Linear analysis of auto-organization in Hebbian neural networks

The self-organization of neurotopies where neural connections follow Hebbian dynamics is framed in terms of linear operator theory. A general and exact equation describing the time evolution of the overall synaptic strength connecting two neural laminae is derived. This linear matricial equation, which is similar to the equations used to describe oscillating systems in physics, is modified by the introduction of non-linear terms, in order to capture self-organizing (or auto-organizing) processes. The behavior of a simple and small system, that contains a non-linearity that mimics a metabolic constraint, is analyzed by computer simulations. The emergence of a simple ®order® (or degree of organization) in this low-dimensionality model system is discussed

Brain, language and the origin of human mental functions

We propose that to understand the biological and neurophysiological processes that give rise to human mental phenomena it is necessary to consider them as behavioral relational phenomena. In particular, we propose that: a) these phenomena take place in the relational manner of living that human language constitutes, and b) that they arise as recursive operations in such behavioral domain. Accordingly, we maintain that these phenomena do not take place in the brain, nor are they the result of a unique operation of the human brain, but arise with the participation of the brain as it generates the behavioral relational dynamics that constitutes language