Abstract Deep Neural Networks (DNNs) are formidable instruments that have demonstrated exceptional performance across various domains, from identifying patterns to tackling intricate challenges in robotics. However, their complex structures and opacity pose risks when they're used in practical settings. In this regard, Formal Verification (FV) of DNNs has become an essential approach to ensure reliable assurances regarding their safety features. Yet,... Deep Neural Networks (DNNs) are formidable instruments that have demonstrated exceptional performance across various domains, from identifying patterns to tackling intricate challenges in robotics. However, their complex structures and opacity pose risks when they're used in practical settings. In this regard, Formal Verification (FV) of DNNs has become an essential approach to ensure reliable assurances regarding their safety features. Yet, the simple yes-or-no responses (safe or unsafe) may not provide sufficient information for immediate safety actions like ranking safety models or choosing the best one. To overcome this, the FV challenge has been broadened to include a counting version, known as #DNNVerification, aimed at determining the number of unsafe areas within a specified safety property's area. However, the problem's complexity makes it difficult for current solutions to handle large and complex DNNs in real-world robotic environments. To tackle this issue, we draw inspiration from recent developments in FV and introduce a new approach that combines reachability analysis with Symbolic Linear Relaxation and parallel computing to improve the effectiveness of both exact and approximate FV for DNN counter tasks. Our experimental tests on established FV benchmarks and realistic robotic scenarios reveal a significant enhancement in both scalability and efficiency, making it possible to apply these methods to complex robotic tasks. Read More Read Less

Abstract After the reform and opening up, China’s economy has entered a high-speed development road, and urban infrastructure construction has rapidly expanded. With the development of cities, the increase in population and the richness of city functions, the environment is becoming increasingly complex. Still, the design of the city guide needs to be revised. The actual role of the existing design is... After the reform and opening up, China’s economy has entered a high-speed development road, and urban infrastructure construction has rapidly expanded. With the development of cities, the increase in population and the richness of city functions, the environment is becoming increasingly complex. Still, the design of the city guide needs to be revised. The actual role of the existing design is minimal, so it does not meet the current wizard needs. An excellent guide system can provide excellent guidance service to people and become a window for people to observe the city, thereby increasing people’s good impression of the town. Based on the above points, the backward plane symbols’ backwards design ideas were discarded in this paper, and more advanced information technologies and B/S architecture were used to design a set of city vision transmission digital guidance systems. A better information interaction model was intended from the new angle of visual transmission of urban information. Read More Read Less

Abstract Regarding sports facilities, we have considered factors such as quantity, type, quality, and availability. Regarding sports activities, we focus on factors such as the frequency, scale, level, and participation of events. Regarding sports training, we have considered factors such as the type, frequency, quality, and effectiveness of training. Regarding sports guidance, we focus on factors such as professionalism, timeliness, effectiveness,... Regarding sports facilities, we have considered factors such as quantity, type, quality, and availability. Regarding sports activities, we focus on factors such as the frequency, scale, level, and participation of events. Regarding sports training, we have considered factors such as the type, frequency, quality, and effectiveness of training. Regarding sports guidance, we focus on factors such as professionalism, timeliness, effectiveness, and personalization of guidance. Based on the fuzzy evaluation, this article analyzes the factors influencing weight in urban sports services. Firstly, we have constructed an evaluation system for urban sports services, including sports facilities, sports activities, sports training, sports guidance, and other aspects. Then, we used the fuzzy mathematics method to evaluate each aspect’s weights. Read More Read Less