Novel technologies for the acquisition of protein expression data at the single cell level are emerging rapidly. Although there exists a substantial body of computational algorithms and tools for the analysis of single cell gene expression (scRNAseq) data, tools for even basic tasks such as clustering or cell type identification for single cell proteomic (scProteomics) data are relatively scarce. Adoption of algorithms that have been developed for scRNAseq into scProteomics is challenged by the larger number of drop-outs, missing data, and noise in single cell proteomic data. Graph contrastive learning (GCL) on cell-to-cell similarity graphs derived from single cell protein expression profiles show promise in cell type identification. However, missing edges and noise in the cell-to-cell similarity graph requires careful design of convolution matrices to overcome the imperfections in these graphs. Here, we introduce scProfiterole (Single Cell Proteomics Clustering via Spectral Filters), a computational framework to facilitate effective use of spectral graph filters in GCL-based clustering of single cell proteomic data. Since clustering assumes a homophilic network topology, we consider three types of homophilic filters: (i) random walks, (ii) heat kernels (HK), (iii) beta kernels (BK). Direct implementation of these filters is computationally prohibitive, thus, the filters are either truncated or approximated in practice. To overcome this limitation, scProfiterole uses Arnoldi orthonormalization to implement polynomial interpolations of any given spectral graph filter. Our results on comprehensive single cell proteomic data show that (i) GCL with learnable polynomial coefficients that are carefully initialized improves the effectiveness and robustness of cell type identification, (ii) HK and BK improve clustering performance over adjacency matrices or random walks, and (iii) polynomial interpolation of spectral filters outperforms approximation or truncation. The source code for scProfiterole and Supplementary Data are available at https://github.com/mustafaCoskunAgu/scProfiterole.

High-throughput sequence analysis commonly relies on k-mers and sampling schemes to improve scalability and data locality. Among these, local schemes are widely used and are typically evaluated by their density, the expected fraction of selected positions. Minimizers are the most common example, but recent near-tight lower bounds suggest diminishing room for improvement under the classical notion of density. Here, we revisit density and broaden its scope. First, we establish a direct link between density and the distance between consecutive selected positions. Under the sole assumption that these distances are identically distributed, we show that density is exactly the inverse of their expected distance, without assumptions on the selection mechanism. This provides a new way to analyze schemes beyond classical local models. Second, we introduce multiminimizers, a meta-scheme combining N minimizer schemes and selecting the candidate whose extends farthest. Multiminimizers are not local schemes, but under independent random component orders and locally distinct m-mers, their expected density converges exponentially to the optimum. Experiments with random minimizers and open-closed mod-minimizers confirm a controllable computation-density trade-off. Third, we introduce deduplicated density, measuring the fraction of distinct minimizers needed to cover all k-mers in a sequence set. We show that multiminimizers also improve this metric, prove that global optimization is NP-complete, and propose an effective local heuristic. Finally, we provide an efficient SIMD-accelerated Rust implementation and demonstrate reduced memory usage on core sequence-analysis tasks.

Accurately identifying topologically associated domains (TADs) from high-throughput chromosome conformation capture (Hi-C) contact maps is fundamental to decoding chromatin architecture and its regulatory functions. Despite numerous existing tools, achieving a balance between computational time and the mathematical optimality of TAD partitions remains a significant challenge. In this study, we formulate TAD identification as a graph partitioning problem guided by the principle of Infomap entropy minimization. We introduce InfoTAD, a novel algorithm that models the hierarchical organization of chromatin interactions through an Infomap entropy encoding tree. A primary theoretical contribution of this work is the rigorous proof that finding an optimal encoding tree with minimal Infomap entropy is Nondeterministic Polynomial-time hard (NP-hard). To circumvent this complexity, we propose an efficient approximation algorithm that integrates a discretization strategy with dynamic programming, specifically tailored to the linear constraints of Hi-C contact maps. Comparative benchmarks on simulated datasets show that InfoTAD consistently achieves higher accuracy and lower Infomap entropy than other methods. Furthermore, application to real Hi-C contact matrices from human cell lines (GM12878 and IMR90) reveals that the boundaries identified by InfoTAD are significantly enriched with structural proteins, underscoring its biological precision and potential for advancing genomic research.

