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  1. Free, publicly-accessible full text available October 4, 2022
  2. Since its publication, the authors of Wang et al. (2021) have brought to our attention an error in their article. A grant awarded by the National Science Foundation (grant no. MCB 1817985) to author Elizabeth Vierling was omitted from the Acknowledgements section. The correct Acknowledgements section is shown below. Acknowledgements We thank Suiwen Hou (Lanzhou University) and Zhaojun Ding (Shandong University) for providing the seeds used in this study. We thank Xiaoping Gou (Lanzhou University) and Ravishankar Palanivelu (University of Arizona) for critically reading the manuscript and for suggestions regarding the article. This work was supported by grants from Nationalmore »Natural Science Foundation of China (31870298) to SX, the US Department of Agriculture (USDA-CSREES-NRI-001030) and the National Science Foundation (MCB 1817985) to EV, and the Youth 1000-Talent Program of China (A279021801) to LY.« less
  3. Complex analyses involving multiple, dependent random quantities often lead to graphical models—a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical analyses for graphical data, especially towards generative modeling, one needs mathematical representations and metrics for matching and comparing graphs, and subsequent tools, such as geodesics, means, and covariances. This paper utilizes a quotient structure to develop efficient algorithms for computing these quantities, leading to useful statistical tools, including principal component analysis, statistical testing, and modeling. We demonstrate the efficacy of this framework using datasets taken from several problem areas, includingmore »letters, biochemical structures, and social networks.« less
  4. Free, publicly-accessible full text available June 1, 2023