{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T17:56:28Z","timestamp":1791309388011,"version":"4.3.1"},"reference-count":68,"publisher":"Public Library of Science (PLoS)","issue":"10","license":[{"start":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T00:00:00Z","timestamp":1791244800000},"content-version":"am","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100018692","name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","doi-asserted-by":"publisher","award":["CDSN - Maug\u00e9 Yann"],"award-info":[{"award-number":["CDSN - Maug\u00e9 Yann"]}],"id":[{"id":"10.13039\/501100018692","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    A key challenge in inferring gene regulatory networks (GRNs) governing cellular processes such as differentiation and reprogramming from experimental data lies in the impossibility of directly measuring protein dynamics at the single-cell level, which prevents establishing causal relationships between regulator activity and target responses. In earlier work, we introduced CARDAMOM, an algorithm that uses temporal snapshots of scRNA-seq data to calibrate a GRN-driven mechanistic model of gene expression. However, this method had several limitations: it could only rely on the relative ordering of time points rather than their exact labels, imposed restrictive quasi-stationary assumptions on protein dynamics, and depended on multiple hyperparameters. Here, we present CardamomOT, a new method based on the same mechanistic model that jointly reconstructs the GRN and unobserved protein trajectories from the data within a mechanistic optimal transport framework. By incorporating exact time labels and priors on protein kinetic rates from the literature, and substantially reducing the number of required hyperparameters, our approach addresses these limitations and substantially improves the accuracy and robustness of GRN calibration. We validate our framework on both\n                    <jats:italic>in silico<\/jats:italic>\n                    and experimental datasets, demonstrating computational scalability and consistently improved performance over state-of-the-art methods in both GRN and trajectory reconstruction on simulated datasets, and, on experimental datasets, reconstruction of cellular trajectories, velocity fields and latent protein levels that are mutually consistent, together with GRN structures consistent with known biology. We also show that these improvements make the calibrated mechanistic model suitable to be used as a generative model to generate testable predictions of cellular responses to unseen perturbations. To our knowledge, this is among the first methods to explicitly integrate mechanistic GRN inference, trajectory reconstruction, and simulation of realistic datasets into a unified framework for scRNA-seq time series analysis.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1014838","type":"journal-article","created":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T17:44:32Z","timestamp":1791308672000},"page":"e1014838","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["CardamomOT: A mechanistic optimal transport-based framework for gene regulatory network inference, trajectory reconstruction and generative modeling"],"prefix":"10.1371","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-8453-0841","authenticated-orcid":true,"given":"Yann","family":"Maug\u00e9","sequence":"first","affiliation":[{"name":"Aix-Marseille Universit\u00e9, SouthROCK Center of Excellence in Pediatric Oncology Research","place":["Marseille, France"],"department":["COMPO, Inria M\u00e9diterran\u00e9e, Cancer Research Center of Marseille, Inserm UMR1068, CNRS UMR7258, UM105"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3863-2199","authenticated-orcid":true,"given":"Elias","family":"Ventre","sequence":"additional","affiliation":[{"name":"Aix-Marseille Universit\u00e9, SouthROCK Center of Excellence in Pediatric Oncology Research","place":["Marseille, France"],"department":["COMPO, Inria M\u00e9diterran\u00e9e, Cancer Research Center of Marseille, Inserm UMR1068, CNRS UMR7258, UM105"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,10,6]]},"reference":[{"issue":"12","key":"pcbi.1014838.ref001","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pbio.2000640","article-title":"Cell Fate Decision as High-Dimensional Critical State