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Models of Neural Development


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:

Piepenbrock, C. and Obermayer, K. (2000). The Effect of Intracortical Competition on the Formation of Topographic Maps in Models of Hebbian Learning. Biological Cybernetics, 82, 345 – 353.

Piepenbrock, C. and Obermayer, K. (1999). The Role of Lateral Cortical Competition in Ocular Dominance Development. Advances in Neural Information Processing Systems 11. MIT Press, 139 – 145.,

Piepenbrock, C., Ritter, H. and Obermayer, K. (1997). The Joint Development of Orientation and Ocular Dominance: role of Constraints. Neural Computation, 9, 959 – 970.

Weber, C., Ritter, H., Cowan, J. and Obermayer, K. (1997). Development and Regeneration of the Retinotectal Map in Goldfish: A Computational Study. Philosophical Transaction of the Royal Society B, 352, 1603 – 1623.

Erwin, E., Obermayer, K. and Schulten, K. (1995). Models of Orientation and Ocular Dominance Columns in the Visual Cortex: A Critical Comparison. Neural Computation, 7, 425 – 468.

Obermayer, K., Blasdel, G. and Schulten, K. (1992). A Statistical Mechanical Analysis of Self-Organization and Pattern Formation during the Development of Visual Maps. Physical Review A, 45, 7568 – 89.

Obermayer, K., Ritter, H. and Schulten, K. (1990). A Principle for the Formation of the Spatial Structure of Cortical Feature Maps. Proceedings of the National Academy of Sciences of the United States of America, 8345 – 8349.

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