The need for improved models that can accurately predict COVID-19 dynamics is vital to managing the pandemic and its consequences. We use machine learning techniques to design an adaptive learner that, based on epidemiological data available at any given time, produces a model that accurately forecasts the number of reported COVID-19 deaths and cases in the United States, up to 10 weeks into the future with a mean absolute percentage error of 9%. In addition to being the most accurate long-range COVID predictor so far developed, it captures the observed periodicity in daily reported numbers. Its effectiveness is based on three design features: (1) producing different model parameters to predict the number of COVID deaths (and cases) from each time and for a given number of weeks into the future, (2) systematically searching over the available covariates and their historical values to find an effective combination, and (3) training the model using “last-fold partitioning”, where each proposed model is validated on only the last instance of the training dataset, rather than being cross-validated. Assessments against many other published COVID predictors show that this predictor is 19–48% more accurate.
We give an asymptotic formula for the minimum number of edges contained in triangles in a graph having n vertices and e edges. Our main tool is a generalization of Zykov's symmetrization method that can be applied for several graphs simultaneously.
Abstract:A k−clique covering of a simple graph G is a collection of cliques of G covering all the edges of G such that each vertex is contained in at most k cliques. The smallest k for which G admits a k−clique covering is called the local clique cover number of G and is denoted by lcc(G). Local clique cover number can be viewed as the local counterpart of the clique cover number that is equal to the minimum total number of cliques covering all edges. In this article, several aspects of the local clique covering problem are studied and its relationships to other well-known problems are discussed. In particular, it is proved that the local clique cover number of every claw-free graph is at most c / log , where is the maximum degree of the graph and c is a constant. It is also shown that the bound is tight, up to a constant factor. Moreover, regarding a conjecture by Chen et al. (Clique covering the edges of a locally cobipartite graph, Discrete Math 219(1-3)(2000), 17-26), we prove that the clique cover number of every connected claw-free graph on n vertices with the minimum degree δ, is at most n + c δ 4/3 log
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.