Appendix X

Notation

v1.0

14 Nov 2018

Harland Harrison


http://harlandh.cnc.net/Philosophy


The formulas express four different things


Structure

Plasticity

Signals

Math


"Structure" describes  the connections between neurons, principally across synapses


"Plasticity" describes changes in structure


"Signals" are data traveling over the structure.


"Math" includes symbolic logic and algebraic expressions


Structure:


Letters, A...z, denote neurons or "pathways" of neurons


-> denotes synapses connecting axon to dendrite


X->Y denotes a pathway connecting neuron X to Y which may be a single neuron or another pathway


X<->Y  is equivalent to X->Y,Y->X 


~-> indicates a synaptic connection does not exist or has been lost


Plasticity:


=>  shows the structure description on the left creates or changes to that on the right


+-> indicates a synapse strengthened by a plastic change


--> indicates a synapse weakened by a plastic change


Signals:


X(t) indicates the signal out of X, varying over time.

The signal is considered digital

Time is normalized to integers of pulse frequency or delay time


T(A->B) is the time delay for a signal to pass through a pathway

Generally, normalized to 1 for two neurons in the same structure


Math:


Ordinary math which conflicts with the special notation should be

enclosed in quotes:


"ax+bi=-1"  " (a->b) -> (b | ~a)"



General:


{ S } is equivalent to S0,S1...Sn for any set of neurons or pathways


| X | is equivalent to X0,X1...Xn for any expression X


X,Y [operator] Z  is equivalent to X [operator] Z,  Y [operator] Z

where  [operator] could be any of ->,  => , <-> etc


...  indicates more expressions in the similar pattern

eg s0(t)=s1(t+1)=s2(t+2)...=sn(t+n)


M( X ) or m( X) is the number of items in X




(More to come)


harlandh@harlandh.cnc.net