The growing interest in k-mer-based methods across bioinformatics calls for compact k-mer set representations that can be optimized for specific downstream applications. Recently, masked superstrings (MS) have provided such flexibility by moving beyond de Bruijn graph paths to general k-mer superstrings equipped with a binary mask, thereby subsuming Spectrum-Preserving String Sets and achieving compactness on arbitrary k-mer sets. However, existing methods optimize superstring length and mask properties in two separate steps, possibly missing solutions where a small increase in superstring length yields a substantial reduction in mask complexity. Here, we introduce the first method for Pareto optimization of k-mer superstrings and masks, and apply it to the problem of compressing pan-genome k-mer sets. We model the compressibility of MS using an objective that combines superstring length and the number of runs in the mask. We prove that the resulting optimization problem is NP-hard and develop a heuristic based on iterative deepening search in the Aho-Corasick automaton. Using microbial pan-genome datasets, we characterize the Pareto front in the superstring-length/mask-run space and show that the front contains points that Pareto-dominate simplitigs and matchtigs. Finally, we demonstrate that Pareto-optimized MS improve pan-genome k-mer set compressibility by 12%-19% when combined with neural-network compressors, achieving less than 1.2 bits per k-mer in common scenarios.

Approximate membership query structures are used throughout sequence bioinformatics, from read screening and metagenomic classification to assembly, indexing, and error correction. Among them, Bloom filters remain the default choice. They are not the most efficient structures in either time or memory, but they provide an effective compromise between compactness, speed, simplicity, and dynamic insertions, which explains their widespread adoption in practice. Their main drawback is poor cache locality, since each query typically requires several random memory accesses. Blocked Bloom filters alleviate this issue by restricting accesses for any given element to a single memory block, but this usually comes with a loss in accuracy at fixed memory. In this work, we introduce the Super Bloom Filter, a Bloom filter variant designed for streaming k-mer queries on biological sequences. Super Bloom uses minimizers to group adjacent k-mers into super-k-mers and assigns all k-mers of a group to the same memory block, thereby amortizing random accesses over consecutive k-mer queries and improving cache efficiency. We further combine this layout with the findere scheme, which reduces false positives by requiring consistent evidence across overlapping subwords. We provide a theoretical analysis of the construction of Super Bloom filters, showing how minimizer density controls the expected reduction in memory transfers, and derive a practical parameterization strategy linking memory budget, block size, collision overhead, and the number of hash functions to robust false-positive control. Across a broad range of memory budgets and numbers of hash functions, Super Bloom consistently outperforms existing Bloom filter implementations, with several-fold time improvements. As a practical validation, we integrated it into a Rust reimplementation of BioBloom Tools, a sequence screening tool that builds filters from reference genomes and classifies reads through k-mer membership queries for applications such as host removal and contamination filtering. This replacement yields substantially faster indexing and querying than both the original C++ implementation and Rust variants based on Bloom filters and blocked Bloom filters. The findere scheme also reduces false positives by several orders of magnitude, with some configurations yielding no observed false positives among 109 randomly queried k-mers. Code is available at https://github.com/EtienneC-K/SuperBloom and https://github.com/Malfoy/SBB.

Single-cell RNA-seq provides detailed molecular snapshots of individual cells but is notoriously noisy. Variability stems from biological differences and technical factors, such as amplification bias and limited RNA capture efficiency, making it challenging to adapt computational pipelines to heterogeneous datasets or evolving technologies. As a result, most studies still rely on principal component analysis (PCA) for dimensionality reduction, valued for its interpretability and robustness, in spite of its known bias in high dimensions. Here, we improve upon PCA with a random matrix theory (RMT)-based approach that guides the inference of sparse principal components using existing sparse PCA algorithms. We first introduce a novel biwhitening algorithm that self-consistently estimates the magnitude of transcriptomic noise affecting each gene in individual cells, without assuming a specific noise distribution. This enables the use of an RMT-based criterion to automatically select the sparsity level, rendering sparse PCA nearly parameter-free. Our mathematically grounded approach retains the interpretability of PCA while enabling robust, hands-off inference of sparse principal components. Across seven single-cell RNA-seq technologies and four sparse PCA algorithms, we show that this method systematically improves the reconstruction of the principal subspace and consistently outperforms PCA-, autoencoder-, and diffusion-based methods in cell type classification tasks.

