Collective Sensitivity and Collective Accessibility of Non-Autonomous Discrete Dynamical Systems

The concepts of collectively accessible, collectively sensitive, collectively infinitely sensitive, and collectively Li–Yorke sensitive are defined in non-autonomous discrete systems. It is proved that, if the mapping sequence h1,∞=(h1,h2,…) is W-chaotic, then hn,∞=(hn,hn+1,…)(∀n∈N={1,2,…}) would also be W-chaotic. W-chaos represents one of the following five properties: collectively accessible, sensitive, collectively sensitive, collectively infinitely sensitive, and collectively Li–Yorke sensitive. Then, the relationship of chaotic properties between the product system (H1×H2,f1,∞×g1,∞) and factor systems (H1,f1,∞) and (H2,g1,∞) was presented. Furthermore, in this paper, it is also proved that, if the autonomous discrete system (X,h^) induced by the p-periodic discrete system (H,h1,∞) is W-chaotic, then the p-periodic discrete system (H,f1,∞) would also be W-chaotic

Collective Sensitivity and Collective Accessibility of Non-Autonomous Discrete Dynamical Systems

The concepts of collectively accessible, collectively sensitive, collectively infinitely sensitive, and collectively Li–Yorke sensitive are defined in non-autonomous discrete systems. It is proved that, if the mapping sequence h1,∞=(h1,h2,…) is W-chaotic, then hn,∞=(hn,hn+1,…)(∀n∈N={1,2,…}) would also be W-chaotic. W-chaos represents one of the following five properties: collectively accessible, sensitive, collectively sensitive, collectively infinitely sensitive, and collectively Li–Yorke sensitive. Then, the relationship of chaotic properties between the product system (H1×H2,f1,∞×g1,∞) and factor systems (H1,f1,∞) and (H2,g1,∞) was presented. Furthermore, in this paper, it is also proved that, if the autonomous discrete system (X,h^) induced by the p-periodic discrete system (H,h1,∞) is W-chaotic, then the p-periodic discrete system (H,f1,∞) would also be W-chaotic

Transitivity and Shadowing Properties of Nonautonomous Discrete Dynamical Systems

This paper proves that some shadowing properties are sufficient conditions for being transitive or point-transitive for a nonautonomous discrete dynamical system. Moreover, considering weak mixing property and transitivity via Furstenberg family, this paper reveals the relationship for transitivity and mixing between [Formula: see text]-periodic systems and their induced autonomous discrete dynamical systems. </jats:p

The Retentivity of Four Kinds of Shadowing Properties in Non-Autonomous Discrete Dynamical Systems

In this paper, four kinds of shadowing properties in non-autonomous discrete dynamical systems (NDDSs) are discussed. It is pointed out that if an NDDS has a F-shadowing property (resp. ergodic shadowing property, d¯ shadowing property, d̲ shadowing property), then the compound systems, conjugate systems, and product systems all have accordant shadowing properties. Moreover, the set-valued system (K(X),f¯1,∞) induced by the NDDS (X,f1,∞) has the above four shadowing properties, implying that the NDDS (X,f1,∞) has these properties.</jats:p

Three Types of Distributional Chaos for a Sequence of Uniformly Convergent Continuous Maps

Let h s s = 1 ∞ be a sequence of continuous maps on a compact metric space W which converges uniformly to a continuous map h on W . In this paper, some equivalence conditions or necessary conditions for the limit map h to be distributional chaotic are obtained (where distributional chaoticity includes distributional chaotic in a sequence, distributional chaos of type 1 (DC1), distributional chaos of type 2 (DC2), and distributional chaos of type 3 (DC3)).</jats:p

Three Types of Distributional Chaos for a Sequence of Uniformly Convergent Continuous Maps

Let hss=1∞ be a sequence of continuous maps on a compact metric space W which converges uniformly to a continuous map h on W. In this paper, some equivalence conditions or necessary conditions for the limit map h to be distributional chaotic are obtained (where distributional chaoticity includes distributional chaotic in a sequence, distributional chaos of type 1 (DC1), distributional chaos of type 2 (DC2), and distributional chaos of type 3 (DC3))

The Retentivity of Four Kinds of Shadowing Properties in Non-Autonomous Discrete Dynamical Systems

In this paper, four kinds of shadowing properties in non-autonomous discrete dynamical systems (NDDSs) are discussed. It is pointed out that if an NDDS has a F-shadowing property (resp. ergodic shadowing property, d&macr; shadowing property, d&#818; shadowing property), then the compound systems, conjugate systems, and product systems all have accordant shadowing properties. Moreover, the set-valued system (K(X),f&macr;1,&infin;) induced by the NDDS (X,f1,&infin;) has the above four shadowing properties, implying that the NDDS (X,f1,&infin;) has these properties

Finite Chaoticity and Pairwise Sensitivity of a Strong-Mixing Measure-Preserving Semi-Flow

Chaos is a common phenomenon in nature and social sciences. As is well known, chaos has multiple definitions, and there are both differences and connections between them. The unique properties of chaotic systems can be leveraged to address challenges in communication, security, data processing, system analysis, and control across different domains. For semi-flows, this paper introduces two important concepts corresponding to discrete dynamical systems, finitely chaotic and pairwise sensitivity. Since Tent map and its induced suspended semi-flows both have these two properties, then these two concepts on the semi-flows have extensive and important applications and meanings in information security, finance, artificial intelligence and other fields. This paper extends the vast majority of corresponding results in discrete dynamical systems to semi-flows

Targeted next-generation sequencing and long-read HiFi sequencing provide novel insights into clinically significant KLF1 variants

Abstract Background Krüppel-like factor 1 (KLF1), a crucial erythroid transcription factor, plays a significant role in various erythroid changes and haemolytic diseases. The rare erythrocyte Lutheran inhibitor (In(Lu)) blood group phenotype serves as an effective model for identifying KLF1 hypomorphic and loss-of-function variants. In this study, we aimed to analyse the genetic background of the In(Lu) phenotype in a population-based sample group by high-throughput technologies to find potentially clinically significant KLF1 variants. Results We included 62 samples with In(Lu) phenotype, screened from over 300,000 Chinese blood donors. Among them, 36 samples were sequenced using targeted Next Generation Sequencing (NGS), whereas 19 samples were sequenced using High Fidelity (HiFi) technology. In addition, seven samples were simply sequenced using Sanger sequencing. A total of 29 hypomorphic or loss-of-function variants of KLF1 were identified, 21 of which were newly discovered. All new variants discovered by targeted NGS or HiFi sequencing were validated through Sanger sequencing, and the obtained results were found to be consistent. The KLF1 haplotypes of all new variants were further confirmed using clone sequencing or HiFi sequencing. The lack of functional KLF1 variants detected in the four samples indicates the presence of additional regulatory mechanisms. In addition, some samples exhibited BCAM polymorphisms, which encodes antigens of the Lutheran (LU) blood group system. However, no BCAM mutations which leads to the absence of LU proteins were detected. Conclusions High-throughput sequencing methods, particularly HiFi sequencing, were introduced for the first time into genetic analysis of the In(Lu) phenotype. Targeted NGS and HiFi sequencing demonstrated the accuracy of the results, providing additional advantages such as simultaneous analysis of other blood group genes and clarification of haplotypes. Using the In(Lu) phenotype, a powerful model for identifying hypomorphic or loss-of-function KLF1 variants, numerous novel variants have been detected, which have contributed to the comprehensive understanding of KLF1. These clinically significant KLF1 mutations can serve as a valuable reference for the diagnosis of related blood cell diseases