Stability of impulsive infinite delay differential equations

AbstractIn this work, we consider the stability of impulsive infinite delay differential equations. By using Lyapunov functions and the Razumikhin technique, we get some results that are more general than ones given before. And in using the Razumikhin technique, we use a new technique that has been given by Shunian Zhang; we extend this technique to study impulsive systems. An example is also discussed in this work to illustrate the advantage of the results obtained

Attention, Please! Adversarial Defense via Attention Rectification and Preservation

This study provides a new understanding of the adversarial attack problem by examining the correlation between adversarial attack and visual attention change. In particular, we observed that: (1) images with incomplete attention regions are more vulnerable to adversarial attacks; and (2) successful adversarial attacks lead to deviated and scattered attention map. Accordingly, an attention-based adversarial defense framework is designed to simultaneously rectify the attention map for prediction and preserve the attention area between adversarial and original images. The problem of adding iteratively attacked samples is also discussed in the context of visual attention change. We hope the attention-related data analysis and defense solution in this study will shed some light on the mechanism behind the adversarial attack and also facilitate future adversarial defense/attack model design

Stability Analysis of Complex-Valued Nonlinear Differential System

This paper studies the stability of complex-valued nonlinear differential system. The stability criteria of complex-valued nonlinear autonomous system are established. For the general complex-valued nonlinear non-autonomous system, the comparison principle in the context of complex fields is given. Those derived stability criteria not only provide a new method to analyze complex-valued differential system, but also greatly reduce the complexity of analysis and computation

Muti-frequency extended sampling method for the inverse acoustic source problem

We consider the reconstruction of the compact support of an acoustic source given multiple frequency far field data. We propose a multi-frequency extended sampling method (MESM). The MESM computes the solutions of some ill-posed integral equations and constructs an indicator function to image the source. The behavior of the indicator function is justified. The method is fast and easy to implement. Various numerical examples are presented to show the effectiveness of the MESM for both frequency-independent and frequency-dependent sources

ON THE EXISTENCE AND UNIQUENESS OF A LIMIT CYCLE FOR A LIENARD SYSTEM WITH A DISCONTINUITY LINE

In this paper, we investigate the existence and uniqueness of crossing limit cycle for a planar nonlinear Lienard system which is discontinuous along a straight line (called a discontinuity line). By using the Poincare mapping method and some analysis techniques, a criterion for the existence, uniqueness and stability of a crossing limit cycle in the discontinuous differential system is established. An application to Schnakenberg model of an autocatalytic chemical reaction is given to illustrate the effectiveness of our result. We also consider a class of discontinuous piecewise linear differential systems and give a necessary condition of the existence of crossing limit cycle, which can be used to prove the non-existence of crossing limit cycle

Hybrid Impulsive Control for Closed Quantum Systems

The state transfer problem of a class of nonideal quantum systems is investigated. It is known that traditional Lyapunov methods may fail to guarantee convergence for the nonideal case. Hence, a hybrid impulsive control is proposed to accomplish a more accurate convergence. In particular, the largest invariant sets are explicitly characterized, and the convergence of quantum impulsive control systems is analyzed accordingly. Numerical simulation is also presented to demonstrate the improvement of the control performance

Towards Better Fairness-Utility Trade-off: A Comprehensive Measurement-Based Reinforcement Learning Framework

Machine learning is widely used to make decisions with societal impact such as bank loan approving, criminal sentencing, and resume filtering. How to ensure its fairness while maintaining utility is a challenging but crucial issue. Fairness is a complex and context-dependent concept with over 70 different measurement metrics. Since existing regulations are often vague in terms of which metric to use and different organizations may prefer different fairness metrics, it is important to have means of improving fairness comprehensively. Existing mitigation techniques often target at one specific fairness metric and have limitations in improving multiple notions of fairness simultaneously. In this work, we propose CFU (Comprehensive Fairness-Utility), a reinforcement learning-based framework, to efficiently improve the fairness-utility trade-off in machine learning classifiers. A comprehensive measurement that can simultaneously consider multiple fairness notions as well as utility is established, and new metrics are proposed based on an in-depth analysis of the relationship between different fairness metrics. The reward function of CFU is constructed with comprehensive measurement and new metrics. We conduct extensive experiments to evaluate CFU on 6 tasks, 3 machine learning models, and 15 fairness-utility measurements. The results demonstrate that CFU can improve the classifier on multiple fairness metrics without sacrificing its utility. It outperforms all state-of-the-art techniques and has witnessed a 37.5% improvement on average

Profiles of cyclin B and cdc2 during ovarian and embryonic development in <em>Exopalaemon carinicauda</em>

Mitosis-promoting factor (MPF) is a complex formed by cyclin B (cyclin B) and cyclin-dependent kinase (cdc2). To investigate the role of MPF in the reproduction of Exopalaemon carinicauda, we cloned its full-length cDNA of the Ec-cyclin B and Ec-cdc2 genes. We analyzed their molecular characteristics and expression profiles during ovarian and embryonic development. The results showed that the Ec-cyclin B gene was 1194 bp long and encoded a 397 amino acid (aa) long protein. However, Ec-cdc2 was 900 bp long, which encoded 299 aa with a conserved cyclin binding motif PSTAIRE. The phylogenetic tree analysis showed that Ec-cyclin B had the highest homology with the cyclin B of Macrobrachium rosenbergii (81.06%). In comparison, Ec-cdc2 had the highest homology with the cdc2 of E. modestus (96.80%). Ec-cyclin B showed the highest expression in the ovary, whereas Ec-cdc2 was the highest in the hepatopancreas, followed by the ovary. In the five stages of ovarian development, Ec-cyclin B and Ec-cdc2 expression levels reach the highest at stage Ⅴ(p < 0.05). Overall, the expression of these two genes first increased and then decreased at different embryonic developmental stages. Therefore, these findings suggested that cyclin B and cdc2 played an essential role in the ovarian and embryonic development of E. carinicauda

Hybrid Impulsive Control for Closed Quantum Systems

The state transfer problem of a class of nonideal quantum systems is investigated. It is known that traditional Lyapunov methods may fail to guarantee convergence for the non-ideal case. Hence, a hybrid impulsive control is proposed to accomplish a more accurate convergence. In particular, the largest invariant sets are explicitly characterized, and the convergence of quantum impulsive control systems is analyzed accordingly. Numerical simulation is also presented to demonstrate the improvement of the control performance