 53rd Conference on Decision and Control (CDC14), Los Angeles, USA, Dec. 2014.

[1] Zhang, F., Ramazi, P. and Cao, M. “Distributed concurrent targeting for linear arrays of point sources.” In Proc. of the 19th IFAC World Congress, Cape Town, South Africa, Aug. 2014.

Current Teaching

  • MATH 2P08 (Ordinary differential equations) Winter 2021