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PROLONG: penalized regression for outcome guided longitudinal omics analysis with network and group constraints.

MOTIVATION: There is a growing interest in longitudinal omics data paired with some longitudinal clinical outcome. Given a large set of continuous omics variables and some continuous clinical outcome, each measured for a few subjects at only a few time points, we seek to identify those variables that co-vary over time with the outcome. To motivate this problem we study a dataset with hundreds of urinary metabolites along with Tuberculosis mycobacterial load as our clinical outcome, with the objective of identifying potential biomarkers for disease progression. For such data clinicians usually apply simple linear mixed effects models which often lack power given the low number of replicates and time points. We propose a penalized regression approach on the first differences of the data that extends the lasso + Laplacian method [Li and Li (Network-constrained regularization and variable selection for analysis of genomic data. Bioinformatics 2008;24:1175-82.)] to a longitudinal group lasso + Laplacian approach. Our method, PROLONG, leverages the first differences of the data to increase power by pairing the consecutive time points. The Laplacian penalty incorporates the dependence structure of the variables, and the group lasso penalty induces sparsity while grouping together all contemporaneous and lag terms for each omic variable in the model. RESULTS: With an automated selection of model hyper-parameters, PROLONG correctly selects target metabolites with high specificity and sensitivity across a wide range of scenarios. PROLONG selects a set of metabolites from the real data that includes interesting targets identified during EDA. AVAILABILITY AND IMPLEMENTATION: An R package implementing described methods called "prolong" is available at https://github.com/stevebroll/prolong. Code snapshot available at 10.5281/zenodo.14804245.

Humans

Unicorn: enhancing single-cell Hi-C data with blind super-resolution for 3D genome structure reconstruction.

MOTIVATION: Single-cell Hi-C (scHi-C) data provide critical insights into chromatin interactions at individual cell levels, uncovering unique genomic 3D structures. However, scHi-C datasets are characterized by sparsity and noise, complicating efforts to accurately reconstruct high-resolution chromosomal structures. In this study, we present ScUnicorn, a novel blind super-resolution framework for scHi-C data enhancement. ScUnicorn uses an iterative degradation kernel optimization process, unlike traditional super-resolution approaches, which rely on downsampling, predefined degradation ratios, or constant assumptions about the input data to reconstruct high-resolution interaction matrices. Hence, our approach more reliably preserves critical biological patterns and minimizes noise. Additionally, we propose 3DUnicorn, a maximum likelihood algorithm that leverages the enhanced scHi-C data to infer precise 3D chromosomal structures. RESULTS: Our evaluation demonstrates that ScUnicorn achieves superior performance over the state-of-the-art methods in terms of Peak Signal-to-Noise Ratio, Structural Similarity Index Measure, and GenomeDisco scores. Moreover, 3DUnicorn's reconstructed structures align closely with experimental 3D-FISH data, underscoring its biological relevance. Together, ScUnicorn and 3DUnicorn provide a robust framework for advancing genomic research by enhancing scHi-C data fidelity and enabling accurate 3D genome structure reconstruction. AVAILABILITY AND IMPLEMENTATION: Unicorn implementation is publicly accessible at https://github.com/OluwadareLab/Unicorn.

Single-Cell Analysis

MutBERT: probabilistic genome representation improves genomics foundation models.

MOTIVATION: Understanding the genomic foundation of human diversity and disease requires models that effectively capture sequence variation, such as single nucleotide polymorphisms (SNPs). While recent genomic foundation models have scaled to larger datasets and multi-species inputs, they often fail to account for the sparsity and redundancy inherent in human population data, such as those in the 1000 Genomes Project. SNPs are rare in humans, and current masked language models (MLMs) trained directly on whole-genome sequences may struggle to efficiently learn these variations. Additionally, training on the entire dataset without prioritizing regions of genetic variation results in inefficiencies and negligible gains in performance. RESULTS: We present MutBERT, a probabilistic genome-based masked language model that efficiently utilizes SNP information from population-scale genomic data. By representing the entire genome as a probabilistic distribution over observed allele frequencies, MutBERT focuses on informative genomic variations while maintaining computational efficiency. We evaluated MutBERT against DNABERT-2, various versions of Nucleotide Transformer, and modified versions of MutBERT across multiple downstream prediction tasks. MutBERT consistently ranked as one of the top-performing models, demonstrating that this novel representation strategy enables better utilization of biobank-scale genomic data in building pretrained genomic foundation models. AVAILABILITY AND IMPLEMENTATION: https://github.com/ai4nucleome/mutBERT.

