Jung-Chao Ban

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This work investigates three-dimensional pattern generation problems and their applications to three-dimensional Cellular Neural Networks (3DCNN). An ordering matrix for the set of all local patterns is established to derive a recursive formula for the ordering matrix of a larger finite lattice. For a given admissible set of local patterns, the transition(More)
This paper aims to characterize whether a multi-layer cellular neural network is of deep architecture; namely, when can an n-layer cellular neural network be replaced by an m-layer cellular neural network for m<n yet still preserve the same output phenomena? From a mathematical point of view, such characterization involves investigating whether the(More)
This study demonstrates the devil's staircase structure of topological entropy functions for one-dimensional symmetric unimodal maps with a gap inside. The results are obtained by using kneading theory and helpful in investigating the communication of chaos. Work partially supported by the NSC under Grant No. 89-2115-M-008-029 and the National Center for(More)
This study investigates the complexity of the global set of output patterns for one-dimensional multi-layer cellular neural networks with input. 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(More)
This work investigates mosaic patterns for the one-dimensional cellular neural networks with various boundary conditions. These patterns can be formed by combining the basic patterns. The parameter space is partitioned so that the existence of basic patterns can be determined for each parameter region. The mosaic patterns can then be completely(More)
In this paper, we study the quantitative behavior of one-dimensional linear cellular automata Tf [−r,r], defined by local rule f(x−r, . . . , xr) = r ∑ i=−r λixi (mod m), acting on the space of all doubly infinite sequences with values in a finite ring Zm, m ≥ 2. Once generalize the formulas given by Ban et al. [J. Cellular Automata 6 (2011) 385-397] for(More)
Inhomogeneous multi-layer neural networks (IHMNNs) have been applied in various fields, for example, biological and ecological contexts. This work studies the learning problem of IHMNNs with an activation function $$f(x) = \dfrac{1}{2} (|x+1| - |x-1|)$$ f ( x ) = 1 2 ( | x + 1 | - | x - 1 | ) that derives from cellular neural networks, which can be adapted(More)