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Computational Cognitive Neuroscience
Neuron
Kristína Rebrová
Kristína Rebrová Computational Cognitive NeuroscienceNeuron
Neuron as detector
Kristína Rebrová Computational Cognitive NeuroscienceNeuron
Dynamics of Integration: tug-of-war
Kristína Rebrová Computational Cognitive NeuroscienceNeuron
Neurons variables
gi : inhibitory conductance
Ei : inhibitory driving potential
Θ: action potential threshold
Vm: membrane...
Neural integration
Vm(t) = Vm(t−1)+dtvm[ge(Ee−Vm)+gi (Ei −Vm)+gl (El −Vm)]
Ie = ge(Ee − Vm)
Ii = gi (Ei − Vm)
Il = gl (El ...
Equilibrium Membrane Potential
ge(t) =
1
n
i
xi wi
xi = input to the neuron
wi = weight of the neuron
a weight defines how ...
Generating Output
If Vm gets over threshold, neuron fires a spike.
Spike resets membrane potential back to rest.
Vm has to ...
Rate Code Approximation to Spiking
spikes to rates
instantaneous and steady – smaller, faster models
definitely lose severa...
The end
Thank you for your attention
kristina.rebrova@gmail.com
Kristína Rebrová Computational Cognitive NeuroscienceNeuron
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CCNExcercises:Neuron

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Slides for 2nd Excercise in Computational Cognitive Neuroscience
dai.fmph.uniba.sk/courses/CCN/

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CCNExcercises:Neuron

  1. 1. Computational Cognitive Neuroscience Neuron Kristína Rebrová Kristína Rebrová Computational Cognitive NeuroscienceNeuron
  2. 2. Neuron as detector Kristína Rebrová Computational Cognitive NeuroscienceNeuron
  3. 3. Dynamics of Integration: tug-of-war Kristína Rebrová Computational Cognitive NeuroscienceNeuron
  4. 4. Neurons variables gi : inhibitory conductance Ei : inhibitory driving potential Θ: action potential threshold Vm: membrane potential Ee: excitatory driving potential ge: excitatory conductance Ee: leak driving potential ge: leak conductance ¯g: maximum conductance Kristína Rebrová Computational Cognitive NeuroscienceNeuron
  5. 5. Neural integration Vm(t) = Vm(t−1)+dtvm[ge(Ee−Vm)+gi (Ei −Vm)+gl (El −Vm)] Ie = ge(Ee − Vm) Ii = gi (Ei − Vm) Il = gl (El − Vm) Inet = Ie + Ii + Il Vm(t) = Vm(t − 1) + dtvmInet Kristína Rebrová Computational Cognitive NeuroscienceNeuron
  6. 6. Equilibrium Membrane Potential ge(t) = 1 n i xi wi xi = input to the neuron wi = weight of the neuron a weight defines how much unit listens to given input weights determine what the neuron detects = everything is encoded in weights Vm = ¯gege(t) ¯gege(t) + ¯gi gi (t) + ¯gl Ee + ¯gi gi (t) ¯gege(t) + ¯gi gi (t) + ¯gl Ei + ¯gl ¯gege(t) + ¯gi gi (t) + ¯gl El Kristína Rebrová Computational Cognitive NeuroscienceNeuron
  7. 7. Generating Output If Vm gets over threshold, neuron fires a spike. Spike resets membrane potential back to rest. Vm has to climb back up to threshold to spike again Kristína Rebrová Computational Cognitive NeuroscienceNeuron
  8. 8. Rate Code Approximation to Spiking spikes to rates instantaneous and steady – smaller, faster models definitely lose several important things to find an equation* that makes good approximation of actual spiking rate for same sets of inputs X-over-X-plus-1 (XX1) function Kristína Rebrová Computational Cognitive NeuroscienceNeuron
  9. 9. The end Thank you for your attention kristina.rebrova@gmail.com Kristína Rebrová Computational Cognitive NeuroscienceNeuron

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