Humans

Sparse polygenic risk score inference with the spike-and-slab LASSO.

MOTIVATION: Large-scale biobanks, with rich phenotypic and genomic data across hundreds of thousands of samples, provide ample opportunities to elucidate the genetics of complex traits and diseases. Consequently, there is growing demand for robust and scalable methods for disease risk prediction from genotype data. Inference in this setting is challenging due to the high-dimensionality of genomic data, especially when coupled with smaller sample sizes. Popular Polygenic Risk Score (PRS) inference methods address this challenge by adopting sparse Bayesian priors or penalized regression techniques, such as the Least Absolute Shrinkage and Selection Operator (LASSO). However, the former class of methods are not as scalable and do not produce exact sparsity, while the latter tends to over-shrink large coefficients. RESULTS: In this study, we present SSLPRS, a novel PRS method based on the Spike-and-Slab LASSO (SSL) prior, which offers a theoretical bridge between the two frameworks. We extend previous work to derive a coordinate-ascent inference algorithm that operates on GWAS summary statistics, which is orders-of-magnitude more efficient than corresponding individual-level-based implementations. To illustrate the statistical properties of the proposed model, we conducted experiments involving nine simulation configurations and nine quantitative phenotypes from the UK Biobank. Our results demonstrate that SSLPRS is competitive with state-of-the-art methods in terms of prediction accuracy and exhibits superior variable selection performance, especially in sparse genetic architectures. In simulations, this translates to upwards of 50% improvement in positive predictive value. In analysis of real phenotypes, we show that selected variants are highly enriched for meaningful genomic annotations and have better replication rates in larger meta-analyses. AVAILABILITY AND IMPLEMENTATION: SSLPRS is available in the open-source package https://github.com/li-lab-mcgill/penprs.

Multifactorial Inheritance

CIRCE: a scalable Python package to predict cis-regulatory DNA interactions from single-cell chromatin accessibility data.

MOTIVATION: Chromatin 3D folding creates numerous DNA interactions, participating in gene expression regulation. Single-cell chromatin-accessibility assays now profile hundreds of thousands of cells, challenging existing methods for mapping cis-regulatory interactions. RESULTS: We present CIRCE, a fast and scalable Python package to predict cis-regulatory DNA interactions from single-cell chromatin accessibility data. CIRCE re-implements the Cicero workflow to analyse single-cell atlases, cutting runtime and memory use by several orders of magnitude. We also provide new options to compute metacells, grouping similar cells to reduce data sparsity. We benchmarked CIRCE against Cicero on two datasets of different sizes and demonstrated the improvement from CIRCE's metacells' strategy with promoter capture Hi-C data. We also evaluated how DNA interaction predictions are impacted by different pre-processing. We observed a negative impact of Cicero's count normalization, and the best performance was obtained with the single-cell count matrix directly. Finally, we demonstrated the scalability of CIRCE by processing a dataset of more than 700 000 cells and 1 million DNA regions in less than an hour. CIRCE should greatly facilitate the prediction of DNA region interactions for scverse and Python users, while providing new and up-to-date pre-processing insights. AVAILABILITY AND IMPLEMENTATION: CIRCE is released as an open-source software under the AGPL-3.0 licence. The package source code is available on GitHub at https://github.com/cantinilab/CIRCE, and its documentation is accessible at https://circe.readthedocs.io. The code to reproduce the presented results is available as a Snakemake pipeline at https://github.com/cantinilab/circe_reproducibility.s.

Software

CROP: a feature-independent context-aware method for CRISPR-Cas9 frameshift prediction.

