simple inhibitory signals in the matsumsig model

These are simple enough. It is clear that in the brain some circuits can switch off other circuits when they are active. Here is a simple example in the MatSumSig model:

[ filtered-signal ] = [ pos[x1] ] [ 1 -1 ] [ signal      ]
                                           [ off-current ]

where pos[x] is the simplest of the sigmoids (and also corresponds to the fact that you can't have negative numbers of spikes):

def pos(x):
  if x <= 0:
    return 0
  else:
    return x

and:

signal is a time varying signal.
off-current is a time varying off-current. (In this case an inhibitory signal of roughly the same strength as the signal)
filtered-signal is the result

an example of a strongly inhibitory off-current:

[ filtered-signal ] = [ pos[x1] ] [ 1 -10 ] [ signal      ]
                                            [ off-current ]

an example of a weakly inhibitory off-current:

[ filtered-signal ] = [ pos[x1] ] [ 1 -0.2 ] [ signal      ]
                                             [ off-current ]

And now a BKO example:

M |yes> => |yes> + -1|no>
M |no> => -1|yes> + |no>

sa: matrix[M]
[ no  ] = [  1   -1  ] [ no  ]
[ yes ]   [  -1  1   ] [ yes ]

Now some examples:

sa: drop M |yes>
|yes>

sa: drop M |no>
|no>

sa: drop M (|yes> + |no>)
|>

sa: drop M (0.8|yes> + 0.2|no>)
0.6|yes>

sa: drop M (0.2|yes> + 0.8|no>)
0.6|no>

All simple enough, and corresponds to the case when you have objects/concepts that are mutually exclusive.

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updated: 19/12/2016
by Garry Morrison
email: garry -at- semantic-db.org