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  1. Undergraduate teaching assistants (UTAs) office hours are an approachable way for students to get help, but little is known about why and for what do the students choose to attend office hours. We sought to understand what kind of help the students believe they need by analyzing the problem-solving step students self-reported when joining the office hours queue app. We used the UPIC framework to aggregate course specific problem-solving steps to enable comparing between seven data sets from a CS1 and a data science course across four semesters. We then compared the class-level and student-level phase distributions to understand the differences between the two courses and the two levels in the courses. We found most students have a "primary phase" where a majority of their interactions fall, and there are significant individual differences in their phase distributions. Moreover, we did not find either students' demographics or the context of their first visits to significantly impact their individual differences in the phase distributions, suggesting students may have fixed beliefs on how to approach office hours. Finally, a strong majority of interactions happen within 3 days of the deadline, such that the UPIC distribution for those days looks like the class-level phase distribution. 
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  2. We model the societal task of redistricting political districts as a partitioning problem: Given a set of n points in the plane, each belonging to one of two parties, and a parameter k, our goal is to compute a partition P of the plane into regions so that each region contains roughly s = n/k points. P should satisfy a notion of "local" fairness, which is related to the notion of core, a well-studied concept in cooperative game theory. A region is associated with the majority party in that region, and a point is unhappy in P if it belongs to the minority party. A group D of roughly s contiguous points is called a deviating group with respect to P if majority of points in D are unhappy in P. The partition P is locally fair if there is no deviating group with respect to P.This paper focuses on a restricted case when points lie in 1D. The problem is non-trivial even in this case. We consider both adversarial and "beyond worst-case" settings for this problem. For the former, we characterize the input parameters for which a locally fair partition always exists; we also show that a locally fair partition may not exist for certain parameters. We then consider input models where there are "runs" of red and blue points. For such clustered inputs, we show that a locally fair partition may not exist for certain values of s, but an approximate locally fair partition exists if we allow some regions to have smaller sizes. We finally present a polynomial-time algorithm for computing a locally fair partition if one exists. 
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