Chaotic Behaviors of Symbolic Dynamics about Rule 58 in Cellular Automata

The complex dynamical behaviors of rule 58 in cellular automata are investigated from the viewpoint of symbolic dynamics. The rule is Bernoulli στ-shift rule, which is members of Wolfram’s class II, and it was said to be simple as periodic before. It is worthwhile to study dynamical behaviors of rule 58 and whether it possesses chaotic attractors or not. It is shown that there exist two Bernoulli-measure attractors of rule 58. The dynamical properties of topological entropy and topological mixing of rule 58 are exploited on these two subsystems. According to corresponding strongly connected graph of transition matrices of determinative block systems, we divide determinative block systems into two subsets. In addition, it is shown that rule 58 possesses rich and complicated dynamical behaviors in the space of bi-infinite sequences. Furthermore, we prove that four rules of global equivalence class ε43 of CA are topologically conjugate. We use diagrams to explain the attractors of rule 58, where characteristic function is used to describe that some points fall into Bernoulli-shift map after several times iterations, and we find that these attractors are not global attractors. The Lameray diagram is used to show clearly the iterative process of an attractor

A Novel Scheme for Image Encryption Based on Piecewise Linear Chaotic Map

Abstract-Recently, the chaos based cryptographic algorithms have suggested some meaningful techniques to develop efficient image encryption schemes. In this paper, we propose a new digital image encryption scheme based on the piecewise linear chaotic map (PWLCM) in order to meet the requirements of the secure encryption. The proposed scheme is described in detail, along with the security analyses including key space analysis, sensitivity analysis, information entropy analysis and differential attack analysis. The results show that the suggested image encryption scheme has some properties desirable in a good security cryptosystem

The splicing factor DHX38 enables retinal development through safeguarding genome integrity

DEAH-Box Helicase 38 (DHX38) is a pre-mRNA splicing factor and also a disease-causing gene of autosomal recessive retinitis pigmentosa (arRP). The role of DHX38 in the development and maintenance of the retina remains largely unknown. In this study, by using the dhx38 knockout zebrafish model, wedemonstrated that Dhx38 deficiency causes severe differentiation defects and apoptosis of retinal progenitor cells (RPCs) through disrupted mitosis and increased DNA damage. Furthermore, we found a significant accumulation of R-loops in the dhx38-deficient RPCs and human cell lines. Finally, we found that DNA replication stress is the prerequisite for R-loop-induced DNA damage in the DHX38 knockdown cells. Taken together, our study demonstrates a necessary role of DHX38 in the development of retina and reveals a DHX38/R-loop/replication stress/DNA damage regulatory axis that is relatively independent of the known functions of DHX38 in mitosis control

Stability of Delayed Hopfield Neural Networks with Variable-Time Impulses

In this paper the globally exponential stability criteria of delayed Hopfield neural networks with variable-time impulses are established. The proposed criteria can also be applied in Hopfield neural networks with fixed-time impulses. A numerical example is presented to illustrate the effectiveness of our theoretical results