Due to the Covid-19 pandemic, most university classes were moved to online instruction. This greatly stimulated the need for online learning tools. WeBWorK is an open source online homework system, which has been used extensively in a variety of subjects. However, it has not been widely adopted by the Computer Science education community. In this paper, we discuss our experience using WeBWorK in teaching two large online sections of discrete mathematics. Emphasis is given to how we created randomized and auto-graded problems for many topics. In addition, we summarize student performance and feedback. We conclude with our reflections on using WeBWorK and propose future work for exploring its adaptive learning features.

Mobility models are crucial for the simulation and evaluation of protocols for multihop wireless networks. However, most commonly used mobility models do not reflect the way humans actually move. This significantly affects the reliability of simulation results. In this paper we introduce a new mobility model called the Smoothly Truncated Levy Walk (STLW), which is more realistic than most standard models that appear in the literature. Its main innovations are as follows. First, to take into account dependencies in the direction of motion, it models changes in the direction instead of the standard approach, which directly models the direction and ignores these dependencies. Second, it uses realistic models for pause times, flight lengths, and changes in direction. In particular, it uses tempered stable distributions to model pause times and flight lengths and the beta distribution to model changes in direction. We justify the use of these distributions from both a theoretical and an empirical perspective. In particular, we perform a trace-based validation on several real-world traces from various scenarios. Validation results show that this model is very flexible and can be used to model human movements in a variety of situations.

In this letter, we introduce an estimator of Küllback-Leibler divergence based on two independent samples. We show that on any finite alphabet, this estimator has an exponentially decaying bias and that it is consistent and asymptotically normal. To explain the importance of this estimator, we provide a thorough analysis of the more standard plug-in estimator. We show that it is consistent and asymptotically normal, but with an infinite bias. Moreover, if we modify the plug-in estimator to remove the rare events that cause the bias to become infinite, the bias still decays at a rate no faster than O(1/n). Further, we extend our results to estimating the symmetrized Küllback-Leibler divergence. We conclude by providing simulation results, which show that the asymptotic properties of these estimators hold even for relatively small sample sizes.

Stochastic knapsack problems deal with selecting items with potentially random sizes and rewards so as to maximize the total reward while satisfying certain capacity constraints. A novel variant of this problem, where items are worthless unless collected in bundles, is introduced here. This setup is similar to the Groupon model, where a deal is off unless a minimum number of users sign up for it. Since the optimal algorithm to solve this problem is not practical, several adaptive greedy approaches with reasonable time and memory requirements are studied in detail - theoretically, as well as, experimentally. Worst case performance guarantees are provided for some of these greedy algorithms, while results of experimental evaluation demonstrate that they are much closer to optimal than what the theoretical bounds suggest. Applications include optimizing for online advertising pricing models where advertisers pay only when certain goals, in terms of clicks or conversions, are met. We perform extensive experiments for the situation where there are between two and five ads. For typical ad conversion rates, the greedy policy of selecting items having the highest individual expected reward obtains a value within 5% of optimal over 95% of the time for a wide selection of parameters.