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Article overview
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On the structure of multi-layer cellular neural networks: Complexity between two layers | Jung-Chao Ban
; Chih-Hung Chang
; | Date: |
3 Oct 2015 | Abstract: | Let $mathbf{Y}$ be the solution space of an $n$-layer cellular neural
network, and let $mathbf{Y}^{(i)}$ and $mathbf{Y}^{(j)}$ be the hidden
spaces, where $1 leq i, j leq n$. ($mathbf{Y}^{(n)}$ is called the output
space.) The classification and the existence of factor maps between two hidden
spaces, that reaches the same topological entropies, are investigated in [Ban
et al., J.~Differential Equations extbf{252}, 4563-4597, 2012]. This paper
elucidates the existence of factor maps between those hidden spaces carrying
distinct topological entropies. For either case, the Hausdorff dimension $dim
mathbf{Y}^{(i)}$ and $dim mathbf{Y}^{(j)}$ can be calculated. Furthermore,
the dimension of $mathbf{Y}^{(i)}$ and $mathbf{Y}^{(j)}$ are related upon the
factor map between them. | Source: | arXiv, 1510.0779 | Services: | Forum | Review | PDF | Favorites |
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