Temporal Information

[Fry, Robert L.]

     The establishment of what actually comprises information in biological 
systems is an essential problem since this determination provides the basis 
for the analytical evaluation of the information processing capability of 
neural structures.  In response to the question "What comprises information 
to a neuron?" consider the answer that those quantitites which are 
observable or measureable by a neuron represent information.  Hence what is 
information to one neuron may not necessarily be information to another. 
 Now as  current discussions have pointed out, there are many possibilities 
regarding what exactly these measureable quantites might consist of in the 
way of rate encoding, time-of-arrival, and so on or even possibly 
combinations thereof.  Consider the following simplistic perspective.

     Observable quantities may be measured in both space and in time both of 
which can be conceptually be thought of as being quantized in a neural 
context.  Spatial quantization occurs due to the specificity of synaptic (or 
perhaps axonal input accrding to current understandings of some neural 
structures) for a given neural.  The synaptic efficacies can be viewed as a 
Hermitian measurement operator  giving rise to the somatic measured 
quantity.  In a dual sense, time is also quantized if time-of-arrival is the 
critical measurement temporal quantity of specific action potential which 
either do or do not exist at a given instant in time.  The term "instant" 
used here obviously must be considered in regard to "Bill's" question of 
what the critical time constant is or are for the subject neural assemblies. 
 There is empirical evidence that there are adaptation mechanisms in place 
which serve to modulate time-of-arrival giving rise to a delay vector having 
a one-to-one correspondance with the efficacy vector.  From this perspective 
there is a dual time-space dependency on at least some of the quantites 
observable by an individual neuron.  The observable quantity would then 
consist of a_n*x(t-tau_n) where a_n is the learned connection strength and 
tau_n is the learned delay.  This has been the basis for my research in 
which I have been applying the basic Shannon measures of entropy, mutual 
information , and relative entropy to the study of neural structures which 
are optimal in an information-theoretic sense and have publications and 
papers some of which exist in the neuroprose repository.  With this view, 
the sets {a_n} and {tau_n} are seen to represent  Lagrange vectors which 
serve to maximize the mutual informatioon between neural inputs and output.

     This is of course a personal perspective and obviously there may be 
many other temporal modalities for the inter-neuron exchange of information. 
 It can be argued however, that the above modality is in many ways the most 
simple.  Analytically, it seems a very tractable perspective as opposed to 
rate, latencies, etc.

Robert Fry
Johns Hopkins University/
Applied Physics Laboratory
Johns Hopkins Road
Laurel, MD 20723