Efficient synthesis of large protein libraries is key to making high-throughput biochemistry scalable. Advances in DNA microarray technology now allow more than 170,000 designed oligonucleotides to be synthesized in a single array, dramatically reducing cost and enabling pooled amplification for downstream mutagenesis reactions. Effective amplification of short oligonucleotides into long coding sequences requires efficient primer design (PD) without cross-hybridization. However, no PD method currently guarantees complete coverage of the protein-coding sequences with maximum efficiency and no cross-hybridization over multiple proteins or multiple variants of the same protein. Here, we present PrimerDesigner, a suite of methods to design the most efficient primers for synthesizing large protein libraries with complete protein-coding sequence coverage and without cross-hybridization. We first prove that PD with complete coverage and without cross-hybridization is NP-hard, even for a single protein. As a solution, we formulate the PD problem using integer linear programming (ILP). When no cross-hybridization is possible, we solve the PD problem for a single protein in linear time. Moreover, we extend our ILP formulation to handle multiple variants of the same protein. We demonstrate that PrimerDesigner produces optimal solutions in only a few minutes for a single protein and within a couple of hours for multiple proteins while achieving higher efficiency than a greedy baseline approach. We expect PrimerDesigner to enable the synthesis of large protein libraries at an unprecedented scale and efficiency.

Deconvolution of spatial transcriptomics data returns, for every spot, a full vector of cell type proportions, yet standard spatial domain identification keeps only the dominant cell type assignment (argmax) and discards the remaining composition signal. We present stPularity, a post-deconvolution clustering tool that operates directly on the proportion vectors a deconvolution pipeline already produces: it builds a k-nearest neighbor graph on spatially smoothed cell type proportions and applies a modified Louvain procedure whose objective trades off modularity against a normalized-entropy purity term, automatically determining the number of clusters without ground-truth labels. Its few hyperparameters are set automatically by Bayesian optimization over label-free internal criteria, so the pipeline runs without manual resolution selection. Because stPularity reads only the proportion matrix and spatial coordinates, it is agnostic to the deconvolution method and operates in the low dimensionality of the cell type panel (4-38 cell types). Across four benchmarks, stPularity improves over the dominant-cell-type baseline on three of four datasets, raising the adjusted Rand index (ARI) over argmax by 0.14-0.26. On three of the four datasets, this advantage over argmax persists or widens as the deconvolution proportions are corrupted with increasing noise. An ablation shows that proportion vectors and gene-expression principal component analysis (PCA) embeddings are complementary rather than redundant, their relative strength depending on whether spatial structure is compositional or transcriptomic. Expression-based spatial methods attain higher absolute ARI by reprocessing the full transcriptome; stPularity, instead, targets a distinct goal: recovering interpretable spatial structure from the composition vectors that the argmax workflow would otherwise discard.

Cellular morphological transitions are observed across many diseases, yet their functional role remains unclear because few technologies profile form and function in the same cell. Linking single-cell morphology to transcriptomics is difficult: The two modalities share no feature correspondence and are typically measured in different cells. We present GeoAdvAE, a geometry-aware adversarial autoencoder for diagonal (unpaired) integration of single-cell morphology and single-cell RNA sequencing. GeoAdvAE couples modality-specific variational autoencoders with a Gromov-Wasserstein regularizer and an adversarial discriminator to embed unpaired morphologies and transcriptomes into a shared latent space that preserves both reconstruction fidelity and cross-modal geometry. Using patch-seq neurons with joint morphology-RNA measurements as ground truth, GeoAdvAE attains the best cross-modal cell-type matching accuracy among diagonal integration methods, outperforming optimal-transport, latent-alignment, and adversarial baselines. Applied to 98 CAJAL-quantified microglial morphologies and 31,948 single-cell transcriptomes from the 5xFAD Alzheimer's disease model, GeoAdvAE recovers a one-dimensional axis that aligns the two modalities. Integrated-gradient attribution highlights transcriptomic shifts (DNA repair in ramified microglia; cell killing in amoeboid microglia), nominates gene markers (Ms4a6b; Ftl1/Fth1), and reveals disease-associated microglia signatures that are decoupled from morphology. GeoAdvAE provides a scalable, interpretable approach to connecting cellular "form" and "function" when joint profiling of morphology and transcriptomics is impractical. Our method is publicly available at https://github.com/turbodu222/GeoAdVAE.

