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In this work, we prove a threshold theorem for the 2D Navier-Stokes equations posed on the periodic channel, $$\mathbb{T} \times [-1,1]$$, supplemented with Navier boundary conditions $$\omega|_{y = \pm 1} = 0$$. Initial datum is taken to be a perturbation of Couette in the following sense: the shear component of the perturbation is assumed small (in an appropriate Sobolev space) but importantly is independent of $$\nu$$. On the other hand, the nonzero modes are assumed size $$O(\nu^{\frac12})$$ in an anisotropic Sobolev space. For such datum, we prove nonlinear enhanced dissipation and inviscid damping for the resulting solution. The principal innovation is to capture quantitatively the \textit{inviscid damping}, for which we introduce a new Singular Integral Operator which is a physical space analogue of the usual Fourier multipliers which are used to prove damping. We then include this SIO in the context of a nonlinear hypocoercivity framework. 

Robotics has emerged as one of the most popular subjects in STEM (Science, Technology, Engineering, and Mathematics) education for students in elementary, middle, and high schools, providing them with an opportunity to gain knowledge of engineering and technology. In recent years, flying robots (or drones) have also gained popularity as teaching tool to impart the fundamentals of computer programming to high school students. However, despite completing the programming course, students may still lack an understanding of the working principle of drones. This paper proposes an approach to teach students the basic principles of drone aeronautics through laboratory programming. This course was designed by professors from Vaughn College of Aeronautics and Technology for high school students who work on after-school and weekend programs during the school year or summer. In early 2021, the college applied for and was approved to offer a certificate program in UAS (Unmanned Aerial Systems) Designs, Applications, and Operations to college students by the Education Department of New York State. Later that year, the college also received a grant from the Federal Aviation Administration (FAA) to provide tuition-free early higher education for high school students, allowing them to complete the majority of the credits in the UAS certificate program while still enrolled in high school. The program aims to equip students with the hands-on skills necessary for successful careers as versatile engineers and technicians. Most of the courses in the certificate program are introductory or application-oriented, such as Introduction to Drones, Drone Law, Part 107 License, or Fundamentals of Land Surveying and Photogrammetry. However, one of the courses, Introduction to Drone Aeronautics, is more focused on the theory of drone flight and control. Organizing the lectures and laboratory of the course for high school students who are interested in pursuing the certificate can be a challenge. To create the Introduction to Drone Aeronautics course, a variety of school courses and online resources were examined. After careful consideration, the Robolink Co-drone [1] was chosen as the experimental platform for students to study drone flight, and control and stabilize a drone. However, developing a set of comprehensible lectures proved to be a difficult task. Based on the requirements of the certificate program, the lectures were designed to cover the following topics: (a) an overview of fundamentals of drone flight principles, including the forces acting on a drone such as lift, weight, drag, and thrust, as well as the selection of on-board components and trade-offs for proper payload and force balance; (b) an introduction to the proportional-integral-directive (PID) controller and its role in stabilizing a drone and reducing steady-state errors; (c) an explanation of the forces acting on a drone in different coordinates, along with coordinate transformations; and (d) an opportunity for students to examine the dynamic model of a 3D quadcopter with control parameters, but do not require them to derive the 3D drone dynamic equations. In the future, the course can be improved to cater to the diverse learning needs of the students. More interactive and accessible tools can be developed to help different types of students understand drone aeronautics. For instance, some students may prefer to apply mathematical skills to derive results, while others may find it easier to comprehend the stable flight of a drone by visualizing the continuous changes in forces and balances resulting from the control of DC motor speeds. Despite the differences in students’ mathematical abilities, the course has helped high school students appreciate that mathematics is a powerful tool for solving complex problems in the real world, rather than just a subject of abstract numbers. 

