Large high-performance computing systems are commonly shared among users that submit their workflows to a resource manager and scheduling framework such as SLURM. Most commonly available job schedulers provide built-in algorithms for performing job backfill and placement, where candidate jobs can be run out of order on currently free resources, provided that they do not negatively impact other jobs already waiting in the queue. Backfilling relies on two key requirements: 1) the user's own estimate of the runtime of their job and 2) the ability for the scheduler to create and maintain a future schedule of all jobs in the queue at any one moment. Unfortunately, user-provided estimates are often erroneous, a well-known problem in parallel job scheduling. These estimates cause the scheduler to plan jobs based on inaccurate data, which in turn causes the scheduler-provided estimates of user wait time to be quite inaccurate. As such, in this work, we leverage several machine learning (ML) techniques to provide a more accurate estimate of user waiting time and contrast them across a variety of metrics including wait time and bounded per-processor slowdown using simulated data based on real job workload traces. The presented machine learning models improve overall wait time estimation by a factor of$4.1 \times$over traditional scheduler-provided wait times.

A recent trend in machine learning (ML) is its application to surrogate modeling for computationally intractable simulations. The general approach is to train an ML model using data obtained from the field or extensive results from prior simulations. Although training can be an expensive process, it is typically a one-time requirement and the result can be used to reduce the time otherwise required to calculate the solution. In this work, we train and apply a sophisticated ML model that has both spatial and temporal capabilities to aid in solving a well-known two-dimensional heat transfer finite difference problem which serves as a proxy application for our external funding sponsor, Los Alamos National Laboratory (LANL). Additionally, we train and apply the same model to a 2D boiling water simulation in order to contrast the model's generality in two applications with different levels of mathematical complexity and present the obtained predictive results.

BACKGROUND: Correlation metrics are widely utilized in genomics analysis and often implemented with little regard to assumptions of normality, homoscedasticity, and independence of values. This is especially true when comparing values between replicated sequencing experiments that probe chromatin accessibility, such as assays for transposase-accessible chromatin via sequencing (ATAC-seq). Such data can possess several regions across the human genome with little to no sequencing depth and are thus non-normal with a large portion of zero values. Despite distributed use in the epigenomics field, few studies have evaluated and benchmarked how correlation and association statistics behave across ATAC-seq experiments with known differences or the effects of removing specific outliers from the data. Here, we developed a computational simulation of ATAC-seq data to elucidate the behavior of correlation statistics and to compare their accuracy under set conditions of reproducibility. RESULTS: Using these simulations, we monitored the behavior of several correlation statistics, including the Pearson's R and Spearman's [Formula: see text] coefficients as well as Kendall's [Formula: see text] and Top-Down correlation. We also test the behavior of association measures, including the coefficient of determination R[Formula: see text], Kendall's W, and normalized mutual information. Our experiments reveal an insensitivity of most statistics, including Spearman's [Formula: see text], Kendall's [Formula: see text], and Kendall's W, to increasing differences between simulated ATAC-seq replicates. The removal of co-zeros (regions lacking mapped sequenced reads) between simulated experiments greatly improves the estimates of correlation and association. After removing co-zeros, the R[Formula: see text] coefficient and normalized mutual information display the best performance, having a closer one-to-one relationship with the known portion of shared, enhanced loci between simulated replicates. When comparing values between experimental ATAC-seq data using a random forest model, mutual information best predicts ATAC-seq replicate relationships. CONCLUSIONS: Collectively, this study demonstrates how measures of correlation and association can behave in epigenomics experiments. We provide improved strategies for quantifying relationships in these increasingly prevalent and important chromatin accessibility assays.

The m-adic residue codes are investigated and are found to have many of the strong properties of the quadratic residue codes. A subgroup of the automorphism group and restrictions on the form of the idempotents of the m-adic residue codes are given. It is shown that some m-adic residue codes are self-orthogonal and the duals of some m-adic residue codes are their complements. Bounds on the minimum of the weights of the odd-like vectors in the odd-like codes are given. At some lengths, m-adic residue codes exist for several values of m. Containment relationships between these codes are demonstrated which show that, when m is even, m-adic residue codes inherit properties of quadratic residue codes. A table is included that contains minimum weights of the binary m-adic residue codes of lengths less than or equal to 127.>