A pangenome is a collection of taxonomically related genomes, often from the same species, serving as a representation of their genomic diversity. The study of pangenomes, or pangenomics, aims to quantify and compare this diversity, which has significant relevance in fields such as medicine and biology. Originally conceptualized as sets of genes, pangenomes are now commonly represented as pangenome graphs. These graphs consist of nodes representing genomic sequences and edges connecting consecutive sequences within a genome. Among possible pangenome graphs, a common option is the compacted de Bruijn graph (cdBG). In our work, we focus on the colored cdBG (ccdBG), where each node is associated with a set of colors that indicate the genomes traversing it. In response to the evolution of pangenome representation, we introduce a novel method for comparing pangenomes by their node counts, addressing two main challenges: the variability in node counts arising from graphs constructed with different numbers of genomes and the large influence of rare genomic sequences. We propose an approach for interpolating and extrapolating node counts in ccdBGs, adjusting for the number of genomes. To tackle the influence of rare genomic sequences, we apply Hill numbers, a well-established diversity index previously utilized in ecology and metagenomics for similar purposes, to proportionally weight both rare and common nodes according to the frequency of genomes traversing them.

Single-cell RNA sequencing (scRNA-seq) has significantly advanced our understanding of cardiac cell composition and its underlying pathogenesis. In scRNA-seq data analysis, doublet detection plays a pivotal role in quality control. However, these methods often face challenges related to high computational demands and extended runtimes, particularly in large-scale datasets and rare cell identification. To address these issues, this study introduces the eXtreme-scale Doublet Analyzer (Xoublet) algorithm, which projects single-cell transcriptomic data into principal component analysis space and simulates doublets. Xoublet constructs a hierarchical tree to facilitate rapid screening of similar data, expediting neighborhood searches. Xoublet was compared with Scrublet and DoubletFinder on human-mouse and Cell Hashing datasets with experimentally derived labels, while method-specific calls were examined in an annotated cardiac atlas without independent doublet ground truth. Computational scalability was evaluated separately on HeartMap. Accuracy varied across datasets: Xoublet performed similarly to Scrublet in the cell-line Cell Hashing benchmark but was less discriminative in the human-mouse and peripheral blood mononuclear cell benchmarks. On 2,479,674 HeartMap profiles, Xoublet completed scoring in 574.8 seconds with 4.14 GiB peak resident memory, compared with 1060.6 seconds and 22.81 GiB for the Scrublet core. These findings indicate that Xoublet provides computational advantages for large-scale scoring, although its detection accuracy and sensitivity to specific cell states remain data-dependent.

Multi-assembly methods rely at their core on a flow decomposition problem, namely, decomposing a weighted graph into weighted paths or walks. However, most results over the past decade have focused on decompositions over directed acyclic graphs (DAGs). This limitation has led to either purely heuristic methods or, in applications, transforming a graph with cycles into a DAG via preprocessing heuristics. In this article, we show that flow decomposition problems can also be solved in practice on general graphs with cycles via a framework that yields fast and flexible mixed-integer linear programming (MILP) formulations. Our key technique relies on the graph-theoretical notion of a dominator tree, which we use to find all safe sequences of edges that are guaranteed to appear in some walk of any flow decomposition. We generalize previous results from DAGs to cyclic graphs by showing that maximal safe sequences correspond to extensions of common leaves of two dominator trees, and that all such sequences can be found in time linear in their size. Using these, we can accelerate MILPs for any flow decomposition into walks in general graphs by setting suitable variables encoding solution walks to (at least) 1 and by setting to 0 other walk variables that are nonreachable to and from safe sequences. This reduces model size and eliminates costly linearizations of MILP variable products. We experiment with three decomposition models (minimum flow decomposition, least absolute errors, and minimum path error) on four bacterial datasets. Our preprocessing enables up to 1000-fold speedups and solves many instances that would otherwise time out in under 30 seconds. We thus hope that our dominator-based MILP simplification framework, together with the accompanying software library, can serve as building blocks for multi-assembly applications.

