# Nicolas Brunel

## Professor of Neurobiology

### 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

Neurobiology Training Program awarded by National Institutes of Health (Mentor). 2019 to 2024

Canonical computations for motor learning by the cerebellar cortex micro-circuit awarded by National Institutes of Health (Co-Principal Investigator). 2019 to 2024

Striatal Plasticity in Habit Formation as a Platform to Deconstruct Adaptive Learning awarded by National Institutes of Health (Co Investigator). 2018 to 2023

Investigating ripple oscillations as a mechanism for human memory retrieval awarded by National Institutes of Health (Principal Investigator). 2019 to 2022

Medical Scientist Training Program awarded by National Institutes of Health (Mentor). 1997 to 2022

CRCNS: Multiscale dynamics of cortical circuits for visual recognition & memory awarded by University of Chicago (Principal Investigator). 2017 to 2022

Learning spatio-temporal statistics from the environment in recurrent networks awarded by Office of Naval Research (Principal Investigator). 2017 to 2020

Learning spatio-temporal statistics from the environment in recurrent networks awarded by (Principal Investigator). 2017 to 2020

CRCNS: Multiscale dynamics of cortical circuits for visual recognition & memory awarded by University of Chicago (Principal Investigator). 2017 to 2020

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

## Pages

Brunel, Nicolas, and Vincent Hakim. “Population Density Models..” *Encyclopedia of Computational Neuroscience*, edited by Dieter Jaeger and Ranu Jung, Springer, 2014.

Brunel, Nicolas, and Vincent Hakim. “Fokker-Planck Equation..” *Encyclopedia of Computational Neuroscience*, edited by Dieter Jaeger and Ranu Jung, Springer, 2014.

Brunel, Nicolas. “Dynamics of neural networks.” *Principles of Neural Coding*, 2013, pp. 489–512. *Manual*, doi:10.1201/b14756.
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Brunel, Nicolas, and Vincent Hakim. “Neuronal Dynamics..” *Encyclopedia of Complexity and Systems Science*, edited by Robert A. Meyers, Springer, 2009, pp. 6099–116.

Vaz, Alex P., et al. “Coupled ripple oscillations between the medial temporal lobe and neocortex retrieve human memory..” *Science*, vol. 363, no. 6430, Mar. 2019, pp. 975–78. *Pubmed*, doi:10.1126/science.aau8956.
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Bouvier, Guy, et al. “Cerebellar learning using perturbations..” *Elife*, vol. 7, Nov. 2018. *Pubmed*, doi: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*, vol. 99, no. 1, July 2018, pp. 227-238.e4. *Pubmed*, doi:10.1016/j.neuron.2018.05.038.
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Martí, Daniel, et al. “Correlations between synapses in pairs of neurons slow down dynamics in randomly connected neural networks..” *Phys Rev E*, vol. 97, no. 6–1, June 2018. *Pubmed*, doi: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*, vol. 7, no. 1, Sept. 2017. *Pubmed*, doi:10.1038/s41598-017-12033-y.
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Titley, Heather K., et al. “Toward a Neurocentric View of Learning..” *Neuron*, vol. 95, no. 1, July 2017, pp. 19–32. *Pubmed*, doi:10.1016/j.neuron.2017.05.021.
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Zampini, Valeria, et al. “Mechanisms and functional roles of glutamatergic synapse diversity in a cerebellar circuit..” *Elife*, vol. 5, Sept. 2016. *Pubmed*, doi:10.7554/eLife.15872.
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De Pittà, M., et al. “Astrocytes: Orchestrating synaptic plasticity?.” *Neuroscience*, vol. 323, May 2016, pp. 43–61. *Pubmed*, doi:10.1016/j.neuroscience.2015.04.001.
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Brunel, Nicolas. “Is cortical connectivity optimized for storing information?.” *Nat Neurosci*, vol. 19, no. 5, May 2016, pp. 749–55. *Pubmed*, doi:10.1038/nn.4286.
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Bouvier, Guy, et al. “Burst-Dependent Bidirectional Plasticity in the Cerebellum Is Driven by Presynaptic NMDA Receptors..” *Cell Rep*, vol. 15, no. 1, Apr. 2016, pp. 104–16. *Pubmed*, doi:10.1016/j.celrep.2016.03.004.
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## Pages

Roxin, A., et al. “Rate models with delays and the dynamics of large networks of spiking neurons.” *Progress of Theoretical Physics Supplement*, vol. 161, 2006, pp. 68–85. *Scopus*, doi: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..” *J Comput Neurosci*, vol. 18, no. 3, 2005, pp. 311–21. *Pubmed*, doi:10.1007/s10827-005-0337-8.
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Brunel, N. “Dynamics of networks of randomly connected excitatory and inhibitory spiking neurons..” *J Physiol Paris*, vol. 94, no. 5–6, 2000, pp. 445–63. *Pubmed*, doi: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.” *Neurocomputing*, vol. 32–33, 2000, pp. 307–12. *Scopus*, doi: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.” *European Journal of Neuroscience*, vol. 12, BLACKWELL SCIENCE LTD, 2000, pp. 79–79.

Brunel, N., and J. P. Nadal. “Modeling memory: what do we learn from attractor neural networks?.” *C R Acad Sci Iii*, vol. 321, no. 2–3, 1998, pp. 249–52. *Pubmed*, doi:10.1016/s0764-4469(97)89830-7.
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Brunel, N. “Cross-correlations in sparsely connected recurrent networks of spiking neurons.” *Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*, vol. 1327, 1997, pp. 31–36.

Brunel, Nicolas, and Jean-Pierre Nadal. “Optimal tuning curves for neurons spiking as a Poisson process..” *Esann*, edited by Michel Verleysen, D-Facto public, 1997.

Ninio, J., and N. Brunel. “Time to detect a single difference between two correlated images.” *Perception*, vol. 25, PION LTD, 1996, pp. 89–89.

Brunel, N., and D. J. Amit. “Learning internal representations in an analog attractor neural network.” *International Journal of Neural Systems, Supplementary Issue, 1995*, edited by D. J. Amit et al., WORLD SCIENTIFIC PUBL CO PTE LTD, 1995, pp. 19–23.