Spatial complexity in some class of cellular neural networks

• Main Authors: Chih-Hung Chang, 張志鴻
• Other Authors: Song-Sun Lin
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/40609174901465454499

博士 === 國立交通大學 === 應用數學系所 === 96 === This dissertation consists two parts. The first part investigates the complexity of the global set of output patterns for one-dimensional multi-layer cellular neural networks with input; the second part focus on the dense entropy of two-dimensional inhomogeneous cellular neural networks with/without input. For the first part, applying labeling to the output space produces a sofic shift space. Two invariants, namely spatial entropy and dynamical zeta function, can be exactly computed by studying the induced sofic shift space. This study gives sofic shift a realization through a realistic model. Furthermore, a new phenomenon, the broken of symmetry of entropy, is discovered in multi-layer cellular neural networks with input. The second part is strongly related to the learning problem (or inverse problem); the necessary and sufficient conditions for the admissibility of local patterns must be characterized. The entropy function is dense in $[0, \log 2]$ with respect to the parameter space and the radius of the interacting cells, indicating that, in some sense, such system exhibits a wide range of phenomena.