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Introduction:
Neurons and the Problem of Neural Coding
BOOK: Spiking Neuron Models,
W. Gerstner and W. Kistler
Cambridge University Press, 2002
Chapter 1
Swiss Federal Institute of Technology Lausanne, EPFL
Laboratory of Computational Neuroscience, LCN, CH 1015 Lausanne
Background: Neurons and Synapses
Book: Spiking Neuron Models
Chapter 1.1
Swiss Federal Institute of Technology Lausanne, EPFL
Laboratory of Computational Neuroscience, LCN, CH 1015 Lausanne
motor
cortex
association
cortex
visual
cortex
to motor
output
10 000 neurons
3 km wires
1mm
Signal:
action potential (spike)
action
potential
Molecular basis
-70mV
Na+
K+
Ca2+
Ions/proteins
action
potential
Modeling of Biological neural networks
predict
neurons
molecules
populations
of neurons
behavior
signals
computational
model
ion channels
Swiss Federal Institute of Technology Lausanne, EPFL
Laboratory of Computational Neuroscience, LCN, CH 1015 Lausanne
Background: What is brain-style computation?
Brain
Computer
Systems for computing and information processing
Brain
Computer
memory
CPU
input
Distributed architecture
Von Neumann architecture
10
1 CPU
(10 proc. Elements/neurons)
(10 10 transistors)
No separation of
processing and memory
Systems for computing and information processing
Brain
slow
fast
Computer
Tasks:
Mathematical
 7 
5 cos

 5 
Real world
E.g. complex scenes
fast
slow
Elements of Neuronal Dynamics
Book: Spiking Neuron Models
Chapter 1.2
Swiss Federal Institute of Technology Lausanne, EPFL
Laboratory of Computational Neuroscience, LCN, CH 1015 Lausanne
Phenomenology of spike generation
threshold -> Spike
j
i
Spike reception: EPSP,
summation of EPSPs
ui

Threshold Spike emission
(Action potential)
Spike reception: EPSP
Modeling of Biological neural networks
populations
of neurons
spiking neuron model
behavior
neurons
molecules
signals
computational
model
ion channels
Swiss Federal Institute of Technology Lausanne, EPFL
Laboratory of Computational Neuroscience, LCN, CH 1015 Lausanne
A simple phenomenological neuron model
Book: Spiking Neuron Models
Chapter 1.3
electrode
Swiss Federal Institute of Technology Lausanne, EPFL
Laboratory of Computational Neuroscience, LCN, CH 1015 Lausanne
Introduction
Course (Biological Modeling of Neural Networks)
Chapter 1.1
A first phenomenological model
electrode
Swiss Federal Institute of Technology Lausanne, EPFL
Laboratory of Computational Neuroscience, LCN, CH 1015 Lausanne
Spike Response Model
Spike emission
 t  ti^ 
j
i
Spike reception: EPSP
 t  t
f
j
ui


Spike reception: EPSP
 t  t
Spike emission: AP
 t  t
^
i

Last spike of i
ui t    t  t  
^
i
ui t    

All spikes, all neurons
 w  t  t 
ij
j
Firing:
f
j
f
j
linear
f
t t
^
i
threshold
Integrate-and-fire Model
Spike emission
j
i
ui
I

d
  ui  ui  RI (t )
dt
ui t     Fire+reset
Spike reception: EPSP
f reset
 t  t j
linear
threshold


The Problem of Neuronal Coding
Book: Spiking Neuron Models
Chapter 1.4
Swiss Federal Institute of Technology Lausanne, EPFL
Laboratory of Computational Neuroscience, LCN, CH 1015 Lausanne
The Problem of Neuronal Coding
Book: Spiking Neuron Models
Chapter 1.4
nsp
T
stim
nsp (t ; t  T )
 
T
Rate defined as temporal average
Rate
Swiss Federal Institute of Technology Lausanne, EPFL
Laboratory of Computational Neuroscience, LCN, CH 1015 Lausanne
The Problem of Neuronal Coding
Rate defined as average over stimulus repetitions
Peri-Stimulus Time Histogram
Stim(t)
PSTH(t)
t
K=500 trials
n(t ; t  t )
PSTH (t ) 
K t
Swiss Federal Institute of Technology Lausanne, EPFL
Laboratory of Computational Neuroscience, LCN, CH 1015 Lausanne
The problem of neural coding:
population activity - rate defined by population average
t
?
I(t)
population dynamics?
t
population
activity
n(t; t  t )
A(t ) 
Nt
The problem of neural coding:
temporal codes
Time to first spike after input
t
correlations
Phase with respect to oscillation
Reverse Correlations
I(t)
fluctuating input
Swiss Federal Institute of Technology Lausanne, EPFL
Laboratory of Computational Neuroscience, LCN, CH 1015 Lausanne
Reverse-Correlation Experiments
I (t )
after 1000
25000spikes
spikes
(simulations)
Stimulus Reconstruction
I(t)
fluctuating input
Swiss Federal Institute of Technology Lausanne, EPFL
Laboratory of Computational Neuroscience, LCN, CH 1015 Lausanne
Stimulus Reconstruction
Bialek et al
The problem of neural coding:
What is the code used by neurons?
Constraints from reaction time experiments
How fast is neuronal signal processing?
animal -- no animal
Simon Thorpe
Nature, 1996
Reaction time experiment
Visual processing
eye
Memory/association
Output/movement
How fast is neuronal signal processing?
Simon Thorpe
Nature, 1996
animal -- no animal
# of
images
Reaction time
400 ms
Visual processing
Reaction time
Memory/association
eye
Recognition time 150ms
Output/movement
If we want to avoid prior
assumptions about neural coding,
we need to model neurons
on the level of action potentials:
spiking neuron models