Chaotic Properties of Subshifts Generated by a Non-Periodic Recurrent Orbit

The chaotic properties of some subshift maps are investigated. These subshifts are the orbit closures of certain non-periodic recurrent points of a shift map. We first provide a review of basic concepts for dynamics of continuous maps in metric spaces. These concepts include nonwandering point, recurrent point, eventually periodic point, scrambled set, sensitive dependence on initial conditions, Robinson chaos, and topological entropy. Next we review the notion of shift maps and subshifts. Then we show that the one-sided subshifts generated by a non-periodic recurrent point are chaotic in the sense of Robinson. Moreover, we show that such a subshift has an infinite scrambled set if it has a periodic point. Finally, we give some examples and discuss the topological entropy of these subshifts, and present two open problems on the dynamics of subshifts

Reasoning cartographic knowledge in deep learning-based map generalization with explainable AI

Cartographic map generalization involves complex rules, and a full automation has still not been achieved, despite many efforts over the past few decades. Pioneering studies show that some map generalization tasks can be partially automated by deep neural networks (DNNs). However, DNNs are still used as black-box models in previous studies. We argue that integrating explainable AI (XAI) into a DL-based map generalization process can give more insights to develop and refine the DNNs by understanding what cartographic knowledge exactly is learned. Following an XAI framework for an empirical case study, visual analytics and quantitative experiments were applied to explain the importance of input features regarding the prediction of a pre-trained ResU-Net model. This experimental case study finds that the XAI-based visualization results can easily be interpreted by human experts. With the proposed XAI workflow, we further find that the DNN pays more attention to the building boundaries than the interior parts of the buildings. We thus suggest that boundary intersection over union is a better evaluation metric than commonly used intersection over union in qualifying raster-based map generalization results. Overall, this study shows the necessity and feasibility of integrating XAI as part of future DL-based map generalization development frameworks

The juxtamembrane and carboxy-terminal domains of Arabidopsis PRK2 are critical for ROP-induced growth in pollen tubes.

Polarized growth of pollen tubes is a critical step for successful reproduction in angiosperms and is controlled by ROP GTPases. Spatiotemporal activation of ROP (Rho GTPases of plants) necessitates a complex and sophisticated regulatory system, in which guanine nucleotide exchange factors (RopGEFs) are key components. It was previously shown that a leucine-rich repeat receptor-like kinase, Arabidopsis pollen receptor kinase 2 (AtPRK2), interacted with RopGEF12 for its membrane recruitment. However, the mechanisms underlying AtPRK2-mediated ROP activation in vivo are yet to be defined. It is reported here that over-expression of AtPRK2 induced tube bulging that was accompanied by the ectopic localization of ROP-GTP and the ectopic distribution of actin microfilaments. Tube depolarization was also induced by a potentially kinase-dead mutant, AtPRK2K366R, suggesting that the over-expression effect of AtPRK2 did not require its kinase activity. By contrast, deletions of non-catalytic domains in AtPRK2, i.e. the juxtamembrane (JM) and carboxy-terminal (CT) domains, abolished its ability to affect tube polarization. Notably, AtPRK2K366R retained the ability to interact with RopGEF12, whereas AtPRK2 truncations of these non-catalytic domains did not. Lastly, it has been shown that the JM and CT domains of AtPRK2 were not only critical for its interaction with RopGEF12 but also critical for its distribution at the plasma membrane. These results thus provide further insight into pollen receptor kinase-mediated ROP activation during pollen tube growth

The Quantum Phase-Dynamical Properties of the Squeezed Vacuum State Intensity-Couple Interacting with the Atom

The Phase-dynamical properties of the squeezed vacuum state intensity-couple interacting with the two-level atom in an ideal cavity are studied using the Hermitian phase operator formalism. Exact general expressions for the phase distribution and the associated expectation value and variance of the phase operator have been derived. we have also obtained the analytic results of the phase variance for two special cases-weakly and strongly squeezed vacuum. The results calculated numerically show that squeezing has a significant effect on the phase properties of squeezed vacuum

Inversion formula of multifractal energy dissipation in 3D fully developed turbulence

The concept of inverse statistics in turbulence has attracted much attention in the recent years. It is argued that the scaling exponents of the direct structure functions and the inverse structure functions satisfy an inversion formula. This proposition has already been verified by numerical data using the shell model. However, no direct evidence was reported for experimental three dimensional turbulence. We propose to test the inversion formula using experimental data of three dimensional fully developed turbulence by considering the energy dissipation rates in stead of the usual efforts on the structure functions. The moments of the exit distances are shown to exhibit nice multifractality. The inversion formula between the direct and inverse exponents is then verified.Comment: 3 RevTex pages including 3 eps figure

Fault diagnosis for rotating machinery based on multi-differential empirical mode decomposition

The fault diagnosis of rotating machinery has crucial significance for the safety of modern industry, and the fault feature extraction is the key link of the diagnosis process. As an effective time-frequency method, Empirical Mode Decomposition (EMD) has been widely used in signal processing and feature extraction. However, the mode mixing phenomenon may lead to confusion in the identification of multi frequency signals and restricts the applications of EMD. In this paper, a novel method based on Multi-Differential Empirical Mode Decomposition (MDEMD) was proposed to extract the energy distribution characteristics of fault signals. Firstly, multi-order differential signals were deduced and decomposed by EMD. Then, their energy distribution characteristics were extracted and utilized to construct the feature matrix. Finally, taking the feature matrix as input, the classifiers were applied to diagnosis the existence and severity of rotating machinery faults. Simulative and practical experiments were implemented respectively, and the results demonstrated that the proposed method, i.e. MDEMD, is able to eliminate the mode mixing effectively, and the feature matrix extracted by MDEMD has high separability and universality, furthermore, the fault diagnosis based on MDEMD can be accomplished more effectively and efficiently with satisfactory accuracy