The growth of metagenomics-derived amino acid sequence data has transformed our understanding of protein function, microbial diversity, and evolutionary relationships. However, the vast majority of these proteins remain functionally uncharacterized. Grouping the millions of such uncharacterized sequences with the few experimentally characterized ones allows the transfer of annotations, while the inspection of conserved residues with multiple sequence alignments can provide clues to function, even in the absence of existing functional information. To address the challenges associated with this data surge and the need to group sequences, we present a scalable, open-source, parametrizable Nextflow pipeline (nf-core/proteinfamilies) that generates nascent protein families or assigns new proteins to existing families. The computational benchmarks demonstrated that resource usage scales approximately linearly with input size, and the biological benchmarks showed that the generated protein families closely resemble manually curated families in widely used databases.

Computation of correlation functions is a key operation in Lattice quantum chromodynamics (LQCD) simulations to extract nuclear physics observables. These functions involve many binary batch tensor contractions, each tensor possibly occupying hundreds of MBs of memory. Performing these contractions on GPU accelerators poses the challenge of scheduling them as to optimize tensor reuse and reduce data traffic. In this work we propose two fast novel scheduling algorithms that reorder contractions to increase temporal locality via input/intermediate tensor reuse. Our schedulers take advantage of application-specific features, such as contractions being binary and locality within contraction trees, to optimize the objective of minimizing peak memory. We integrate them into the LQCD analysis software suite Redstar and improve time-to-solution. Our schedulers attain upto 2.1x improvement in peak memory, which is reflected by a reduction of upto 4.2x in evictions, upto 1.8x in data traffic, resulting in upto 1.9x faster correlation function computation time.

The plant root microbiome is vital in plant health, nutrient uptake, and environmental resilience. To explore and harness this diversity, we present metagRoot, a specialized and enriched database focused on the protein families of the plant root microbiome. MetagRoot integrates metagenomic, metatranscriptomic, and reference genome-derived protein data to characterize 71 091 enriched protein families, each containing at least 100 sequences. These families are annotated with multiple sequence alignments, CRISPR elements, hidden Markov models, taxonomic and functional classifications, ecosystem and geolocation metadata, and predicted 3D structures using AlphaFold2. MetagRoot is a powerful tool for decoding the molecular landscape of root-associated microbial communities and advancing microbiome-informed agricultural practices by enriching protein family information with ecological and structural context. The database is available at https://pavlopoulos-lab.org/metagroot/ or https://www.metagroot.org.

The approximate minimum degree algorithm is widely used before numerical factorization to reduce fill-in for sparse matrices. While considerable attention has been given to the numerical factorization process, less focus has been placed on parallelizing the approximate minimum degree algorithm itself. In this paper, we explore different parallelization strategies, and introduce a novel parallel framework that leverages multiple elimination on distance-2 independent sets. Our evaluation shows that parallelism within individual elimination steps is limited due to low computational workload and significant memory contention. In contrast, our proposed framework overcomes these challenges by parallelizing the work across elimination steps. To the best of our knowledge, our implementation is the first scalable shared memory implementation of the approximate minimum degree algorithm. Experimental results show that we achieve up to a 7.29x speedup using 64 threads over the state-of-the-art sequential implementation in SuiteSparse.

Multiplication of a sparse matrix with another (dense or sparse) matrix is a fundamental operation that captures the computational patterns of many data science applications, including but not limited to graph algorithms, sparsely connected neural networks, graph neural networks, clustering, and many-to-many comparisons of biological sequencing data. In many application scenarios, the matrix multiplication takes places on an arbitrary algebraic semiring where the scalar operations are overloaded with user-defined functions with certain properties or a more general heterogenous algebra where even the domains of the input matrices can be different. Here, we provide a unifying treatment of the sparse matrix-matrix operation and its rich application space including machine learning, computational biology and chemistry, graph algorithms, and scientific computing.

