The H\"older continuity of Lyapunov exponents for a class of Cos-type quasiperiodic Schr\"odinger cocycles

In this paper we obtain exact $\frac{1}{2}$-H\"older continuity of the Lyapunov exponents for quasi-periodic Sch\"odinger cocycles with $C^2$ cos-type potentials, large coupling constants, and fixed Diophantine frequency. Moreover, we prove the locally Lipschitz continuity of the Lyapunov exponent for a full measure spectral set. Furthermore, for any given $r$ between $\frac{1}{2}$ to $1$, we can find some energy on the spectrum and on which Lyapunov exponent is exactly $r$-H\"older continuous.Comment: 88 Page

Kibble-Zurek dynamics in an array of coupled binary Bose condensates

Universal dynamics of spontaneous symmetry breaking is central to understanding the universal behavior of spontaneous defect formation in various system from the early universe, condensed-matter systems to ultracold atomic systems. We explore the universal real-time dynamics in an array of coupled binary atomic Bose-Einstein condensates in optical lattices, which undergo a spontaneous symmetry breaking from the symmetric Rabi oscillation to the broken-symmetry self-trapping. In addition to Goldstone modes, there exist gapped Higgs mode whose excitation gap vanishes at the critical point. In the slow passage through the critical point, we analytically find that the symmetry-breaking dynamics obeys the Kibble-Zurek mechanism. From the scalings of bifurcation delay and domain formation, we numerically extract two Kibble-Zurek exponents $b_{1}=\nu/(1+\nu z)$ and $b_{2}=1/(1+\nu z)$, which give the static correlation-length critical exponent $\nu$ and the dynamic critical exponent $z$. Our approach provides an efficient way to simultaneous determination of the critical exponents $\nu$ and $z$ for a continuous phase transition.Comment: 6 pages, 4 figures, accepted for publication in EPL (Europhysics Letters

Unravelling the ageing effects of PDMS‐based triboelectric nanogenerators

Ageing of elastomeric materials in triboelectric nanogenerators (TENGs) often leads to compromised electrical performance and can greatly affect their real-world application as next-generation energy harvesters and self-powered sensors. Herein, the ageing behavior of PDMS-based TENGs is investigated by probing the dielectric and mechanical properties of the membrane materials. Over time, ageing of PDMS after 17 months is evinced by a decline by 71%, 68% and 52% in open-circuit voltage, short-circuit current and charge transfer, respectively, and an increase by 6.8 times in surface charge decay rate. The reduced electrical performance can be attributed to a decrease in work function, dielectric constant, surface adhesion and heterogeneity in stiffness, as well as an increase in loss tangent. The effect of chemical chain scission on the PDMS surface is confirmed through nearfield infrared nanospectroscopy. This study gives insights into the underlying mechanism behind the ageing of PDMS-based TENGs, paving the way to future work for ameliorating these ageing-related issues with the aim to ensure long-term stability of practical triboelectric devices

Pay gap and bank performance

This paper takes the 2007-2016 listed banks in China as a research sample to study the impact of the internal compensation gap of the senior management team and the salary gap between the senior management team and the ordinary employees on the performance of different types of banks. Through model regression and the introduction of quadratic items, the two pay gaps have a positive impact on bank performance but show a trend of “reverse U”, indicating that this effect has a range effect. Therefore, according to the nature of the bank, we divided the listed commercial banks into joint-stock commercial banks, state-owned commercial banks and city commercial banks for regression analysis. The results show that the internal compensation gap of executives has significant impact on only in joint-stock commercial banks; the compensation gap between executives and ordinary employees has an inverted “U”-type relationship among various banks, indicating that it is very important for banks to maintain a reasonable salary gap. Based on the results, the paper proposes suggestions for incentive mechanisms for different types of banks. Keywords: Pay Gap, Bank Performance, Chinese Banking Sector, Tournament Theory, Behavioral Theory, Psychological Contract Theory

LA-HCN: Label-based Attention for Hierarchical Multi-label TextClassification Neural Network

Hierarchical multi-label text classification (HMTC) has been gaining popularity in recent years thanks to its applicability to a plethora of real-world applications. The existing HMTC algorithms largely focus on the design of classifiers, such as the local, global, or a combination of them. However, very few studies have focused on hierarchical feature extraction and explore the association between the hierarchical labels and the text. In this paper, we propose a Label-based Attention for Hierarchical Mutlti-label Text Classification Neural Network (LA-HCN), where the novel label-based attention module is designed to hierarchically extract important information from the text based on the labels from different hierarchy levels. Besides, hierarchical information is shared across levels while preserving the hierarchical label-based information. Separate local and global document embeddings are obtained and used to facilitate the respective local and global classifications. In our experiments, LA-HCN outperforms other state-of-the-art neural network-based HMTC algorithms on four public HMTC datasets. The ablation study also demonstrates the effectiveness of the proposed label-based attention module as well as the novel local and global embeddings and classifications. By visualizing the learned attention (words), we find that LA-HCN is able to extract meaningful information corresponding to the different labels which provides explainability that may be helpful for the human analyst.Comment: code is available at https://github.com/XinyiZ001/LA-HC