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Abstract Astrocytes, a subtype of glial cells with a complex morphological structure, are active players in many aspects of the physiology of the central nervous system (CNS). However, due to their highly involved interaction with other cells in the CNS, made possible by their morphological complexity, the precise mechanisms regulating astrocyte function within the CNS are still poorly understood. This knowledge gap is also due to the current limitations of existing quantitative image analysis tools that are unable to detect and analyze images of astrocyte with sufficient accuracy and efficiency. To address this need, we introduce a new deep learning framework for the automated detection of GFAP-immunolabeled astrocytes in brightfield or fluorescent micrographs. A major novelty of our approach is the applications of YOLOv5, a sophisticated deep learning platform designed for object detection, that we customized to derive optimized classification models for the task of astrocyte detection. Extensive numerical experiments using multiple image datasets show that our method performs very competitively against both conventional and state-of-the-art methods, including the case of images where astrocytes are very dense. In the spirit of reproducible research, our numerical code and annotated data are released open source and freely available to the scientific community. 

This paper considers a random component-wise variant of the unnormalized power method, which is similar to the regular power iteration except that only a random subset of indices is updated in each iteration. For the case of normal matrices, it was previously shown that random component-wise updates converge in the mean-squared sense to an eigenvector of eigenvalue 1 of the underlying matrix even in the case of the matrix having spectral radius larger than unity. In addition to the enlarged convergence regions, this study shows that the eigenvalue gap does not directly aect the convergence rate of the randomized updates unlike the regular power method. In particular, it is shown that the rate of convergence is aected by the phase of the eigenvalues in the case of random component-wise updates, and the randomized updates favor negative eigenvalues over positive ones. As an application, this study considers a reformulation of the component-wise updates revealing a randomized algorithm that is proven to converge to the dominant left and right singular vectors of a normalized data matrix. The algorithm is also extended to handle large-scale distributed data when computing an arbitrary rank approximation of an arbitrary data matrix. Numerical simulations verify the convergence of the proposed algorithms under dierent parameter settings.