Reading the Neural Code

1
Reading the Neural Code
2
Dynamical Channel
s(t)
r(t) h(x(t))
Analog signals come into a neural system from
the environment this is s(t). Spike trains
(often) come out of individual neural receptors
or networks carrying information onward. Can we
read the spike train and reconstruct s(t)?
3
(No Transcript)
4
(No Transcript)
5
(No Transcript)
6
From the response data r(t), we form the vector
7
Separate map for each region K of R(t) space
8
If the stimulus s(t) is very fast compared to
the spiking rate, or 1/ISI, we would expect that
the stimulus would not be sampled enough by the
neural activity. Also, if the neural activity is
tonic spikingI.e. stable limit cycle actionthen
very small signals s(t) would simply modulate the
firing frequency, and the reconstruction of s(t)
from observing the response r(t) would be linear.
However, if the amplitude is large, then there
will be large excursions from the limit cycle,
and if the neural activity is chaotic, it may be
distorted by the input, and a nonlinear
stimulus/response relationship would be needed.
The local reconstruction of the s(t)/r(t)
relation encompasses both. Using some fraction
of the data, learn the maps R(t)?s(t). Then use
part of the remainder of the data to give s(t),
the stimulus input, given a new output vector
R(t).
9
Often this is truncated at n1, so it is a global
linear relationship. This works reasonably well
for very small signals in regions where inputs
are modulating tonic spiking. The dynamics is
in the kernel function. No sense of the dynamics
of a system in many dimensions.
10
Prediction of the firing rate for an H1 neuron
responding to a moving visual image. A) The
velocity of the image used to stimulate the
neuron. B) Two of the 100 spike sequences used in
this experiment. C) Comparison of the measured
and computed firing rates. The dashed line is the
firing rate extracted directly from the spike
trains. The solid line is an estimate of the
firing rate constructed by linearly filtering the
stimulus with an optimal kernel. (Adapted from
Rieke et al., 1997.)
11
We did a little experiment to demonstrate this
idea. Our input was the x(t) output from a Lorenz
model We used d7 for the R(t) space. We
used T 3, and we used a local quadratic map.
12
(No Transcript)
13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
(No Transcript)
30
(No Transcript)
31
(No Transcript)
32
(No Transcript)
33
(No Transcript)
34
(No Transcript)
35
(No Transcript)
36
(No Transcript)
37
(No Transcript)
38
(No Transcript)
39
(No Transcript)
40
(No Transcript)
41
(No Transcript)
42
(No Transcript)
43
D 7 T 3 Order is 2 Learn 50,000 Predict
15,000
44
D 7 T 3 Order is 2 Learn 50,000 Predict
15,000
45
(No Transcript)
46
(No Transcript)