- Y. Hu, J. Trousdale, K. Josic, and E. Shea-Brown. Motif Statistics and Spike Correlations in Neuronal Networks. ArXiv q-Bio.NC/1206.3537 and
*J. Statistical Mechanics*P03012:1-51, 2013. -
N. Cain, A. Barreiro, M. Shadlen, and E. Shea-Brown. Neural integrators for decision making: A favorable tradeoff between robustness and sensitivity. ArXiv q-Bio.NC/1111.6573, and

*J. Neurophysiology*, 109(10):2542-59, 2013.J. Trousdale, Y. Hu, E. Shea-Brown, and K. Josic. Impact of network structure and cellular response on spike time correlations. PLOS Computational Biology, 8(3): e1002408, 2012, and ArXiv q-Bio.NC/1110.4914, 2011.

A. Barreiro, E. Thilo, and E. Shea-Brown. The A-current and Type I / Type II transition determine collective spiking from common input. ArXiv q-Bio.NC/1106.0863 and

*J. Neurophysiology*, 108(6):1631-45, 2012. - M. Matell, E. Shea-Brown, 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. Shea-Brown, and J. Rubinstein. Encoding and decoding amplitude-modulated cochlear implant stimuli – a point process analysis.
*J. Comp. Neuroscience*, Volume 28, Number 3, 405-424, 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 (peer-reviewed):
*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), 577-583, 2011.

## Papers and Preprints

Stefano Recanatesi, Matthew Farrell, Madhu Advani, Timothy Moore, Guillaume Lajoie, Eric Shea-Brown. Dimensionality compression and expansion in Deep Neural Networks ArXiv, 2019.Matthew Farrell, Stefano Recanatesi, Guillaume Lajoie, and Eric Shea-Brown. Dynamic compression and expansion in a classifying recurrent network BioRXiv, 2019.

Stefano Recanatesi, Gabe Ocker, Michael Buice, and Eric Shea-Brown. Dimensionality in recurrent spiking networks: global trends in activity and local origins in connectivity BioRXiv and to appear, PLOS Computational Biology, 2019.

Stefano Recanatesi, Matthew Farrell, Guillaume Lajoie, Sophie Deneve, Mattia Rigotti, and Eric Shea-Brown. Signatures and mechanisms of low-dimensional neural predictive manifolds. BioRXiv and submitted, 2018.

Y. Hu, S. Brunton, N. Cain, S. Mihalas, J. N. Kutz, E. Shea-Brown. Feedback through graph motifs relates structure and function in complex networks. ArXiv q-Bio.NC/1605.09073, and to appear, PRE, 2018.

A. Cayco-Gajic, J. Zylberberg, and E. Shea-Brown. A moment-based maximum entropy model for fitting higher-order interactions in neural data. Entropy 20, 489, 2018.

J. Knox, K. Harris, N. Graddis, J. Whitesell, H. Zeng, J. Harris, E. Shea-Brown, S. Mihalas. High resolution data-driven model of the mouse connectome. BioRxiv and to appear, Network Neuroscience, 2018.

B. Brinkman, F. Rieke, E. Shea-Brown, M. Buice. Predicting How and When Hidden Neurons Skew Measured Synaptic Interactions. ArXiv q-Bio.NC/1702.00865, and PLOS Computational Biology 14(10): e10064902018.

R. Kass, (~20 authors), E. Shea-Brown, …, and M. Kramer. Computational neuroscience: mathematical and statistical perspectives. To appear, Annual Review of Statistics and Its Application, 5, 2018.

A.Fyall, Y. El-Shamayleh, H. Choi, E. Shea-Brown, and A. Pasupathy. Dynamic representation of occluded objects in primate prefrontal and visual cortices. eLife 6:e25784, 2017.

