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
NONLINEARITY IN PSYCHOPHYSICS
Two lectures
by Giorgio Careri
Dipartimento di Fisica
Universita' di Roma La Sapienza
Roma, Italy
MIDIT-seminar 443
NOTE THE CHANGE IN DATE
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.