Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy

MIDIT                               OFD                           CATS
Modelling, Nonlinear Dynamics       Optics and Fluid Dynamics     Chaos and Turbulence Studies
and Irreversible Thermodynamics     Risø National Laboratory      Niels Bohr Institute and 
Technical University of Denmark     Building 128                  Department of Chemistry
Building 321                        P.O. Box 49                   University of Copenhagen 
DK-2800 Lyngby                      DK-4000 Roskilde              DK-2100 Copenhagen Ø
Denmark                             Denmark                       Denmark


Two lectures

by Giorgio Careri
Dipartimento di Fisica
Universita' di Roma La Sapienza
Roma, Italy

MIDIT-seminar 443

Tuesday April 13, 1999, 15.00 h and 16.00 h.
at MIDIT, IMM Building 305, room 053

Lecture 1: Nonlinear Neuronal Responses

Abstract: The sigmoid input-output relationship displayed by sensory cells and by cortical neurons should be responsible for the threshold-dependent encoding of sensory informations. To this end, the complex processes occuring in a single neuron in different time scales are briefly reviewed, and the faster signaling is identified in cooperative interactions among events at the dendritic membrane. This phenomenology is modelled by a random 2-dimensional lattice where sources (sites) and channels of interaction (bonds) are treated according to statistical physics (percolation theory) , thus offering a sigmoid response centered on a critical value (threshold) where long range connectivity finally emerges.

Lecture 2: Percolative Model for Psycophysical Laws

Abstract: The neural correlates of sensory information are still a matter of concern in cognitive sciences. Convincing evidence for the experimental validity of Steven's power law between sensation magnitude (output) versus stimuli intensity (input) is briefly reviewed. Next, by modelling a dendritic assembly by a percolating network, both the power law above a critical threshold and the numerical values of the exponent are derived, and apparent discrepancies of Steven's data explained as finite size effects. It is suggested that perceptron-like neuronal units can operate according to percolative laws, thus using the same scale-invariant pattern for the hierarchical emergence of a long range cluster of active neuronal units.