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Models of Neural Development

Lupe

Topographic projections between neural sheets, orientation columns and ocular dominance columns in early visual areas have served as paradigmatic model systems for understanding the mechanisms underlying neural plasticity and development. Using mathematical models and computer simulations we investigated how activity driven and intrinsic processes interact in order to generate the observed anatomical connectivity patterns and response properties of neurons. We describe the development of those patterns as a goal-oriented (in the sense of underlying cost-functions) self-organizing process, which extracts information from the environment and imprints this knowledge into neural circuits. Particular emphasis was given to competitive networks including the Self-Organizing Map, which are known to trade smoothness vs. completeness of representations and which lead to patterns which fit experimental data surprisingly well.The mathematical properties of self-organizing maps were also analysed in a machine learning context. For details see "Research" page "Learning Vector Quantization and Self-organizing Maps"

Acknowledgements: Research was funded by BMBF, DFG, and the Technische Universität Berlin.

Selected Publications:

A Statistical Mechanical Analysis of Self-Organization and Pattern Formation during the Development of Visual Maps
Citation key Obermayer1992b
Author Obermayer, K. and Blasdel, G.G. and Schulten, K.
Pages 7568 – 89
Year 1992
DOI 10.1103/PhysRevA.45.7568
Journal Physical Review A
Volume 45
Number 10
Publisher APS
Abstract We report a detailed analytical and numerical model study of pattern formation during the development of visual maps, namely, the formation of topographic maps and orientation and ocular dominance columns in the striate cortex. Pattern formation is described by a stimulus-driven Markovian process, the self-organizing feature map. This algorithm generates topologically correct maps between a space of (visual) input signals and an array of formal ‘‘neurons,’’ which in our model represents the cortex. We define order parameters that are a function of the set of visual stimuli an animal perceives, and we demonstrate that the formation of orientation and ocular dominance columns is the result of a global instability of the retinoptic projection above a critical value of these order parameters. We characterize the spatial structure of the emerging patterns by power spectra, correlation functions, and Gabor transforms, and we compare model predictions with experimental data obtained from the striate cortex of the macaque monkey with optical imaging. Above the critical value of the order parameters the model predicts a lateral segregation of the striate cortex into (i) binocular regions with linear changes in orientation preference, where iso-orientation slabs run perpendicular to the ocular dominance bands, and (ii) monocular regions with low orientation specificity, which contain the singularities of the orientation map. Some of these predictions have already been verified by experiments.
Bibtex Type of Publication Selected:development
Link to original publication Download Bibtex entry

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