I am an assistant professor at the University of Washington Applied Mathematics Department. My interests span a wide set of topics in mathematical neuroscience and biological dynamics. Current and recent projects focus on optimal signal processing and decision making in simple neural networks, the dynamics of neural populations in interval timing tasks, correlations and reliability in simple neural circuits, and properties of oscillator networks with generalized symmetries. This work is supported by the Burroughs-Wellcome Fund (BWF) Scientific Interfaces Program.

Before coming to UW, I was a postdoctoral fellow in mathematical neuroscience at NYU's Courant Institute and Center for Neural Science with Prof. John Rinzel as my mentor. This work was supported by NSF (Div. Math. Sci.) and BWF fellowships. In 2004, I completed my Ph.D in Princeton's Program in Applied and Computational Mathematics, working with Prof. Phil Holmes. My thesis work was on neural dynamics and cognitive control. The goal here is to understand the dynamics of low-dimensional and symmetric stochastic neural networks, and how these systems might be controlled to explain fascinating data from brain recordings and task performance. My work at Princeton was in close collaboration with Prof. Jonathan Cohen and the Center for the Study of Mind, Brain, and Behavior. Over my first two years at Princeton I also did a project reviewing and posing open problems in the control of quantum dynamics with Prof. Hersch Rabitz, who is still an active collaborator. My graduate work was supported by the National Science Foundation, the Burroughs-Wellcome Fund, and Princeton's Graduate School. Before I moved to Princeton, I worked at the Lawrence Livermore National Laboratory and studied Engineering Physics at UC-Berkeley. Outside of applied math, I have worked on science policy issues, and I regularly take some time off to go rock and ice climbing.

CV (pdf)

Papers and preprints:

K. Josic, E. Shea-Brown, B. Doiron, and J. de la Rocha. Stimulus-dependent correlations and population codes. ArXiV:q-bio.NC/0810.2152, 2008.

E. Shea-Brown, K. Josic, J. de la Rocha, and B. Doiron. Correlation and synchrony transfer in integrate-and-fire neurons: basic properties and consequences for coding. Physical Review Letters 100, 108102, 2008. Also: ArXiV.

E. Shea-Brown, M. Gilzenrat, and J.D. Cohen. Optimization of decision making in multilayer networks: The role of Locus Coeruleus Neural Computation 20:2863-2894, 2008.

K. Lin, E. Shea-Brown, and L-S. Young. Reliability of coupled oscillators I: Two-oscillator systems. ArXiV nlin.CD/0708.3061.

K. Lin, E. Shea-Brown, and L-S. Young. Reliability of coupled oscillators II: Larger networks. ArXiV nlin.CD/0708.3063.

J. de la Rocha, B. Doiron, E. Shea-Brown, K. Josic, and A. Reyes. Correlation between neural spike trains increases with firing rate. Nature 448, 802-806, 2007.

X. Feng, E. Shea-Brown, H. Rabitz, B. Greenwald, and R. Kosut. Optimal deep brain stimulation of the subthalamic nucleus -- a computational study. Journal of Computational Neuroscience , 2007. (journal ed.)

X. Feng, E. Shea-Brown, H. Rabitz, B. Greenwald, and R. Kosut. Toward Closed-Loop Optimization of Deep Brain Stimulation for Parkinson's Disease: Concepts and Lessons from a Computational Model. Journal of Neuroengineering , 4: L14-L21, 2007

K. Lin, E. Shea-Brown, and L-S. Young. Reliable and unreliable dynamics in driven coupled oscillators. ArXiV nlin.CD/0608021.

S. Coombes, B. Doiron, K. Josic, and E. Shea-Brown. Toward blueprints for network architecture, biophysical dynamics, and signal transduction. To appear, Proc. Royal. Society, 2006.

J. Moehlis, E. Shea-Brown, and H. Rabitz. Optimal inputs for phase models of spiking neurons. ASME Journal of Computational and Nonlinear Dynamics 1(4): 358-367, 2006.

R. Bogacz, E. Brown, J. Moehlis, P. Hu, P. Holmes and J.D. Cohen (2006) The physics of optimal decision making: A formal analysis of models of performance in two-alternative forced choice tasks. Psychological Review 113: 700-765, 2006.

E. Shea-Brown, J. Rinzel, B. Rakitin, C. Malapani. A firing-rate model of Parkinsonian deficits in interval timing. Brain Research, 1070 (2006), 189-201.

