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Statistics of spike trains: A dynamical systems
perspective.
 Bruno Cessac, Horacio Rostro, 
Juan­Carlos Vasquez, Thierry Viéville
●Multiples scales.
●Non linear and collective dynamics.
● Adaptation.
● Interwoven evolution.
Neural network activity.
● Spontaneous activity; ●Multiples scales.
● Response to external stimuli ; ●Non linear and collective dynamics.
● Response to excitations from ● Adaptation.
other neurons... ● Interwoven evolution.
Neural network activity.
● Spontaneous activity; ●Multiples scales.
● Response to external stimuli ; ●Non linear and collective dynamics.
● Response to excitations from ● Adaptation.
other neurons... ● Interwoven evolution.
Neural network activity. Spike generation.
(t)=1 if i fires at t
i
=0 otherwise.
A raster plot is a sequence
~ ={(t)}, i=1...N, t=1...
i
● Spontaneous activity; ●Multiples scales.
● Response to external stimuli ; ●Non linear and collective dynamics.
● Response to excitations from ● Adaptation.
other neurons... ● Interwoven evolution.
Neural network activity. Spike generation.
(t)=1 if i fires at t
i
=0 otherwise.
A raster plot is a sequence
~ ={(t)}, i=1...N, t=1...
i
● Spontaneous activity; ●Multiples scales.
● Response to external stimuli ; ●Non linear and collective dynnaammiiccss..
● Response to excitations from ● Adaptation.
other neurons... ● Interwoven evolution.
Neural response to some stimulus ?
Neural network activity. Spike generation.
(t)=1 if i fires at t
i
=0 otherwise.
A raster plot is a sequence
~ ={(t)}, i=1...N, t=1...
i
● Spontaneous activity; ●Multiples scales.
● Response to external stimuli ; ●Non linear and collective dynnaammiiccss..
● Response to excitations from ● Adaptation.
other neurons... ● Interwoven evolution.
Neural response to some stimulus ?
● Definite succession of
spikes during a definite time
period.
Neural network activity. Spike generation.
(t)=1 if i fires at t
i
=0 otherwise.
A raster plot is a sequence
~ ={(t)}, i=1...N, t=1...
i
● Spontaneous activity; ●Multiples scales.
● Response to external stimuli ; ●Non linear and collective dynnaammiiccss..
● Response to excitations from ● Adaptation.
other neurons... ● Interwoven evolution.
Neural response to some stimulus ?
● Definite succession of
spikes during a definite time
period.
●Statistical “coding”.
Spikes: Exploring the Neural Code.
F Rieke, D Warland, R de Ruyter van
Steveninck & W Bialek (MIT Press,
Cambridge, 1997). Neural network activity. Spike generation.
(t)=1 if i fires at t
i
=0 otherwise.
A raster plot is a sequence
~ ={(t)}, i=1...N, t=1...
i
● Spontaneous activity; ●Multiples scales.
● Response to external stimuli ; ●Non linear and collective dynnaammiiccss..
● Response to excitations from ● Adaptation.
other neurons... ● Interwoven evolution.
Neural response to some stimulus ?
● Definite succession of
spikes during a definite time
period.
●Statistical “coding”.
Spikes: Exploring the Neural Code.
F Rieke, D Warland, R de Ruyter van
Steveninck & W Bialek (MIT Press,
Cambridge, 1997). Neural network activity. Spike generation.
(t)=1 if i fires at t
i
=0 otherwise.
A raster plot is a sequence
~ ={(t)}, i=1...N, t=1...
i
● Spontaneous activity; ●Multiples scales.
● Response to external stimuli ; ●Non linear and collective dynnaammiiccss..
● Response to excitations from ● Adaptation.
other neurons... ● Interwoven evolution.
Neural response to some stimulus ?
● Definite succession of
spikes during a definite time
period.
●Statistical “coding”.
Spikes: Exploring the Neural Code.
F Rieke, D Warland, R de Ruyter van
Steveninck & W Bialek (MIT Press,
Cambridge, 1997).