G. Ocker, Y. Hu, M. Buice, B. Doiron, K. Josic, R. Rosenbaum, E. Shea-Brown. From the statistics of connectivity to the statistics of spike times in neuronal networks. ArXiv q-Bio.NC/1703.03132, and Current Opinion in Neurobiology 46: 109-119, 2017.

G. Ocker, K. Josic, E. Shea-Brown, M. Buice. Linking structure and activity in nonlinear spiking networks. ArXiv q-Bio.NC/03828, and PLOS Computational Biology 13(6): e1005583, 2017.

Joel Zylberberg, Alexandre Pouget, Peter E. Latham, Eric Shea-Brown. Robust information propagation through noisy neural circuits ArXiv q-Bio.NC/1608.05706 and PLOS Computational Biology 13(4): e1005497, 2017.

K. Harris, T. Dashevskiy, J. Mendoza, A. Garcia, J. Ramirez, and E. Shea-Brown Differential roles for inhibition in excitatory rhythm generators ArXiv q-Bio.NC/1610.04258, and J. Neurophysiology 118: 2070-2088, 2017.

B. Brinkman, A. Weber, F. Rieke, and E. Shea-Brown. 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. Shea-Brown. Nonnegative spline regression of incomplete tracing data reveals high resolution neural connectivity. ArXiv q-Bio.NC/1605.08031, and NIPS, 2016.

G. Lajoie, K. Lin, J.-P. Thivierge, and E. Shea-Brown. Revisiting chaos in stimulus-driven spiking networks: signal encoding and discrimination. ArXiv q-Bio.NC/ 1604.07497, and PLOS Computational Biology, 2016.

J. Zylberberg, J. Cafaro, M. Turner, E. Shea-Brown, and F. Rieke. Direction-selective circuits shape noise to ensure a precise population code. Neuron 89: 369-383, 2016.

J. Zylberberg and E. Shea-Brown. Input nonlinearities can shape beyond-pairwise correlations and improve information transmission by neural populations. ArXiv q-Bio.NC/1212.3549 and Physical Review E 92: 062707, 2015.

D. Leen and E. Shea-Brown. A simple mechanism for higher-order correlations in integrate-and-fire neurons. ArXiv q-Bio.NC/1306.5275 and Journal of Mathematical Neuroscience 5:17, 2015

M. Schwemmer, A. Fairhall, S. Deneve, and E. Shea-Brown. Constructing precisely computing networks with biophysical spiking neurons. ArXiv q-Bio.NC/1411.1391, and *J. Neurosci. 35(28):10112–10134, 2015.*

A. Cayco Gajic, J. Zylberberg, and E. Shea-Brown. Impact of triplet correlations on neural population codes. ArXiv q-Bio.NC/1412.0363, and *Neural Computation*, 2015.

Y. Hu, J. Zylberberg, and E. Shea-Brown. The sign rule and beyond: Boundary effects, flexibility, and optimal noise correlations in neural population codes. ArXiv q-Bio/1307.3235, and *PLOS Comp. Biology 10(2): e1003469*, 2014.

A. Barreiro, E. Shea-Brown. When do feedforward microcircuits produce beyond-pairwise correlations? ArXiv q-Bio/1011.2797, and *Frontiers in Comp. Neuroscience *8:10*,* 2014.

G. Lajoie, J.P. Thivierge, and E. Shea-Brown. Structured chaos shapes spike-response noise entropy in balanced neural networks. ArXiv qBio/1311.7128 and *Frontiers in Comp. Neuroscience *8:123*,* 2014.

J. Trousdale, Y. Hu, E. Shea-Brown, and K. Josic. A generative spike train model with time-structured higher order correlations. ArXiv q-Bio/1305.4160, *Frontiers Comp. Neuroscience*, 7:84, 10.3389, 2013.

Y. Hu, J. Trousdale, E. Shea-Brown, and K. Josic. Local paths to global coherence: cutting networks down to size. ArXiv q-Bio/1212.4239, 2013 and * Physical Review E* 89: 032802, 2014.