Summarizing a collection P of related RNA secondary structures is a key challenge in applications like evolutionary analysis, alternative fold studies and mRNA vaccine design. This requires both clustering the input structures into similar groups and identifying the core structural motifs on which they agree or differ. Existing methods fail by focusing on only one of these goals: clustering methods do not output shared motifs, while consensus methods overlook the structural diversity present in the collection. Here, we introduce the Maximum Agreement Secondary Structures (MASS) problem, which seeks the largest set F of structural features present in P that partition the input structures into a user-specified number τ of distinct clusters. We prove that MASS is NP-hard and also establish its equivalence to a constrained binary matrix projection problem. We present an exact integer linear program, an exact combinatorial algorithm, and a scalable beam-search heuristic. Using simulations we demonstrate the performance of these exact algorithms and heuristics relative to baseline methods that focus on either clustering or identifying a single consensus tree. On real data, we demonstrate that MASS identifies conserved scaffolds in conformational datasets, reveals conserved structural motifs in different species within RNA families, and recovers shared structural features among synonymous transcripts encoding the same protein. MASS provides a general and interpretable framework for summarizing RNA structural organization.

RNA-sequencing (RNA-seq) relies on Unique Molecular Identifiers (UMIs) to accurately quantify gene expression after PCR amplification. Longer UMIs minimize collisions, where two distinct transcripts are assigned the same UMI, at the expense of increased sequencing and synthesis costs. However, it is not clear how long UMIs need to be in practice, especially given the nonuniformity of the empirical UMI distribution. In this work, we develop a method-of-moments estimator that accounts for UMI collisions, accurately quantifying gene expression and preserving downstream biological insights. We show that UMIs need not be unique: shorter UMIs can be used with a more sophisticated estimator.

Accurate survival prediction in cancer remains challenging due to the sparsity of somatic mutation profiles and the failure of existing models to capture higher-order gene-gene dependencies. Network diffusion methods such as Random Walk with Restart (RWR) can propagate mutation signals across protein-protein interaction (PPI) networks to address sparsity, yet their integration within a deep learning Cox survival framework has not been comprehensively benchmarked across multiple cancer cohorts. We present RCoxNet, a deep learning framework that maps somatic mutation profiles onto a ConsensusPathDB-derived PPI network via RWR, selects prognostic genes by log-rank filtering, and processes network-informed mutation scores through three fully connected hidden layers feeding into a Cox proportional hazards output. RCoxNet was evaluated on The Cancer Genome Atlas (TCGA) cohorts for four cancer types (breast invasive carcinoma [BRCA], lung adenocarcinoma [LUNG], glioblastoma multiforme [GBM], and ovarian serous cystadenocarcinoma [OV]) using 20 independent random splits. The model achieved mean C-index values of 0.807 ± 0.044 (BRCA), 0.750 ± 0.039 (LUNG), 0.704 ± 0.041 (GBM), and 0.668 ± 0.036 (OV), consistently outperforming DeepSurv, Cox-nnet, SurvivalNet, Cox Elastic-Net (Cox-EN), and DeepHit, with statistically significant gains over Cox-EN, Cox-nnet, SurvivalNet, and DeepHit across the majority of cohorts. RCoxNet demonstrates that embedding sparse mutation profiles into a PPI network context substantially improves cancer survival prediction and yields biologically interpretable prognostic features relevant to precision oncology.