The video memory of the cerebellum

Part 2.8 The video memory of the cerebellum

Before introducing the somewhat time-critical functioning of a (possible) neural video memory, we should examine another time-critical process in the Cerebellum more closely.

What output does the Cerebellum deliver during the period of time we call the imprinting of a Purkinje cell or group of Purkinje?

This question is very important because the output of the cerebellar nuclei is used to enable sequential storage. What output do the output neurons of the cerebellum provide during this imprinting phase?

According to theorem 1.41, the nuclear neurons of an uncoined Purkinje group deliver the zero signal fKN_,U= 0 as output. According to theorem 1.41, the nuclear neurons of a coined Purkinje group deliver a firing rate fKN_,G= fP + ½ min( fP; fR). Here, fp is the signal strength of the embossed signal of the Purkinje group, while fR represents the residual signal strength.

We must therefore assume that the rate of fire of the output neurons (nuclear neurons) of a Purkinje group increases during the imprinting phase from the value fKN_,U = 0 to the value fKN_,G= fP + ½ min( fP; fR). The output depends on the signal applied. The part of the input that is a partial signal of the Purkinj group's own signal increases the firing rate of the output, while the part that must be assigned to the external signal reduces the firing rate proportionately.

The more the (relatively short) duration of imprinting approaches its end, the more the associated output of the nuclear neurons approaches the value of an end imprinted Purkinje group. Since the inhibition signal for the associated climbing fiber is derived from the output of the negative nuclear neuron, this inhibition is stronger with increasing embossing and is complete at the embossing end. The climbing fibre inhibition prevents the applied embossing signal from embossing another Purkinje group with the same signal. This means that a Purkinje group switches off the associated (embossing) climbing fibre signal completely during embossing exactly when the embossing phase is finished.

Theorem 2.18: Output of the cerebellar nuclear neurons of a Purkinj group during imprinting

At the beginning of the imprinting of a Purkinje group, the output of the nuclear neurons is the zero signal. During the imprinting process, it gradually approaches the value that the final imprinted Purkinje group provides as output.

After these considerations, it seems necessary to think about the principles of making a video film as such. Let us assume, for example, that we have a video camera that takes 30 pictures per second.

Do we want to save every image? Or do we want to select only those pictures from the series that are different from each other.

The result will depend on it. For example, if we film a forest with a stationary tripod, in complete silence of the wind, each image will first look like its predecessor image and like its successor image. So instead of many thousands of pictures per hour, one single (still) picture is sufficient. But if wind moves the trees, birds fly around or the forester with his hunting dog leaves the forest, we have to decide: Should every image be selected for saving or should we refrain from saving if the previous image is very similar to the current one?

It would be advantageous to determine how much may change from one image to another, so that we consider the new image to be worth storing. The evaluation of the "image similarity" should determine an algorithm.

We call such a procedure similarity compression. From a sequence of images only those successive images are used for selection for storage, whose similarity is not too great. Thus, the total number of images is significantly smaller compared to time-based storage. With the latter, the images are recorded at a constant frame rate.

We decide to develop a neuronal circuit for a video memory, which realizes the similarity compression. For a new image to be stored, it must be dissimilar to the previously stored image.

The interaction of the cerebellum's own signal detectors with the external signal detectors helps us here. A stored own signal is still recognized if the external signal component is not greater than the own signal component. So if at least 50 percent of the content in the image changes, a Purkinje cell will no longer recognize this image and leave its automatic storage to the neighboring, free Purkinje group. 50 percent appears relatively large. But in a Purkinje group we only store a small section of the image, perhaps the size of a stamp. This small area corresponds to the receptive field of the corresponding cortex cluster. And about 1000 times 1000 such small receptive fields could make up the whole picture. When a small bird approaches, it will completely cover the entire stamp area (i.e. the receptive field), the Purkinje cell will not recognize the previously stored image content of this small image section and will cause the new image content to be stored in the neighbouring group.