The known universe of protein families represents only a small fraction of nature's molecular diversity. From 40.3 billion sequences across 40,446 metagenomes, 9,540 metatranscriptomes, and 539 million proteins from 167,415 reference genomes, we identified 608,258 previously uncharacterized protein families with >=100 members and 6.5 million families with >=25 members, none matching known Pfam domains or reference proteins. This effort doubles the known repertoire of large families and quadruples that of smaller families. Integration of AlphaFold2-based structural predictions with gene-neighborhood and taxonomic analyses enables the characterization of previously unannotated proteins, revealing candidates for both novel and known biological functions in understudied microbial lineages and biomes. This expanded repertoire provides insights into microbial adaptation and broadens the molecular toolkit available for biotechnology, highlighting the power of global metagenomics to uncover hidden protein diversity. ### Competing Interest Statement The authors have declared no competing interest. Hellenic Foundation for Research and Innovation (H.F.R.I.) under the ‘Third Call for H.F.R.I. Research Projects to support faculty members and researchers’ [23592-EMISSION], 23592-EMISSION Hellenic Foundation for Research and Innovation (H.F.R.I.) under the ‘4th Call for H.F.R.I. Research Project to support Postdoctoral Researchers’ [28787-VIROMINE], 28787-VIROMINE ARISE program from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 945405, 945405 US Department of Energy Joint Genome Institute (https://ror.org/04xm1d337), DE-AC02-05CH11231

Rotation equivariant graph neural networks, i.e., networks designed to guarantee certain geometric relations between their inputs and outputs, yield state-of-the-art performance on spatial deep learning tasks. They exhibit high data efficiency during training and significantly reduced inference time for interatomic potential calculations compared to classical approaches. Key to these models is the Clebsch-Gordon (CG) tensor product, a kernel that contracts two dense feature vectors with a highly structured sparse tensor to produce a dense output vector. The operation, which may be repeated millions of times for typical equivariant models, is a costly and inefficient bottleneck. We introduce a GPU sparse kernel generator for the CG tensor product that provides significant speedup over the best existing open and closed-source implementations. Our implementation achieves high performance by carefully managing GPU shared memory through static analysis at model compile-time, minimizing reads and writes to global memory. We break the tensor product into a series of kernels with operands that fit entirely into registers, enabling us to emit long arithmetic instruction streams that maximize instruction-level parallelism. By fusing the CG tensor product with a subsequent graph convolution, we reduce both intermediate storage and global memory traffic over naive approaches that duplicate input data. We also provide optimized kernels for the gradient of the CG tensor product and a novel identity for the higher partial derivatives required to predict interatomic forces. Our fused kernels offer up to 4.5x speedup for the forward pass and 3x for the backward pass over NVIDIA cuEquivariance, as well as >10x speedup over the widely-used e3nn package. We offer up to 5.3x inference-time speedup for the MACE chemistry foundation model over the original unoptimized version.

Clonal evolution of cancer results in intratumor heterogeneity (ITH), making treatment and cure challenging. Single-cell sequencing has advanced our understanding of ITH, but tracing subclonal evolution using mutational profiles of cells is limited by scale and noise. Moreover, available tumor progression tree inference methods usually offer a single tree to explain the progression of a tumor, and do not inform about alternative evolutionary scenarios. In this paper we introduce the partition function for a tumor progression tree, to assess the reliability of any proposed subclonal structure in a single-cell sequenced tumor. Given that tumor progression can be represented as a perfect phylogeny, the partition function for a given set of cells, R, and a given mutation, ρ , is defined as the likelihood that ρ is present exclusively in R. As such, the partition function evaluates whether R forms a subclone with ρ as a possible subclonal driver, which is especially useful if the cells of R are biologically or clinically significant, e.g., have aggressive growth, therapy resistance, or metastatic potential. We also present an algorithm to estimate the partition function and provide theoretical proofs that our algorithm asymptotically approaches the ground truth. In addition, we present empirical evidence of its accuracy on simulated data, as well as its practical value in analyzing the progression history of real tumors. The implementation is available at: https://github.com/algo-cancer/Partition-Function/ .