M. Golubitsky, K. Josic, and E. Shea-Brown. Winding Numbers and Average Frequencies in Phase Oscillator Networks. Journal of Nonlinear Science, 16, 201-231, 2006.

P. Holmes, E. Shea-Brown, J. Moehlis, R. Bogacz, J. Gao, G. Aston-Jones, E. Clayton, J. Rajkowski, and J.D. Cohen. Optimal decisions: From neural spikes, through stochastic differential equations, to behavior. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Science , 88 (10), 2496-2503, 2005.

E. Brown, M. Gilzenrat, and J. D. Cohen. The locus coeruleus, adaptive gain, and the optimization of simple decision tasks. Technical Report #04-02, Center for the Study of Mind, Brain, and Behavior, Princeton University (2004).

J. Moehlis, E. Brown, R. Bogacz, P. Holmes, J. D. Cohen. Optimizing reward rate in two alternative forced choice tasks: mathematical formalism. Technical Report #04-01, Center for the Study of Mind, Brain, and Behavior, Princeton University (2004).

E. Brown, J. Gao, P. Holmes, R. Bogacz, M. Gilzenrat and J.D. Cohen. Simple neural networks that optimize decisions. Int. J. Bifurcation and Chaos, Vol. 15, No. 3 (2005) 803-826. (see comment in Nature journal club.)

E. Brown, J. Moehlis, P. Holmes, E. Clayton, J. Rajkowski, and G. Aston-Jones. The influence of spike rate and stimulus duration on noradrenergic neurons. J. Comp . Neurosci. 17 (1), 5-21 , 2004 .

E. Brown, J. Moehlis, and P. Holmes. On the phase reduction and response dynamics of neural oscillator populations. Neural Computation 16:673-715, 2004.

E. Brown, P. Holmes, and J. Moehlis. Globally coupled oscillator networks. In: Perspectives and Problems in Nonlinear Science: A Celebratory Volume in Honor of Larry Sirovich, E. Kaplan, J. Marsden, K. Sreenivasan, Eds., p. 183-215. Springer, New York, 2003

E. Brown and H. Rabitz, Some mathematical and algorithmic challenges in the control of quantum dynamics. J. Math. Chem. 31(1):17-63, 2002.

R. Cho, L. Nystrom, E. Brown, A. Jones, T. Braver, P. Holmes, and J. Cohen. Mechanisms underlying performance dependencies on stimulus history in a two-alternative forced choice task. Cognitive, Affective, and Behavioral Neuroscience, Dec. 2002.

E. Brown and P. Holmes, Modeling a simple choice task: stochastic dynamics of mutually inhibitory neural groups, Stochastics and Dynamics 1(2):159-191, 2001.

Other papers (please contact me):

H. Rabitz, G. Turinici, and E. Brown. Control of Molecular Motion: Concepts, Procedures, and Future Prospects. Ch. 14 in Handbook of Numerical Analysis, Volume X, P. Ciarlet and J. Lions, Eds., Elsevier, Amsterdam, 2003.

E. Brown, S. Doss, F. Hoffman, R. Gelinas, K. Fox, and J. O’Boyle. Adaptive-Grid Computational Model of VOC Transport Across Fine-and Coarse-grained sediment Contacts. Report, Lawrence Livermore National Laboratory (UCRL-ID-129845), pp. 5.1-5.37, Livermore, CA, 1998. 

 

Dissertation:

Neural oscillators and integrators in the dynamics of decision tasks. Applied and Computational Mathematics, Princeton University. June 2004.

 

Scholarpedia articles:

with Philip Holmes, Jeff Moehlis and Kresimir Josic (peer-reviewed): Isochrons, Periodic Orbits, and Stability .

Sample an animated talk:

[click on compressed images for animations; plug-ins for your version of Adobe Acrobat or Reader may be required]

How architecture restricts spiking patterns in networks of phase oscillators. Int'l Workshop on Applied Dynamical Systems, Montreal (2005).

From Spikes to Speed-Accuracy via the brainstem . Courant Institute Applied Mathematics Seminar (2004).

If you're also going, let's meet and talk about science at:

2008 SIAM Annual Meeting, San Diego (Jul 7-11)

European Congress of Mathematics, Amsterdam (Jul 14-18)

 

or please reach me at:

(as of Jan 1, 2008). Department of Applied Mathematics, University of Washington, 414 Guggenheim Hall, Seattle, WA 98195-2420.