Cortical Functionality Emergence :

The human genotype represents at most ten billion binary informations, whereas the human brain contains more than a million times a billion synapses. So a diierentiated brain structure is essentially due to self-organization. Such self-organization is relevant for areas ranging from medicine to the design of intelligent complex systems. Many brain structures emerge as collective phenomenon of a microscopic neurosynaptic dynamics: a stochastic dynamics mimics the neuronal action potentials, while the synaptic dynamics is modeled by a local coupling dynamics of type Hebb-rule, that is, a synaptic eeciency increases after coincident spiking of pre-and postsynaptic neuron. The microscopic dynamics is transformed to a collective dynamics reminiscent of hydrodynamics. The theory models empirical ndings quantitatively: Topology preserving neuronal maps were assumed by Descartes in 1664; their self-organization was suggested by Weiss in 1928; their empirical observation was reported by Marshall in 1941; it is shown that they are neurosynaptically stable due to ubiquitous innnitesimal short range electrical or chemical leakage. In the visual cortex, neuronal stimulus orientation preference emerges; empirically measured orientation patterns are determined by the Poisson equation of electrostatics; this Poisson equation orientation pattern emergence is derived here. Complex cognitive abilities emerge when the basic local synaptic changes are regulated by valuation, emergent valuation, attention, attention focus or combination of subnetworks. Altogether a general theory is presented for the emergence of functionality from synaptic growth in neuro-biological systems. The theory provides a transformation to a collective dynamics and is used for quantitative modeling of empirical data.