Sparse matrix-sparse matrix multiplication (SpGEMM) is a key kernel in many scientific applications and graph workloads. Unfortunately, SpGEMM is bottlenecked by data movement due to its irregular memory access patterns. Significant work has been devoted to developing row reordering schemes towards improving locality in sparse operations, but prior studies mostly focus on the case of sparse-matrix vector multiplication (SpMV). In this paper, we address these issues with hierarchical clustering for SpGEMM that leverages both row reordering and cluster-wise computation to improve reuse in the second input (B) matrix with a novel row-clustered matrix format and access pattern in the first input (A) matrix. We find that hierarchical clustering can speed up SpGEMM by 1.39x on average with low preprocessing cost (less than 20x the cost of a single SpGEMM on about 90% of inputs). Furthermore, we decouple the reordering algorithm from the clustered matrix format so they can be applied as independent optimizations. Additionally, this paper sheds light on the role of both row reordering and clustering independently and together for SpGEMM with a comprehensive empirical study of the effect of 10 different reordering algorithms and 3 clustering schemes on SpGEMM performance on a suite of 110 matrices. We find that reordering based on graph partitioning provides better SpGEMM performance than existing alternatives at the cost of high preprocessing time. The evaluation demonstrates that the proposed hierarchical clustering method achieves greater average speedup compared to other reordering schemes with similar preprocessing times.

We introduce a parallel algorithm to construct a preconditioner for solving a large, sparse linear system where the coefficient matrix is a Laplacian matrix (a.k.a., graph Laplacian). Such a linear system arises from applications such as discretization of a partial differential equation, spectral graph partitioning, and learning problems on graphs. The preconditioner belongs to the family of incomplete factorizations and is purely algebraic. Unlike traditional incomplete factorizations, the new method employs randomization to determine whether or not to keep fill-ins, i.e., newly generated nonzero elements during Gaussian elimination. Since the sparsity pattern of the randomized factorization is unknown, computing such a factorization in parallel is extremely challenging, especially on many-core architectures such as GPUs. Our parallel algorithm dynamically computes the dependency among row/column indices of the Laplacian matrix to be factorized and processes the independent indices in parallel. Furthermore, unlike previous approaches, our method requires little pre-processing time. We implemented the parallel algorithm for multi-core CPUs and GPUs, and we compare their performance to other state-of-the-art methods.

In lower-upper (LU) factorization of a sparse matrix in the form of A = LU, symbolic factorization is a pre-processing stage usually performed to discover the sparsity structure of the factors. A is usually not equal to L + U due to the fill-ins (the nonzeros that do not appear in A but element of L or U) introduced in the factorization. The symbolic factorization can be performed using only the pattern of A and the existing algorithms for that purpose usually utilize graphs by relying on the duality of graphs and matrices. In this work, we assess the viability of utilizing GraphBLAS for symbolic factorization. GraphBLAS defines a standard way to express operations on graphs in the language of linear algebra. We express edge-based and path-based symbolic factorization of the coefficient matrix using common graph operations and investigate utilization of masks and elimination trees for optimization. Our goal is to obtain a performant symbolic factorization, which can then be used on any hardware in a portable manner for which the GraphBLAS standard is realized. We demonstrate our approach on various non-symmetric sparse matrices by running symbolic factorization on multi-core and many-core architectures efficiently.

Particle track reconstruction is an important problem in high-energy physics (HEP), necessary to study properties of subatomic particles. Traditional track reconstruction algorithms scale poorly with the number of particles within the accelerator. The Exa.TrkX project, to alleviate this computational burden, introduces a pipeline that reduces particle track reconstruction to edge classification on a graph, and uses graph neural networks (GNNs) to produce particle tracks. However, this GNN-based approach is memory-prohibitive and skips graphs that would exceed GPU memory. We introduce improvements to the Exa.TrkX pipeline to train on samples of input particle graphs, and show that these improvements generalize to higher precision and recall. In addition, we adapt performance optimizations, introduced for GNN training, to fit our augmented Exa.TrkX pipeline. These optimizations provide a $2\times$ speedup over our baseline implementation in PyTorch Geometric.

