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Physical oriented models of Nerve Nets -
hypothetic models and examples (Part 1)

Gerd Heinz


The decisive question of how the nervous system can be identified is how it is networked. How do we imagine a connection between different communicating units? Is it a direct connection like a line connecting bell button and bell ("bell wire model")? If we reduce this idea, it would mean that every neuron would have to be able to potentially connect to every other neuron (of a few billion) in a universally learning nerve network. Consequently, if it must be assumed that potentially every neuron must be able to communicate with everyone else, this means that every neuron must be connected to everyone else. This in turn has the consequence that all 100 billion neurons ring when a bell button (excited neuron) is pressed. Consequently, nerve systems cannot be described with bell wire models of any kind. But how then?

The neural network theory brought forth a new approach since the 1940s. Threshold logic ("Threshold Logic", Jan Lukasiewicz 1920/1922) gave rise to the idea of only (connecting or) exciting neurons if a threshold value is exceeded, which comes from the simultaneous firing of different neurons. At least small, homogeneous, clocked networks could be described with this idea.

However, the limits of these models are reached when code or noise processing is required, or when signals pass through channels (chiasma opticum, homunculus).

If we include spatial coordinates and delay times on all paths in a model, we arrive at interference networks. But how should communication take place? About interference integrals, of course, about the relative simultaneity of the arrival of pulses. Relative means that it doesn't matter when a pulse started somewhere. The only important thing is that it and its twin brothers arrive at a destination at the same time. Then the goal is uncertain: it is only defined by the simultaneity, by delays.

The railway network is suitable as a conceptual model. Train stations stand for neurons, routes for nerves, trains for pulses. May trains commimg from Magdeburg, Rostock, Leipzig or Dresden arrive at Berlin Central Station. If passengers will be able to transfer between the trains, it would be necessary for the trains to arrive in Berlin at exactly the same time. In order for trains to be able to arrive in Berlin at the same time, they have to start at different times from the places of departure, if we assume that they generally have different travel routes and times.

Places of high interference (local overlapping of many wave crests) require a very precise, spatio-temporal timing of the elementary waves involved. Pulses can come from anywhere. The wave front only have to arrive at the exact destination at the same time to meet other wave fronts. We suddenly conceive a nerve web as the most brilliant, decentralized machine in the universe. We also understand that interference networks are a group of complicated networks that have the property of associating several transmitting neurons with corresponding receiving neurons. And we understand that we are still at the very beginning of their knowledge. We will call networks that do this "projecting networks" or "interference networks".

The author was lucky enough to discover some of them.

Thumb Experiment

If the thumb is electrically stimulated, the progressing impulse can be picked up on two non-invasive accessible nerve tracts (n. radialis and n. medianus) (NLG/EEG averager set at least 10 times; arrange the shielding electrode between the stimulus and sensor electrodes).

A small change in the position of the thumb causes that the time difference between the arrival of both pulse parts varies by around 0.5 milliseconds. The wavefront of the impulse passes the sensor electrodes more or less obliquely. The picture even shows a sign reversal of the wavefront when the thumb is pointing inwards.

The right part of the picture shows mappings that vary with the position of the thumb on a hypothetical reception field.

Bild: Thumb experiment, G. Heinz, 1992

An introductionary experiment by the author, measured by Electro-Encephalography. Stimulation of thumb by ring electrodes and recording of two nerves (n.radialis and n.medianus) shows the forthcoming of impulses in dependence of the position/location of the thumb. (Use a guard ring between thumb-electrode and sensor-electrodes to avoid artefacts. Averaging: 10-times minimum).

If the thumb position changes, the delay-difference between the sensor electrodes changes too. The wave frontier passes more or less diagonally the sensor electrodes. When we suppose, that elsewhere in the body (medulla spinalis, ganglion spinalis...) lay neurones in a circuit in a real distance (s), we can calculate the properties of this interference circuit with real velocities. Interference circuits can be any fast - but only at the transmission wires (v, w).

This simple interference circuit had already demonstrated a mirrored projection (red to red, blue to blue), (Measurement from December 16th, 1992, Landesklinik Teupitz; Dr. Gerd Heinz/ Dr. Torsten Griepentrog). So Christmas 1992 became the most sleepless celebration of my life. Now the thoughts "only" had to be sorted and written down.

The first publication was the IWK-paper "Relativität elektrischer Impulsausbreitung als Schlüssel zur Informatik biologischer Systeme. 39.IWK Ilmenau (PDF, german), (HTML, german) translation (HTML, english).

See further details in the web-publication "Beobachtbare Relativität neuronaler Impulsausbreitung - Ein Versuch mit Konsequenzen für die Neuroinformatik" (PDF german).

Three Elementary Functions of Neurons: Bursts as Neural Adresses and Neighborhood Inhibition

Circuit drawing with equations

In organisms we find at different places pulses grouped to bursts (d). We know, that nerves connect tree-like (b) in different ways. Acknowledged, that "The velocity along the axon varies directly with its diameter, from less than one millimeter per second in thin axons, which are usually short, to more than 120 meters per second in thick axons", nerves with the smallest diameter have the smallest velocities.

