Oliver Serang’s research while affiliated with University of Montana and other places

The first worst-case linear-time algorithm for selection was discovered in 1973; however, linear-time binary heap construction was first published in 1964. Here we describe another worst-case linear selection algorithm,which is simply implemented and uses binary heap construction as its principal engine. The algorithm is implemented in place, and shown to perform similarly to in-place median of medians.

Generative-adversarial networks (GANs) have been used to produce data closely resembling example data in a compressed, latent space that is close to sufficient for reconstruction in the original vector space. The Wasserstein metric has been used as an alternative to binary cross-entropy, producing more numerically stable GANs with greater mode covering behavior. Here, a generalization of the Wasserstein distance, using higher-order moments than the mean, is derived. Training a GAN with this higher-order Wasserstein metric is demonstrated to exhibit superior performance, even when adjusted for slightly higher computational cost. This is illustrated generating synthetic antibody sequences.

Selection and sorting the Cartesian sum, X + Y, are classic and important problems. Here, a new algorithm is presented, which generates the top k values of the form X i + Y j . The algorithm relies on layer-ordered heaps, partial orderings of exponentially sized layers. The algorithm relies only on median-of-medians and is simple to implement. Furthermore, it uses data structures contiguous in memory, cache efficient, and fast in practice. The presented algorithm is demonstrated to be theoretically optimal.

Selection on the Cartesian product is a classic problem in computer science. Recently, an optimal algorithm for selection on A + B, based on soft heaps, was introduced. By combining this approach with layer-ordered heaps (LOHs), an algorithm using a balanced binary tree of A + B selections was proposed to perform selection on X1 + X2 + ⋯ + X m in o(n⋅m + k⋅m), where X i have length n. Here, that o(n⋅m + k⋅m) algorithm is combined with a novel, optimal LOH-based algorithm for selection on A + B (without a soft heap). Performance of algorithms for selection on X1 + X2 + ⋯ + X m are compared empirically, demonstrating the benefit of the algorithm proposed here.

Nonparametric statistical tests are an integral part of scientific experiments in a diverse range of fields. When performing such tests, it is standard to sort values; however, this requires Ω(n log(n)) time to sort n values. Thus given enough data, sorting becomes the computational bottleneck, even with very optimized implementations such as the C++ standard library routine, std::sort. Frequently, a nonparametric statistical test is only used to partition values above and below a threshold in the sorted ordering, where the threshold corresponds to a significant statistical result. Linear-time selection and partitioning algorithms cannot be directly used because the selection and partitioning are performed on the transformed statistical significance values rather than on the sorted statistics. Usually, those transformed statistical significance values (e.g., the p value when investigating the family-wise error rate and q values when investigating the false discovery rate (FDR)) can only be computed at a threshold. Because this threshold is unknown, this leads to sorting the data. Layer-ordered heaps, which can be constructed in O(n), only partially sort values and thus can be used to get around the slow runtime required to fully sort. Here we introduce a layer-ordering-based method for selection and partitioning on the transformed values (e.g., p values or q values). We demonstrate the use of this method to partition peptides using an FDR threshold. This approach is applied to speed up Percolator, a postprocessing algorithm used in mass-spectrometry-based proteomics to evaluate the quality of peptide-spectrum matches (PSMs), by >70% on data sets with 100 million PSMs.

Selection on the Cartesian product is a classic problem in computer science. Recently, an optimal algorithm for selection on X+Y, based on soft heaps, was introduced. By combining this approach with layer-ordered heaps (LOHs), an algorithm using a balanced binary tree of X+Y selections was proposed to perform k-selection on $X_1+X_2+\cdots+X_m$ in $o(n\cdot m + k\cdot m)$, where $X_i$ have length n. Here, that $o(n\cdot m + k\cdot m)$ algorithm is combined with a novel, optimal LOH-based algorithm for selection on X+Y (without a soft heap). Performance of algorithms for selection on $X_1+X_2+\cdots+X_m$ are compared empirically, demonstrating the benefit of the algorithm proposed here.

The layer-ordered heap (LOH) is a simple, recently proposed data structure used in optimal selection on X+Y, thealgorithm with the best known runtime for selection on $X_1+X_2+\cdots+X_m$, and the fastest method in practice for computing the most abundant isotope peaks in a chemical compound. Here, we introduce a few algorithms for constructing LOHs, analyze their complexity, and demonstrate that one algorithm is optimal for building a LOH of any rank $\alpha$. These results are shown to correspond with empirical experiments of runtimes when applying the LOH construction algorithms to a common task in machine learning.

Computation of the isotopic distribution of compounds is crucial to applications of mass spectrometry, particularly as machine precision continues to improve. In the last decade, several tools have been created for doing so. In this paper we present a novel algorithm for calculating the most abundant k isotopologue peaks of a compound. The algorithm uses Serang's optimal method of selection on Cartesian products. The method is significantly faster than the state-of-the-art on large compounds (\emph{e.g.}, Titin protein) and on compounds whose elements have many isotopes (\emph{e.g.}, Palladium alloys).

The theoretical computation of isotopic distribution of compounds is crucial in many important applications of mass spectrometry, especially as machine precision grows. A considerable amount of good tools have been created in the last decade for doing so. In this paper we present a novel algorithm for calculating the top k peaks of a given compound. The algorithm takes advantage of layer-ordered heaps used in an optimal method of selection on X+Y and is able to efficiently calculate the top k peaks on very large molecules. Among its peers, this algorithm shows a significant speedup on molecules whose elements have many isotopes. The algorithm obtains a speedup of more than 31x when compared to \textsc{IsoSpec} on \ch{Au2Ca10Ga10Pd76} when computing 47409787 peaks, which covers 0.999 of the total abundance.

Selection on the Cartesian sum, A+B, is a classic and important problem. Frederickson's 1993 algorithm produced the first algorithm that made possible an optimal runtime. Kaplan \emph{et al.}'s recent 2018 paper descibed an alternative optimal algorithm by using Chazelle's soft heaps. These extant optimal algorithms are very complex; this complexity can lead to difficulty implementing them and to poor performance in practice. Here, a new optimal algorithm is presented, which uses layer-ordered heaps. This new algorithm is both simple to implement and practically efficient.