 Y. Hu, J. Trousdale, K. Josic, and E. SheaBrown. Motif Statistics and Spike Correlations in Neuronal Networks. ArXiv qBio.NC/1206.3537 and J. Statistical Mechanics P03012:151, 2013.

N. Cain, A. Barreiro, M. Shadlen, and E. SheaBrown. Neural integrators for decision making: A favorable tradeoff between robustness and sensitivity. ArXiv qBio.NC/1111.6573, and J. Neurophysiology, 109(10):254259, 2013.
J. Trousdale, Y. Hu, E. SheaBrown, and K. Josic. Impact of network structure and cellular response on spike time correlations. PLOS Computational Biology, 8(3): e1002408, 2012, and ArXiv qBio.NC/1110.4914, 2011.
A. Barreiro, E. Thilo, and E. SheaBrown. The Acurrent and Type I / Type II transition determine collective spiking from common input. ArXiv qBio.NC/1106.0863 and J. Neurophysiology, 108(6):163145, 2012.
 M. Matell, E. SheaBrown, A. Wilson, C. Gooch, and J. Rinzel. A heterogeneous population code for elapsed time in rat medial agranular cortex. Behavioral Neuroscience, 125(1): 54–73, 2011. Winner, 2011 D.G. Marquis Award for best paper of year in Behavioral Neuroscience.
 J. Goldwyn, E. SheaBrown, and J. Rubinstein. Encoding and decoding amplitudemodulated cochlear implant stimuli – a point process analysis. J. Comp. Neuroscience, Volume 28, Number 3, 405424, 2010.

E. Brown, Neural oscillators and integrators in the dynamics of decision tasks. Applied and Computational Mathematics, Princeton University. June 2004.
 with Philip Holmes, Jeff Moehlis and Kresimir Josic (peerreviewed): Isochrons, Periodic Orbits, and Stability .
 We wrote this
SIAM News article on our work: Exploring Connectivity in the Brain’s Network of Neurons, 2014.
Featured book review with K. Josic, on Two books in mathematical neuroscience and the state of the field, SIAM Review 53(3), 577583, 2011.

Papers and Preprints
A.Fyall, Y. ElShamayleh, H. Choi, E. SheaBrown, and A. Pasupathy. Dynamic representation of occluded objects in primate prefrontal and visual cortices. eLife 6:e25784, 2017B. Brinkman, F. Rieke, E. SheaBrown, M. Buice. Effective synaptic interactions in subsampled nonlinear networks with strong coupling. ArXiv qBio.NC/1702.00865, and submitted, 2017.
R. Kass, (~20 authors), E. SheaBrown, …, and M. Kramer. Computational neuroscience: mathematical and statistical perspectives. To appear, Annual Review of Statistics and Its Application, 5, March 2018
G. Ocker, Y. Hu, M. Buice, B. Doiron, K. Josic, R. Rosenbaum, E. SheaBrown. From the statistics of connectivity to the statistics of spike times in neuronal networks. ArXiv qBio.NC/1703.03132, and Current Opinion in Neurobiology 46: 109119, 2017.
G. Ocker, K. Josic, E. SheaBrown, M. Buice. Linking structure and activity in nonlinear spiking networks. ArXiv qBio.NC/03828, and PLOS Computational Biology 13(6): e1005583, 2017.
Joel Zylberberg, Alexandre Pouget, Peter E. Latham, Eric SheaBrown. Robust information propagation through noisy neural circuits ArXiv qBio.NC/1608.05706 and PLOS Computational Biology 13(4): e1005497, 2017.
K. Harris, T. Dashevskiy, J. Mendoza, A. Garcia, J. Ramirez, and E. SheaBrown Differential roles for inhibition in excitatory rhythm generators ArXiv qBio.NC/1610.04258, and J. Neurophysiology 118: 20702088, 2017.
B. Brinkman, A. Weber, F. Rieke, and E. SheaBrown. How Do Efficient Coding Strategies Depend on Origins of Noise in Neural Circuits? PLOS Computational Biology, 12(10): e1005150, 2016.
K. Harris, S. Mihalas, and E. SheaBrown. Nonnegative spline regression of incomplete tracing data reveals high resolution neural connectivity. ArXiv qBio.NC/1605.08031, and NIPS, 2016.
Y. Hu, S. Brunton, N. Cain, S. Mihalas, J. N. Kutz, E. SheaBrown. Feedback through graph motifs relates structure and function in complex networks. ArXiv qBio.NC/1605.09073, 2016.