The software and data in this repository are a snapshot of the software and data that were used in the research reported on in the paper Sempervirens: A Fast Reconstruction Algorithm for Noisy and Incomplete Binary Matrix Representations of Trees. The snapshot is based on this SHA in the development repository.

Computing fixed-radius near-neighbor graphs is an important first step for many data analysis algorithms. Near-neighbor graphs connect points that are close under some metric, endowing point clouds with a combinatorial structure. As computing power and data acquisition methods advance, diverse sources of large scientific datasets would greatly benefit from scalable solutions to this common subroutine for downstream analysis. Prior work on parallel nearest neighbors has made great progress in problems like k-nearest and approximate nearest neighbor search problems, with particular attention on Euclidean spaces. Yet many applications need exact solutions and non-Euclidean metrics. This paper presents a scalable sparsity-aware distributed memory algorithm using cover trees to compute near-neighbor graphs in general metric spaces. We provide a shared-memory algorithm for cover tree construction and demonstrate its competitiveness with state-of-the-art fixed-radius search data structures. We then introduce two distributed-memory algorithms for the near-neighbor graph problem, a simple point-partitioning strategy and a spatial-partitioning strategy, which leverage the cover tree algorithm on each node. Our algorithms exhibit parallel scaling across a variety of real and synthetic datasets for both traditional and non-traditional metrics. On real world high dimensional datasets with one million points, we achieve speedups up to 678.34x over the state-of-the-art using 1024 cores for graphs with 70 neighbors per vertex (on average), and up to 1590.99x using 4096 cores for graphs with 500 neighbors per vertex (on average).

Applications such as reconstructing cell lineage trees (represented as phylogenetic trees) from single-cell sequencing data require reconstructing a [Formula: see text]-matrix that has many errors and missing entries. We introduce Sempervirens, a very fast matrix reconstruction algorithm for noisy and incomplete matrix representations of phylogenetic trees. Sempervirens uses an iterative maximum-likelihood approach to determine the topology tree represented by the corrupted data. We show that Sempervirens is at least three orders of magnitude faster than other methods on thousand by thousand matrices, with the speed gap widening with larger matrices. We also show that Sempervirens matches state-of-the-art methods in reconstruction accuracy. The speed of Sempervirens enables it to be tractably applied to reconstructing much larger matrices than those that other methods can reconstruct. In addition to experimental results, we justify the algorithm with a mathematical treatment of its subprocedures. History: Accepted by J. Paul Brooks, Area Editor for Applications in Biology, Medicine, and Healthcare. Funding: This work was supported by the Office of Science of the Department of Energy [Contract DE-AC02-05CH11231]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0373 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0373 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Metagenomic binning, the process of grouping DNA sequences into taxonomic units, is critical for understanding the functions, interactions, and evolutionary dynamics of microbial communities. We propose a deep learning approach to binning using two neural networks, one based on composition and another on environmental abundance, dynamically weighting the contribution of each based on characteristics of the input data. Trained on over 43,000 prokaryotic genomes, our network for composition-based binning is inspired by metric learning techniques used for facial recognition.Using a task-specific, multi-GPU accelerated algorithm to cluster the embeddings produced by our network, our binner leverages marker genes observed to be universally present in nearly all taxa to grade and select optimal clusters of sequences from a hierarchy of candidates.We evaluate our approach on four simulated datasets with known ground truth. Our linear time integration of marker genes recovers more near complete genomes than state of the art but computationally infeasible solutions using them, while being over an order of magnitude faster. Finally, we demonstrate the scalability and acuity of our approach by testing it on three of the largest metagenome assemblies ever performed. Compared to other binners, we produced 47%-183% more near complete genomes. From these datasets, we find over the genomes of over 3000 new candidate species which have never been previously cataloged, representing a potential 4% expansion of the known bacterial tree of life.### Competing Interest StatementThe authors have declared no competing interest.

