Browsing by Author "Huang, Nai-Zhu"

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Decidability of Irreducible Tree Shifts of Finite Type
(1970-01-01)
Ban, Jung-Chao
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Chang, Chih-Hung
;
Huang, Nai-Zhu
;
Wu, Yu-Liang
;
應用數學系
We reveal an algorithm for determining the complete prefix code irreducibility (CPC-irreducibility) of dyadic trees labeled by a finite alphabet. By introducing an extended directed graph representation of tree shift of finite type (TSFT), we show that the CPC-irreducibility of TSFTs is related to the connectivity of its graph representation, which is a similar result to one-dimensional shifts of finite type.
Entropy Bifurcation of Neural Networks on Cayley Trees
(2020-01-01)
Ban, Jung-Chao
;
Chang, Chih-Hung
;
Huang, Nai-Zhu
;
應用數學系
;
Department of Applied Mathematics
It has been demonstrated that excitable media with a tree structure performed better than other network topologies, therefore it is natural to consider neural networks defined on Cayley trees. The investigation of a symbolic space called tree-shift of finite type is important when it comes to the discussion of the equilibrium solutions of neural networks on Cayley trees. Entropy is a frequently used invariant for measuring the complexity of a system, and constant entropy for an open set of coupling weights between neurons means that the specific network is stable. This paper gives a complete characterization of entropy spectrum of neural networks on Cayley trees and reveals whether the entropy bifurcates when the coupling weights change.
Entropy dimension of shift spaces on monoids
(2020-07-01)
Ban, Jung-Chao
;
Chang, Chih-Hung
;
Huang, Nai-Zhu
;
應用數學系
;
Department of Applied Mathematics
We consider the entropy dimension of G-shifts of finite type for the case where G is a non-Abelian monoid. Entropy dimension tells us whether a shift space has zero topological entropy. Suppose the Cayley graph C-G of G has a finite representation (that is, {C-gG : g is an element of G} is a finite set up to graph isomorphism), and relations among generators of G are determined by a matrix A. We reveal an association between the characteristic polynomial of A and the finite representation of the Cayley graph. After introducing an algorithm for the computation of the entropy dimension, the set of entropy dimensions is related to a collection of matrices in which the sum of each row of every matrix is bounded by the number of leaves of the graph. Furthermore, the algorithm extends to G having finitely many free-followers.