Single-cell RNA sequencing (scRNA-seq) has provided a high-dimensional catalog of millions of cells across species and diseases. These data have spurred the development of hundreds of computational tools to derive nov...
Single-cell RNA sequencing (scRNA-seq) has provided a high-dimensional catalog of millions of cells across species and diseases. These data have spurred the development of hundreds of computational tools to derive novel biological insights. Here, we outline the components of scRNA-seq analytical pipelines and the computational methods that underlie these steps. We describe available methods, highlight well-executed benchmarking studies, and identify opportunities for additional benchmarking studies and computational methods. As the biochemical approaches for single-cell omics advance, we propose coupled development of robust analytical pipelines suited for the challenges that new data present and principled selection of analytical methods that are suited for the biological questions to be addressed.
Three abstract optimization problems are presented along with doubly iterative algorithms for their numerical solution. These algorithms are generalizations of particular algorithms described by Barr and Gilbert [19],...
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Three abstract optimization problems are presented along with doubly iterative algorithms for their numerical solution. These algorithms are generalizations of particular algorithms described by Barr and Gilbert [19], [21] and Fujisawa and Yasuda [22]. The supporting theory is fully developed along with proofs of convergence. Practical aspects of computations are considered and procedures which insure rapid convergence are discussed. Two applications to discrete-time optimal control problems are described.
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