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In monocular visual-inertial navigation, it is desirable to initialize the system as quickly and robustly as possible. A state-of-the-art initialization method typically constructs a linear system to find a closed-form solution using the image features and inertial measurements and then refines the states with a nonlinear optimization. These methods generally require a few seconds of data, which however can be expedited (less than a second) by adding constraints from a robust but only up-to-scale monocular depth network in the nonlinear optimization. To further accelerate this process, in this work, we leverage the scale-less depth measurements instead in the linear initialization step that is performed prior to the nonlinear one, which only requires a single depth image for the first frame. Importantly, we show that the typical estimation of all feature states independently in the closed-form solution can be modeled as estimating only the scale and bias parameters of the learned depth map. As such, our formulation enables building a smaller minimal problem than the state of the art, which can be seamlessly integrated into RANSAC for robust estimation. Experiments show that our method has state-of-the-art initialization performance in simulation as well as on popular real-world datasets (TUM-VI, and EuRoC MAV). For the TUM-VI dataset in simulation as well as real-world, we demonstrate the superior initialization performance with only a 0.3 s window of data, which is the smallest ever reported, and validate that our method can initialize more often, robustly, and accurately in different challenging scenarios. 

The outbreak of COVID-19 resulted in high death tolls all over the world. The aim of this paper is to show how a simple SEIR model was used to make quick predictions for New Jersey in early March 2020 and call for action based on data from China and Italy. A more refined model, which accounts for social distancing, testing, contact tracing and quarantining, is then proposed to identify containment measures to minimize the economic cost of the pandemic. The latter is obtained taking into account all the involved costs including reduced economic activities due to lockdown and quarantining as well as the cost for hospitalization and deaths. The proposed model allows one to find optimal strategies as combinations of implementing various non-pharmaceutical interventions and study different scenarios and likely initial conditions.