# Nicolas Brunel

## Professor of Physics

### Overview

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.

### Selected Grants

An Integrated Nonparametric Bayesian and Deep Neural Network Framework for Biologically-Inspired Lifelong Learning awarded by Defense Advanced Research Projects Agency (Co Investigator). 2018 to 2020

Learning spatio-temporal statistics from the environment in recurrent networks awarded by Office of Naval Research (Principal Investigator). 2017 to 2019

Large-scale, neuronal ensemble recordings in motor cortex of the behaving marmoset awarded by University of Chicago (Principal Investigator). 2018

Learning spatio-temporal statistics from the environment in recurrent networks awarded by University of Texas Health Science Center at Houston (Principal Investigator). 2017 to 2018

CRCNS: US-French Research Proposal: Synaptic plasticity rules under physiological conditions for hippocampus and cerebellum awarded by National Science Foundation (Principal Investigator). 2017

Brunel, N, and Hakim, V. "Population Density Models." *Encyclopedia of Computational Neuroscience.* Ed. D Jaeger and R Jung. Springer, 2014.

Brunel, N, and Hakim, V. "Fokker-Planck Equation." *Encyclopedia of Computational Neuroscience.* Ed. D Jaeger and R Jung. Springer, 2014.

Brunel, N, and Hakim, V. "Neuronal Dynamics." *Encyclopedia of Complexity and Systems Science.* Ed. RA Meyers. Springer, 2009. 6099-6116.

Tartaglia, EM, and Brunel, N. "Bistability and up/down state alternations in inhibition-dominated randomly connected networks of LIF neurons." *Scientific reports* 7.1 (September 20, 2017): 11916-.
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Titley, HK, Brunel, N, and Hansel, C. "Toward a Neurocentric View of Learning." *Neuron* 95.1 (July 2017): 19-32. (Review)
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Zampini, V, Liu, JK, Diana, MA, Maldonado, PP, Brunel, N, and Dieudonné, S. "Mechanisms and functional roles of glutamatergic synapse diversity in a cerebellar circuit." *eLife* 5 (September 19, 2016).
Full Text Open Access Copy

Brunel, N. "Is cortical connectivity optimized for storing information?." *Nature neuroscience* 19.5 (May 2016): 749-755.
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De Pittà, M, Brunel, N, and Volterra, A. "Astrocytes: Orchestrating synaptic plasticity?." *Neuroscience* 323 (May 2016): 43-61. (Review)
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Dubreuil, AM, and Brunel, N. "Storing structured sparse memories in a multi-modular cortical network model." *Journal of computational neuroscience* 40.2 (April 2016): 157-175.
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Bouvier, G, Higgins, D, Spolidoro, M, Carrel, D, Mathieu, B, Léna, C, Dieudonné, S, Barbour, B, Brunel, N, and Casado, M. "Burst-Dependent Bidirectional Plasticity in the Cerebellum Is Driven by Presynaptic NMDA Receptors." *Cell reports* 15.1 (April 2016): 104-116.
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De Pittà, M, and Brunel, N. "Modulation of Synaptic Plasticity by Glutamatergic Gliotransmission: A Modeling Study." *Neural plasticity* 2016 (January 2016): 7607924-.
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Lim, S, McKee, JL, Woloszyn, L, Amit, Y, Freedman, DJ, Sheinberg, DL, and Brunel, N. "Inferring learning rules from distributions of firing rates in cortical neurons." *Nature neuroscience* 18.12 (December 2015): 1804-1810.
Full Text Open Access Copy

Alemi, A, Baldassi, C, Brunel, N, and Zecchina, R. "A Three-Threshold Learning Rule Approaches the Maximal Capacity of Recurrent Neural Networks." *PLoS computational biology* 11.8 (August 20, 2015): e1004439-.
Full Text Open Access Copy

## Pages

Roxin, A, Brunel, N, and Hansel, D. "Rate Models with Delays and the Dynamics of Large Networks of Spiking Neurons." 2006. Full Text

Fourcaud-Trocmé, N, and Brunel, N. "Dynamics of the instantaneous firing rate in response to changes in input statistics." June 2005. Full Text

Brunel, N. "Dynamics of networks of randomly connected excitatory and inhibitory spiking neurons." September 2000. Full Text

Brunel, N. "Phase diagrams of sparsely connected networks of excitatory and inhibitory spiking neurons." June 2000. Full Text

Brunel, N, and Wang, XJ. "Fast network oscillations with intermittent principal cell firing in a model of a recurrent excitatory-inhibitory circuit." 2000.

Brunel, N, and Nadal, JP. "Modeling memory: what do we learn from attractor neural networks?." February 1998. Full Text

Brunel, N. "Cross-correlations in sparsely connected recurrent networks of spiking neurons." January 1, 1997.

Brunel, N, and Nadal, J-P. "Optimal tuning curves for neurons spiking as a Poisson process." D-Facto public, 1997.

Ninio, J, and Brunel, N. "Time to detect a single difference between two correlated images." 1996.

Brunel, N, and Amit, DJ. "Learning internal representations in an analog attractor neural network." 1995.