Linear maps on nonnegative symmetric matrices preserving a given independence number

The independence number of a square matrix $A$, denoted by $\alpha(A)$, is the maximum order of its principal zero submatrices. Let $S_n^{+}$ be the set of $n\times n$ nonnegative symmetric matrices with zero trace, and let $J_n$ be the $n\times n$ matrix with all entries equal to one. Given any integers $n,t$ with $2\le t\le n-1$, we prove that a linear map $\phi: S_n^+\rightarrow S_n^+$ satisfies $\phi(J_n-I_n)=J_n-I_n$ and $$\alpha(\phi(X))=t~\iff \alpha(X)=t {~~~~\rm for~ all~}X\in S_n^+$$ if and only if there is a permutation matrix $P$ such that $$\phi(X)=P^TXP{~~~~\rm for~ all~}X\in S_n^+.$

Work-family conflict mediation effect on the relations between emotional dissonance and emotional exhaustion: a study of civil servants in China

JEL: J53; M100The aim of the present study is to investigate the level of emotional exhaustion in civil servant of China and also to examine the relationship among emotional dissonance, work-family conflict and emotional exhaustion. Data were collected through self-report questionnaires (N=254), targeting groups of civil servants in China. The findings indicate that there is a significant high level of emotional exhaustion in Chinese civil servants. The result also shows that work-family conflict mediates the relationship between emotional dissonance and emotional exhaustion. Management implications of the findings, limitations, and suggestions for future research are discussed.O objetivo do presente estudo é investigar o nível de exaustão emocional dos funcionários públicos da China e também para examinar a relação entre a dissonânci emocional, o conflito trabalho-família e a exaustão emocional. Os dados foram recolhidos através de questionários (N=254), destinados a grupos de funcionários públicos na China. As descobertas indicam que há um alto nível de exaustão emocional nos funcionário públicos chineses. Os resultados também mostram que o conflito trabalho-família medeia a relação entre dissonância emocional e exaustão emocional. As implicações das descobertas, limitações e sugestões para investigação futura são discutidas

A sensitivity study of artificial viscosity in a defect-deferred correction method for the coupled Stokes/Darcy model

This paper analyzes the sensitivity of the artificial viscosity in the defect deferred correction method for the non-stationary coupled Stokes/Darcy model. For the defect step and the deferred correction step of the defect deferred correction method, we respectively give the corresponding sensitivity systems related to the change of artificial viscosity. Finite element schemes are devised for computing solutions to the sensitivity systems. Finally, we will verify the theoretical analysis results through numerical experiments. Our results reveal that the solution is sensitive for small values of the artificial viscosity, and when the viscosity/hydraulic conductivity coefficients are small

What are Public Concerns about ChatGPT? A Novel Self-Supervised Neural Topic Model Tells You

The recently released artificial intelligence conversational agent, ChatGPT, has gained significant attention in academia and real life. A multitude of early ChatGPT users eagerly explore its capabilities and share their opinions on it via social media. Both user queries and social media posts express public concerns regarding this advanced dialogue system. To mine public concerns about ChatGPT, a novel Self-Supervised neural Topic Model (SSTM), which formalizes topic modeling as a representation learning procedure, is proposed in this paper. Extensive experiments have been conducted on Twitter posts about ChatGPT and queries asked by ChatGPT users. And experimental results demonstrate that the proposed approach could extract higher quality public concerns with improved interpretability and diversity, surpassing the performance of state-of-the-art approaches

Current-cycle iterative learning control for high-precision position tracking of piezoelectric actuator system via active disturbance rejection control for hysteresis compensation

As a typical smart structure, piezoelectric actuator (PEA) is an essential constituent component in piezoelectric-driven positioning stages. Nevertheless, the positioning precision is severely degraded by its innate rate-dependent hysteretic nonlinearity. In this paper, an innovative control method which combines active disturbance rejection control (ADRC) and current-cycle iterative learning control (CILC) is proposed by constructing PEA as a second-order disturbance-based (SODB) structure to handle both hysteretic nonlinearities and dynamic uncertainties of PEA. The proposed method differs from the prevalent model-inverse solution in hysteresis compensation, where the control performance of the latter extremely relies on the accurateness of the hysteretic model while the former does not require a mathematical model of hysteresis since it is considered as a general disturbance and eliminated. Compared with the existing hysteresis compensation via pure ADRC method, the proposed method has improved robustness by incorporating an additional ILC loop to ADRC. Comparative experimentations are executed on a PEA system and results imply that the proposed approach has better control performance than pure proportionalintegral (PI) control and ADRC

Iterative learning of human partner's desired trajectory for proactive human-robot collaboration

A period-varying iterative learning control scheme is proposed for a robotic manipulator to learn a target trajectory that is planned by a human partner but unknown to the robot, which is a typical scenario in many applications. The proposed method updates the robot’s reference trajectory in an iterative manner to minimize the interaction force applied by the human. Although a repetitive human–robot collaboration task is considered, the task period is subject to uncertainty introduced by the human. To address this issue, a novel learning mechanism is proposed to achieve the control objective. Theoretical analysis is performed to prove the performance of the learning algorithm and robot controller. Selective simulations and experiments on a robotic arm are carried out to show the effectiveness of the proposed method in human–robot collaboration