G. Lajoie, K. Lin, J.P. Thivierge, and E. SheaBrown. Revisiting chaos in stimulusdriven spiking networks: signal encoding and discrimination. ArXiv qBio.NC/ 1604.07497, and PLOS Computational Biology, 2016.
J. Zylberberg, J. Cafaro, M. Turner, E. SheaBrown, and F. Rieke. Directionselective circuits shape noise to ensure a precise population code. Neuron 89: 369383, 2016.
J. Zylberberg and E. SheaBrown. Input nonlinearities can shape beyondpairwise correlations and improve information transmission by neural populations. ArXiv qBio.NC/1212.3549 and Physical Review E 92: 062707, 2015.
D. Leen and E. SheaBrown. A simple mechanism for higherorder correlations in integrateandfire neurons. ArXiv qBio.NC/1306.5275 and Journal of Mathematical Neuroscience 5:17, 2015
M. Schwemmer, A. Fairhall, S. Deneve, and E. SheaBrown. Constructing precisely computing networks with biophysical spiking neurons. ArXiv qBio.NC/1411.1391, and J. Neurosci. 35(28):10112–10134, 2015.
A. Cayco Gajic, J. Zylberberg, and E. SheaBrown. Impact of triplet correlations on neural population codes. ArXiv qBio.NC/1412.0363, and Neural Computation, 2015.
Y. Hu, J. Zylberberg, and E. SheaBrown. The sign rule and beyond: Boundary effects, flexibility, and optimal noise correlations in neural population codes. ArXiv qBio/1307.3235, and PLOS Comp. Biology 10(2): e1003469, 2014.
A. Barreiro, E. SheaBrown. When do feedforward microcircuits produce beyondpairwise correlations? ArXiv qBio/1011.2797, and Frontiers in Comp. Neuroscience 8:10, 2014.
G. Lajoie, J.P. Thivierge, and E. SheaBrown. Structured chaos shapes spikeresponse noise entropy in balanced neural networks. ArXiv qBio/1311.7128 and Frontiers in Comp. Neuroscience 8:123, 2014.
J. Trousdale, Y. Hu, E. SheaBrown, and K. Josic. A generative spike train model with timestructured higher order correlations. ArXiv qBio/1305.4160, Frontiers Comp. Neuroscience, 7:84, 10.3389, 2013.
Y. Hu, J. Trousdale, E. SheaBrown, and K. Josic. Local paths to global coherence: cutting networks down to size. ArXiv qBio/1212.4239, 2013 and Physical Review E 89: 032802, 2014.
J. Zylberberg and E. SheaBrown. Input nonlinearities shape beyondpairwise correlations and improve information transmission by neural populations. ArXiv qBio/1212.3549, 2012.
A. Cayco Gajic and E. SheaBrown. Neutral stability, rate propagation, and critical branching in feedforward networks. ArXiv qBio/1210.8406, and to appear, Neural Computation, 2013.
G. Lajoie, K. Lin, and E. SheaBrown. Chaos and reliability in balanced spiking networks. ArXiv nlin/1209.3051, 2012 and Physical Review E, 87:052901052913, 2013.
N. Cain and E. SheaBrown. Impact of correlated neural activity on decision making performance. ArXiv qBio.NC/1207.5159, and Neural Computation 13(25) 2: 289–327, 2013.
A. Fairhall, E. SheaBrown, and A Barreiro. Information theoretic approaches to understanding circuit function. Curr. Opinion in Neurobiology 22(4): 653659, 2012.
N. Cain and E. SheaBrown. Computational models of decision making: integration, nonlinearity, and noise. Curr. Opinion in Neurobiology 22:1–7, 2012.
J. Goldwyn, J. Rubinstein, and E. SheaBrown. A point process framework for modeling electrical stimulation of the auditory nerve. ArXiv qBio.NC/1201.5428 and J. Neurophysiology, 108:14301452, 2012
J. Goldwyn and E. SheaBrown. The what and where of adding channel noise to the HodgkinHuxley equations. PLOS Comp. Biol. 7:1002247, 2011.
J. Goldwyn, N. Imennov, M. Famulare, and E. SheaBrown. On stochastic differential equation models for ion channel noise in HodgkinHuxley neurons. Phys. Rev. E 83, 041908, 2011. Also: ArXiv qBio/1009.4172, 2010.
