It has been rigorously shown in [Ruelle, 2005] that the complex susceptibility of chaotic maps of the interval can have a pole in the upper-half complex plane. We develop a numerical procedure allowing to exhibit this pole from time series. We then apply the same analysis to the Henon map and conjecture that the complex susceptibility has also...
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2007 (v1)Journal articleUploaded on: December 4, 2022
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May 14, 2014 (v1)Publication
We review methods from statistical physics and dynamical systems theory for the analysis of mean-field models in neuroscience.
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October 8, 2019 (v1)Journal article
We review two examples where the linear response of a neuronal network submitted to an external stimulus can be derived explicitly, including network parameters dependence. This is done in a statistical physics-like approach where one associates to the spontaneous dynamics of the model a natural notion of Gibbs distribution inherited from...
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2012 (v1)Conference paper
no abstract
Uploaded on: December 3, 2022 -
2011 (v1)Conference paper
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May 19, 2015 (v1)Conference paper
Recent advances in multi-electrodes array acquisition have made it possible to record the activity ofup to several hundreds of neurons at the same time and to register their collective activity (spiketrains). For the retina, this opens up new perspectives in understanding how retinal structure and ganglion cells encode information about a...
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September 7, 2020 (v1)Conference paper
International audience
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2004 (v1)Publication
The concept of Self-Organized Criticality (SOC) was proposed in an attempt to explain the widespread appearance of power-law in nature. It describes a mechanism in which a system reaches spontaneously a state where the characteristic events (avalanches) are distributed according to a power law. We present a dynamical systems approach to...
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January 14, 2019 (v1)Publication
Doctoral
Uploaded on: December 4, 2022 -
January 14, 2019 (v1)Publication
Doctoral
Uploaded on: February 23, 2023 -
2008 (v1)Journal article
We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in \cite{BMS}. Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one correspondence with sequences of spikes patterns (``raster plots''). Moreover, though the dynamics is generically...
Uploaded on: December 3, 2022 -
June 8, 2021 (v1)Publication
Available at https://www.youtube.com/watch?v=BJ-5O-HJg_Y
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2010 (v1)Conference paper
no abstract
Uploaded on: December 3, 2022 -
June 20, 2014 (v1)Conference paper
La rétine est la partie de l'oeil qui transforme les scènes visuelles du monde extérieur en trains d'impulsions (potentiels d'action neuronaux) transmis au cerveau via le nerf optique. Mais c'est bien plus qu'une caméra puisque la rétine est capable de détecter des caractéristiques telles que mouvement différentiel, mouvement d'approche, ...;...
Uploaded on: March 25, 2023 -
2006 (v1)Publication
It has been rigorously shown in \cite{CMP} that the complex susceptibility for chaotic maps of the interval can have a pole in the upper complex plane. I develop a numerical procedure allowing to exhibit this pole from time series. I then apply the same analysis to the Hénon map and conjecture that the complex susceptibility has also a pole in...
Uploaded on: December 3, 2022 -
January 11, 2018 (v1)Conference paper
National audience
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January 31, 2022 (v1)Publication
International audience
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2012 (v1)Conference paper
no abstract
Uploaded on: December 2, 2022 -
2011 (v1)Conference paper
no abstract
Uploaded on: December 4, 2022 -
2011 (v1)Conference paper
no abstract
Uploaded on: December 4, 2022 -
September 12, 2022 (v1)Conference paper
International audience
Uploaded on: December 3, 2022 -
March 27, 2014 (v1)Conference paper
Recent advances in multi-electrodes array acquisition has made it possible torecord the activity of up to several hundreds of neurons at the same time andto register their collective spiking activity. This opens up new perspectivesin understanding how a neuronal network encodes the response to a stimulus, andwhat a spike train tells up about...
Uploaded on: March 25, 2023 -
December 4, 2017 (v1)Conference paper
International audience
Uploaded on: March 25, 2023 -
2011 (v1)Journal article
We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky integrate and fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties....
Uploaded on: December 3, 2022 -
January 9, 2017 (v1)Conference paper
International audience
Uploaded on: March 25, 2023