Transition","volume":"14","author":"M Mojtahedi","year":"2016","journal-title":"PLoS Biol"},{"issue":"12","key":"pcbi.1014838.ref002","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pbio.1002585","article-title":"Single-Cell-Based Analysis Highlights a Surge in Cell-to-Cell Molecular Variability Preceding Irreversible Commitment in a Differentiation Process","volume":"14","author":"A Richard","year":"2016","journal-title":"PLoS Biol"},{"issue":"1","key":"pcbi.1014838.ref003","doi-asserted-by":"crossref","first-page":"1096","DOI":"10.1038\/s41467-017-01076-4","article-title":"Dynamics of lineage commitment revealed by single-cell transcriptomics of differentiating embryonic stem cells","volume":"8","author":"S Semrau","year":"2017","journal-title":"Nat Commun"},{"issue":"3","key":"pcbi.1014838.ref004","article-title":"Stem Cell Differentiation as a Non-Markov Stochastic Process","volume":"5","author":"PS Stumpf","year":"2017","journal-title":"Cell Syst"},{"issue":"1","key":"pcbi.1014838.ref005","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/s12551-018-0494-4","article-title":"The rise of the distributions: why non-normality is important for understanding the transcriptome and beyond","volume":"11","author":"JC Mar","year":"2019","journal-title":"Biophys Rev"},{"issue":"10","key":"pcbi.1014838.ref006","doi-asserted-by":"crossref","first-page":"2965","DOI":"10.1039\/C6MB00388E","article-title":"Cellular identity at the single-cell level","volume":"12","author":"AF Coskun","year":"2016","journal-title":"Mol Biosyst"},{"key":"pcbi.1014838.ref007","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-1-4939-8882-2_1","article-title":"Gene Regulatory Network Inference: An Introductory Survey","volume":"1883","author":"VA Huynh-Thu","year":"2019","journal-title":"Methods Mol Biol"},{"issue":"9","key":"pcbi.1014838.ref008","article-title":"Inferring regulatory networks from expression data using tree-based methods","volume":"5","author":"VA Huynh-Thu","year":"2010","journal-title":"PLoS One"},{"issue":"11","key":"pcbi.1014838.ref009","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1038\/nmeth.4463","article-title":"SCENIC: single-cell regulatory network inference and clustering","volume":"14","author":"S Aibar","year":"2017","journal-title":"Nat Methods"},{"issue":"1","key":"pcbi.1014838.ref010","doi-asserted-by":"crossref","first-page":"3384","DOI":"10.1038\/s41598-018-21715-0","article-title":"dynGENIE3: dynamical GENIE3 for the inference of gene networks from time series expression data","volume":"8","author":"VA Huynh-Thu","year":"2018","journal-title":"Sci Rep"},{"issue":"3","key":"pcbi.1014838.ref011","article-title":"Inferring Causal Gene Regulatory Networks from Coupled Single-Cell Expression Dynamics Using Scribe","volume":"10","author":"X Qiu","year":"2020","journal-title":"Cell Syst"},{"issue":"7924","key":"pcbi.1014838.ref012","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1038\/s41586-022-05046-9","article-title":"Live-seq enables temporal transcriptomic recording of single cells","volume":"608","author":"W Chen","year":"2022","journal-title":"Nature"},{"issue":"11","key":"pcbi.1014838.ref013","doi-asserted-by":"crossref","first-page":"1726","DOI":"10.1038\/s41587-023-02082-2","article-title":"Prediction of single-cell RNA expression profiles in live cells by Raman microscopy with Raman2RNA","volume":"42","author":"KJ Kobayashi-Kirschvink","year":"2024","journal-title":"Nat Biotechnol"},{"key":"pcbi.1014838.ref014","doi-asserted-by":"crossref","unstructured":"Santambrogio F. Optimal transport for applied mathematicians. 2015;87.","DOI":"10.1007\/978-3-319-20828-2"},{"issue":"4","key":"pcbi.1014838.ref015","doi-asserted-by":"crossref","DOI":"10.1016\/j.cell.2019.01.006","article-title":"Optimal-Transport Analysis of Single-Cell Gene Expression Identifies Developmental Trajectories in Reprogramming","volume":"176","author":"G Schiebinger","year":"2019","journal-title":"Cell"},{"key":"pcbi.1014838.ref016","unstructured":"Lavenant H, Zhang S, Kim Y-H, Schiebinger G. Towards a mathematical theory of trajectory inference. In: 2021. https:\/\/arxiv.org\/abs\/2102.09204"},{"issue":"4","key":"pcbi.1014838.ref017","article-title":"Mapping transcriptomic vector fields of single cells","volume":"185","author":"X