Robert, A. (1999); "Lamination and Within-Area Integration in the Neocortex";
Doctoral Dissertation, University of California at San Diego, Cognitive Science Department.
My doctoral dissertation focuses on bridging from cortical anatomy to computational models for Hebbian development in non-primary cortex. After a review of neocortical evolution, inter-species and inter-area cytoarchitectural variation, and major theories of the role feedforward and feedback connections in sensory processing, it describes how I compiled cell distribution and connection data focusing on rat primary sensory cortex and built two detailed models from it using single-compartment spiking cells, both of which were compared with slice experiments. The second model reduced the number of layers and cell populations from the first, and I then simplified this into an architecture with 3 (non-spiking) cell layers and a 3 x 3 matrix of "lateral" interactions within and between them. Under Hebbian learning algorithms similar to those employed for studying development of orientation selectivity in primary visual cortex, I show that the 3-layer structure is better able to integrate multiple inputs with different arbor widths and strengths as are seen in real neocortical feedforward and feedback connections. Dr. Martin I. Sereno was my advisor.
Robert, A. (1999); "Pyramidal Arborizations and Activity Spread in Neocortex";
in Neurocomputing 26-27:483-90.
This journal/conference paper provides a compressed version of the first third or so of the work described above in connection with my dissertation. A cortical model with 3 layers and 13 spiking cell populations was constructed from anatomical data and compared with slice experiments. Interlayer interaction functions suitable for use in non-spiking and Hebbian learning models are calculated.
Robert, A. (2002); "Laminated Models of Within-Area Integration in the Neocortex";
This manuscript submitted for publication is an expanded version of the previous paper.
Robert, A. (1998); "Blending and Other Conceptual Operations in the Interpretation of Mathematical Proofs";
in Koenig, J.P. (ed.), Discourse and Cognition: Bridging the Gap, pp. 337-50.
This paper describes the application of notions from cognitive semantics - image schemas and metaphorical mapping - to understanding mathematical reasoning. Professor Gilles Fauconnier has played a major role in helping me develop these ideas.
Robert, A. (2002); "Cognitive Structures and Processes in the Interpretation of Mathematical Proofs";
A longer exposition of the work described in the paper above, including several extensions. Submitted to a journal but required revision. Offered as-is for anyone who is interested. Feedback, particularly from practicing mathematicians, is welcome.
Robert, A. (1997); "From Contour Completion to Image Schemas: A Modern Perspective on Gestalt Psychology";
UCSD Department of Cognitive Science Technical Report 97-02.
This technical report assesses the Gestalt grouping laws and the principles behind them in the light of experimental data and modeling results from modern neuroscience. It suggests that although the grouping principles are in need of revision, the general philosophy of the Gestalt approach -- that energy minimization acting at the level of dynamic neural activity underlies a wide range of psychological phenomena -- is valid and useful in the context of contemporary cognitive science. In particular, the Gestalt theory is highly compatible with present concepts and theoretical constructs in cognitive semantics, itself a framework tying together diverse cognitive phenomena.
See my research page for more information.
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