dopamine DA serotonin 5-HT noradrenaline NA acetylchol. ACh

I(S,R)=Σs,rP(s,r)ln2[P(s,r)/P(s)P(r)] H(S) = - ΣsP(s)ln2P(s) 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)]

I(S,R) is further limited by the s  r mapping precision θ θ s ROC curves False alarms Hits But note: ROC curves are symmetrical for ‘normal’ signals

‘High-threshold’ processes lead to asymmetrical ROCs θ s ROC curves False alarms Hits (remember this when we discuss hippocampus and neocortex..)

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 If r is linear, e.g. r = k (s + δ) (Gaussian σs, σδ)  I(S,R) = ½ ln2 (1+ω2) with ω = σs / σδ (signal-to-noise)

a threshold-linear unit is limited both by its response sparsity (a) and by its signal-to-noise (ω)

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

Distributed Representations (rat CA1 place cells, from simultaneous recordings by Wilson & McNaughton)

I(S,R)=Σs,rP(s,r)ln2[P(s,r)/P(s)P(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?

I(S,S’) < I(S,R) (if decoding is honest) 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

A Simplified History of Neural Complexity Symbolic  ({ri}) (Noam Chomsky) 106 107 108 109 yrs Memory ri (x,t) (David Marr) Spatial r (x,t) (e.g. Joseph Atick) Chemical r (t) (e.g. Peter Dayan)

 ({ri}) ri (x,t) r (x,t) r (t) A Simplified History of Neural Complexity Symbolic  ({ri}) (Noam Chomsky) 3 106 107 108 109 yrs         mammalian species         echidna CA1 CA3 DG platypus Memory ri (x,t) (David Marr) lizard 2 1 Spatial r (x,t) (e.g. Joseph Atick) Chemical r (t) (e.g. Peter Dayan)

Metric

The goal: + colour… to account for data on contrast sensitivity in single neurons + colour…

Decorrelation in the absence of noise: Spatial autocorrelation in the inputs In Fourier space, for natural images

Decorrelation in the presence of noise: (a simplified treatment; the full one in Atick and Redlich, 1990)

goldfish primates double opponency single opponency !!

Juergen Haag and Alexander Borst 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.