MOTIVATION: The CRISPR-Cas9 complex has revolutionized genome-editing technologies. By designing a 20 nt-long guide RNA, a Cas9 nuclease can be guided to cleave almost any genomic target site (followed by NGG). The cleavage induces double-stranded DNA breaks, which are then repaired by cellular pathways. Accurate CRISPR-Cas9 repair-outcome prediction is essential for designing guide RNAs with desired genomic effects, such as gene knockout. A central challenge is quantifying the rate of frameshifts, i.e. repair-outcomes that lead to a change in the local length that is not a multiple of three. Previous methods for frameshift-rate prediction were trained on only a few experimental or cellular contexts, mostly relied on manually defined microhomology features, and were limited by sparse features and class labels. RESULTS: We developed CROP, a feature-independent context-aware repair-outcome prediction method. By aggregating specific repair outcomes as Δlength classes, CROP overcomes class sparsity. We designed CROP to work with variable input sequence lengths and output classes to utilize multiple datasets simultaneously. We benchmarked CROP against state-of-the-art repair-outcome prediction methods over 18 datasets, which we curated and standardized from various studies. Across all datasets, CROP outperformed all competing methods in frameshift-rate prediction. We performed cross-experiment and cross-cellular frameshift-rate predictions to investigate the generalizability of repair mechanisms. Finally, we show that CROP learned microhomology principles from raw sequences without explicit feature engineering, establishing an end-to-end architecture for CRISPR-Cas9 repair-outcome prediction that learns from multiple datasets. AVAILABILITY AND IMPLEMENTATION: CROP is available at https://github.com/OrensteinLab/CROP.

CRISPR-Cas Systems

LAML-Pro: joint maximum likelihood inference of cell genotypes and cell lineage trees.

MOTIVATION: Recent dynamic lineage tracing technologies use genome editing to induce heritable mutations, or edits, that accumulate across successive cell divisions. These edits are measured using single-cell sequencing or imaging, providing data to reconstruct cell lineages at single-cell resolution. Current computational approaches to infer cell lineage trees, or phylogenies, from these data perform two separate steps: (i) Identify each cell's edits (genotype) from the raw sequencing or imaging data; (ii) Infer a cell lineage tree from the cell genotypes. However, genotyping cells is an inexact process and genotype errors can yield an inaccurate lineage tree. For example, using fluorescence based-imaging to measure edits results in a high fraction (≈25%-50%) of uncertain or erroneous genotypes. RESULTS: We introduce Lineage Analysis via Maximum Likelihood with PRobabilistic Observations (LAML-Pro), an algorithm that jointly infers cell genotypes and a cell lineage tree. LAML-Pro is based on the Probabilistic Mixed-type Missing Observation (PMMO) model, which we derive to describe both the genome editing and genotype observation processes. LAML-Pro constructs lineage trees from thousands of cells in under an hour by leveraging the sparsity of transitions under the PMMO model. On simulated data, we demonstrate that LAML-Pro corrects genotype errors and infers substantially more accurate trees than existing methods which are vulnerable to genotype errors. Applied to data from two recent imaging-based lineage tracing systems, LAML-Pro reduces genotype errors by 5-fold and produces more spatially coherent lineage trees compared to existing methods. AVAILABILITY AND IMPLEMENTATION: LAML-Pro is implemented in C++ and is available as both a command-line interface and as a Python library at: github.com/raphael-group/LAML-Pro.

Cell Lineage

Predicting gene-specific regulation with transcriptomic and epigenetic single-cell data.

MOTIVATION: Analysis of single cell ATAC-seq and RNA-seq data has allowed to gain unprecedented insights into gene regulation by allowing to define cell type-specific regulatory regions and their effects on gene expression. While powerful, such analysis is challenging due to the inherent sparsity of single cell data. RESULTS: We present a new approach, MetaFR, to learn gene-specific models that link open-chromatin variation from scATAC-seq data to gene expression from scRNA-seq. Using efficient regression trees, we illustrate that accurate expression prediction models can be learned on the single-cell or meta-cell level. Validation was done using fine-mapped eQTLs. Meta-cell models were found to outperform single-cell models for most genes. Comparison to the SOTA method SCARlink revealed advantages of MetaFR in terms of runtime and prediction performance. MetaFR thus allows time-efficient analysis and obtains reliable models of gene expression prediction, which can be used to study gene regulation in any organism for which scRNA-seq and scATAC-seq data is available. AVAILABILITY AND IMPLEMENTATION: MetaFR is available under https://github.com/SchulzLab/MetaFR.

Single-Cell Analysis

Network methods for diagonal integration of unpaired single-cell multiomics data: a review.

