Nicolas Brunel | Scholars@Duke

Nicolas Brunel
Professor of Neurobiology

We use theoretical models of brain systems to investigate how they process and learn information from their inputs. Our current work focuses on the mechanisms of learning and memory, from the synapse to the network level, in collaboration with various experimental groups. Using methods from
statistical physics, we have shown recently that the synaptic
connectivity of a network that maximizes storage capacity reproduces
two key experimentally observed features: low connection probability
and strong overrepresentation of bidirectionnally connected pairs of
neurons. We have also inferred `synaptic plasticity rules' (a
mathematical description of how synaptic strength depends on the
activity of pre and post-synaptic neurons) from data, and shown that
networks endowed with a plasticity rule inferred from data have a
storage capacity that is close to the optimal bound.

Current Appointments & Affiliations

Professor of Neurobiology, Neurobiology, Basic Science Departments 2017
Professor of Physics, Physics, Trinity College of Arts & Sciences 2017
Faculty Network Member of the Duke Institute for Brain Sciences, Duke Institute for Brain Sciences, University Institutes and Centers 2018
Member of the Center for Cognitive Neuroscience, Center for Cognitive Neuroscience, Duke Institute for Brain Sciences 2018

Contact Information

311 Research Drive, Durham, NC 27710
nicolas.brunel@duke.edu (919) 684-8684
Neurobiology page
Physics page

Background
Education, Training, & Certifications
- Ph.D., Pierre and Marie Curie University (France) 1993
Academic Positions Outside Duke
- Professor, The University of Chicago. 2012 - 2017
- Directeur de Recherches, CNRS, Universite Paris Descartes. 2005 - 2012
- Charge de Recherches, CNRS, Universite Paris Descartes. 2001 - 2005
- Charge de Recherches, CNRS, Ecole Normale Superieure. 1995 - 2001
Recognition
Awards & Honors
- Prime d'excellence scientifique. CNRS. 2011
Research
Selected Grants
- Neurobiology Training Program awarded by National Institutes of Health 2019 - 2024
- Canonical computations for motor learning by the cerebellar cortex micro-circuit awarded by National Institutes of Health 2019 - 2024
- Striatal Plasticity in Habit Formation as a Platform to Deconstruct Adaptive Learning awarded by National Institutes of Health 2018 - 2023
- Investigating ripple oscillations as a mechanism for human memory retrieval awarded by National Institutes of Health 2019 - 2022
- Medical Scientist Training Program awarded by National Institutes of Health 1997 - 2022
- Learning spatio-temporal statistics from the environment in recurrent networks awarded by Office of Naval Research 2017 - 2020
- Learning spatio-temporal statistics from the environment in recurrent networks 2017 - 2020
- Circuitry underlying response summation in mouse and primate: theory and experiment 2018 - 2020
- An Integrated Nonparametric Bayesian and Deep Neural Network Framework for Biologically-Inspired Lifelong Learning awarded by Defense Advanced Research Projects Agency 2018 - 2020
- CRCNS: Multiscale dynamics of cortical circuits for visual recognition & memory awarded by University of Chicago 2017 - 2020
- Large-scale, neuronal ensemble recordings in motor cortex of the behaving marmoset awarded by University of Chicago 2018 - 2019
- CRCNS: US-French Research Proposal: Synaptic plasticity rules under physiological conditions for hippocampus and cerebellum awarded by National Science Foundation 2017
Publications & Artistic Works
Selected Publications
- Academic Articles
  - Vaz, Alex P., Sara K. Inati, Nicolas Brunel, and Kareem A. Zaghloul. “Coupled ripple oscillations between the medial temporal lobe and neocortex retrieve human memory..” Science 363, no. 6430 (March 1, 2019): 975–78. https://doi.org/10.1126/science.aau8956.
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  - Bouvier, Guy, Johnatan Aljadeff, Claudia Clopath, Célian Bimbard, Jonas Ranft, Antonin Blot, Jean-Pierre Nadal, Nicolas Brunel, Vincent Hakim, and Boris Barbour. “Cerebellar learning using perturbations..” Elife 7 (November 12, 2018). https://doi.org/10.7554/eLife.31599.
