ISBN
978-3-00-037458-6
ISBN 978-3-00-042153-2
Monograph of Dr. rer. nat. Andreas Heinrich Malczan
The input that neuronal nuclei receive, like their output, can be interpreted in terms of set theory. Switching nuclei receive their input from a finite number of neurons. These can - at least theoretically - be numbered. Then the input neurons form a well-ordered set. Each neuron can be clearly identified by its number - the Index.
If we consider the output of each neuron as the signal of that neuron, we get a set of signals that matches the set of neurons. If you assign to each signal exactly the Index of the generating neuron, you also get a well-ordered set of signals.
The neuron Nk corresponds to its signal Sk.
The neurons form the neuron set N = { Nk}k = 1...n.
The signals form the signal set S = { Sk }k = 1...n.
A negation neuron forms the negated signal ~Sk to a signal Sk.
The sign ~ stands for the negation operator.
A negation nucleus now forms the signal-theoretical negation of the input set S.
K = K ({ Sk }) = { ~Sk } K Core operator
The result set of a negation nucleus is therefore the set of negated signals. In this respect, a negation kernel is the material embodiment of a function operator that maps a set of input signals to a set of output signals in such a way that each element of the original set is mapped to its negation.
Analogously, a switch-over core forms the signal set S1 = { S1,k }, whose generating neurons use the transmitter T1, to a signal set S2 = { S2,k }, whose generating neurons use the transmitter T2.
Likewise, an inversion kernel Ki maps a set of signals S = { Sk } to the set of signals S* = { Sk* } which are inverse to it.
If the generation of the output of a neuron nucleus is interpreted in terms of set theory, it becomes clear that nature also needs an ordering principle. In our case, this ordering principle was the good order of input quantity and output quantity, which we achieved by numbering (Indexing).
Only in this way can a topology be retained. This topology preservation is extremely important for neuronal nuclei and, as recent research shows, it is achieved, among other things, by gradients of marker substances. Depending on their concentration in the neuronal nucleus, these marker substances control the pathfinding of the axons so that input and output remain topologically well-ordered and a complete signal chaos is prevented.
ISBN
978-3-00-037458-6
ISBN 978-3-00-042153-2
Monografie von Dr. rer. nat. Andreas Heinrich Malczan