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Wave Packet Construction from Binary Trees


Work Sheet   2020-1-7
This worksheet will try to expand coverage on the fundamental
contents on this webpage.


Comments on intuition and aesthetic justification.  Elucidate intution,
and aesthetics.  Connect basis coefficients to neural coefficients (ie.,
weights, and temporal bints.  Explain synapse more.

Waves ...

The wave packet formulation is a practical methodology because it combines
the intrinsically intuitive wave model of energy propagation with a built
in natural structure for information processing using the binary tree.


Neural Waves ...

Using wave packets to describe locally isolated bundles of energy waves
is aesthetically pleasing because of its mathematical simplicity, and
ubiquitous existence in Nature.


Wavepackets compaction and dispersion.  Characterize a solition by
its median frequency and the refractive index of the medium (density,
temperature or energy).  Refractive index is related to how much
you can make the wave coherent in an inhomogeneous medium.  Wave
interference period is related to coherence, and the medium.



Synapse ...

The measurement of a single spike is subject to the uncertainty principle.


Synapse as a pulse.
Minimum uncertainty is dE/df, from dE * dt = h.
Coherence length, L, is  C * dE/df  (use f because it's what's
really measured on an oscilloscope ... in pulses use h or dt).


Elucidate for Karl Popper that uncertainty principle can be used to
create a theory of neurons communicating.  The elucidation above
is intuitive.  Apply to synapses and synaptic waves ...
Bruce Hutcheon's article: Resonance in Neurons.



The Syntactic Neuron

Programming Sequences ...

S(t) = c dS(t)/dt is a Markov sequence.

A TRIE is a neuron.  The prefixed binary tree, TRIE, in a cluster
of TRIEs, is a neuron.