Control Group

Cambridge University Department of Engineering

Dr M. Rule

Priorities - Research - Background - Publications

Position: Leverhulme and Isaac Newton Trust Fellow

E-mail: mer49 [at]

Office Location: BN4-76

[Profile on Google Scholar]

Research Priorities

I'm currently looking for experimental and clinical collaborators interested in formalizing control-theoretic models of disorders of the motor system. I am especially interested in rare movement disorders involving less-studied brainstem and subcortical structures. Please feel free to contact me you are if interested in collaborating.

Research Interests

My research focuses on how neurons work together to generate emergent collective dynamics. I specialize in computational modelling of large-scale neuronal recordings from the sensorimotor system. My previous theoretical research focused on machine-learning methods as algorithmic metaphors for neural computation, and the mathematical foundations of statistical tools for systems neuroscience. My ongoing research focuses on studying sensorimotor representations via brain-machine interfaces, building statistical tools for systems neuroscience, and building theoretical models of ongoing learning in closed-loop.

My research philosophy falls within the tradition of biological cybernetics and computational neurophysiology. I aim to understand the algorithms that the nervous system uses for adaptive sensorimotor control. This understanding is vital for the principled design and optimization of therapeutic interventions for disorders of the motor system, ranging from brain-machine interfaces for paralyses, to improving the functional control outcomes of deep-brain stimulation for movement disorders.


I studied computer science, biology, and computational neuroscience at Carnegie Mellon University and the Pittsburgh Center for the Neural Basis of Cognition, and hold a Ph.D. in neuroscience from Brown University, where I worked with applied mathematician Dr. Wilson Truccolo and the lab of Dr. J. P. Donogue applying computational statistics to collective dynamics in primate motor cortex ( 1, 2, 3, 4).

I worked on mathematical models of spatiotemporal wave dynamics in cortex ( 1, 2) with Drs. Bard Ermentrout and Stuart Heitmann, and developed theoretical connections between these models and machine-learning methods ( 1, 2) with Drs. Guido Sanguinetti and Matthias Hennig at the Institute for Adaptive and Neural Computation at the University of Edinburgh. With the Hennig group, I studied the statistical physics of artificial neural networks as a metaphor for neural coding ( 1, 2).

Since joining the Control Group, I've focused on learning and plasticity in sensorimotor cortex. I've studied how neural population codes over time ( 1, 2), and proposed theory of homeostasis that could explain how the brain keeps consolidated and plastic representations integrated.

I am currently looking for faculty and/or group leader tenure-track positions.


Rule, M.E. and O’Leary, T., 2022. Self-healing codes: How stable neural populations can track continually reconfiguring neural representations. Proceedings of the National Academy of Sciences, 119(7), p.e2106692119. [ PDF ]

Scholl, C., Rule, M.E. and Hennig, M.H., 2021. The information theory of developmental pruning: Optimizing global network architectures using local synaptic rules. PLoS computational biology, 17(10), p.e1009458. [ PDF ]

Sorrell, E., Rule, M.E. and O'Leary, T., 2021. Brain–machine interfaces: Closed-loop control in an adaptive system. Annual Review of Control, Robotics, and Autonomous Systems, 4, pp.167-189. [ PDF ]

Rule, M.E., Loback, A.R., Raman, D.V., Driscoll, L.N., Harvey, C.D. and O'Leary, T., 2020. Stable task information from an unstable neural population. Elife, 9, p.e51121. [ PDF ]

Rule, M.E., Sorbaro, M. and Hennig, M.H., 2020. Optimal encoding in stochastic latent-variable Models. Entropy, 22(7), p.714. [ PDF ]

Rule, M.E., O’Leary, T. and Harvey, C.D., 2019. Causes and consequences of representational drift. Current opinion in neurobiology , 58 , pp.141-147. [ PDF ]

Rule, M.E., Schnoerr, D., Hennig, M.H. and Sanguinetti, G., 2019. Neural field models for latent state inference: Application to large-scale neuronal recordings. PLoS computational biology, 15(11), p.e1007442. [ PDF ]

Rule, M. and Sanguinetti, G., 2018. Autoregressive point processes as latent state-space models: A moment-closure approach to fluctuations and autocorrelations. Neural Computation, 30(10), pp.2757-2780. [ PDF ]

Rule, M.E., Vargas-Irwin, C., Donoghue, J.P. and Truccolo, W., 2018. Phase reorganization leads to transient β-LFP spatial wave patterns in motor cortex during steady-state movement preparation. Journal of neurophysiology, 119(6), pp.2212-2228. [ PDF ]

Heitmann, S., Rule, M., Truccolo, W. and Ermentrout, B., 2017. Optogenetic stimulation shifts the excitability of cerebral cortex from type I to type II: oscillation onset and wave propagation. PLoS computational biology, 13(1), p.e1005349. [ PDF ]

Rule, M.E., Vargas-Irwin, C.E., Donoghue, J.P. and Truccolo, W., 2017. Dissociation between sustained single-neuron spiking and transient β-LFP oscillations in primate motor cortex. Journal of neurophysiology, 117(4), pp.1524-1543. [ PDF ]

Rule, M. (2016). Collective neural dynamics in primate motor cortex. (Ph.D. Thesis) Brown University, Providence, Rhode Island. Available at Brown University Library, [ PDF ]

Guler, S.D. and Rule, M.E., 2013, June. Invent-abling: enabling inventiveness through craft. In Proceedings of the 12th International Conference on Interaction Design and Children (pp. 368-371). [ PDF ]

Rule, M.E., Vargas-Irwin, C., Donoghue, J.P. and Truccolo, W., 2015. Contribution of LFP dynamics to single-neuron spiking variability in motor cortex during movement execution. Frontiers in systems neuroscience, 9, p.89. [ PDF ]

Rule, M., Stoffregen, M. and Ermentrout, B., 2011. A model for the origin and properties of flicker-induced geometric phosphenes. PLoS Comput Biol, 7(9), p.e1002158. [ PDF ]

Nain, A.S., Chung, F., Rule, M., Jadlowiec, J.A., Campbell, P.G., Amon, C. and Sitti, M., 2007, April. Microrobotically fabricated biological scaffolds for tissue engineering. In Proceedings 2007 IEEE International Conference on Robotics and Automation (pp. 1918-1923). IEEE. [ PDF ]