J. Zylberberg and E. Shea-Brown. Input nonlinearities shape beyond-pairwise correlations and improve information transmission by neural populations. ArXiv q-Bio/1212.3549, 2012.

A. Cayco Gajic and E. Shea-Brown. Neutral stability, rate propagation, and critical branching in feedforward networks. ArXiv q-Bio/1210.8406, and to appear, Neural Computation, 2013.

G. Lajoie, K. Lin, and E. Shea-Brown. Chaos and reliability in balanced spiking networks. ArXiv nlin/1209.3051, 2012 and Physical Review E, 87:052901-052913, 2013.

N. Cain and E. Shea-Brown. Impact of correlated neural activity on decision making performance. ArXiv q-Bio.NC/1207.5159, and *Neural Computation *13(25) 2: 289–327, 2013.

A. Fairhall, E. Shea-Brown, and A Barreiro. Information theoretic approaches to understanding circuit function. * Curr. Opinion in Neurobiology *22(4): 653-659*,* 2012.

N. Cain and E. Shea-Brown. Computational models of decision making: integration, nonlinearity, and noise. *Curr. Opinion in Neurobiology* 22:1–7, 2012.

J. Goldwyn, J. Rubinstein, and E. Shea-Brown. A point process framework for modeling electrical stimulation of the auditory nerve. ArXiv q-Bio.NC/1201.5428 and *J. Neurophysiology*, 108:1430-1452, 2012

J. Goldwyn and E. Shea-Brown. The what and where of adding channel noise to the Hodgkin-Huxley equations. *PLOS Comp. Biol.* 7:1002247, 2011.

J. Goldwyn, N. Imennov, M. Famulare, and E. Shea-Brown. On stochastic differential equation models for ion channel noise in Hodgkin-Huxley neurons. Phys. Rev. E 83, 041908, 2011. Also: ArXiv q-Bio/1009.4172, 2010.

A. Barreiro, E. Shea-Brown. When do feedforward microcircuits produce beyond-pairwise correlations? ArXiv q-Bio/1011.2797, and to appear, *Frontiers in Comp. Neuroscience,* 2014.

G. Lajoie and E. Shea-Brown. Shared inputs and desynchrony in elliptic bursters: from slow passage to discontinuous circle maps. SIAM J. App. Dyn. Sys. (10): 1232-1271*,* 2011, and ArXiv math.DS/1010.2809.

A. Barreiro, E. Shea-Brown, and E. Thilo. Timescales of spike-train correlation for neural oscillators with common drive. *Phys. Rev. E, * 81, 011916, 2010 and ArXiv q-Bio/0907.3924.

K. Lin, E. Shea-Brown, and L-S. Young. Spike-time reliability of layered neural oscillator networks. * Journal of Computational Neuroscience *, 27(1): 135, 2009, and ArXiv. Builds on: K. Lin, E. Shea-Brown, and L-S. Young. Reliability of layered neural oscillator networks. * Fast communication in Comm. Math. Sci., 7(1): 239-247, 2009. *

K. Josic, E. Shea-Brown, B. Doiron, and J. de la Rocha. Stimulus-dependent correlations and population codes.* Neural Computation, *21(10): 2774-2804, 2009 and ArXiv.

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. Some additional material: *ArXiV version*.

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. *J. Nonlin. Sci.*, 19(5): 497-545, 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. Shea-Brown, K. Josic, and A. Reyes. Correlation between neural spike trains increases with firing rate. * Nature* 448, 802-806, 2007(+ supplemental material).

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.

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

S. Coombes, B. Doiron, K. Josic, and E. Shea-Brown. Toward blueprints for network architecture, biophysical dynamics, and signal transduction.* Phil. Trans. Royal Soc. A*, 364: 3301-3318, 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, 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. Preprint version. (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. 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. 183-215. 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):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. Preprint.

## Eric's Dissertation

## Scholarpedia Articles

## etc.