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  - Pereira, Ulises, and Nicolas Brunel. “Attractor Dynamics in Networks with Learning Rules Inferred from In Vivo Data..” Neuron 99, no. 1 (July 11, 2018): 227-238.e4. https://doi.org/10.1016/j.neuron.2018.05.038.
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  - Martí, Daniel, Nicolas Brunel, and Srdjan Ostojic. “Correlations between synapses in pairs of neurons slow down dynamics in randomly connected neural networks..” Phys Rev E 97, no. 6–1 (June 2018). https://doi.org/10.1103/PhysRevE.97.062314.
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  - Tartaglia, Elisa M., and Nicolas Brunel. “Bistability and up/down state alternations in inhibition-dominated randomly connected networks of LIF neurons..” Sci Rep 7, no. 1 (September 20, 2017). https://doi.org/10.1038/s41598-017-12033-y.
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  - Titley, Heather K., Nicolas Brunel, and Christian Hansel. “Toward a Neurocentric View of Learning..” Neuron 95, no. 1 (July 5, 2017): 19–32. https://doi.org/10.1016/j.neuron.2017.05.021.
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  - Zampini, Valeria, Jian K. Liu, Marco A. Diana, Paloma P. Maldonado, Nicolas Brunel, and Stéphane Dieudonné. “Mechanisms and functional roles of glutamatergic synapse diversity in a cerebellar circuit..” Elife 5 (September 19, 2016). https://doi.org/10.7554/eLife.15872.
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  - De Pittà, M., N. Brunel, and A. Volterra. “Astrocytes: Orchestrating synaptic plasticity?.” Neuroscience 323 (May 26, 2016): 43–61. https://doi.org/10.1016/j.neuroscience.2015.04.001.
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  - Brunel, Nicolas. “Is cortical connectivity optimized for storing information?.” Nat Neurosci 19, no. 5 (May 2016): 749–55. https://doi.org/10.1038/nn.4286.
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  - Bouvier, Guy, David Higgins, Maria Spolidoro, Damien Carrel, Benjamin Mathieu, Clément Léna, Stéphane Dieudonné, Boris Barbour, Nicolas Brunel, and Mariano Casado. “Burst-Dependent Bidirectional Plasticity in the Cerebellum Is Driven by Presynaptic NMDA Receptors..” Cell Rep 15, no. 1 (April 5, 2016): 104–16. https://doi.org/10.1016/j.celrep.2016.03.004.
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  - Dubreuil, Alexis M., and Nicolas Brunel. “Storing structured sparse memories in a multi-modular cortical network model..” J Comput Neurosci 40, no. 2 (April 2016): 157–75. https://doi.org/10.1007/s10827-016-0590-z.
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  - De Pittà, Maurizio, and Nicolas Brunel. “Modulation of Synaptic Plasticity by Glutamatergic Gliotransmission: A Modeling Study..” Neural Plast 2016 (2016). https://doi.org/10.1155/2016/7607924.
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  - Lim, Sukbin, Jillian L. McKee, Luke Woloszyn, Yali Amit, David J. Freedman, David L. Sheinberg, and Nicolas Brunel. “Inferring learning rules from distributions of firing rates in cortical neurons..” Nat Neurosci 18, no. 12 (December 2015): 1804–10. https://doi.org/10.1038/nn.4158.
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  - Alemi, Alireza, Carlo Baldassi, Nicolas Brunel, and Riccardo Zecchina. “A Three-Threshold Learning Rule Approaches the Maximal Capacity of Recurrent Neural Networks..” Plos Comput Biol 11, no. 8 (August 2015). https://doi.org/10.1371/journal.pcbi.1004439.
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  - Ostojic, Srdjan, Germán Szapiro, Eric Schwartz, Boris Barbour, Nicolas Brunel, and Vincent Hakim. “Neuronal morphology generates high-frequency firing resonance..” J Neurosci 35, no. 18 (May 6, 2015): 7056–68. https://doi.org/10.1523/JNEUROSCI.3924-14.2015.
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  - Tartaglia, Elisa M., Nicolas Brunel, and Gianluigi Mongillo. “Modulation of network excitability by persistent activity: how working memory affects the response to incoming stimuli..” Plos Comput Biol 11, no. 2 (February 2015). https://doi.org/10.1371/journal.pcbi.1004059.
