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Social learning, i.e., students learning from each other through social interactions, has the potential to significantly scale up instruction in online education. In many cases, such as in massive open online courses (MOOCs), social learning is facilitated through discussion forums hosted by course providers. In this paper, we propose a probabilistic model for the process of learners posting on such forums, using point processes. Different from existing works, our method integrates topic modeling of the post text, timescale modeling of the decay in post activity over time, and learner topic interest modeling into a single model, and infers this information from user data. Our method also varies the excitation levels induced by posts according to the thread structure, to reflect typical notification settings in discussion forums. We experimentally validate the proposed model on three real-world MOOC datasets, with the largest one containing up to 6,000 learners making 40,000 posts in 5,000 threads. Results show that our model excels at thread recommendation, achieving significant improvement over a number of baselines, thus showing promise of being able to direct learners to threads that they are interested in more efficiently. Moreover, we demonstrate analytics that our model parameters can provide, such as the timescales of different topic categories in a course.

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Airborne collision detection is a difficult problem due to inherent noise, errors in prediction, and challenges associated with modeling the dynamics of the intruder aircraft. Moreover, onboard limited computational resources, fast closing speeds, and unanticipated maneuvers make it challenging to detect collision without creating too many false alarms. In this paper, an innovative approach is presented to quantify likely intruder trajectories and estimate the probability of collision risk for a pair of aircraft flying at the same altitude and in close proximity given the state estimates provided by an airborne radar sensor. The proposed approach is formulated in a probabilistic framework using the reachable set concept and the statistical data contained in the uncorrelated encounter model developed by Lincoln Laboratory, Massachusetts Institute of Technology. Monte-Carlo-based simulation is used to evaluate and compare the performance of the proposed approach with linearly extrapolated collision-detection logic.