MOTIVATION: Advances in single-cell sequencing have enabled multiomics profiling at unprecedented resolution; however, mass spectrometry-based single-cell proteomics (scMS) remains inherently destructive, precluding simultaneous transcriptomic capture. Unlike antibody-based methods such as CITE-seq, which permit paired profiling but are restricted to targeted protein panels, scMS provides unbiased, genome-scale coverage of the intracellular proteome yet necessitates post hoc integration of unpaired datasets. This diagonal integration challenge, where transcriptomes and proteomes are measured in separate cells lacking shared anchors, remains underserved by existing reviews, which focus predominantly on vertical integration strategies enabled by non-destructive assays. RESULTS: We survey the complete computational pipeline for constructing mechanistic proteogenomic networks from unpaired single-cell data, covering: (i) unimodal network inference such as knowledge-based approaches, probabilistic graphical models, temporal directionality inference, and generative and foundation model strategies that establish the transcriptomic scaffold; (ii) cross-modal integration architectures such as network propagation, graph neural networks (scMRDR, scmFormer, scCotag), and consensus frameworks designed explicitly for the unpaired proteomics setting; and (iii) benchmarking paradigms spanning network reconstruction (BEELINE, GRETA, CausalBench) and multi-task integration evaluation (scMultiBench, SCMMIB), with guidance on metric selection under network sparsity and class imbalance. We identify three principal axes of future development: generative proteomic translation from transcriptomic precursors, inductive prior embedding in next-generation architectures, and perturbation-based causal benchmarking. AVAILABILITY AND IMPLEMENTATION: This is a review article; no novel software is distributed. A curated benchmark resource table, methods starter guide, and per-method bottleneck annotations are provided in the Supplementary Material.

Multiomics

BioNeuralNet: a graph neural network based Multi-Omics network data analysis tool.

SUMMARY: Multi-omics data offer unprecedented insights into complex biological systems, yet their high dimensionality, sparsity, and intricate interactions pose significant analytical challenges. Network-based approaches have advanced multi-omics research by effectively capturing biologically relevant relationships among molecular features (e.g., genes, proteins, metabolites). While these methods are powerful for representing molecular interactions, there remains a need for tools specifically designed to effectively utilize these network representations across diverse downstream analyses. To fulfill this need, we introduce BioNeuralNet, a flexible and modular Python framework tailored for end-to-end network-based multi-omics data analysis. BioNeuralNet leverages Graph Neural Networks (GNNs) to learn biologically meaningful low-dimensional representations from multi-omics networks, converting these complex molecular networks into versatile embeddings. BioNeuralNet supports all major stages of multi-omics network analysis, including several network construction techniques, generation of low-dimensional representations, and a broad range of downstream analytical tasks. Its extensive utilities, including diverse GNN architectures, and compatibility with established Python packages (e.g., scikit-learn, PyTorch, NetworkX), enhance usability and facilitate quick adoption. BioNeuralNet is an open-source, user-friendly, and extensively documented framework designed to support flexible and reproducible multi-omics network analysis in precision medicine. AVAILABILITY AND IMPLEMENTATION: The BioNeuralNet library is available via The Python Package Index (PyPI). Source code, documentation, tutorials, and workflows are hosted at https://bioneuralnet.readthedocs.io. Code archived at https://doi.org/10.5281/zenodo.17503083.

Graph Neural Networks

BaGGLS: a Bayesian shrinkage framework for interpretable modeling of interactions in high-dimensional biological data.

MOTIVATION: Biological data is often high dimensional, noisy, and governed by complex interactions among sparse signals. This poses major challenges for interpretability and reliable feature selection. Tasks such as identifying motif interactions in genomics exemplify these difficulties, as only a small subset of biologically relevant features (e.g. motifs) are typically active, and their effects are often non-linear and context-dependent. While statistical approaches often result in more interpretable models, deep learning models have proven effective in modeling complex interactions and prediction accuracy, yet their black-box nature limits interpretability. RESULTS: We introduce BaGGLS, a flexible and interpretable probabilistic binary regression model designed for high-dimensional biological inference involving feature interactions. BaGGLS incorporates a Bayesian group global-local shrinkage prior, aligned with the group structure introduced by interaction terms. This prior encourages sparsity while retaining interpretability, helping to isolate meaningful signals and suppress noise. To enable scalable inference, we employ a partially factorized variational approximation that captures posterior skewness and supports efficient learning even in large feature spaces. In extensive simulations, we compare BaGGLS to frequentist probit regressions (unconstrained and with L1-penalty) as well as a probit model with Markov Chain Monte Carlo (MCMC) sampling under a horseshoe prior. We can show that BaGGLS outperforms the other methods with regard to interaction detection and is many times faster than MCMC sampling under the horseshoe prior. We also demonstrate the usefulness of BaGGLS in the context of interaction discovery from motif scanner outputs (e.g. Find Individual Motif Occurrences (FIMO)) and noisy attribution scores from deep learning models. This shows that BaGGLS is a promising approach for uncovering biologically relevant interaction patterns, with potential applicability across a range of high-dimensional tasks in computational biology. AVAILABILITY: Code is available at gitlab.com/dacs-hpi/baggls.