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  - Barbieri, Francesca, Alberto Mazzoni, Nikos K. Logothetis, Stefano Panzeri, and Nicolas Brunel. “Stimulus dependence of local field potential spectra: experiment versus theory..” J Neurosci 34, no. 44 (October 29, 2014): 14589–605. https://doi.org/10.1523/JNEUROSCI.5365-13.2014.
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  - Higgins, David, Michael Graupner, and Nicolas Brunel. “Memory maintenance in synapses with calcium-based plasticity in the presence of background activity..” Plos Comput Biol 10, no. 10 (October 2014). https://doi.org/10.1371/journal.pcbi.1003834.
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  - Dubreuil, Alexis M., Yali Amit, and Nicolas Brunel. “Memory capacity of networks with stochastic binary synapses..” Plos Comput Biol 10, no. 8 (August 2014). https://doi.org/10.1371/journal.pcbi.1003727.
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  - Clopath, Claudia, Aleksandra Badura, Chris I. De Zeeuw, and Nicolas Brunel. “A cerebellar learning model of vestibulo-ocular reflex adaptation in wild-type and mutant mice..” J Neurosci 34, no. 21 (May 21, 2014): 7203–15. https://doi.org/10.1523/JNEUROSCI.2791-13.2014.
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  - Brunel, Nicolas, Vincent Hakim, and Magnus J. E. Richardson. “Single neuron dynamics and computation..” Curr Opin Neurobiol 25 (April 2014): 149–55. https://doi.org/10.1016/j.conb.2014.01.005.
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  - Hertäg, Loreen, Daniel Durstewitz, and Nicolas Brunel. “Analytical approximations of the firing rate of an adaptive exponential integrate-and-fire neuron in the presence of synaptic noise..” Front Comput Neurosci 8 (2014). https://doi.org/10.3389/fncom.2014.00116.
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  - Tartaglia, Elisa M., Gianluigi Mongillo, and Nicolas Brunel. “On the relationship between persistent delay activity, repetition enhancement and priming..” Front Psychol 5 (2014). https://doi.org/10.3389/fpsyg.2014.01590.
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  - Clopath, Claudia, and Nicolas Brunel. “Optimal properties of analog perceptrons with excitatory weights..” Plos Comput Biol 9, no. 2 (2013). https://doi.org/10.1371/journal.pcbi.1002919.
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  - Graupner, Michael, and Nicolas Brunel. “Calcium-based plasticity model explains sensitivity of synaptic changes to spike pattern, rate, and dendritic location..” Proc Natl Acad Sci U S A 109, no. 10 (March 6, 2012): 3991–96. https://doi.org/10.1073/pnas.1109359109.
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  - Clopath, Claudia, Jean-Pierre Nadal, and Nicolas Brunel. “Storage of correlated patterns in standard and bistable Purkinje cell models..” Plos Comput Biol 8, no. 4 (2012). https://doi.org/10.1371/journal.pcbi.1002448.
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  - Roxin, Alex, Nicolas Brunel, David Hansel, Gianluigi Mongillo, and Carl van Vreeswijk. “On the distribution of firing rates in networks of cortical neurons..” J Neurosci 31, no. 45 (November 9, 2011): 16217–26. https://doi.org/10.1523/JNEUROSCI.1677-11.2011.
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  - Ostojic, Srdjan, and Nicolas Brunel. “From spiking neuron models to linear-nonlinear models..” Plos Comput Biol 7, no. 1 (January 20, 2011). https://doi.org/10.1371/journal.pcbi.1001056.
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  - Hamaguchi, Kosuke, Alexa Riehle, and Nicolas Brunel. “Estimating network parameters from combined dynamics of firing rate and irregularity of single neurons..” J Neurophysiol 105, no. 1 (January 2011): 487–500. https://doi.org/10.1152/jn.00858.2009.
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  - Ledoux, Erwan, and Nicolas Brunel. “Dynamics of networks of excitatory and inhibitory neurons in response to time-dependent inputs..” Front Comput Neurosci 5 (2011). https://doi.org/10.3389/fncom.2011.00025.
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  - Mazzoni, Alberto, Nicolas Brunel, Stefano Cavallari, Nikos K. Logothetis, and Stefano Panzeri. “Cortical dynamics during naturalistic sensory stimulations: experiments and models..” J Physiol Paris 105, no. 1–3 (January 2011): 2–15. https://doi.org/10.1016/j.jphysparis.2011.07.014.