Our modern age is being forged by industrialization and automation. Processes that once required tedious handwork can now be completed with higher efficiency and consistent quality by machines and facilities that perform their operations automatically. Examples of automation technology in our daily lives are found in households where washing machines are used, on the streets where traffic lights regulate traffic, or even in buildings that use air-conditioning units and automatic lighting systems. Open-loop control systems or closed-loop control systems are used in all these systems to determine a predefined sequence of processing steps. The Industrial Manufacturing System (IMS) developed at the college intends to address the need for education. This project introduces how the production assembly line develops. The system consists of Sorting, Assembly, Processing, Testing, Storage, and Buffering operations. The Siemens Simatic PLC (Programmable Logic Controller) S7-300 is used in the manufacturing system and TIA (Total Integrated Automation) Portal is used as the programming environment. This project focuses on the automation of an industrial manufacturing system through several tools such as PLC, TIA PORTAL (V16), and PROFIBUS. The control of the whole system is implemented by using Siemens Sematic PLC. The main objective of this project is to create a fully automated production line for college education. The system consists of Buffering, Sorting, Assembly, Processing, Testing, Handling, and Storage to minimize the risk to workers’ health [1] and the occurrence of accidents and increase production efficiency. 

Abstract BackgroundMeasuring parathyroid hormone-related peptide (PTHrP) helps diagnose the humoral hypercalcemia of malignancy, but is often ordered for patients with low pretest probability, resulting in poor test utilization. Manual review of results to identify inappropriate PTHrP orders is a cumbersome process. MethodsUsing a dataset of 1330 patients from a single institute, we developed a machine learning (ML) model to predict abnormal PTHrP results. We then evaluated the performance of the model on two external datasets. Different strategies (model transporting, retraining, rebuilding, and fine-tuning) were investigated to improve model generalizability. Maximum mean discrepancy (MMD) was adopted to quantify the shift of data distributions across different datasets. ResultsThe model achieved an area under the receiver operating characteristic curve (AUROC) of 0.936, and a specificity of 0.842 at 0.900 sensitivity in the development cohort. Directly transporting this model to two external datasets resulted in a deterioration of AUROC to 0.838 and 0.737, with the latter having a larger MMD corresponding to a greater data shift compared to the original dataset. Model rebuilding using site-specific data improved AUROC to 0.891 and 0.837 on the two sites, respectively. When external data is insufficient for retraining, a fine-tuning strategy also improved model utility. ConclusionsML offers promise to improve PTHrP test utilization while relieving the burden of manual review. Transporting a ready-made model to external datasets may lead to performance deterioration due to data distribution shift. Model retraining or rebuilding could improve generalizability when there are enough data, and model fine-tuning may be favorable when site-specific data is limited. 

In this paper, we propose MetaMobi, a novel spatio-temporal multi-dots connectivity-aware modeling and Meta model update approach for crowd Mobility learning. MetaMobi analyzes real-world Wi-Fi association data collected from our campus wireless infrastructure, with the goal towards enabling a smart connected campus. Specifically, MetaMobi aims at addressing the following two major challenges with existing crowd mobility sensing system designs: (a) how to handle the spatially, temporally, and contextually varying features in large-scale human crowd mobility distributions; and (b) how to adapt to the impacts of such crowd mobility patterns as well as the dynamic changes in crowd sensing infrastructures. To handle the first challenge, we design a novel multi-dots connectivity-aware learning approach, which jointly learns the crowd flow time series of multiple buildings with fusion of spatial graph connectivities and temporal attention mechanisms. Furthermore, to overcome the adaptivity issues due to changes in the crowd sensing infrastructures (e.g., installation of new ac- cess points), we further design a novel meta model update approach with Bernoulli dropout, which mitigates the over- fitting behaviors of the model given few-shot distributions of new crowd mobility datasets. Extensive experimental evaluations based on the real-world campus wireless dataset (including over 76 million Wi-Fi association and disassociation records) demonstrate the accuracy, effectiveness, and adaptivity of MetaMobi in forecasting the campus crowd flows, with 30% higher accuracy compared to the state-of-the-art approaches.