A comparison between the Avila-Gou\"ezel-Yoccoz norm and the Teichm\"uller norm

We give a comparison between the Avila-Gou\"ezel-Yoccoz norm and the Teichm\"uller norm on the principal stratum of holomorphic quadratic differentials.Comment: 10 pages,2 figur

Challenges, advances and future directions in protection of hybrid AC/DC microgrids

Hybrid microgrids which consist of AC and DC subgrids interconnected by power electronic interfaces have attracted much attention in recent years. They not only can integrate the main benefits of both AC and DC configurations, but also can reduce the number of converters in connection of Distributed Generation (DG) sources, Energy Storage Systems (ESSs) and loads to AC or DC buses. In this paper, the structure of hybrid microgrids is discussed, and then a broad overview of the available protection devices and approaches for AC and DC subgrids is presented. After description, analysis and classification of the existing schemes, some research directions including communication infrastructures, combined control and protection schemes, and promising devices for the realisation of future hybrid AC/DC microgrids are pointed out

Few-shot Online Anomaly Detection and Segmentation

Detecting anomaly patterns from images is a crucial artificial intelligence technique in industrial applications. Recent research in this domain has emphasized the necessity of a large volume of training data, overlooking the practical scenario where, post-deployment of the model, unlabeled data containing both normal and abnormal samples can be utilized to enhance the model's performance. Consequently, this paper focuses on addressing the challenging yet practical few-shot online anomaly detection and segmentation (FOADS) task. Under the FOADS framework, models are trained on a few-shot normal dataset, followed by inspection and improvement of their capabilities by leveraging unlabeled streaming data containing both normal and abnormal samples simultaneously. To tackle this issue, we propose modeling the feature distribution of normal images using a Neural Gas network, which offers the flexibility to adapt the topology structure to identify outliers in the data flow. In order to achieve improved performance with limited training samples, we employ multi-scale feature embedding extracted from a CNN pre-trained on ImageNet to obtain a robust representation. Furthermore, we introduce an algorithm that can incrementally update parameters without the need to store previous samples. Comprehensive experimental results demonstrate that our method can achieve substantial performance under the FOADS setting, while ensuring that the time complexity remains within an acceptable range on MVTec AD and BTAD datasets

Dynamical Behaviors of a Stochastic Susceptible-Infected-Treated-Recovered-Susceptible Cholera Model with Ornstein-Uhlenbeck Process

In this study, a cholera infection model with a bilinear infection rate is developed by considering the perturbation of the infection rate by the mean-reverting process. First of all, we give the existence of a globally unique positive solution for a stochastic system at an arbitrary initial value. On this basis, the sufficient condition for the model to have an ergodic stationary distribution is given by constructing proper Lyapunov functions and tight sets. This indicates in a biological sense the long-term persistence of cholera infection. Furthermore, after transforming the stochastic model to a relevant linearized system, an accurate expression for the probability density function of the stochastic model around a quasi-endemic equilibrium is derived. Subsequently, the sufficient condition to make the disease extinct is also derived. Eventually, the theoretical findings are shown by numerical simulations. Numerical simulations show the impact of regression speed and fluctuation intensity on stochastic systems