dopamine
serotonin
DA
5-HT
noradrenaline
NA
acetylchol. ACh
s
H(S) = - ΣsP(s)ln2P(s)
r
H(R)
if P(s1,s2)=P(s1)P(s2) then H(s1,s2)=H(s1)+H(s2)
I(S,R)=Σs,rP(s,r)ln2[P(s,r)/P(s)P(r)]
If r is binary, e.g.
P(r=1)=a
P(r=0)=1-a
H(R) = a ln2 (1/a) + (1-a) ln2 [1/(1-a)]
Binary
1.20000
1.00000
bits
0.80000
0.60000
0.40000
0.20000
0.00000
0.00000
0.20000
0.40000
0.60000
a (sparsity)
0.80000
1.00000

I(S,R) is further limited by the s  r mapping precision
θ
ROC curves
θ
s
Hits
But note: ROC curves are
symmetrical for ‘normal’
signals
False alarms
‘High-threshold’ processes lead to asymmetrical ROCs
θ
ROC curves
s
Hits
(remember this when we
discuss hippocampus and
neocortex..)
False alarms
If r is binary, e.g.
P(r=1)=a

P(r=0)=1-a
H(R) = a ln2 (1/a) + (1-a) ln2 [1/(1-a)]
I(S,R) is further limited by the s  r mapping precision
Binary
1.4
1.20000
1.2
1.00000
1
bits
If r is linear, e.g.
0.80000
r = k (s + δ) (Gaussian σs, σδ) 
0.8
0.60000
I(S,R) = ½ ln20.40000
(1+ω2)
0.20000
0.00000
0.00000
0.6
with ω = σs / σδ (signal-to-noise)
0.4
0.2
0
0.20000
0.40000
0.60000
a (sparsity)
0.80000
1.00000
a threshold-linear unit is limited both by its response
sparsity (a) and by its signal-to-noise (ω)
k ( s    T ) s    T
r
0
s   T


1
I   ( ) ln 2 [1   2 ]
2
1
2

 ( )
2 ln 2
1  2
  (  ) ln 2  (  )
  d ( ) (  ) ln 2  (  )
s  T
 s2   2
   1   2  
[ ( )   ( )]2
a
(1   2 ) ( )   ( )
 ( )  e
 2 / 2

/ 2
 ( )    ( )d

Walsh patterns
Use a basis for all possible
stimuli to characterize
fully neuronal responses
Try then an information theoretic description
How?
Extract principal components
much more info in the
temporal waveform
T012 >> Ts !
Was it just
an artifact?
Finite size bias 
need to correct for it
Some temporal course
of information…
Distributed
Representations
(rat CA1 place cells, from simultaneous
recordings by Wilson & McNaughton)
s
r
H(S) = - ΣsP(s)ln2P(s)
H(R)
I(S,R)=Σs,rP(s,r)ln2[P(s,r)/P(s)P(r)]
I(S,R) < H(S)
I(S,R) < H(R)
What if {r} is complex, or just high-dimensional?
s
s’
r
Neural code
Decoding
One possible approach
I(S,S’) < I(S,R)
(if decoding is honest)
Pro: reduced complexity H(R)  H(S)
Con: dependence on decoding algorithm
+ colour…
Decorrelation in the absence of noise:
Decorrelation in the presence of noise:
The Journal of Neuroscience, April 15, 2002, 22(8):3227-3233
Dendro-Dendritic Interactions between Motion-Sensitive Large-Field Neurons in the Fly
Juergen Haag and Alexander Borst
For visual course control, flies rely on a set of motion-sensitive neurons called lobula plate tangential cells
(LPTCs). Among these cells, the so-called CH (centrifugal horizontal) cells shape by their inhibitory action
the receptive field properties of other LPTCs called FD (figure detection) cells specialized for figure-ground
discrimination based on relative motion. Studying the ipsilateral input circuitry of CH cells by means of
dual-electrode and combined electrical-optical recordings, we find that CH cells receive graded input from
HS (large-field horizontal system) cells via dendro-dendritic electrical synapses. This particular wiring scheme
leads to a spatial blur of the motion image on the CH cell dendrite, and, after inhibiting FD cells, to an
enhancement of motion contrast. This could be crucial for enabling FD cells to discriminate object from self motion.