On weakly ss-permutably embedded subgroups

summary:Suppose $G$ is a finite group and $H$ is a subgroup of $G$. $H$ is said to be $s$-permutably embedded in $G$ if for each prime $p$ dividing $|H|$, a Sylow $p$-subgroup of $H$ is also a Sylow $p$-subgroup of some $s$-permutable subgroup of $G$; $H$ is called weakly $s$-permutably embedded in $G$ if there are a subnormal subgroup $T$ of $G$ and an $s$-permutably embedded subgroup $H_{se}$ of $G$ contained in $H$ such that $G=HT$ and $H\cap T\leq H_{se}$. We investigate the influence of weakly $s$-permutably embedded subgroups on the $p$-nilpotency and $p$-supersolvability of finite groups

A note on weakly ss-normal subgroups of finite groups

In this paper, we investigate the influence of the certain subgroups of fixed prime power order on the $p$-supersolubility of finite groups. Many recent results are extended

The influence of weakly s-permutably embedded subgroups on the p-nilpotency of finite groups

The research was partly supported by the NSF of China (grant no. 11071229) andthe NSF of the Jiangsu Higher Education Institutions (grant no. 10KJD110004)

Information Theory-Guided Heuristic Progressive Multi-View Coding

Multi-view representation learning aims to capture comprehensive information from multiple views of a shared context. Recent works intuitively apply contrastive learning to different views in a pairwise manner, which is still scalable: view-specific noise is not filtered in learning view-shared representations; the fake negative pairs, where the negative terms are actually within the same class as the positive, and the real negative pairs are coequally treated; evenly measuring the similarities between terms might interfere with optimization. Importantly, few works study the theoretical framework of generalized self-supervised multi-view learning, especially for more than two views. To this end, we rethink the existing multi-view learning paradigm from the perspective of information theory and then propose a novel information theoretical framework for generalized multi-view learning. Guided by it, we build a multi-view coding method with a three-tier progressive architecture, namely Information theory-guided hierarchical Progressive Multi-view Coding (IPMC). In the distribution-tier, IPMC aligns the distribution between views to reduce view-specific noise. In the set-tier, IPMC constructs self-adjusted contrasting pools, which are adaptively modified by a view filter. Lastly, in the instance-tier, we adopt a designed unified loss to learn representations and reduce the gradient interference. Theoretically and empirically, we demonstrate the superiority of IPMC over state-of-the-art methods.Comment: This paper is accepted by the jourcal of Neural Networks (Elsevier) by 2023. A revised manuscript of arXiv:2109.0234

Simulation-based Validation for Autonomous Driving Systems

Simulation is essential to validate autonomous driving systems. However, a simple simulation, even for an extremely high number of simulated miles or hours, is not sufficient. We need well-founded criteria showing that simulation does indeed cover a large fraction of the relevant real-world situations. In addition, the validation must concern not only incidents, but also the detection of any type of potentially dangerous situation, such as traffic violations. We investigate a rigorous simulation and testing-based validation method for autonomous driving systems that integrates an existing industrial simulator and a formally defined testing environment. The environment includes a scenario generator that drives the simulation process and a monitor that checks at runtime the observed behavior of the system against a set of system properties to be validated. The validation method consists in extracting from the simulator a semantic model of the simulated system including a metric graph, which is a mathematical model of the environment in which the vehicles of the system evolve. The monitor can verify properties formalized in a first-order linear temporal logic and provide diagnostics explaining their non satisfaction. Instead of exploring the system behavior randomly as many simulators do, we propose a method to systematically generate sets of scenarios that cover potentially risky situations, especially for different types of junctions where specific traffic rules must be respected. We show that the systematic exploration of risky situations has uncovered many flaws in the real simulator that would have been very difficult to discover by a random exploration process

The Visualization and Analysis of Spatial Distribution of Foreign Restaurants : A Case Study of Tokyo Wards Area

University of Tokyo(東京大学

T2MAC: Targeted and Trusted Multi-Agent Communication through Selective Engagement and Evidence-Driven Integration

Communication stands as a potent mechanism to harmonize the behaviors of multiple agents. However, existing works primarily concentrate on broadcast communication, which not only lacks practicality, but also leads to information redundancy. This surplus, one-fits-all information could adversely impact the communication efficiency. Furthermore, existing works often resort to basic mechanisms to integrate observed and received information, impairing the learning process. To tackle these difficulties, we propose Targeted and Trusted Multi-Agent Communication (T2MAC), a straightforward yet effective method that enables agents to learn selective engagement and evidence-driven integration. With T2MAC, agents have the capability to craft individualized messages, pinpoint ideal communication windows, and engage with reliable partners, thereby refining communication efficiency. Following the reception of messages, the agents integrate information observed and received from different sources at an evidence level. This process enables agents to collectively use evidence garnered from multiple perspectives, fostering trusted and cooperative behaviors. We evaluate our method on a diverse set of cooperative multi-agent tasks, with varying difficulties, involving different scales and ranging from Hallway, MPE to SMAC. The experiments indicate that the proposed model not only surpasses the state-of-the-art methods in terms of cooperative performance and communication efficiency, but also exhibits impressive generalization.Comment: AAAI2