Everyone knows what resonance is. When a truck drives by, the windows shake. When enough people rhythmically pounding over a bridge, it may begin to vibrate visibly and amplified to the maximum amplitude and finally breaks apart. If you hit the C at the piano while pedaling, the upper and lower C, then the fifths and thirds and eventually the whole string system will resonate. We can only hear because of the sound source and our inner ear resonate. All oscillations or even time cycles can, if they hit a suitable system, produce this resonance, e.g., Atoms, photons, electrons, celestial bodies, etc. Resonance is always a temporal event. One system imposes on the other its natural frequency, its own time.





How could one visualize or imagine the resonance in the neuronal area?

The following figure (after Helmholtz) illustrates a very simplified form of resonance in the neural domain.

Earlier conjectures on how information travels through the brain were unrealistic: Either the idea of strong connections between distant brain areas (for which, however, there was no scientific evidence) or assumed a global mechanism in the brain that stimulated different brain areas to common vibrations. Nobody could explain precisely how these processes came about.

Resonance could be the key to long-distance communication, among other things. Not all nerve cells stimulate others to become active. On the contrary, some of them are inhibiting. The resulting interaction between arousal and inhibition makes the activity of a network swing by a certain amount. Naturally, networks have a frequency at which these vibrations are particularly pronounced. Similar to a piano string that has a preferred frequency. If the activity oscillates at precisely this frequency, then the impulses propagate much further than if this is not the case. This type of resonance enhancement (vibrating signals) seems to be the only way communication over long distances in the brain could occur.

What kind of holistic effect does the whole thing have on a neural network?

The main difference lies in the area of information representation. There are two approaches:

1. the Euclidean-Geometric

2. the Fourier harmonic approach

In the geometric approach, points and lines are considered as primary features of the system. At this level, one tries to represent complex and higher-dimensioned neural mechanisms. The complexity of such a system can grow very fast to the point of uncontrollability. The whole approach is strictly causal, deterministic and reductionist. In most cases, the processes in such systems are reversible.

When a harmonic analysis is chosen as an approach, the neurons function as "strings" tuned to a particular bandwidth of frequencies. The ensemble of strings "composes" the resonators or active filters as is the case in most musical instruments. Thus, it is clear that a single neuron or nerve cell alone has no significant function. Only in combination (triggered by the resonance) takes place an information transfer and processing. This approach would be a non-linear implementation.

If my thoughts on this subject are too naive, then I apologize.

Murat

I originally published this article in German: Resonanz in neuronalen Netzen

Note:

For those who want to be more detailed with the topic: I can highly recommend this demanding technical article.

http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1003811

For the above article, there is also a Python implementation that you can experiment with.

https://github.com/afbujan/ctr