A. Barreiro, E. SheaBrown. When do feedforward microcircuits produce beyondpairwise correlations? ArXiv qBio/1011.2797, and to appear, Frontiers in Comp. Neuroscience, 2014.
G. Lajoie and E. SheaBrown. Shared inputs and desynchrony in elliptic bursters: from slow passage to discontinuous circle maps. SIAM J. App. Dyn. Sys. (10): 12321271, 2011, and ArXiv math.DS/1010.2809.
A. Barreiro, E. SheaBrown, and E. Thilo. Timescales of spiketrain correlation for neural oscillators with common drive. Phys. Rev. E, 81, 011916, 2010 and ArXiv qBio/0907.3924.
K. Lin, E. SheaBrown, and LS. Young. Spiketime reliability of layered neural oscillator networks. Journal of Computational Neuroscience , 27(1): 135, 2009, and ArXiv. Builds on: K. Lin, E. SheaBrown, and LS. Young. Reliability of layered neural oscillator networks. Fast communication in Comm. Math. Sci., 7(1): 239247, 2009.
K. Josic, E. SheaBrown, B. Doiron, and J. de la Rocha. Stimulusdependent correlations and population codes. Neural Computation, 21(10): 27742804, 2009 and ArXiv.
E. SheaBrown, K. Josic, J. de la Rocha, and B. Doiron. Correlation and synchrony transfer in integrateandfire neurons: basic properties and consequences for coding. Physical Review Letters 100, 108102, 2008. Some additional material: ArXiV version.
E. SheaBrown, M. Gilzenrat, and J.D. Cohen. Optimization of decision making in multilayer networks: The role of Locus Coeruleus Neural Computation 20:28632894, 2008.
K. Lin, E. SheaBrown, and LS. Young. Reliability of coupled oscillators. J. Nonlin. Sci., 19(5): 497545, 2009 and ArXiV. Additional umpublished material in: Reliability of coupled oscillators II: Larger networks. ArXiV nlin.CD/0708.3063.
J. de la Rocha, B. Doiron, E. SheaBrown, K. Josic, and A. Reyes. Correlation between neural spike trains increases with firing rate. Nature 448, 802806, 2007(+ supplemental material).
X. Feng, E. SheaBrown, H. Rabitz, B. Greenwald, and R. Kosut. Optimal deep brain stimulation of the subthalamic nucleus  a computational study. Journal of Computational Neuroscience , 2007.
X. Feng, E. SheaBrown, H. Rabitz, B. Greenwald, and R. Kosut. Toward ClosedLoop Optimization of Deep Brain Stimulation for Parkinson's Disease: Concepts and Lessons from a Computational Model. Journal of Neuroengineering , 4: L14L21, 2007
S. Coombes, B. Doiron, K. Josic, and E. SheaBrown. Toward blueprints for network architecture, biophysical dynamics, and signal transduction. Phil. Trans. Royal Soc. A, 364: 33013318, 2006.
J. Moehlis, E. SheaBrown, and H. Rabitz. Optimal inputs for phase models of spiking neurons. ASME Journal of Computational and Nonlinear Dynamics 1(4): 358367, 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 twoalternative forced choice tasks. Psychological Review 113: 700765, 2006.
E. SheaBrown, J. Rinzel, B. Rakitin, C. Malapani. A firingrate model of Parkinsonian deficits in interval timing. Brain Research, 1070 (2006), 189201.
M. Golubitsky, K. Josic, and E. SheaBrown. Winding Numbers and Average Frequencies in Phase Oscillator Networks. Journal of Nonlinear Science, 16, 201231, 2006.
P. Holmes, E. SheaBrown, J. Moehlis, R. Bogacz, J. Gao, G. AstonJones, 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), 24962503, 2005.
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) 803826. Preprint version. (see comment in Nature journal club.)
E. Brown, J. Moehlis, P. Holmes, E. Clayton, J. Rajkowski, and G. AstonJones. The influence of spike rate and stimulus duration on noradrenergic neurons. J. Comp . Neurosci. 17 (1), 521 , 2004.
E. Brown, J. Moehlis, and P. Holmes. On the phase reduction and response dynamics of neural oscillator populations. Neural Computation 16:673715, 2004. Preprint.
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. 183215. Springer, New York, 2003
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 and H. Rabitz, Some mathematical and algorithmic challenges in the control of quantum dynamics phenomena. J. Math. Chem. 31(1):1763, 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 twoalternative 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):159191, 2001. Preprint.
Eric's Dissertation
Scholarpedia Articles
etc.