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  - Mazzoni, Alberto, Kevin Whittingstall, Nicolas Brunel, Nikos K. Logothetis, and Stefano Panzeri. “Understanding the relationships between spike rate and delta/gamma frequency bands of LFPs and EEGs using a local cortical network model..” Neuroimage 52, no. 3 (September 2010): 956–72. https://doi.org/10.1016/j.neuroimage.2009.12.040.
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  - Panzeri, Stefano, Nicolas Brunel, Nikos K. Logothetis, and Christoph Kayser. “Sensory neural codes using multiplexed temporal scales..” Trends Neurosci 33, no. 3 (March 2010): 111–20. https://doi.org/10.1016/j.tins.2009.12.001.
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  - Graupner, Michael, and Nicolas Brunel. “Mechanisms of induction and maintenance of spike-timing dependent plasticity in biophysical synapse models..” Front Comput Neurosci 4 (2010). https://doi.org/10.3389/fncom.2010.00136.
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  - Brunel, Nicolas, and Frédéric Lavigne. “Semantic priming in a cortical network model..” J Cogn Neurosci 21, no. 12 (December 2009): 2300–2319. https://doi.org/10.1162/jocn.2008.21156.
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  - Graupner, Michael, and Nicolas Brunel. “A bitable synaptic model with transitions between states induced by calcium dynamics: theory vs experiment.” Bmc Neuroscience 10, no. S1 (September 2009). https://doi.org/10.1186/1471-2202-10-s1-o15.
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  - Ostojic, Srdjan, Nicolas Brunel, and Vincent Hakim. “How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains..” J Neurosci 29, no. 33 (August 19, 2009): 10234–53. https://doi.org/10.1523/JNEUROSCI.1275-09.2009.
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  - Ostojic, Srdjan, Nicolas Brunel, and Vincent Hakim. “Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities..” J Comput Neurosci 26, no. 3 (June 2009): 369–92. https://doi.org/10.1007/s10827-008-0117-3.
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  - Zillmer, Rüdiger, Nicolas Brunel, and David Hansel. “Very long transients, irregular firing, and chaotic dynamics in networks of randomly connected inhibitory integrate-and-fire neurons..” Phys Rev E Stat Nonlin Soft Matter Phys 79, no. 3 Pt 1 (March 2009). https://doi.org/10.1103/PhysRevE.79.031909.
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  - Dugué, Guillaume P., Nicolas Brunel, Vincent Hakim, Eric Schwartz, Mireille Chat, Maxime Lévesque, Richard Courtemanche, Clément Léna, and Stéphane Dieudonné. “Electrical coupling mediates tunable low-frequency oscillations and resonance in the cerebellar Golgi cell network..” Neuron 61, no. 1 (January 15, 2009): 126–39. https://doi.org/10.1016/j.neuron.2008.11.028.
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  - Mazzoni, Alberto, Stefano Panzeri, Nikos K. Logothetis, and Nicolas Brunel. “Encoding of naturalistic stimuli by local field potential spectra in networks of excitatory and inhibitory neurons..” Plos Comput Biol 4, no. 12 (December 2008). https://doi.org/10.1371/journal.pcbi.1000239.
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  - Roxin, Alex, Vincent Hakim, and Nicolas Brunel. “The statistics of repeating patterns of cortical activity can be reproduced by a model network of stochastic binary neurons..” J Neurosci 28, no. 42 (October 15, 2008): 10734–45. https://doi.org/10.1523/JNEUROSCI.1016-08.2008.
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  - Barbieri, Francesca, and Nicolas Brunel. “Can attractor network models account for the statistics of firing during persistent activity in prefrontal cortex?.” Front Neurosci 2, no. 1 (July 2008): 114–22. https://doi.org/10.3389/neuro.01.003.2008.
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  - Solages, Camille de, Germán Szapiro, Nicolas Brunel, Vincent Hakim, Philippe Isope, Pierre Buisseret, Charly Rousseau, Boris Barbour, and Clément Léna. “High-frequency organization and synchrony of activity in the purkinje cell layer of the cerebellum..” Neuron 58, no. 5 (June 12, 2008): 775–88. https://doi.org/10.1016/j.neuron.2008.05.008.