For storage we use the Purkinje cells of the cerebellum. Their image input comes from the cortex, for example from the primary visual fields. To simplify matters, we restrict ourselves to a cortex cluster, i.e. we "film" only a small part of our visual field. Since this principle is applied to all cortex clusters, we still get a video image of the entire environment. It is similar to using dozens or hundreds of cameras, each of which films only a small square of the visible field of view. Putting the many films together on a big screen would again give the whole picture as if it had been filmed with only one camera.

The climbing fiber signal for storing the first partial image in the first Purkinje group originates from the cortex cluster. Its magnocellular activity neuron monitors the signal activity in the cluster and initiates the climbing fibre signal as soon as the average signal level is sufficiently strong. Switching on the climbing fiber signal corresponds to switching on the camera. It requires signals in the cortex cluster. From the output of the averaging activity neuron, the striosome system forms the climbing fiber signal for the first image of the video memory as described above.

This climbing fiber signal affects the first free video Purkinje group. When it has acted for about one second, the embossing of the embossable signals is finished. Those parallel fiber signals are embossable which were sufficiently active during this embossing period, i.e. which had the minimum firing rate for embossing.

Here we remember a special feature of the climbing fiber signal. It consisted of a high-frequency fundamental oscillation which was totally suppressed about five times per second for a duration of about 1/10 second. Its envelope frequency was about five hertz.

Per second of stamping, we have five "stamping gaps" of about 1/10 second duration each. In these embossing gaps the Purkinje cell can decide whether the embossing of the embossing signal was already strong enough or still needs to be continued. If the imprinting was strong enough, the group of Purkinje cells supplied by this climbing fibre signal will respond with a response. An imprinted Purkinje cell (or Purkinje group) completely stops inhibiting the cerebellar nucleus neurons when it recognizes its imprinting signal. And it is exactly this imprinting signal that is present in the Purkinje cells together with the climbing fibre signal.

So after the (shorter or longer) exposure to the "image signals", the imprintable ones of them will be stored in the Purkinje group and this group will recognize exactly this signal. In this case, the corresponding excitatory nuclear neuron in the cerebellar nucleus reports that the image has been recognized and the imprinting process is therefore complete.

Immediately, the GABAergic nuclear neuron of the cerebellar nucleus inhibits the associated climbing fiber signal in the olive, so that the same image cannot be stored in another Purkinj group. Thus the first image of our video memory is ready.

We want to assume that nothing changes in the image in the first few seconds because we are filming the forest, for example. Then the first Purkinje group will recognize the current image after its final imprint and will communicate this to the thalamus. Likewise, the negative nuclear neuron inhibits the current climbing fiber signal.

When suddenly the forester comes out of the forest and suddenly stops, we have the second image worthy of storage. The forester with his dog is the foreign signal, which now leads to non-recognition in the corresponding image detail. Therefore, the first Purkinje group will not recognize the forest picture with the forester and his dog, if the edge of the forest is not too far away and the forester appears "very small". If the signal is not recognized, however, it will be stored as a new signal in the neighboring Purkinje group ... etc.

With this method the Cerebellum can work as a primitive video memory. Each image, which differs more clearly from the previous images, is stored - in relation to the different cortex clusters.

Nevertheless, this cerebellar video memory is different from a real video memory. This is explained by a small example.

If a certain sequence of movements is repeated continuously, the cerebellar video memory will only store the sequence once. If a pendulum clock is filmed with a conventional video camera, the pendulum swings back and forth in the film for as long as the film lasts. This is not the case with the Cerebellum. For example, when the pendulum of the clock reaches its lowest position for the first time and thus hangs completely vertically, a cerebral image is burned into a Purkinje cell. If the pendulum returns to the same position after exactly half a swing, the responsible Purkinje cell recognizes this and immediately reports: Image recognized. This suppresses the climbing fibre signal as long as the pendulum is in this (and similar, directly adjacent) position. In the described cerebellar, primitive video memory, an image is thus only stored if it has never occurred before. This causes the intelligent compression, but the temporal connection can be lost. Therefore this model of video memory is really only a model. Its basic functioning is set out in a theorem.

