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Harrison Schramm, Isaac Rubin and Norah Schramm investigate the impact distance learning may have had on the grades of students at a California high school., (© 2021 The Royal Statistical Society.)

We develop an extension to differential equation models of dynamical systems to allow us to analyze probabilistic threshold dynamics that fundamentally and globally change system behavior. We apply our novel modeling approach to two cases of interest: a model of infectious disease modified for malware where a detection event drastically changes dynamics by introducing a new class in competition with the original infection; and the Lanchester model of armed conflict, where the loss of a key capability drastically changes the effectiveness of one of the sides. We derive and demonstrate a step-by-step, repeatable method for applying our novel modeling approach to an arbitrary system, and we compare the resulting differential equations to simulations of the system's random progression. Our work leads to a simple and easily implemented method for analyzing probabilistic threshold dynamics using differential equations., (Published by Elsevier Inc.)

Introduction: This paper aims to provide insights into human perception, navigation performance, and confidence in helicopter overland navigation. Helicopter overland navigation is a challenging mission area because it is a complex cognitive task, and failing to recognize when the aircraft is off-course can lead to operational failures and mishaps., Methods: A human-in-the-loop experiment to investigate pilot perception during simulated overland navigation by analyzing actual navigation trajectory, pilots' perceived location, and corresponding confidence levels was designed. There were 15 military officers with prior overland navigation experience who completed 4 simulated low-level navigation routes, 2 of which entailed auto-navigation. This route was paused roughly every 30 s for the subject to mark their perceived location on the map and their confidence level using a customized program., Results: Analysis shows that there is no correlation between perceived and actual location of the aircraft, nor between confidence level and actual location. There is, however, some evidence that there is a correlation (rho = -0.60 to approximately 0.65) between perceived location and intended route of flight, suggesting that there is a bias toward believing one is on the intended flight route., Discussion: If aviation personnel can proactively identify the circumstances in which usual misperceptions occur in navigation, they may reduce mission failure and accident rate. Fleet squadrons and instructional commands can benefit from this study to improve operations that require low-level flight while also improving crew resource management.