PhD Defense Kang Li

Title: Novel Mathematical neural models for visuel attention

Visual attention has been extensively studied in psychology, but some fundamental questions remain controversial. We focus on two questions in this study. First, we investigate how a neuron in visual cortex responds to multiple stimuli inside the receptive field, described by either a response-averaging or a probability-mixing model. Second, we discuss how stimuli are processed during visual search, explained by either a serial or a parallel mechanism.

Here we present novel mathematical methods to answer the psychology questions from a neural perspective, combining the formulation of neural explanations for the visual attention theories and spiking neuron models for single spike trains. Statistical inference and model selection are performed and various numerical methods are explored. The designed methods also give a framework for neural coding under visual attention theories. We conduct both analysis on real data and theoretical study with simulations.

Our findings are shown in separate projects. First, the probability-mixing model is favored over the response-averaging model, shown by analysis on experimental data from monkeys. Second, both parallel and serial processing exist, with a tendency of being parallel in the beginning and a tendency of being serial later on, shown by another set of experimental data from monkeys. Third, we show that the probability-mixing and response-averaging model can be separated and parameters can be successfully estimated for either model in a more realistic biophysical system, supported by simulation study. Finally, we present the decoding of multiple temporal stimuli under these visual attention theories, also in a realistic biophysical situation with simulations.

Supervisor: Prof. Susanne Ditlevsen, Math, University of Copenhagen

Co.-supervisor: Søren Kyllingsbæk, Department of psychology, SAMF

Assessment committee:

Prof. Bo Markussen, Math, Chairman, University of Copenhagen

Directeur  de Recherche Patricia Reynaud-Bouret, Université de Nice Sophia-Antipolis

Prof. Dr. Hans Colonius, Carl von Ossietzky Universität Oldenburg