Theorem 2.19: Primitive video memory of the cerebellum

The cortex signals from the cortex clusters of the primary visual fields cause an automatic storage of all sufficiently different images in the cere-bellum in the order of their first temporal occurrence. A multiple storage of identical images does not occur, resulting in a similarity compression, which can, however, lead to the loss of the temporal coherence of the individual images.

The question of the video format in the brain will not be answered until part 3 of this monograph on the subject of digitizing analog signals is completed. Then you will see that the neural video format is not too different from the digital format.

With regard to the inverse video memory, which can replay stored video sequences so that they appear to us in a dream, for example, we need two new terms. One is the concept of similarity concatenation.

The concept of "sufficiently different" images implies that video sequences are at least often piecewise continuous. In this case two successive images are different, but have common image contents, e.g. the common image background. We call such images "similarity chained". If such images are stored in two successive Purkinj groups, they have a common subset of moss fibres from which they are both excited simultaneously.

If one of the images in a Purkinje group with the number k is recognized later, the signal detectors of the neighboring groups of this kth group are also partially excited. This excitation of the own signal detectors (basket cells, star cells, golgi cells, nuclear neurons) of the neighboring groups via the common moss fibers is called secondary excitation. The strength of the secondary excitation depends on the number of common moss fibres. Side excited Purkinj groups have the binary value 1 at several equal bit positions in their digital signature, exactly there their own signal detectors use the input of the same moss fibers.

The similarity concatenation and the resulting secondary excitation are one of three causes for the functioning of inverse video memories in the brain. Therefore, we summarize this finding in a separate theorem.

With regard to the output, it can be noted that side-excited Basket, Star, Golgi cells and nuclear neurons are more strongly excited as a result, while the Purkinje cells are more strongly inhibited by these self-signal detectors.

Theorem 2.20: Similarity concatenation and secondary excitation

If adjacent Purkinj groups of a cerebellar memory chain are similarly concatenated, signal detection in one Purkinj group will lead in parallel to a secondary excitation of the intrinsic signal detectors of the similarly concatenated neighbouring groups, because common partial signals and thus jointly used moss fibre signals are used as parts of the intrinsic signals of the adjacent Purkinj groups.

It is known that there are places in the brain where synchronicity with the course of the day is observed, we have an internal clock. So if an analog quantity in the brain represents the time of day, which is digitalized accordingly, this digital quantity would be available as a signal on the parallel fibers of the cerebellum. If this signal has a sufficient number of bits, i.e. parallel fibres, it is stored with the video signal. During the storage of the images, the signal value of the time signal changes and is also stored. This means that video images are now also stored which are visually completely identical if they only have a sufficiently different time signal. This is the case if they are further apart in time, e.g. at least 20 seconds. The prerequisite is that the time signal really does occupy a larger number of binary digits and thus of parallel fibres. This would eliminate the above deficiency: The same video signals at different times are stored in the order of their temporal occurrence. The existence of neuronal time in the brain has already been proven. It must be shown in chapter 3 how this analog time quantity is converted into a digital time quantity, so that this extended variant of the video memory is close to reality.

Moreover, the inclusion of auditory input would have similar effects. If the sound signal is stored together with the image signal, images may be the same as long as their sound differs, in order to be stored nevertheless. For in view of the two hundred thousand parallel fibres, it is quite conceivable that visual and auditory signals could end up in the same Purkinje cells, perhaps even olfactory (olfactory signals) and so on.

If we (purely hypothetically) assume here the existence of a digitized time signal in the brain, we should state the reasons for this assumption.