Bayes Theorem

Middle Eastern intestinal lymphoma: report of a case and review of the literature.

A 20-year-old Persian man with Middle Eastern lymphoma is described, and 84 additional cases from the literature are reviewed. Basically, the disease is a malignant lymphoma which involves the upper small intestine (duodenum and proximal jejunum). It is associated with clubbing of the fingers, abdominal pain, weight loss, diarrhea, vomiting, and malabsorption, and frequently occurs in a younger age group than "Western Hemisphere" intestinal lymphoma. Some patients also have alpha heavy chain disease. The sex ratio is equal, and the disease occurs only in Middle Eastern and North African Moslems and Jews. Upper gastrointestinal radiographs are frequently diagnostic, and per oral small intestinal biopsy is nearly always diagnostic. Pathologically, the following features are characteristic for Middle Eastern lymphoma: partial or total villous atrophy with only mildly abnormal surface epithelium, sparsity of crypts, lymphatic dilatation, and infiltration of lamina propria by pleomorphic mononuclear cells which pepetrate the muscularis mucosa. The etiology and pathogenesis of this disease are unknown, but several hypotheses are discussed. Treatment by a variety of modalities is far from satisfactory, and the prognosis is much poorer than that observed in patients with the "Western" form of intestinal lymphoma. Other differences between Middle Eastern lymphoma and Western lymphoma are described in detail,

Adult

Unifying multimodal single-cell data with a mixture-of-experts β-variational autoencoder framework.

Multimodal single-cell assays profile complementary layers of cell state, but integration is complicated by modality mismatch, sparsity, and uneven cohort coverage. Here, we present Unified Variational Inference (UniVI), a scalable mixture-of-experts β-variational autoencoder that learns a shared latent space while preserving modality-specific structure. UniVI couples modality-specific encoders/decoders with a shared latent prior and a symmetric cross-modal alignment objective, enabling consistent integration of paired measurements without curated feature-link graphs or preannotated reference atlases; optional supervised heads can be added when labels are available. Across paired RNA-protein (CITE-seq) and RNA-chromatin (10x Genomics Multiome, SHARE-seq) data spanning human PBMCs and mouse back skin-a nonhematopoietic tissue with continuous differentiation hierarchies-UniVI produces coherent embeddings, improves label transfer, and enables cross-modal reconstruction and denoising. Extending to trimodal measurements, UniVI maintains robust three-way alignment among RNA, chromatin accessibility, and surface proteins (TEA-seq), and accommodates DNA methylation in a paired scNMT-seq mouse gastrulation proof-of-concept under beta-binomial likelihoods. Performance degrades gracefully under severe cell type imbalance and in the presence of modality-exclusive populations. In an acute myeloid leukemia mosaic design, a paired RNA-protein bridge anchors independent RNA-only and protein+genotype cohorts, revealing genotype-associated neighborhoods that sharpen with mutation-aware fine-tuning. UniVI thus provides a flexible, interpretable framework for multimodal integration across paired, trimodal, and mosaic study designs and supports practical reference-to-query projection in partially observed studies.

Journal Article

Differential patterns of elastic fibers in scarring and non-scarring alopecias.

