Research

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We study applications of mathematics and statistics to problems in neuroscience, with particular emphasis on:

• Human seizures

  What features characterize the multi-scale dynamics of the seizing human brain?

Example publication: M. A. Kramer, Wilson Truccolo, Uri T. Eden, Kyle Q. Lepage, Leigh R. Hochberg, Emad N. Eskandar, Joseph R. Madsen, Jong W. Lee, Atul Maheshwari, Eric Halgren, Catherine J. Chu, Sydney S. Cash, Human seizures self-terminate across spatial scales via a critical transition, Proc Nat Acad Sci USA, 109 (51) 21116-21121, 2012.

Example publication: L. R. Gonzalez-Ramirez, O. J. Ahmed, S. S. Cash, C. E. Wayne, and M. A. Kramer, A Biologically Constrained, Mathematical Model of Cortical Wave Propagation Preceding Seizure Termination, PLoS Comput Biol 11(2):e1004065, 2015.

• Brain networks

  What features govern functional network evolution in the brain?

Example publication: Chu CJ, Tanaka N, Diaz J, Edlow BL, Wu O, Hamalainen M, Stufflebeam S, Cash SS, Kramer MA, EEG functional connectivity is partially predicted by underlying white matter connectivity, Neuroimage, 108, 23-33, 2015.

Example publication: E. Stephen, K. Lepage, U. Eden, J. Brumberg, F. Guenther, M. Kramer, Assessing dynamics, spatial scale, and uncertainty in task-related brain network analyses, Front. Comput. Neurosci. 8:31, 2014.

• Connecting data and models

  How do we rigorously link "expert knowledge" captured in a computational model with observed brain data?

  Example publication: L. Meng, M. Kramer, S. Middleton, M. Whittington, U. Eden, A unified approach to linking experimental, statistical and computational analysis of spike train data, PLoS ONE 9(1): e85269, 2014.

  Example publication: L. Meng, M. A. Kramer, U. T. Eden, A sequential Monte Carlo approach to estimate biophysical neural models from spikes, J Neural Eng, 8:065006, 2011.

• Data analysis

  How do we chararacterize observed brain activity?

Example publication: M. Kramer, U. Eden, Assessment of cross-frequency coupling with confidence using generalized linear models, J Neurosci Methods, 220(1):64-74, 2013.

Example publication: K. Q. Lepage, M. A. Kramer, U. T. Eden, Some sampling properties of common phase estimators, Neural Computation, 25, 1-21, 2012.

• Neuronal rhythms

  What mechanisms pace brain rhythms?

Example publication: N. Kopell, M. A. Whittington, M. A. Kramer, Neuronal assembly dynamics in the beta1 frequency range permits short-term memory, Proc Nat Acad Sci USA, 108(9):3779-84, 2011.

Example publication: M. A. Kramer, Anita K. Roopun, Lucy M. Carracedo, Roger D. Traub, Miles A. Whittington, and Nancy J. Kopell, Rhythm Generation through Period Concatenation in Rat Somatosensory Cortex, PLOS Comp Bio, 4(9): e1000169, 2008.

• Dynamical systems

  What dynamical mechanisms underlie neuronal activity?

Example publication: J. Burke, M. Desroches, A. M. Barry, T. J. Kaper, M. A. Kramer, A showcase of torus canards in neuronal bursters, J Math Neuro, 2:3 doi:10.1186/2190-8567-2-3, 2012.

• Education

  How do we develop the skills necessary to make sense of neural data?

Example publication: M. A. Kramer and U. T. Eden, Case Studies in Neural Data Analysis: A Guide for the Practicing Neuroscientist, MIT Press, 2016.