We find agglomerations of U.S. counties that are partitioned by commuting patterns by representing inter-county commuting patterns as a weighted network. To do so, we develop a community detection method based on the configuration model to identify significant clusters of nodes in a weighted network that prominently feature self-loops which represent same-county commuting. Application of this method to county level commuting data from 2010 yielded regions that are significantly different from existing delineations such as Metropolitian Statistical Areas and Megaregions. Our method identifies regions with varying sizes as well as highly overlapping regions. Some counties may singularly define a region, while others may be part of multiple regions. Our results offer an alternative way of categorizing economic regions from existing methods and suggest that geographical delineations should be rethought.
Iterative random sketching (IRS) offers a computationally expedient approach to solving linear systems. However, IRS' benefits can only be realized if the procedure can be appropriately tracked and stopped-otherwise, the algorithm may stop before the desired accuracy is achieved, or it may run longer than necessary. Unfortunately, IRS solvers cannot access the residual norm without undermining their computational efficiency. While iterative random sketching solvers have access to noisy estimates of the residual, such estimates turn out to be insufficient to generate accurate estimates and confidence bounds for the true residual. Thus, in this work, we propose a moving average estimator for the system's residual, and rigorously develop practical uncertainty sets for our estimator. We then demonstrate the accuracy of our methods on a number of linear systems problems.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.