In the book "The Brain" by Richard F. Thompson from Spektrum Akademischer Verlag, 3rd edition 2001, which has already been quoted several times, there is a very interesting chapter on the subject of "Biorhythms". There, many measurable parameters are even graphically displayed as a function of the course of the day. It explains that rectal temperature, plasma level of 17-hydroxy-corticosteroids, grip strength, dopamine level, catecholamine level and optical reaction time follow a daily rhythm that is repeated every 24 hours. The diurnal rhythm, which neurologists call the circadian activity rhythm, is due to the action of an internal clock. We read about this on page 216 of the work just mentioned:

(begin quote)

"A superior clock in the mammalian brain has only recently been identified. It is a structure in the hypothalamus known as the suprachiasmatic nucleus or nucleus suprachiasmaticus; because of its paired arrangement it is often referred to as two suprachiasmatic nuclei or SCN. As the name suggests, the SCN are located immediately above the optic chiasma, the junction of the two optic nerves. The relative size and structure of these small hypothalamic nuclei appear to be essentially the same in organisms as different as mice and humans. Obviously, they perform their function in all mammals in the same way. If the SCN is destroyed, the circadian activity rhythm is completely lost in mammals (Figure 7.10)".

(end of quote)

Thus, there are daytime activity variations in the brain, the digitalization of which could provide the input for a neuronal time signal in the parallel fibers of the cerebellum. In addition to the circadian rhythm, there are also longer-term, but also shorter rhythms whose periods are significantly longer or significantly shorter than the 24-hour rhythm. The principle of digitizing such quantities into neuronal signals will be shown later. At this point, the existence of such binary time signals in the brain is already assumed, because we know an application example for this.

We put our knowledge into a new theorem.

Theorem 2.21. Video memory with digital time signal

If, in addition to the visual signals from the cortex, a digitized time variable is also stored, then the same or similar image signals which occur one after the other can also be stored one after the other, if the digitized time signal component has a sufficient bit width as an inherent signal, i.e. if sufficient moss fibres are used. Identical image contents then have a different time signal component in the intrinsic signal and represent different and distinguishable signals for the Purkinj groups. This also applies to the coupling of video signals with auditory, gustatory, olfactory or motor binary signals.

It will become apparent that there are several workable versions of a video memory, which could have a certain reality value for circuitry reasons. May neurologists decide which of the possible variants has been realized in which brains. Because video storage is certainly already found in the animal kingdom. Here we want to tackle the biggest shortcoming of this primitive video memory. It is a clear deficiency: we can only store images that do not change significantly for the shortest possible imprinting period of at least one second.

However, since we are physically able to detect very fast changes in, for example, video clips, our primitive video memory needs a system-theoretical improvement. If a signal only lasts a tenth of a second, this is not enough for imprinting. How could we extend the exposure time of this signal?

This is where the hippocampus comes into play again. It is capable of generating a longer lasting signal from a short signal. First, it generates from the original signal a lot of primary echoes with different pause duration. Afterwards it combines these into a secondary echo which lasts much longer than the original signal. So may the hippocampus help to make the video memory more realistic.

Any cortex signal from the primary visual fields that is suitable for video may therefore reach the hippocampus. The hippocampus should generate ten echoes for each signal of 0.1 second duration. The signal of each cortex neuron of the cluster runs along its own moss fibre of the hippocampus. The speed of the associated action potentials is low, e.g. 0.1 m/s.

If the moss fibre has a length of 100 millimetres, each action potential needs one second for this distance.

If this moss fiber is tapped at ten points, the propagation delay on the tap lines results in a total of 10 signals, the first of which is delayed by 0.1 second. The second tapped signal arrives with a delay of 0.2 seconds. The last one already has a time delay of one second.

All of these tapping lines - referred to by neurologists as Schaffer collaterals - converge by means of better myelinated axon lines to a common CA1 neuron, which combines the ten time-delayed primary echoes of 0.1 second duration each into a secondary echo of one second duration.

Every signal neuron of every cortex cluster in the visual field now has exactly one such CA1 neuron in the hippocampus *), which generates an echo of about one second duration for each input. This hippocampal output projects into assigned fields in the cerebral cortex. It has already been proven that the hippocampus projects via the territory anterius of the thalamus into the cerebral cortex, which is called the cinguli gyrus. It is the lowest, innermost coil of the cerebrum.

