Transcript MATLAB tutorial - Weizmann Institute of Science

MATLAB tutorial
online version
Methods in Computational Neuroscience
Obidos, 2004
Thanks to Oren Shriki, Oren Farber
and Barak Blumenfeld
Capabilities
• Numerical calculations. Matrix manipulations.
MATLAB = MATrix LABoratory
• Data Analysis
• Data Visualisation
• Simulations
Neuronal models
Network models
• Analytical calculations
• User interfaces
• ....
• ....
Starting MATLAB
• Desktop Demo
type demo matlab desktop in the prompt ,and then start a „desktop
environment“ demo
First steps. Learning by doing
• Matrix Manipulations
Data analysis
• Importing Data
type demo matlab desktop in the prompt ,and then start a „importing
data“
• Data Analysis Demo
• Interpolation Demo
3-D plots
• Mexican hat function
f (r)  AE e
|r|/  E
 AI e
0.1
|r|/  I
0.05
0
-50
-25
0
25
50
Poisson spike train generator
• Exercise 3
Spike times: ti
Interspike interval distribution: P[τ ≤ ti+1 - ti < τ +Δt] = rΔt exp(rτ).
Formula for generation:
Relative refractory period:
ti+1 = ti - ln(xrand)/r.
 ref
dr
 r0  r
dt
T
Autocorrelation function
1
Q( )   dt(  (t )  r )( (t   )  r )
T0
n
 ( )   (t  ti )
i 1
Ring neural network model


 m i   mi  g   Jij m j 
 y

g(x)
T
• Weak coupling with homogeneous input
• Weak coupling with noisy tuned input
• Strong coupling with noisy tuned input
• Strong coupling with nonspecific input
Orientation maps
Orientation maps
0

z x  
 2 i k
 f k x  e
n
135
k 1

 2i
z x   z x  e
90
45
Preferred orientation φ
Selectivity

z x 
0
2-D network of visual cortex
(courtesy of Barak Blumenfeld)


 m x    m x   g   J x, y m ( y )
 y

g(x)
T