European Union Human Brain Project
Monograph of Dr. rer. nat. Andreas Heinrich Malczan
ISBN 978-3-00-068559-0Published only in German
of all brain activity is the propagation of neuronal excitations. In
the cortex, which forms the highest subsystem, the signals from most
receptors arrive in the form of neuronal excitations in the input
neurons of the fourth layer. Via axons of the neurons and interneurons,
the incoming excitations propagate in the cortex layer and overlap
additively. This results in a distance-dependent damping of the
neuronal excitation, which corresponds to a concave transfer function.
This is concave for each individual input neuron and has a negatively
definite Hessian matrix in a sufficiently large environment. The
additive superposition of any linear combination with positive factors
(firing rates are positive!) again results in a concave overall
excitation function, which always has a global maximum within a certain
superposition area. This global excitation maximum moves back and forth
when the firing rates of the input neurons change, i.e. the strength of
the primordial variables that excite the signal-providing receptors
change. Thus, changes in joint angles in circular movements lead to the
rotation of cortical excitation maxima around a fixed centre.
Similarly, movements of inclined straight lines lead to excitation
maxima that are arranged windmill-like around a centre and whose neuron
populations are called orientation columns.
In the cortex, many signals are represented by maximally excited populations of neurons, and the location of the maxima encodes the parameters of investigation involved. Maximum coding is a basic principle of the brain. The application of extreme value methods enables the determination of the parameters that cause these maxima. Differential calculus provides the tools to understand why researchers observe excitation maxima at the cortex surface, and it provides the relationship between the maximum excitation and its cause. Only then can we understand how the brain internally represents and processes signals. The basis of signal processing in the cortex are divergence modules, in which the input is distributed partly vertically, partly in the plane and partly spatially, overlapping and leading to excitation maxima. The output represents maximum-encoded signals whose maxima represent new modalities, e.g. brightnesses, colours, joint angles, line elements, etc.