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  - Brunel, Nicolas, and Vincent Hakim. “Sparsely synchronized neuronal oscillations..” Chaos 18, no. 1 (March 2008). https://doi.org/10.1063/1.2779858.
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  - Brunel, Nicolas. “Daniel Amit (1938-2007)..” Network 19, no. 1 (2008): 3–8. https://doi.org/10.1080/09548980801915391.
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  - Battaglia, Demian, Nicolas Brunel, and David Hansel. “Temporal decorrelation of collective oscillations in neural networks with local inhibition and long-range excitation..” Phys Rev Lett 99, no. 23 (December 7, 2007). https://doi.org/10.1103/PhysRevLett.99.238106.
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  - Barbour, Boris, Nicolas Brunel, Vincent Hakim, and Jean-Pierre Nadal. “What can we learn from synaptic weight distributions?.” Trends Neurosci 30, no. 12 (December 2007): 622–29. https://doi.org/10.1016/j.tins.2007.09.005.
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  - Brunel, Nicolas, and Mark C. W. van Rossum. “Lapicque's 1907 paper: from frogs to integrate-and-fire..” Biol Cybern 97, no. 5–6 (December 2007): 337–39. https://doi.org/10.1007/s00422-007-0190-0.
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  - Graupner, Michael, and Nicolas Brunel. “STDP in a bistable synapse model based on CaMKII and associated signaling pathways..” Plos Comput Biol 3, no. 11 (November 2007). https://doi.org/10.1371/journal.pcbi.0030221.
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  - Baldassi, Carlo, Alfredo Braunstein, Nicolas Brunel, and Riccardo Zecchina. “Efficient supervised learning in networks with binary synapses..” Proc Natl Acad Sci U S A 104, no. 26 (June 26, 2007): 11079–84. https://doi.org/10.1073/pnas.0700324104.
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  - Baldassi, Carlo, Alfredo Braunstein, Nicolas Brunel, and Riccardo Zecchina. “Efficient supervised learning in networks with binary synapses..” Proc. Natl. Acad. Sci. U.S.A. 104 (2007): 11079–84.
  - Barbieri, Francesca, and Nicolas Brunel. “Irregular persistent activity induced by synaptic excitatory feedback..” Front Comput Neurosci 1 (2007). https://doi.org/10.3389/neuro.10.005.2007.
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  - Brunel, Nicolas, and David Hansel. “How noise affects the synchronization properties of recurrent networks of inhibitory neurons..” Neural Comput 18, no. 5 (May 2006): 1066–1110. https://doi.org/10.1162/089976606776241048.
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  - Geisler, Caroline, Nicolas Brunel, and Xiao-Jing Wang. “Contributions of intrinsic membrane dynamics to fast network oscillations with irregular neuronal discharges..” J Neurophysiol 94, no. 6 (December 2005): 4344–61. https://doi.org/10.1152/jn.00510.2004.
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  - Roxin, Alex, Nicolas Brunel, and David Hansel. “Role of delays in shaping spatiotemporal dynamics of neuronal activity in large networks..” Phys Rev Lett 94, no. 23 (June 17, 2005). https://doi.org/10.1103/PhysRevLett.94.238103.
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  - Boucheny, Christian, Nicolas Brunel, and Angelo Arleo. “A continuous attractor network model without recurrent excitation: maintenance and integration in the head direction cell system..” J Comput Neurosci 18, no. 2 (March 2005): 205–27. https://doi.org/10.1007/s10827-005-6559-y.
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  - Brunel, N. “Course 10 Network models of memory” 80, no. C (January 1, 2005): 407–76. https://doi.org/10.1016/S0924-8099(05)80016-2.
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  - Brunel, Nicolas, Vincent Hakim, Philippe Isope, Jean-Pierre Nadal, and Boris Barbour. “Optimal information storage and the distribution of synaptic weights: perceptron versus Purkinje cell..” Neuron 43, no. 5 (September 2, 2004): 745–57. https://doi.org/10.1016/j.neuron.2004.08.023.
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  - Fourcaud-Trocmé, Nicolas, David Hansel, Carl van Vreeswijk, and Nicolas Brunel. “How spike generation mechanisms determine the neuronal response to fluctuating inputs..” J Neurosci 23, no. 37 (December 17, 2003): 11628–40.