Elastic fiber stain (acid alcoholic orcein) reveals diagnostically significant differences between several types of alopecia of the scalp. A short outline of elastic fiber distribution on the normal hair follicle emphasizes the elastic coat of the follicular isthmus, the sparsity of elastic fibers on the cyclic lower portion of the hair root, and the presence in the neck of the dermal papilla of an elastin-like body which is formed anew with each hair cycle. This body provides a marker of the gradual shortening of successive anagen hairs in male pattern alopecia. Patterns of elastic fibers in the perifollicular and interfollicular dermis are helpful in differentiating idiopathic pseudopelade of Brocq from pseudopeladic states secondary to lupus erythematosus and other disease processes. Within the idiopathic group, the development of elastic fibres on the lower cyclic portion of the hair root identifies a sub-group that may have a different, non-inflammatory pathogenesis and is provisionally designated as fibrosing alopecia.

Alopecia

A study of excitatory neuromuscular transmission in the bovine trachea.

1. The excitatory innervation of bovine tracheal smooth muscle has been studied with the sucrose-gap apparatus.2. Single 2 ms electrical stimuli applied to the whole tissue excited intrinsic nerves, and produced a small transient depolarization of the smooth muscle, the excitatory junction potential (e.j.p.). The e.j.p. caused a twitch-type contraction; twitches and e.j.p.s summated during repetitive stimulation but facilitation was not observed, and action potentials were never elicited.3. The effects of electrical stimulation could be abolished by atropine (5 x 10(-7) mol/l) and augmented by neostigmine (4 x 10(-6) mol/l), and were mimicked by exogenous acetylcholine (1.0 mug/ml).4. With the electron microscope, the density of innervation was found to be low (one axon per ninety smooth muscle cells). Axons were found in small groups in the clefts between bundles of cells, but no axons penetrated within the muscle bundles. Naked axon varicosities containing agranular vesicles were seen, but no axon approached within 200 nm of a smooth muscle cell.5. It is difficult to reconcile the sparsity of innervation with the dependence of the tissue on nerve excitation to initiate activity.

Acetylcholine

Cartilage hair hypoplasia.

Six cases of cartilage hair hypoplasia from five kindreds are described. They demonstrate variation in the expression of clinical features such as sparsity of hair, hair calibre, radiological changes, short stature and the extent of the disproportion between sitting height and stature.

Age Factors

Microvascular procedures in the management of lymphedema.

The burgeoning field of lymphatic research, and the applications of surgical and microsurgical techniques to the problem of lymphedema have been briefly reviewed. The chronicity of this symptom complex and the relative sparsity of cases in developed countries make controlled clinical trials of treatment unfeasable and comparisons of present regimens difficult. However, continued investigation will undoubtedly be fruitful.

Humans

scFANCL: Dual contrastive learning with false-negative correction at cell level for single-cell RNA-seq clustering.

BACKGROUND: Single-cell RNA sequencing (scRNA-seq) enables cellular characterization at single-cell resolution. However, its high dimensionality, sparsity, and noise make clustering challenging. Approaches utilizing contrastive learning and data augmentation have been introduced to improve representation quality for scRNA-seq clustering. In particular, dual contrastive frameworks combining instance- and cluster-level objectives can capture both cell-cell similarities and inter-cluster variations. However, existing dual contrastive frameworks focus primarily on discrete cluster boundaries, neglecting the biological continuity inherent in scRNA-seq data. METHODS: We propose scFANCL, a dual contrastive framework designed to capture biological continuity in scRNA data. Rather than treating all non-augmented samples as negatives, scFANCL applies a cosine-similarity-based threshold to exclude cells of the same type from the negative pool, preserving continuous transcriptional relationships among them while maintaining inter-cluster separation. RESULTS: Extensive experiments across seven publicly available scRNA-seq datasets demonstrated that scFANCL achieves competitive clustering performance compared with existing baseline methods, consistently yielding high ARI and NMI scores across datasets of varying size and complexity. Ablation studies further confirmed the contribution of the false negative filtering component, showing measurable improvements over variants without filtering. Downstream analyses further suggest that the learned embeddings may reflect biologically meaningful transcriptional transitions, including continuous differentiation trajectories within related cell types. The source code is available at https://github.com/mjuailab/scFANCL . CONCLUSIONS: scFANCL addresses a key limitation of conventional contrastive learning by applying a cosine-similarity-based threshold to exclude cells of the same type from the negative pool, thereby preserving biological continuity within cell types while maintaining inter-cluster separation. Evaluations across seven benchmark scRNA-seq datasets demonstrate competitive clustering performance, with learned embeddings capturing biologically meaningful transcriptional structure and characteristics of rare cell populations.

Clustering Algorithms