2017/07/05 by Jung‐Chao Ban, Ban, Jung-Chao, Chih-Hung Chang +1 · 1 citation
Computer Science · Neuroscience · #37A35 #37B10 #92B20 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Neural Networks and Applications #Neural dynamics and brain function
paper · pdf · doi:10.48550/arxiv.1707.02227
openalex publication_date 2017/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper investigates the coloring problem on Fibonacci-Cayley tree, which is a Cayley graph whose vertex set is the Fibonacci sequence. More precisely, we elucidate the complexity of shifts of finite type defined on Fibonacci-Cayley tree via an invariant called entropy. It comes that computing the entropy of a Fibonacci tree-shift of finite type is equivalent to studying a nonlinear recursive system. After proposing an algorithm for the computation of entropy, we apply the result to neural networks defined on Fibonacci-Cayley tree, which reflect those neural systems with neuronal dysfunction. Aside from demonstrating a surprising phenomenon that there are only two possibilities of entropy for neural networks on Fibonacci-Cayley tree, we reveal the formula of the boundary in the parameter space.