| Summary: | 碩士 === 國立東華大學 === 應用數學研究所 === 85 ===
In this paper, a new self-organizing algorithm is developed by using the technique of simulated annealing. By following the Conwey's argument for the principle of self-organization, criteria for self-organizing task are defined and theoretically quantified to obtain an objective energyderived from the same energy function by using a hybrid relaxation method of gradient descent and mean field annealing. In pursuit of efficent computational models, we develop topology invariant operations on solution configurations of a self- organization task by analogy with the three elemetary operations in Knot theory. Relaxation of the energy function for a self-organization task can thus turn to operate in the way of simulated annealing. The resulting dimensing-reducing mappings posses a highly reliable topology preservation such that the nearby elements in the parameter space are ordered as similarly as possible on the cortex-like map. By the convenient implementation of the topology invariant operations in string manipulations on a sequential digital computer, the new self-organizing algorithm can efficiently generate a high reliable coherent map, of which the number of cortical points is more than 10000, in large scale. All numerical simulations use personal computers.
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