Late last April I borrowed a portable oscilloscope from Mark Tilden (thanks
again, Mark) and spent two weeks fiddling with a six neuron loop.  I left
everything running for those two weeks and messed around by changing bias
resistors, replacing a bias resistor with an IR-sensitive photodiode,
breaking the loop and feeding an increasingly high frequency signal into
the beginning neuron and stuff like that.  In particular, I hand-copied two
traces: one characterizing a single neuron and another showing how the
events flowed in the entire loop.  You can see these at:

     http://www.trail.com/~aubois/neuron.jpg

and

     http://www.trail.com/~aubois/loop.jpg

Because I only scanned in these pages from my notebook with relatively low
resolution, here is the (edited) text of the notes:

neuron.jpg
On trace A
   To the far left it indicates that the signal varies
   between .2 and 5 volts

   2.22 S (between arrows,) underneath is says
   "close; within measurement error"

   The diagram to the right shows the schematic of the
   circuit under test; it shows that trace A is at the
   input, that trace B is at the bias point and that
   trace C is the output

On trace B
   2.18 S (between arrows,) the dotted line that
   intercepts the second decay curve is annoted
   with "about 1 volt" -- in other words, this is approx.
   the low threshold of the Schmitt trigger

   To the far left it indicates that the peak of the
   decay curve ranged from 4.5 to 5 volts.  It is possible
   that this range is due to aliasing in the 'scope.  It
   also might be that this is an artifact of this system
   being quasi-periodic rather than periodic.

On trace C
   Between arrows indicating width of the low-active pulse
   is annotated with 360 to 380 mS, wider (that is, longer)
   with bigger resistance and that this delay is the 't' of
   figure 6 in the patent (total neuron delay.)

   In the middle of the curve are some notes concerning the
   negative excursion of trace B.  The first indicates that
   the curve generally looked like an 'S'.  The second says
   that this part of the drawing is not to scale (in fact,
   it is exaggerated;) that the sign of the curvature sometimes
   changes; it sometimes only looks like a cap discharge curve
   but it is occurring just when trace A goes low which
   makes its negative value reasonable.  It probably represents
   the charge on the capacitor discharging with the current
   flowing towards point A and that it is probably being
   clipped (attenuated) by the internal protection diodes on
   the 74HCT14 chip.

Summary:
   There are three important points to be made with this
   drawing.  The first is that when the input goes low it
   sort of is like "cocking" the trigger, getting it ready.
   The second is that when the input goes high again, that
   is this TRAILING edge of the pulse that causes the neuron
   to "fire".  Finally, when the curve gets down to the low
   threshold voltage, the neuron stops "firing".


loop.jpg
   You will note that there are six basic traces, labelled A
   through F, all of which represent neuron outputs.  In order
   to show how things work when the signal has gone through all
   six neurons, I've "unrolled" the loop to produce traces A'
   to F' and A''.  In fact, A' is really same as A but with five
   neuron delays in between.

   The curved arrows show how the transition in one output causes
   activity in the next, primarily that the rising edge (which,
   as I wrote before, is the TRAILING edge of the process) is the
   one that triggers the next neuron.  To total period of the
   entire six neuron quasi-periodic oscillator ought to be approx.
   six times the delay of one.  In fact, calculated delay
   was .354 seconds; six times this gives 2.12 seconds; the actual
   measurement was 2.16 seconds which agrees within 2% (that's
   really quite good)

   I got the calculated delay by solving

      1 volt = 5 volts * e^(-t/RC) for t which ends up
      being t = -R * C ln(.2))
      where R was 1 Meg ohm and C was .22 microfarad

   1 volt represents Vth(low) the low threshold voltage and 5 volts
   represents the peak of the decay curve.

Subject:Nu interconnections (from MWT himself!!!)
Date:Wed, 31 Mar 1999 00:30:31 -0600
From:Richard Piotter 
To:beam 

This was from Mark Tilden (sent back on March 9th)