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  - Brunel, Nicolas. “Dynamics and plasticity of stimulus-selective persistent activity in cortical network models..” Cereb Cortex 13, no. 11 (November 2003): 1151–61. https://doi.org/10.1093/cercor/bhg096.
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  - Brunel, Nicolas, and Peter E. Latham. “Firing rate of the noisy quadratic integrate-and-fire neuron..” Neural Comput 15, no. 10 (October 2003): 2281–2306. https://doi.org/10.1162/089976603322362365.
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  - Mongillo, Gianluigi, Daniel J. Amit, and Nicolas Brunel. “Retrospective and prospective persistent activity induced by Hebbian learning in a recurrent cortical network..” Eur J Neurosci 18, no. 7 (October 2003): 2011–24. https://doi.org/10.1046/j.1460-9568.2003.02908.x.
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  - Brunel, Nicolas, Yves Frégnac, Claude Meunier, and Jean-Pierre Nadal. “Neuroscience and computation..” J Physiol Paris 97, no. 4–6 (July 2003): 387–90. https://doi.org/10.1016/j.jphysparis.2004.02.001.
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  - Brunel, Nicolas, and Xiao-Jing Wang. “What determines the frequency of fast network oscillations with irregular neural discharges? I. Synaptic dynamics and excitation-inhibition balance..” J Neurophysiol 90, no. 1 (July 2003): 415–30. https://doi.org/10.1152/jn.01095.2002.
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  - Brunel, Nicolas, Vincent Hakim, and Magnus J. E. Richardson. “Firing-rate resonance in a generalized integrate-and-fire neuron with subthreshold resonance..” Phys Rev E Stat Nonlin Soft Matter Phys 67, no. 5 Pt 1 (May 2003). https://doi.org/10.1103/PhysRevE.67.051916.
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  - Richardson, Magnus J. E., Nicolas Brunel, and Vincent Hakim. “From subthreshold to firing-rate resonance..” J Neurophysiol 89, no. 5 (May 2003): 2538–54. https://doi.org/10.1152/jn.00955.2002.
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  - Fourcaud, Nicolas, and Nicolas Brunel. “Dynamics of the firing probability of noisy integrate-and-fire neurons..” Neural Comput 14, no. 9 (September 2002): 2057–2110. https://doi.org/10.1162/089976602320264015.
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  - Brunel, N., and X. J. Wang. “Effects of neuromodulation in a cortical network model of object working memory dominated by recurrent inhibition..” J Comput Neurosci 11, no. 1 (July 2001): 63–85. https://doi.org/10.1023/a:1011204814320.
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  - Brunel, N., F. S. Chance, N. Fourcaud, and L. F. Abbott. “Effects of synaptic noise and filtering on the frequency response of spiking neurons..” Phys Rev Lett 86, no. 10 (March 5, 2001): 2186–89. https://doi.org/10.1103/PhysRevLett.86.2186.
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  - Brunel, N. “Persistent activity and the single-cell frequency-current curve in a cortical network model..” Network 11, no. 4 (November 2000): 261–80.
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  - Compte, A., N. Brunel, P. S. Goldman-Rakic, and X. J. Wang. “Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model..” Cereb Cortex 10, no. 9 (September 2000): 910–23. https://doi.org/10.1093/cercor/10.9.910.
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  - Brunel, N. “Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons..” J Comput Neurosci 8, no. 3 (May 2000): 183–208. https://doi.org/10.1023/a:1008925309027.
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  - Brunel, N., and V. Hakim. “Fast global oscillations in networks of integrate-and-fire neurons with low firing rates..” Neural Comput 11, no. 7 (October 1, 1999): 1621–71. https://doi.org/10.1162/089976699300016179.
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  - Brunel, N., and S. Sergi. “Firing frequency of leaky intergrate-and-fire neurons with synaptic current dynamics..” J Theor Biol 195, no. 1 (November 7, 1998): 87–95. https://doi.org/10.1006/jtbi.1998.0782.
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  - Brunel, N., and J. P. Nadal. “Mutual information, Fisher information, and population coding..” Neural Comput 10, no. 7 (October 1, 1998): 1731–57. https://doi.org/10.1162/089976698300017115.
