Statistics of spike trains: A dynamical systems Statistics of spike - PowerPoint PPT Presentation

Statistics of spike trains: A dynamical systems Statistics of spike trains: A dynamical systems perspective. perspective. Bruno Cessac, Horacio Rostro, Juan-Carlos 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. ω i (t)=1 if i fires at t =0 otherwise. A raster plot is a sequence ~ ={ ω i (t)}, i=1...N, t=1... ω ● 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. ω i (t)=1 if i fires at t =0 otherwise. A raster plot is a sequence ~ ={ ω i (t)}, i=1...N, t=1... ω ● Spontaneous activity Spontaneous activity ; ● Multiples scales. ● Response to external stimuli Response to external stimuli ; ● Non linear and collective dynamics. Non linear and collective dynamics. ● Response to excitations from Response to excitations from ● Adaptation. other neurons... other neurons ● Interwoven evolution. Neural response to some stimulus ? Neural response to some stimulus ?

Neural network activity. Spike generation. ω i (t)=1 if i fires at t =0 otherwise. A raster plot is a sequence ~ ={ ω i (t)}, i=1...N, t=1... ω ● Spontaneous activity Spontaneous activity ; ● Multiples scales. ● Response to external stimuli Response to external stimuli ; ● Non linear and collective dynamics. Non linear and collective dynamics. ● Response to excitations from Response to excitations from ● Adaptation. other neurons... other neurons ● Interwoven evolution. Neural response to some stimulus ? Neural response to some stimulus ? ● Definite succession of spikes during a definite time period.

Neural network activity. Spike generation. ω i (t)=1 if i fires at t =0 otherwise. A raster plot is a sequence ~ ={ ω i (t)}, i=1...N, t=1... ω ● Spontaneous activity Spontaneous activity ; ● Multiples scales. ● Response to external stimuli Response to external stimuli ; ● Non linear and collective dynamics. Non linear and collective dynamics. ● Response to excitations from Response to excitations from ● Adaptation. other neurons... other neurons ● Interwoven evolution. Neural response to some stimulus ? 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. ω i (t)=1 if i fires at t =0 otherwise. A raster plot is a sequence ~ ={ ω i (t)}, i=1...N, t=1... ω ● Spontaneous activity Spontaneous activity ; ● Multiples scales. ● Response to external stimuli Response to external stimuli ; ● Non linear and collective dynamics. Non linear and collective dynamics. ● Response to excitations from Response to excitations from ● Adaptation. other neurons... other neurons ● Interwoven evolution. Neural response to some stimulus ? 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. ω i (t)=1 if i fires at t =0 otherwise. A raster plot is a sequence ~ ={ ω i (t)}, i=1...N, t=1... ω ● Spontaneous activity Spontaneous activity ; ● Multiples scales. ● Response to external stimuli Response to external stimuli ; ● Non linear and collective dynamics. Non linear and collective dynamics. ● Response to excitations from Response to excitations from ● Adaptation. other neurons... other neurons ● Interwoven evolution. Neural response to some stimulus ? 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. ω i (t)=1 if i fires at t =0 otherwise. A raster plot is a sequence ~ ={ ω i (t)}, i=1...N, t=1... ω ● Spontaneous activity Spontaneous activity ; ● Multiples scales. ● Response to external stimuli Response to external stimuli ; ● Non linear and collective dynamics. Non linear and collective dynamics. ● Response to excitations from Response to excitations from ● Adaptation. other neurons... other neurons ● Interwoven evolution. Neural response to some stimulus ? Neural response to some stimulus ? ● Definite succession of spikes during a definite time period. ● Statistical “coding”. The probability of The probability of Spikes: Exploring the Neural Code. occurrence of R depends on occurrence of R depends on F Rieke, D Warland, R de Ruyter van Steveninck & W Bialek (MIT Press, the stimulus and on system the stimulus and on system Cambridge, 1997). parameters. parameters.

Neural network activity. Spike generation. ω i (t)=1 if i fires at t =0 otherwise. A raster plot is a sequence ~ ={ ω i (t)}, i=1...N, t=1... ω ● Spontaneous activity Spontaneous activity ; ● Multiples scales. ● Response to external stimuli Response to external stimuli ; ● Non linear and collective dynamics. Non linear and collective dynamics. ● Response to excitations from Response to excitations from ● Adaptation. other neurons... other neurons ● Interwoven evolution. Neural response to some stimulus ? Neural response to some stimulus ? How to compute P(R|S) ? How to compute P(R|S) ? The probability of The probability of occurrence of R depends on occurrence of R depends on the stimulus and on system the stimulus and on system parameters. parameters.

Neural network activity. Spike generation. ω i (t)=1 if i fires at t =0 otherwise. A raster plot is a sequence ~ ={ ω i (t)}, i=1...N, t=1... ω ● Spontaneous activity Spontaneous activity ; ● Multiples scales. ● Response to external stimuli Response to external stimuli ; ● Non linear and collective dynamics. Non linear and collective dynamics. ● Response to excitations from Response to excitations from ● Adaptation. other neurons... other neurons ● Interwoven evolution. Neural response to some stimulus ? Neural response to some stimulus ? How to compute P(R|S) ? How to compute P(R|S) ? Sample averaging. Sample averaging. The probability of The probability of occurrence of R depends on occurrence of R depends on the stimulus and on system the stimulus and on system parameters. parameters.

Neural network activity. Spike generation. ω i (t)=1 if i fires at t =0 otherwise. A raster plot is a sequence ~ ={ ω i (t)}, i=1...N, t=1... ω ● Spontaneous activity Spontaneous activity ; ● Multiples scales. ● Response to external stimuli Response to external stimuli ; ● Non linear and collective dynamics. Non linear and collective dynamics. ● Response to excitations from Response to excitations from ● Adaptation. other neurons... other neurons ● Interwoven evolution. Neural response to some stimulus ? Neural response to some stimulus ? How to compute P(R|S) ? How to compute P(R|S) ? Time averaging. Time averaging. The probability of The probability of occurrence of R depends on occurrence of R depends on the stimulus and on system the stimulus and on system parameters. parameters.

Neural network activity. Spike generation. ω i (t)=1 if i fires at t =0 otherwise. A raster plot is a sequence ~ ={ ω i (t)}, i=1...N, t=1... ω ● Spontaneous activity Spontaneous activity ; ● Multiples scales. ● Response to external stimuli Response to external stimuli ; ● Non linear and collective dynamics. Non linear and collective dynamics. ● Response to excitations from Response to excitations from ● Adaptation. other neurons... other neurons ● Interwoven evolution. Neural response to some stimulus ? Neural response to some stimulus ? How to compute P(R|S) ? How to compute P(R|S) ? Time averaging. Time averaging. The probability of The probability of occurrence of R depends on occurrence of R depends on the stimulus and on system the stimulus and on system parameters. parameters.

Neural network activity. Spike generation. ω i (t)=1 if i fires at t =0 otherwise. A raster plot is a sequence ~ ={ ω i (t)}, i=1...N, t=1... ω ● Spontaneous activity Spontaneous activity ; ● Multiples scales. ● Response to external stimuli Response to external stimuli ; ● Non linear and collective dynamics. Non linear and collective dynamics. ● Response to excitations from Response to excitations from ● Adaptation. other neurons... other neurons ● Interwoven evolution. Which type of probability distribution can we expect ? Which type of probability distribution can we expect ?