"Mark W. Tilden" wrote:
> 
> >Hello. I've been wanting to do a lot of new work with Nu/Nv circuits. I've
> >read
> >on the BEAM tech FAQ how to make "sensory" Nu neurons, however, in the Living
> >Machines paper, there are interconnected Nu units that have bidirectional
> >connections between each other and are in "contact" with Nv neurons. I'm very
> >curious how these neurons are interconnected between each other. I've
> >looked and
> >can find little information other than the indidual units, but no
> >information on
> >how they connect between each other. Do you have any papers with more detailed
> >examples of such circuits. I'm familiar with Lobster's structure, but as I
> >said,
> >there are many questions.
> 
> Hey Richard.  Good to hear from you.
> 
> Lobster was an attempt at putting an Nv ring inside a homogeneous Nu ring,
> where the outputs of the Nu+'s feed trough a resistor into the bias input
> of an Nv.  At the time, I thought I was making direct "learning Nv's" by
> this coupled association.  However, it failed because the responsiveness of
> the Nv's was far higher than that of the Nu's, so at higher process numbers
> the adaptive benefits of the Nu network just cut out or became detrimental.
> Another lesson of the difficulty in making reactive-adaptive devices,
> lobster was and is a really good "bad" example of autonomous control
> higherarchies.  That's why I never published further details on it.
> 
> That diagram is also embarassing as the lexicon for describing Nv nets has
> advanced significantly over the years.  A more appopriate and accurate
> picture would be as follows:
>
> >   | R0          |
> >  ---           _|_
> > /Nu+\____R1__|/Nv-\
> > \___/        |\___/
> >  ---           /|\
> >   |             |
> >   |R2           |
> >   |             |
> >  ___            |
> >  ---           _|_
> > /Nu-\         /Nv-\
> > \___/         \___/
> >  ---           /|\
> >   |R3           |
>
> Where plates indicate an implied or resistive connection, and arrows the
> connections between Nv outputs and the capacitor inputs of the subsequent
> neuron  (the "primary axion").
> 
> >...It appears neurons
> >have plain lines (presumably the output), and it has tries and circles on
> >other
> >lines. Some neurons (only a few) are in contact, much like the Nu and Nv pairs
> >on Lobster. If you can 1, tell me if there is some sort of standard, as to
> >what
> >the symbols mean (excitatory or inhibitory presumably), then that'd be
> >appreciated. Second, the neurons in this network seem to have both excitatory
> >and inhibitory inputs. Is it possible to recreate this in BEAM technology?
> >
> >        ___
> >       /   \>-----
> > -----o\___/
> >           \
> >            `-----
>
> Yes.  Circles are excitory, triangles are inhibitory, and wires are
> dendritic outputs, by neurobiological convention.  The behavior of a brain
> cell is very much like the basic solarengine with multiple valued resistors
> feeding onto the PNP base junction.  Generally, when the neuron has reached
> it's "presynaptic threshold" (gets a charge), a small excess stimulis on
> the membrane wall will result in a one-shot spike or spike-sequence from
> the neuron amplifier.  In biology, inputs are sparsely valued, and can in
> fact be pre-empted as in the following example.
>
> >    \    |
> >     \--<|
> >   \     |>-------
> >    \   _o_
> >       /   \>-----
>
> Where the excitory effect of a dendrite is inhibited on the dendrite itself
> by several inhibitory junctions.  This discovery has led to the new trend
> of analysing the dendrites for processing abilities in the brain, not just
> the neurons.  The "dendritic processing model" as it's called is one of the
> newest fields in neurobiological research, and it's a bitch because of the
> four additional orders of complexity it involves.
> 
> You must also realize that the "plain line" of a dendrite or axion is
> anything like an electric wire.  It is a carefully regulated tube through
> which a calcium wave passes like a bubble through a straw.  As such, when
> it is amplified or inhibited, it really is a physical speeding, expanding,
> or slowing and shrinking of the wave signal.  The electric field measured
> by EEGs and other things just monitor the electrical side effect of what is
> primarily a chemical reaction in our heads.  Biomech tech is thus different
> but related.  How is controversial because of the many acedemic egos
> involved, but i say if the neuron works...
> 
> Nv systems that use Shmitt triggers are different from real biological
> neuron processes as they are threshold symetric: that is, you can make +ve
> or -ve biased Nv networks and they'll still behave the same, just inverted.
> In biology there is no choice but to use the one type of grounded neuron.
> The power of advanced Nv systems takes advantage of the fact that the
> symettric sum bias of an Nv determines its polarity, and thus it's phase
> and interaction with surrounding Nvs.  "Excitory" and "Inhibitory" thus
> mean different things in symetric networks as their operation completely
> switches based upon what that particular Nv is doing at the moment.
> 
> Unfortunately, currently there is no simple circuit that can show this
> without significant hand-convergence of parameters and robot morphology.
> Every year I test my new circuits on the "small gods" at our conference,
> and if they don't get it, well there's just no point in publishing.  I get
> enough "is my solarengine resistor in the right way round?" emails as it is.
> 
> You can wait for my book (getting fatter all the time), or better yet, make
> the discoveries it seems you're well on your way to finding.  Don't forget,
> BEAM is the educational branch, but if you're into application, then
> biomech tech is what we call Nv engineering.
> 
> >Also, where is the next BEAM games going to be held?
> 
> Sorry, I've been meaning to update the mailout.  Next small workshop is
> scheduled for Los Alamos NM first full week in April.  Availability is
> limited.  Contact Paul Argo (pargo@lanl.gov) for details.  As well, the
> next olympics are scheduled for Santa Fe NM next summer 2000, details
> pending.
> 
> Happy botting.
> 
> markt.

-- 


Richard Piotter
richfile@rconnect.com

The Richfiles Robotics & TI web page:
http://richfiles.calc.org

For the BEAM Robotics list:
BEAM Robotics Tek FAQ
http://people.ne.mediaone.net/bushbo/beam/FAQ.html