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  - Nadal, J. P., N. Brunel, and N. Parga. “Nonlinear feedforward networks with stochastic outputs: infomax implies redundancy reduction..” Network 9, no. 2 (May 1998): 207–17.
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  - Brunel, N., F. Carusi, and S. Fusi. “Slow stochastic Hebbian learning of classes of stimuli in a recurrent neural network..” Network 9, no. 1 (February 1998): 123–52.
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  - Brunel, N., and O. Trullier. “Plasticity of directional place fields in a model of rodent CA3..” Hippocampus 8, no. 6 (1998): 651–65. https://doi.org/10.1002/(SICI)1098-1063(1998)8:6<651::AID-HIPO8>3.0.CO;2-L.
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  - Brunel, N., and J. Ninio. “Time to detect the difference between two images presented side by side..” Brain Res Cogn Brain Res 5, no. 4 (June 1997): 273–82. https://doi.org/10.1016/s0926-6410(97)00003-7.
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  - Amit, D. J., and N. Brunel. “Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex..” Cereb Cortex 7, no. 3 (April 1997): 237–52. https://doi.org/10.1093/cercor/7.3.237.
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  - Amit, Daniel, and Nicolas Brunel. “Dynamics of a recurrent network of spiking neurons before and following learning.” Network: Computation in Neural Systems 8, no. 4 (January 1, 1997): 373–404. https://doi.org/10.1088/0954-898X_8_4_003.
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  - Brunel, N. “Hebbian learning of context in recurrent neural networks..” Neural Comput 8, no. 8 (November 15, 1996): 1677–1710. https://doi.org/10.1162/neco.1996.8.8.1677.
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  - Brunel, Nicolas, and Riccardo Zecchina. “A SIMPLE GEOMETRICAL BOUND FOR REPLICA SYMMETRY STABILITY IN NEURAL NETWORKS MODELS.” Modern Physics Letters B 09, no. 18 (August 10, 1995): 1159–64. https://doi.org/10.1142/s0217984995001157.
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  - Amit, Daniel, and Nicolas Brunel. “Learning internal representations in an attractor neural network with analogue neurons.” Network: Computation in Neural Systems 6, no. 3 (August 1, 1995): 359–88. https://doi.org/10.1088/0954-898x/6/3/004.
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  - Brunel, Nicolas. “Storage capacity of neural networks: Effect of the fluctuations of the number of active neurons per memory.” Journal of Physics A: Mathematical and General 27, no. 14 (December 1, 1994): 4783–89. https://doi.org/10.1088/0305-4470/27/14/009.
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  - Amit, D. J., N. Brunel, and M. V. Tsodyks. “Correlations of cortical Hebbian reverberations: theory versus experiment..” J Neurosci 14, no. 11 Pt 1 (November 1994): 6435–45.
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  - Brunel, Nicolas. “Dynamics of an attractor neural network converting temporal into spatial correlations.” Network: Computation in Neural Systems 5, no. 4 (November 1, 1994): 449–70. https://doi.org/10.1088/0954-898x/5/4/003.
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  - Brunel, N., and R. Zecchina. “Response functions improving performance in analog attractor neural networks..” Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 49, no. 3 (March 1994): R1823–26. https://doi.org/10.1103/physreve.49.r1823.
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  - Brunel, N. “Effect of synapse dilution on the memory retrieval in structured attractor neural networks.” Journal De Physique I 3, no. 8 (August 1993): 1693–1715. https://doi.org/10.1051/jp1:1993210.
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  - Amit, D. J., and N. Brunel. “Adequate input for learning in attractor neural networks.” Network: Computation in Neural Systems 4, no. 2 (January 1, 1993): 177–94. https://doi.org/10.1088/0954-898X_4_2_003.
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  - Brunel, Nicolas, Jean-Pierre Nadal, and Gerard Toulouse. “Information capacity of a perceptron.” Journal of Physics A: Mathematical and General 25, no. 19 (December 1, 1992): 5017–38. https://doi.org/10.1088/0305-4470/25/19/015.
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- Book Sections
  - Brunel, Nicolas, and Vincent Hakim. “Population Density Models..” In Encyclopedia of Computational Neuroscience, edited by Dieter Jaeger and Ranu Jung. Springer, 2014.