It will be necessary, to create a substitute circuit (a) for such a connection. Circuit (a) produces on a single input pulse x(t) a burst with a delay mask M, if it has a low bias (OR-type). Also it can produce nothing with a high bias (AND-type). This neuron selects only a definitive pulse group, called burst.

Is it possible, to find two nerve cells with the masks dependency M + M* = T, so the first neurone produces a burst, which only can receive the second neurone. The second neurone in (c) transforms the burst back to a single impulse.

We can observe different things:

  1. Neurons only can communicate with bursts, if they have complementary masks (M + M* = T).
  2. Nature have found a simple principle to address different data streams on a single axon. I suggest, to call this principle "neural data addressing".
  3. With the same effect nature can use a principle to avoid neighborhood excitement: Only neurones speak together, that have complementary masks. I propose, to call this method "neighborhood inhibition".

So we found three elementary functions of neurons:

  1. Code generation
  2. Code detection
  3. DC-level generation

First simulations (oct. 20th 1994, simulator Neuronet, FHTW Berlin, Heinz, Gerd; Puschmann, Peter and Schoel, Gunnar) can be found at the publications directory.
An overview about some details gives the IWK-paper "Wave Interference Technology - Übergänge zwischen Raum und Zeit" (PDF, german).
See also the chapter "Projections and Coding in Pulspropagating Networks - Virtual Experiments", pages 18 and 23 (PDF, english).
Further details are in the papers "Modelling Inherent Communication Principles of Biological Pulse Networks" SAMS1994 (PDF, english) and
"Signalrekonstruktion in leitungsgebundenen Interferenzsystemen - Virtuelle Experimente (2)" 1998 (PDF, german)

Measurment of Distances by Echo, Worldmodel

Simplified brain of a bat

Simplified interference model to measure any distance by echos. A generator neuron N emittes an excitement, exciting on two paths: one part is transformed into sound by the voice, the other part (red) walks slowly with speed v2 radial around the noise sensor (ear) D. In the moment the echo arrives D, an excitement expands with higher speed v1 circular from D. Then the location of an interference correlates with the distance of the echo-reflecting object. We get an interference map of the outside along the radial fibres.

Localisation of Noise

Jeffress idea according to Konishi 1993

Lloyd A. Jeffress model for noise localisation 1948 - historical the first, intermediale, projective interference circuit. Note, that the generating input map excites mirrored the detector field - the neural network. A more right-hand noise location interferes to a more left-hand neural excitement and visa versa.

Mirrored Projections in the Spinal Cord
'Homunculus' as Hyperbolic Projection

Attention! Please avoid to infect your brain. The following, simplified model seems not to be confirm with surgeons experience nor with neuroanatomic results! It is not possible, to publish or to discuss this model in the academic press.
Against this model speeks: different, seeming right documented break down mechanisms of partial spinal cord accidents; a nerval crossing near the brain stem and the experience of neurosurgery.
The model is confirmed by: the presence of neurons in the spinal cord; a pulsewise information processing; reflexes and mirrored topographic projections. The model creates Penfields Homunculus. Furthermore it produces field-like excitement maps in the brain in general, if we suppose the spinal cord carries more then two axons.
It is possible, that the model plays an important rule in the individual genesis.

Medulla spinalis and gyrus p.-centralis with homunculus

Simplified model of the medulla spinalis, created by the author. It is interesting, that such simple model can create Penfields 'Homunculus'. Without crossover, it produces a mirrored and height- specific projection. With PSI-Tools it can be possible, to map things more detailed, if detailed informations about delays are available.

Balancing the Skeleton

Virtual, simplified, interferential skelett stability circuit

We try to couple 30 bone-elements to create a tower high as a man, where the connection between each two elements is freely moveable. If you find an electronic controller that is able to hold this tower stable, avoid to read the rest!
If it is not possible to find such a control circuit. But in accordance to the thumb-experiment we can use some parallel fibres, carrying a wave front from top to bottom. The simple, local algorithm to get global control is: Each element has to move its direction orthogonal to the wavefront, supposed the wavefront comes periodical.

Chiasma Optikum and Cortical World Model

Wave interference maps in the Chiasma Optikum

We try to change the view between two different objects on our table. Because the relative position of the objects within the eye is not changed, the image must appear at the same place in visual cortex. But: we have to remark the view changes at different positions in our world model of the table too! To get such movement of maps see the 'Moving'-simulation in the picture part. The necessary delay-variation can be created from the control potential of the eye muscles.
Beside: Also the mirrored projections of the optical system appears 'interferential'. The wavelenght of impulses in the visual cortex reaches 0,1 millimeter: No wonder.

Access No. since dec. 12, 1996

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File created sept. 30, 1995. Continued editions.