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Many iterative algorithms in computer science require repeated computation of some algebraic expression whose input varies slightly from one iteration to the next. Although efficient data structures have been proposed for maintaining the solution of such algebraic expressions under low-rank updates, most of these results are only analyzed under exact arithmetic (real-RAM model and finite fields) which may not accurately reflect the more limited complexity guarantees of real computers. In this paper, we analyze the stability and bit complexity of such data structures for expressions that involve the inversion, multiplication, addition, and subtraction of matrices under the word-RAM model. We show that the bit complexity only increases linearly in the number of matrix operations in the expression. In addition, we consider the bit complexity of maintaining the determinant of a matrix expression. We show that the required bit complexity depends on the logarithm of the condition number of matrices instead of the logarithm of their determinant. Finally, we discuss rank maintenance and its connections to determinant maintenance. Our results have wide applications ranging from computational geometry (e.g., computing the volume of a polytope) to optimization (e.g., solving linear programs using the simplex algorithm). 

Female students participate in STEM activities at a low rate compared to males. Educational researchers have called for studies which examine the factors that influence STEM participation. The purpose of this study is to examine how a unique learning structure built on the principals of constructive learning environments might impact students’ sense of belonging and encourage them to participate in more STEM activities. For this qualitative study, interviews were conducted with 12 mentor and 17 student participants. Findings indicated that a constructive learning environment enhanced students’ sense of belonging. Programs which enhance female students’ sense of belonging impact their confidence to participate in more STEM activities. This study contributes to research in learning environment theory and STEM education practice. 

With the rapid growth of online social media and ubiquitous Internet connectivity, social sensing has emerged as a new crowdsourcing application paradigm of collecting observations (often called claims) about the physical environment from humans or devices on their behalf. A fundamental problem in social sensing applications lies in effectively ascertaining the correctness of claims and the reliability of data sources without knowing either of them a priori, which is referred to as truth discovery. While significant progress has been made to solve the truth discovery problem, some important challenges have not been well addressed yet. First, existing truth discovery solutions did not fully solve the dynamic truth discovery problem where the ground truth of claims changes over time. Second, many current solutions are not scalable to large-scale social sensing events because of the centralized nature of their truth discovery algorithms. Third, the heterogeneity and unpredictability of the social sensing data traffic pose additional challenges to the resource allocation and system responsiveness. In this paper, we developed a Scalable Streaming Truth Discovery (SSTD) solution to address the above challenges. In particular, we first developed a dynamic truth discovery scheme based on Hidden Markov Models (HMM) to effectively infer the evolving truth of reported claims. We further developed a distributed framework to imple- ment the dynamic truth discovery scheme using Work Queue in HTCondor system. We also integrated the SSTD scheme with an optimal workload allocation mechanism to dynamically allocate the resources (e.g., cores, memories) to the truth discovery tasks based on their computation requirements. We evaluated SSTD through real world social sensing applications using Twitter data feeds. The evaluation results on three real-world data traces (i.e., Boston Bombing, Paris Shooting and College Football) show that the SSTD scheme is scalable and outperforms the state-of-the- art truth discovery methods in terms of both effectiveness and efficiency.