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1

Bifurcation Analysis of a General Class of Nonlinear Integrate-and-Fire Neurons

Touboul, Jonathan

Journal:

SIAM Journal on Applied Mathematics

Year:

2008

Language:

english

File:

PDF, 2.37 MB

english, 2008

2

Topological and Dynamical Complexity of Random Neural Networks

Wainrib, Gilles, Touboul, Jonathan

Journal:

Physical Review Letters

Year:

2013

Language:

english

File:

PDF, 186 KB

english, 2013

3

Noise-Induced Synchronization and Antiresonance in Interacting Excitable Systems: Applications to Deep Brain Stimulation in Parkinsonâs Disease

Touboul, Jonathan D., Piette, Charlotte, Venance, Laurent, Ermentrout, G. Bard

Journal:

Physical Review X

Year:

2020

Language:

english

File:

PDF, 21.56 MB

english, 2020

4

The spikes trains probability distributions: A stochastic calculus approach

Jonathan Touboul, Olivier Faugeras

Journal:

Journal of Physiology-Paris

Year:

2007

Language:

english

File:

PDF, 930 KB

english, 2007

5

Large Deviations, Dynamics and Phase Transitions in Large Stochastic and Disordered Neural Networks

Cabana, Tanguy, Touboul, Jonathan

Journal:

Journal of Statistical Physics

Year:

2013

Language:

english

File:

PDF, 2.25 MB

english, 2013

6

Bifurcation Analysis of a General Class of Nonlinear Integrate-and-Fire Neurons

Jonathan Touboul

Journal:

SIAM Journal on Applied Mathematics

Year:

2008

Language:

english

File:

PDF, 2.69 MB

english, 2008

7

Pulsatile Localized Dynamics in Delayed Neural Field Equations in Arbitrary Dimension

Faye, Grégory, Touboul, Jonathan

Journal:

SIAM Journal on Applied Mathematics

Year:

2014

Language:

english

File:

PDF, 1.56 MB

english, 2014

8

Dynamics and absorption properties of stochastic equations with Hölder diffusion coefficients

Touboul, Jonathan, Wainrib, Gilles

Journal:

Physica D: Nonlinear Phenomena

Year:

2015

Language:

english

File:

PDF, 2.21 MB

english, 2015

9

Importance of the Cutoff Value in the Quadratic Adaptive Integrate-and-Fire Model

Touboul, Jonathan

Journal:

Neural Computation

Year:

2009

Language:

english

File:

PDF, 148 KB

english, 2009

10

Noise-induced Canard and Mixed-Mode Oscillations in Large-Scale Stochastic Networks

Touboul, Jonathan D., Krupa, Martin, Desroches, Mathieu

Journal:

SIAM Journal on Applied Mathematics

Year:

2015

Language:

english

File:

PDF, 2.66 MB

english, 2015

11

On the complex dynamics of savanna landscapes

Touboul, Jonathan David, Staver, Ann Carla, Levin, Simon Asher

Journal:

Proceedings of the National Academy of Sciences

Year:

2018

Language:

english

File:

PDF, 2.59 MB

english, 2018

12

Symmetry breaking in the embryonic skin triggers directional and sequential plumage patterning

Bailleul, Richard, Curantz, Camille, Desmarquet-Trin Dinh, Carole, Hidalgo, Magdalena, Touboul, Jonathan, Manceau, Marie, Hill, Caroline S.

Journal:

Year:

2019

Language:

english

File:

PDF, 6.16 MB

english, 2019

13

Deep brain stimulation-guided optogenetic rescue of parkinsonian symptoms

Valverde, SÃ©bastien, Vandecasteele, Marie, Piette, Charlotte, Derousseaux, Willy, Gangarossa, Giuseppe, Aristieta Arbelaiz, Asier, Touboul, Jonathan, Degos, Bertrand, Venance, Laurent

Journal:

Nature Communications

Year:

2020

File:

PDF, 9.87 MB

2020

14

Dynamics and bifurcations of the adaptive exponential integrate-and-fire model

Jonathan Touboul, Romain Brette

Journal:

Biological Cybernetics

Year:

2008

Language:

english

File:

PDF, 1.21 MB

english, 2008

15

A Markovian event-based framework for stochastic spiking neural networks

Jonathan D. Touboul, Olivier D. Faugeras

Journal:

Journal of Computational Neuroscience

Year:

2011

Language:

english

File:

PDF, 612 KB

english, 2011

16

Finite-size and correlation-induced effects in mean-field dynamics

Jonathan D. Touboul, G. Bard Ermentrout

Journal:

Journal of Computational Neuroscience

Year:

2011

Language:

english

File:

PDF, 1.52 MB

english, 2011

17

On an explicit representation of the solution of linear stochastic partial differential equations with delays

Mathieu Galtier, Jonathan Touboul

Journal:

Comptes Rendus Mathematique

Year:

2012

Language:

french

File:

PDF, 358 KB

french, 2012

18

Event-driven mathematical framework for noisy integrate-and-fire neuron networks: spike trains statistics via stochastic calculus, network analysis inspired by queuing theory and an event-driven simulator

Jonathan Touboul, Olivier Faugeras, Olivier Rochel

Journal:

BMC Neuroscience

Year:

2007

Language:

english

File:

PDF, 167 KB

english, 2007

19

Mean-field equations for stochastic firing-rate neural fields with delays: Derivation and noise-induced transitions

Jonathan Touboul

Journal:

Physica D: Nonlinear Phenomena

Year:

2012

Language:

english

File:

PDF, 2.92 MB

english, 2012

20

Noise-Induced Behaviors in Neural Mean Field Dynamics

Touboul, Jonathan, Hermann, Geoffroy, Faugeras, Olivier

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2012

Language:

english

File:

PDF, 7.23 MB

english, 2012

21

Spiking Dynamics of Bidimensional Integrate-and-Fire Neurons

Touboul, Jonathan, Brette, Romain

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2009

Language:

english

File:

PDF, 2.30 MB

english, 2009

22

Limits and Dynamics of Stochastic Neuronal Networks with Random Heterogeneous Delays

Touboul, Jonathan

Journal:

Journal of Statistical Physics

Year:

2012

Language:

english

File:

PDF, 3.95 MB

english, 2012

23

Exact Event-Driven Implementation for Recurrent Networks of Stochastic Perfect Integrate-and-Fire Neurons

Taillefumier, Thibaud, Touboul, Jonathan, Magnasco, Marcelo

Journal:

Neural Computation

Year:

2012

Language:

english

File:

PDF, 3.08 MB

english, 2012

24

On the Simulation of Nonlinear Bidimensional Spiking Neuron Models

Touboul, Jonathan

Journal:

Neural Computation

Year:

2011

Language:

english

File:

PDF, 666 KB

english, 2011

25

Synchronization in random balanced networks

García del Molino, Luis Carlos, Pakdaman, Khashayar, Touboul, Jonathan, Wainrib, Gilles

Journal:

Physical Review E

Year:

2013

Language:

english

File:

PDF, 4.35 MB

english, 2013

26

A Characterization of the First Hitting Time of Double Integral Processes to Curved Boundaries

Jonathan Touboul and Olivier Faugeras

Journal:

Advances in Applied Probability

Year:

2008

Language:

english

File:

PDF, 1.97 MB

english, 2008

27

Limits and Dynamics of Randomly Connected Neuronal Networks

Quiñinao, Cristobal, Touboul, Jonathan

Journal:

Acta Applicandae Mathematicae

Year:

2015

Language:

english

File:

PDF, 7.33 MB

english, 2015

28

Spatially Extended Networks with Singular Multi-scale Connectivity Patterns

Touboul, Jonathan

Journal:

Journal of Statistical Physics

Year:

2014

Language:

english

File:

PDF, 481 KB

english, 2014

29

Propagation of chaos in neural fields

Touboul, Jonathan

Journal:

The Annals of Applied Probability

Year:

2014

Language:

english

File:

PDF, 475 KB

english, 2014

30

Heterogeneous Connections Induce Oscillations in Large-Scale Networks

Hermann, Geoffroy, Touboul, Jonathan

Journal:

Physical Review Letters

Year:

2012

Language:

english

File:

PDF, 1.55 MB

english, 2012

31

The heterogeneous gas with singular interaction: generalized circular law and heterogeneous renormalized energy

Molino, Luis Carlos García del, Pakdaman, Khashayar, Touboul, Jonathan

Journal:

Journal of Physics A Mathematical and Theoretical

Year:

2015

Language:

english

File:

PDF, 2.04 MB

english, 2015

32

Neural Mass Activity, Bifurcations, and Epilepsy

Touboul, Jonathan, Wendling, Fabrice, Chauvel, Patrick, Faugeras, Olivier

Journal:

Neural Computation

Year:

2011

Language:

english

File:

PDF, 1.71 MB

english, 2011

33

Index distribution of the Ginibre ensemble

Allez, Romain, Touboul, Jonathan, Wainrib, Gilles

Journal:

Journal of Physics A Mathematical and Theoretical

Year:

2014

Language:

english

File:

PDF, 511 KB

english, 2014

34

Lhx2 regulates the timing of β-catenin-dependent cortical neurogenesis

Hsu, Lea Chia-Ling, Nam, Sean, Cui, Yi, Chang, Ching-Pu, Wang, Chia-Fang, Kuo, Hung-Chih, Touboul, Jonathan D., Chou, Shen-Ju

Journal:

Proceedings of the National Academy of Sciences

Year:

2015

Language:

english

File:

PDF, 1.37 MB

english, 2015

35

Competition and boundary formation in heterogeneous media: Application to neuronal differentiation