Multiplying two sparse matrices (SpGEMM) is a common computational primitive used in many areas including graph algorithms, bioinformatics, algebraic multigrid solvers, and randomized sketching. Distributed-memory parallel algorithms for SpGEMM have mainly focused on sparsity-oblivious approaches that use 2D and 3D partitioning. Sparsity-aware 1D algorithms can theoretically reduce communication by not fetching nonzeros of the sparse matrices that do not participate in the multiplication. Here, we present a distributed-memory 1D SpGEMM algorithm and implementation. It uses MPI RDMA operations to mitigate the cost of packing/unpacking submatrices for communication, and it uses a block fetching strategy to avoid excessive finegrained messaging. Our results show that our 1D implementation outperforms state-of-the-art 2D and 3D implementations within CombBLAS for many configurations, inputs, and use cases, while remaining conceptually simpler.

Graph Neural Networks (GNNs) offer a compact and computationally efficient way to learn embeddings and classifications on graph data. GNN models are frequently large, making distributed minibatch training necessary. The primary contribution of this paper is new methods for reducing communication in the sampling step for distributed GNN training. Here, we propose a matrix-based bulk sampling approach that expresses sampling as a sparse matrix multiplication (SpGEMM) and samples multiple minibatches at once. When the input graph topology does not fit on a single device, our method distributes the graph and use communication-avoiding SpGEMM algorithms to scale GNN minibatch sampling, enabling GNN training on much larger graphs than those that can fit into a single device memory. When the input graph topology (but not the embeddings) fits in the memory of one GPU, our approach (1) performs sampling without communication, (2) amortizes the overheads of sampling a minibatch, and (3) can represent multiple sampling algorithms by simply using different matrix constructions. In addition to new methods for sampling, we introduce a pipeline that uses our matrix-based bulk sampling approach to provide end-to-end training results. We provide experimental results on the largest Open Graph Benchmark (OGB) datasets on $128$ GPUs, and show that our pipeline is $2.5\times$ faster than Quiver (a distributed extension to PyTorch-Geometric) on a $3$-layer GraphSAGE network. On datasets outside of OGB, we show a $8.46\times$ speedup on $128$ GPUs in per-epoch time. Finally, we show scaling when the graph is distributed across GPUs and scaling for both node-wise and layer-wise sampling algorithms.

The Exabiome project seeks to improve the understanding of microbiomes through the development of methods for accelerating metagenomic science using exascale computing. This article gives an overview of scientific impact of the three components of the project: metagenome assembly, protein family detection and comparative analysis of metagenomes. Exabiome developed MetaHipMer, the only metagenome assembler capable of scaling to full exascale systems. MetaHipMer has enabled ground-breaking assemblies on the Frontier supercomputer, with many scientific benefits, such as the discovery of rare species and viral genomes. To investigate protein families, Exabiome developed two exascale tools, PASTIS and HipMCL. Together, these can utilize exascale resources to understand the functional diversity of billions of “dark matter” proteins and novel protein families. For comparative analysis, Exabiome developed kmerprof, a tool that can be used to compare huge metagenomes for many different scientific purposes, for example, grouping human microbiomes according to body location.

The MIT/IEEE/Amazon GraphChallenge encourages community approaches to developing new solutions for analyzing graphs and sparse data derived from social media, sensor feeds, and scientific data to discover relationships between events as they unfold in the field. The anonymized network sensing Graph Challenge seeks to enable large, open, community-based approaches to protecting networks. Many large-scale networking problems can only be solved with community access to very broad data sets with the highest regard for privacy and strong community buy-in. Such approaches often require community-based data sharing. In the broader networking community (commercial, federal, and academia) anonymized source-to-destination traffic matrices with standard data sharing agreements have emerged as a data product that can meet many of these requirements. This challenge provides an opportunity to highlight novel approaches for optimizing the construction and analysis of anonymized traffic matrices using over 100 billion network packets derived from the largest Internet telescope in the world (CAIDA). This challenge specifies the anonymization, construction, and analysis of these traffic matrices. A GraphBLAS reference implementation is provided, but the use of GraphBLAS is not required in this Graph Challenge. As with prior Graph Challenges the goal is to provide a well-defined context for demonstrating innovation. Graph Challenge participants are free to select (with accompanying explanation) the Graph Challenge elements that are appropriate for highlighting their innovations.