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Home-> Computation->Coherence


Coherence

Synapses are the critical events in which information is created or transformed as it moves between neurons. In our synthetic model of the neuron, the synchronized transfer of messages occur within specific time durations. These communicating automata inside the computer can move messages in a timed broadcast method to groups of automata waiting to service the request, or in a synchronous point-to-point fashion from one automaton to the next one.

Real neurons receive "broadcast" messages from chemical releases. For example the release of adrenalin in response to stress is like a broadcast message which is transmitted to a wide class of nerves cells in the heart, lung and legs as well as the brain. But when neurons need to really "compute", they talk directly to each other in a synchronous point-to-point fashion passing messages or synapsing in a relay chain.

Synchronized Synapsing Neurons

Neurons communicate in synchronicity or coherently to increase the rate of information flow, that is, they fire or synapse in step which each other. The signals in these synapses are propagated from one neuron to the other in a point-to-point fashion. I'll first make a hardware analogy between the computer and the human brain, then I'll postulate the reason why neurons synapse in groups together in time like an orchestra playing.

Using a simplicistic analogy, software objects in a computer program can communicate with each other in a orderly sequential fashion or synchronously. The programmer can control when and what objects send and receive messages. The timing of sending of a message in computer can controlled to an accuracy of a micro-second.

The biological neurons in the brain which emit chemical messages and synaptic electric currents cannot transfer information very quickly. If the physical frequency of the rate of information transfer in the brain was increased, the energy required just to "cool" the brain would increase exponentially. Keeping the frequency of the neural circuits low allows less energy to be expanded in the system as a whole. This might explain Nature's strategy of having large set of neurons synapsing coherently [1] to increasing the rate of information transfer.

The effort Nature would have to expand to build a fast serial circuit would probably not be economical. Building a few fast serial processors would still not provide the computational resources to manage the nervous system. It's the same problem computer chip makers face. So Nature builds massively parallel processors which I assume on faith are relatively simple units.

Nature discovered by trail-and-error, probably from primitive cell groups, that causing bursts of electro-chemical signals between themselves could transfer relatively large quantities of information. The greater the number of synchronized synapses, the greater the rate of information transfer. The "engineering" contraints of brain building from a biological viewpoint determined the most efficient architecture for transferring a bulk of information. We still don't know for sure exactly how information transfer works in real neurons.


Synchronizing Synapses in Time


The synapses occurring in the dendritic tree are associated with the signals in the axonal tree if the synapses follow each other in time. The content of information moving from the dendrites to the axon in the neuron are filtered or transformed in the cell nucleus or soma. The synaptic firing delay of the signal moving between neurons is controlled by the soma. This delay causes the signal in the neural chain to be synchronized in the propagation paths or channels in the neural circuits. The analog of the soma's propagation delay factor can be made to the refractive index of a wave moving through a dense medium. The refractive index is a measure of the speed of wave propagation, and also determines the wave's path.

The association or correlation of synaptic signals or messages, might probably be due in part to the physical interference of the waveforms of these messages. The physical interferences of waveforms are caused primarily by propagation delays in the nerve cell soma.


Synchronizing Synapses in Space

The classical neural networks contains more of the spacial model. This is in part because of the initial model's success at visual pattern recognition. When a large set of neurons, an ensemble, all get input signals (i_0, i_1, ..., i_n-1) arriving at each neuron's cell body simultaneously, then we say that the neurons are synapsing coherently. Each input signal, i, contains an associated weight, w, which is a measure of the strength of the signal. However, I've given up development in this spacially oriented model in favor of a temporal one long ago. I feel that the significance of using the parts of spacial model will have a second order effect when used in circuits; one which is small, and does not fit cleanly or simply with the temporal one.


Footnote

1. Remember that coherence means order. Order usually implies a system in which the number of states within system has decreased making the system more certain. An ordered system has less entropy. Intuitively, reducing the number of states in a system increases its order. An extreme example is superconductivity in which the number of states in the system decreases. The same is true for coherent laser light. In terms of synchronization, coherence means how well information can be transferred in a system or between systems. That is, the rate of information transfer is high in a synchronized system.



Jackson Pollock: Lucifer, 1947;
photo: www.maws-gallery.co.uk

2. Coherence, for me, can also be related to aesthetics which has been defined as the ratio of simplicity to complexity. With respect to an entropic or informational definition for coherence, a simple system would appear as if the rate of information being passed to the observer is low, and a complex system would be the opposite. So using this definition, a coherence factor near 1 is aesthetic, and a small (near 0) or large factor is not pleasing. An aesthetic system depends on the rate at which the observer can process incoming information. (Of course there are many other factors that make art beautiful and significant. The sense of the aesthetic with respect to coherence is a narrow one. This is a Jackson Pollock like view of art.)


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