Browsing by Author "Lin, Yin-Heng"

Now showing 1 - 4 of 4

Patterns generation and spatial entropy in two-dimensional lattice models
(2007-09-01)
Ban, Jung-Chao
;
Lin, Song-Sun
;
Lin, Yin-Heng
;
應用數學系
;
Department of Applied Mathematics
Patterns generation problems in two-dimensional lattice models are studied. Let S be the set of p symbols and Z(2lx2l), l >= 1, be a fixed finite square sublattice of Z(2). Function U : Z(2lx2l) -> S is called local pattern. Given a basic set B of local patterns, a unique transition matrix A(2) which is a q(2)xq(2) matrix, q = p(l2), can be defined. The recursive formulae of higher transition matrix A(n) on Z(2lxnl) have already been derived [4]. Now A(n)(m), m >= 1, contains all admissible patterns on Z((m+1)lxnl) which can be generated by B. In this paper, the connecting operator C-m, which comprises all admissible patterns on Z((m+1)lx2l), is carefully arranged. C-m can be used to extend A(n)(m) to A(n+1)(m) recursively for n >= 2. Furthermore, the lower bound of spatial entropy h(A(2)) can be derived through the diagonal part of C-m. This yields a powerful method for verifying the positivity of spatial entropy which is important in examining the complexity of the set of admissible global patterns. The trace operator T-m of C-m can also be introduced. In the case of symmetric A(2), T-2m gives a good estimate of the upper bound on spatial entropy. Combining C-m with T-m helps to understand the patterns generation problems more systematically.
Spatial complexity in multi-layer cellular neural networks
(2009-01-15)
Ban, Jung-Chao
;
Chang, Chih-Hung
;
Lin, Song-Sun
;
Lin, Yin-Heng
;
應用數學系
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 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. (C) 2008 Elsevier Inc. All rights reserved.
Spatial complexity in multi-layer cellular neural networks
(2009-01-15)
Ban, Jung-Chao
;
Chang, Chih-Hung
;
Lin, Song-Sun
;
Lin, Yin-Heng
;
應用數學系
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 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. (C) 2008 Elsevier Inc. All rights reserved.
Three-dimensional Cellular Neural Networks and pattern generation problems
(2008-04-01)
Ban, Jung-Chao
;
Lin, Song-Sun
;
Lin, Yin-Heng
;
應用數學系
;
Department of Applied Mathematics
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 matrix is defined and the recursive formula of high order transition matrix is presented. Then, the spatial entropy is obtained by computing the maximum eigenvalues of a sequence of transition matrices. The connecting operators are used to verify the positivity of the spatial entropy, which is important in determining the complexity of the set of admissible global patterns. The results are useful in studying a set of global stationary solutions in various Lattice Dynamical Systems and Cellular Neural Networks.