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Despite providing high spatial resolution, functional imaging remains largely unsuitable for high-throughput experiments because current practices require cells to be manually identified in a time-consuming procedure. Against this backdrop, we seek to integrate such high-resolution technique in high-throughput workflow by automating the process of cell identification. As a step forward, we attempt to identify mixed retinal cells in time-lapse fluorescent microscopy images. Unfortunately, usual 2D image segmentation as well as other existing methods do not adequately distinguish between time courses of different spatial locations. Here, the task gets further complicated due to the inherent heterogeneity of cell morphology. To overcome such challenge, we propose to use a high-dimensional (HiD) version of DBSCAN (density based spatial clustering of applications with noise) algorithm, where difference in such time courses are appropriately accounted. Significantly, outcome of the proposed method matches manually identified cells with over 80% accuracy, marking more than 50% improvement compared to a reference 2D method.

We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modelled by differential equations. The algorithm relies on judiciously combining a large number of computationally cheap training data on coarse resolutions with a few expensive training samples on fine grid resolutions. Theoretical arguments for lowering the generalisation error, based on reducing the variance of the underlying maps, are provided and numerical evidence, indicating significant gains over underlying single-level machine learning algorithms, are presented. Moreover, we also apply the multi-level algorithm in the context of forward uncertainty quantification and observe a considerable speedup over competing algorithms. [ABSTRACT FROM AUTHOR]

We propose a supervised deep learning algorithm based on low-discrepancy sequences as the training set. By a combination of theoretical arguments and extensive numerical experiments we demonstrate that the proposed algorithm significantly outperforms standard deep learning algorithms that are based on randomly chosen training data for problems in moderately high dimensions. The proposed algorithm provides an efficient method for building inexpensive surrogates for many underlying maps in the context of scientific computing. [ABSTRACT FROM AUTHOR]

We propose a finite volume method for the shallow water equations that accurately approximates the transport of vorticity. The algorithm is based on a predictor-corrector-type projection method. Any consistent finite volume scheme may be used in the prediction step of the algorithm. An elliptic equation is solved and the momentum field is corrected to obtain the correct evolution of vorticity. We describe this projection algorithm for the wave equation and the shallow water equations. The crucial role played by the pseudovorticity transport is highlighted. Numerical experiments demonstrating a considerable gain in computational efficiency with the vorticity projection algorithm are presented. [ABSTRACT FROM AUTHOR]