臺灣博碩士論文加值系統

本文是以模擬退火法建立一個新的自行組織模式。以 Conwey對自行組織原理的論點為衣據，我們首先定義自行組織的品質要件，並進一步轉換為數值化的能量函數。所獲得的能量函數可以具體推導出 Durbin 和 Willshaw 的彈性網方法，並證實該方法是由梯度遞減法和平均場退火法所構成混合收斂模式。為獲至更有效率的計算模式，我們以繩結理論中的三個拓撲不變性運算元素為基礎，在自行組織模式的解答空間中發展相類似的運算元素。新的運算元素在拓撲結構不變的原則下可以配合模擬退火法的收斂方式對能量函數求取最佳解。收斂結果所獲得的維度化約對應具備高信賴度的拓撲保留特性，在參數空間中相臨近的元素，可以在自行組織圖中找到相似排列秩序。新的運算元素可以有效率地在連續性計算機中以字串運算型態模擬，所有的模擬計算都是在個人電腦上施行。

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.