  - Brunel, Nicolas, and Vincent Hakim. “Fokker-Planck Equation..” In Encyclopedia of Computational Neuroscience, edited by Dieter Jaeger and Ranu Jung. Springer, 2014.
  - Brunel, Nicolas. “Dynamics of neural networks.” In Principles of Neural Coding, 489–512, 2013. https://doi.org/10.1201/b14756.
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  - Brunel, Nicolas, and Vincent Hakim. “Neuronal Dynamics..” In Encyclopedia of Complexity and Systems Science, edited by Robert A. Meyers, 6099–6116. Springer, 2009.
- Conference Papers
  - Roxin, A., N. Brunel, and D. Hansel. “Rate models with delays and the dynamics of large networks of spiking neurons.” In Progress of Theoretical Physics Supplement, 161:68–85, 2006. https://doi.org/10.1143/PTPS.161.68.
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  - Fourcaud-Trocmé, Nicolas, and Nicolas Brunel. “Dynamics of the instantaneous firing rate in response to changes in input statistics..” In J Comput Neurosci, 18:311–21, 2005. https://doi.org/10.1007/s10827-005-0337-8.
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  - Brunel, N. “Dynamics of networks of randomly connected excitatory and inhibitory spiking neurons..” In J Physiol Paris, 94:445–63, 2000. https://doi.org/10.1016/s0928-4257(00)01084-6.
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  - Brunel, N. “Phase diagrams of sparsely connected networks of excitatory and inhibitory spiking neurons.” In Neurocomputing, 32–33:307–12, 2000. https://doi.org/10.1016/S0925-2312(00)00179-X.
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  - Brunel, N., and X. J. Wang. “Fast network oscillations with intermittent principal cell firing in a model of a recurrent excitatory-inhibitory circuit.” In European Journal of Neuroscience, 12:79–79. BLACKWELL SCIENCE LTD, 2000.
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  - Brunel, N., and J. P. Nadal. “Modeling memory: what do we learn from attractor neural networks?.” In C R Acad Sci Iii, 321:249–52, 1998. https://doi.org/10.1016/s0764-4469(97)89830-7.
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  - Brunel, N. “Cross-correlations in sparsely connected recurrent networks of spiking neurons.” In Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 1327:31–36, 1997.
  - Brunel, Nicolas, and Jean-Pierre Nadal. “Optimal tuning curves for neurons spiking as a Poisson process..” In Esann, edited by Michel Verleysen. D-Facto public, 1997.
  - Ninio, J., and N. Brunel. “Time to detect a single difference between two correlated images.” In Perception, 25:89–89. PION LTD, 1996.
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  - Brunel, N. “Quantitative modeling of local Hebbian reverberations in primate cortex.” In International Journal of Neural Systems, Supplementary Issue, 1995, edited by D. J. Amit, P. delGiudice, B. Denby, E. T. Rolls, and A. Treves, 13–17. WORLD SCIENTIFIC PUBL CO PTE LTD, 1995.
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  - Brunel, N., and D. J. Amit. “Learning internal representations in an analog attractor neural network.” In International Journal of Neural Systems, Supplementary Issue, 1995, edited by D. J. Amit, P. delGiudice, B. Denby, E. T. Rolls, and A. Treves, 19–23. WORLD SCIENTIFIC PUBL CO PTE LTD, 1995.
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Teaching & Mentoring
Recent Courses
Advising & Mentoring
- Current PhD students:
  - Ulises Pereira (University of Chicago, 2013-2018)
  - Max Gillett (2014-2020)
  Past PhD students:
  - Nicolas Fourcaud-Trocme
  - Michael Graupner
  - Carlo Baldassi
  - Francesca Barbieri
  - Erwan Ledoux
  - David Higgins
  - Alexis Dubreuil
  Current post-docs:
  - Yonatan Aljadeff (2014-2018)
  Past post-docs:
  - Alex Roxin
  - Ruediger Zillmer
  - Kosuke Hamaguchi
  - Srdjan Ostojic
  - Alberto Mazzoni
  - Jian Liu
  - Claudia Clopath
  - Francesca Barbieri
  - Elisa Tartaglia
  - Martin Wiechert
  - Sukbin Lim
  - Maurizio de Pitta
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Advising & Mentoring

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