A class of finite pp-groups and the normalized unit groups of group algebras

Let $p$ be a prime and $\mathbb{F}_p$ be a finite field of $p$ elements. Let $\mathbb{F}_pG$ denote the group algebra of the finite $p$-group $G$ over the field $\mathbb{F}_p$ and $V(\mathbb{F}_pG)$ denote the group of normalized units in $\mathbb{F}_pG$. Suppose that $G$ is a finite $p$-group given by a central extension of the form $$1\longrightarrow \mathbb{Z}_{p^n}\times \mathbb{Z}_{p^m} \longrightarrow G \longrightarrow \mathbb{Z}_p\times \cdots\times \mathbb{Z}_p \longrightarrow 1$$ and $G'\cong \mathbb{Z}_p$, $n, m\geq 1$ and $p$ is odd. In this paper, the structure of $G$ is determined. And the relations of $V(\mathbb{F}_pG)^{p^l}$ and $G^{p^l}$, $\Omega_l(V(\mathbb{F}_pG))$ and $\Omega_l(G)$ are given. Furthermore, there is a direct proof for $V(\mathbb{F}_pG)^p\bigcap G=G^p$

LiPar: A Lightweight Parallel Learning Model for Practical In-Vehicle Network Intrusion Detection

With the development of intelligent transportation systems, vehicles are exposed to a complex network environment. As the main network of in-vehicle networks, the controller area network (CAN) has many potential security hazards, resulting in higher requirements for intrusion detection systems to ensure safety. Among intrusion detection technologies, methods based on deep learning work best without prior expert knowledge. However, they all have a large model size and rely on cloud computing, and are therefore not suitable to be installed on the in-vehicle network. Therefore, we propose a lightweight parallel neural network structure, LiPar, to allocate task loads to multiple electronic control units (ECU). The LiPar model consists of multi-dimensional branch convolution networks, spatial and temporal feature fusion learning, and a resource adaptation algorithm. Through experiments, we prove that LiPar has great detection performance, running efficiency, and lightweight model size, which can be well adapted to the in-vehicle environment practically and protect the in-vehicle CAN bus security.Comment: 13 pages, 13 figures, 6 tables, 51 referenc

Productivity Prediction of Tight Sandstone Reservoir Based on BP Neural Network

To survey He-8 member tight sand reservoir with low porosity and permeability in Mizhi gas field in Ordos basin, using the conventional well log data, this paper proposes the tight sand reservoir productivity prediction model and classification criterion based on BP neural network, getting quick classification of gas well productivity. We can predict sand reserve quantitatively instead qualitatively with the methods．Applications show that the methods of productivity prediction are effective and practical

Anderson Localization from Berry-Curvature Interchange in Quantum Anomalous Hall System

We theoretically investigate the localization mechanism of the quantum anomalous Hall effect (QAHE) in the presence of spin-flip disorders. We show that the QAHE keeps quantized at weak disorders, then enters a Berry-curvature mediated metallic phase at moderate disorders, and finally goes into the Anderson insulating phase at strong disorders. From the phase diagram, we find that at the charge neutrality point although the QAHE is most robust against disorders, the corresponding metallic phase is much easier to be localized into the Anderson insulating phase due to the \textit{interchange} of Berry curvatures carried respectively by the conduction and valence bands. At the end, we provide a phenomenological picture related to the topological charges to better understand the underlying physical origin of the QAHE Anderson localization.Comment: 6 pages, 4 figure