However, since this gyrus cinguli as the cerebral cortex probably has the same structure as all cerebral cortices, there are cortex clusters. These again project over the bridge nuclei into the cerebellum. And the activity neuron of each cortex cluster generates a climbing fiber signal for exactly this associated cerebellum cluster. There the time-stretched signals of the hippocampus are burned into the Purkinje cells.

While the original input of the visual fields also contained rapidly changing sequences of images, whose duration of about 0.1 seconds was too short for embossing, these signals are now stretched to ten times the duration. This makes them suitable for embossing.

*) To be more precise: In the hippocampus there is a whole series of CA1 neurons for each moss fibre input, which form secondary echoes of different durations to this signal. In this case, a secondary echo of about one second is sufficient.

This is an extension of the primitive video memory with the "slow motion" property, the temporal resolution is better.

We summarize our knowledge in our own theorem.

Theorem 2.22. Video memory with increased time resolution

If visual signals of the cortex (possibly in common with other types of signals) are transformed into an echo sequence in the hippocampus by superimposing a series of its own time-shifted echoes on each individual signal, then even signals whose original duration would not have been sufficient for imprinting in the cerebellum can be imprinted. The secondary, time-stretched echo of the original input reaches the cinguli gyrus via the anterior thalamus, from there the associated cortex cluster and acts as input for a cerebellum cluster via the bridge nuclei. In this cerebellum cluster, the time-stretched video signal is stored with higher time resolution.

However, the hippocampus does not only have the task of providing time-stretched signals. The signalling pathways in the limbic system directly indicate this. Another task is to provide primary, short echoes for the comparison of signals with itself in order to detect temporal changes. This is precisely why the CA1 neurons project their short primary echoes into the preoptic region to enable visual motion detection.

A further task would be the imprinting of temporal signal sequences into new complex signals, for example phonemes into words. The hippocampus is also integrated into the dopaminergic limbic system. However, we will perhaps come back to this later because the function of the involved amygdala is not explained in this monograph. The author currently lacks the necessary expertise and inspiration, although there are approaches for a model that should be of particular interest to theoretical mathematicians. According to this model, the amygdala generates a medium current focus in a multi-dimensional but discrete spatial world in which each dimension corresponds to a neural modality. Here, the neuronal modalities can be divided into contrary ones that work against each other.

Examples of such contrasting pairs of modalities are listed here: lusty-hungry, light-dark, warm-cold, tired awake, light-heavy, up-down, front-back, poisonous-edible, sweet-sour, salty-bitter, good-bad, male-female, life-dead.

They can only count as modalities if there are receptors for their perception or if they represent complex signals based on receptor input.

Depending on the activity of the modalities involved, the current focus is "pulled" or "shifted" in one or the other direction of the modality and a corresponding output is generated, which controls the subsequent activities of the different subsystems. The awareness of the "shift of emphasis" corresponds to the "mood". The signals of this system are "mean value signals" and therefore (mostly) correspond to the "feelings".

But the hippocampus also creates images of the past that are available in the present. Only then do we become aware of what happened a few seconds, minutes, hours or days ago and what significance these signals of the past have in this present. This type of memory is also known as long-term memory.

The development of language requires this ability. The meaning of a letter, more precisely of a phoneme, depends directly on the phonemes spoken before. In this case, the hippocampus produces a picture of the past by echoing. A new chapter will be devoted to this method of working. Finally, it would be necessary to analyze what language represents from the perspective of systems theory. It is not just a sequence of phonemes that are acoustically composed of formants. Language is highly meaningful. Its meaning results from the context as an empirical value. The emergence of language as a means of phonetic expression, the acquisition of meaning by sounds in the course of evolution and the use of language as a means of communication provide a wide field for theoretical analysis. Only through the use of language did man become human. Therefore, the development of language is an inseparable part of the process of becoming human.

An essential prerequisite for the emergence of intelligence was named by the theory of neural networks: the learning ability of associative matrices. The next section deals with this.