Perthame, Benoît, Quiñinao, Cristóbal, Touboul, Jonathan

Journal:

Mathematical Models and Methods in Applied Sciences

Year:

2015

Language:

english

File:

PDF, 523 KB

english, 2015

36

Pinwheel-dipole configuration in cat early visual cortex

Ribot, Jérôme, Romagnoni, Alberto, Milleret, Chantal, Bennequin, Daniel, Touboul, Jonathan

Journal:

Year:

2015

Language:

english

File:

PDF, 3.26 MB

english, 2015

37

The Real Ginibre Ensemble with\(k=O(n)\)Real Eigenvalues

del Molino, Luis Carlos García, Pakdaman, Khashayar, Touboul, Jonathan, Wainrib, Gilles

Journal:

Journal of Statistical Physics

Year:

2016

Language:

english

File:

PDF, 774 KB

english, 2016

38

Complex Oscillations in the Delayed FitzHugh–Nagumo Equation

Krupa, Maciej, Touboul, Jonathan D.

Journal:

Journal of Nonlinear Science

Year:

2016

Language:

english

File:

PDF, 3.58 MB

english, 2016

39

Canard Explosion in Delay Differential Equations

Krupa, Maciej, Touboul, Jonathan D.

Journal:

Journal of Dynamics and Differential Equations

Year:

2016

Language:

english

File:

PDF, 1.66 MB

english, 2016

40

Enhanced Abventricular Proliferation Compensates Cell Death in the Embryonic Cerebral Cortex

Freret-Hodara, Betty, Cui, Yi, Griveau, Amélie, Vigier, Lisa, Arai, Yoko, Touboul, Jonathan, Pierani, Alessandra

Journal:

Cerebral Cortex

Year:

2016

Language:

english

File:

PDF, 2.35 MB

english, 2016

41

On the Dynamics of Random Neuronal Networks

Robert, Philippe, Touboul, Jonathan

Journal:

Journal of Statistical Physics

Year:

2016

Language:

english

File:

PDF, 872 KB

english, 2016

42

On the Dynamical Interplay of Positive and Negative Affects

Touboul, Jonathan, Romagnoni, Alberto, Schwartz, Robert

Journal:

Neural Computation

Year:

2017

Language:

english

File:

PDF, 3.25 MB

english, 2017

43

The hemodynamic signal as a first-order low-pass temporal filter: Evidence and implications for neuroimaging studies

Sauvage, Antoine, Hubert, Guillaume, Touboul, Jonathan, Ribot, Jérôme

Journal:

Year:

2017

Language:

english

File:

PDF, 1.80 MB

english, 2017

44

Power-law statistics and universal scaling in the absence of criticality

Touboul, Jonathan, Destexhe, Alain

Journal:

Physical Review E

Year:

2017

Language:

english

File:

PDF, 2.27 MB

english, 2017

45

A characterization of the first hitting time of double integral processes to curved boundaries

Touboul, Jonathan, Faugeras, Olivier

Journal:

Advances in Applied Probability

Year:

2008

Language:

english

File:

PDF, 675 KB

english, 2008

46

Parsimony, Exhaustivity and Balanced Detection in Neocortex

Romagnoni, Alberto, Ribot, Jérôme, Bennequin, Daniel, Touboul, Jonathan, Hilgetag, Claus C.

Journal:

PLoS Computational Biology

Year:

2015

Language:

english

File:

PDF, 2.15 MB

english, 2015

47

A New Safety Concern for Glaucoma Treatment Demonstrated by Mass Spectrometry Imaging of Benzalkonium Chloride Distribution in the Eye, an Experimental Study in Rabbits

Brignole-Baudouin, Françoise, Desbenoit, Nicolas, Hamm, Gregory, Liang, Hong, Both, Jean-Pierre, Brunelle, Alain, Fournier, Isabelle, Guerineau, Vincent, Legouffe, Raphael, Stauber, Jonathan, Touboul,

Journal:

Year:

2012

Language:

english

File:

PDF, 909 KB

english, 2012

48

Macroscopic Equations Governing Noisy Spiking Neuronal Populations with Linear Synapses

Galtier, Mathieu N., Touboul, Jonathan, Lambiotte, Renaud

Journal:

Year:

2013

Language:

english

File:

PDF, 889 KB

english, 2013

49

Multiresolution Hilbert Approach to Multidimensional Gauss-Markov Processes

Taillefumier, Thibaud, Touboul, Jonathan

Journal:

International Journal of Stochastic Analysis

Year:

2011

Language:

english

File:

PDF, 2.98 MB

english, 2011

50

Large deviations for randomly connected neural networks: I. Spatially extended systems

Cabana, Tanguy, Touboul, Jonathan D.

Journal:

Advances in Applied Probability

Year:

2018

Language:

english

File:

PDF, 377 KB

english, 2018

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