Formal Tools for the Analysis of Brain-Like Structures and Dynamics

• Authors: Jürgen Jost
• Venue: Creating Brain-Like Intelligence
• Year: 2009

Brains and artificial brainlike structures are paradigms of complex systems, and as such, they require a wide range of mathematical tools for their analysis. One can analyze their static structure as a network abstracted from neuroanatomical results of the arrangement of neurons and the synaptic connections between them. Such structures could underly, for instance, feature binding when neuronal groups coding for specific properties of objects are linked to neurons that represent the spatial location of the object in question. --- One can then investigate what types of dynamics such abstracted networks can support, and what dynamical phenomena can readily occur. An example is synchronization. In fact, flexible and rapid synchronization between specific groups of neurons has been suggested as a dynamical mechanism for feature binding in brains [54]. In order to identify non-trivial dynamical patterns with complex structures, one needs corresponding complexity measures, as developed in [51,52,5]. Ultimately, however, any such dynamical features derive their meaning from their role in processing information. Neurons filter and select information, encode it by transforming it into an internal representation, and possibly also decode it, for instance by deriving specific motor commands as a reaction to certain sensory information.