Qiu","year":"2022","journal-title":"Cell"},{"issue":"19","key":"pcbi.1014838.ref018","doi-asserted-by":"crossref","DOI":"10.1242\/dev.198614","article-title":"Developmental single-cell transcriptomics in the Lytechinus variegatus sea urchin embryo","volume":"148","author":"AJ Massri","year":"2021","journal-title":"Development"},{"key":"pcbi.1014838.ref019","article-title":"Simulation-free Schr\u00f6dinger bridges via score and flow matching","author":"A Tong","year":"2023","journal-title":"arXiv preprint"},{"key":"pcbi.1014838.ref020","unstructured":"El Rimawi-Fine N, Stecklov A, Nelson L, Blanchette M, Tong A, Zhang SY, et al. Simulation-free structure learning for stochastic dynamics. In: 2025. https:\/\/arxiv.org\/abs\/2510.16656"},{"key":"pcbi.1014838.ref021","unstructured":"Bertin P, Viviano JD, Tejada-Lapuerta A, Wang W, Bauer S, Theis FJ, et al. A scalable gene network model of regulatory dynamics in single cells. In: 2025. https:\/\/doi.org\/10.48550\/arXiv.2503.20027"},{"issue":"4","key":"pcbi.1014838.ref022","doi-asserted-by":"crossref","first-page":"1879","DOI":"10.1016\/j.jfa.2011.11.026","article-title":"From the Schr\u00f6dinger problem to the Monge\u2013Kantorovich problem","volume":"262","author":"C L\u00e9onard","year":"2012","journal-title":"Journal of Functional Analysis"},{"key":"pcbi.1014838.ref023","article-title":"Cell trajectory inference based on Schr\u00f6dinger problem and a mechanistic model of stochastic gene expression","author":"C Fourni\u00e9","year":"2025","journal-title":"bioRxiv"},{"key":"pcbi.1014838.ref024","article-title":"A computational framework for solving wasserstein lagrangian flows","author":"KI Neklyudov","year":"2023","journal-title":"arXiv preprint"},{"key":"pcbi.1014838.ref025","unstructured":"Zhang SY. Joint trajectory and network inference via reference fitting. In: 2024. https:\/\/arxiv.org\/abs\/2409.06879"},{"issue":"8","key":"pcbi.1014838.ref026","doi-asserted-by":"crossref","DOI":"10.1093\/bioinformatics\/btaf394","article-title":"Dynamic gene regulatory network inference from single-cell data using optimal transport","volume":"41","author":"F Lamoline","year":"2025","journal-title":"Bioinformatics"},{"key":"pcbi.1014838.ref027","unstructured":"Guan V, Janssen J, Rahmani H, Warren A, Zhang S, Robeva E, et al. Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots. In: 2024. https:\/\/arxiv.org\/abs\/2410.22729"},{"issue":"28","key":"pcbi.1014838.ref028","doi-asserted-by":"crossref","first-page":"6889","DOI":"10.1007\/s00216-023-04759-8","article-title":"A review of the current state of single-cell proteomics and future perspective","volume":"415","author":"R Ahmad","year":"2023","journal-title":"Anal Bioanal Chem"},{"key":"pcbi.1014838.ref029","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/msb.2010.96","article-title":"Lysogen stability is determined by the frequency of activity bursts from the fate-determining gene","volume":"6","author":"C Zong","year":"2010","journal-title":"Mol Syst Biol"},{"key":"pcbi.1014838.ref030","doi-asserted-by":"crossref","first-page":"7125","DOI":"10.1038\/srep07125","article-title":"Stochastic promoter activation affects Nanog expression variability in mouse embryonic stem cells","volume":"4","author":"H Ochiai","year":"2014","journal-title":"Sci Rep"},{"key":"pcbi.1014838.ref031","unstructured":"Herbach U. Mod\u00e9lisation stochastique de l\u2019expression des g\u00e8nes et inf\u00e9rence de r\u00e9seaux de r\u00e9gulation. 2018."},{"issue":"3","key":"pcbi.1014838.ref032","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1010962","article-title":"One model fits all: Combining inference and simulation of gene regulatory networks","volume":"19","author":"E Ventre","year":"2023","journal-title":"PLoS Comput Biol"},{"issue":"1","key":"pcbi.1014838.ref033","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1186\/s12918-017-0487-0","article-title":"Inferring gene regulatory networks from single-cell data: a mechanistic approach","volume":"11","author":"U Herbach","year":"2017","journal-title":"BMC Syst Biol"},{"issue":"1","key":"pcbi.1014838.ref034","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1186\/s12859-019-2798-1","article-title":"WASABI: a dynamic iterative framework for gene regulatory network inference","volume":"20","author":"A Bonnaffoux","year":"2019","journal-title":"BMC Bioinformatics"},{"key":"pcbi.1014838.ref035","doi-asserted-by":"crossref","first-page":"89","DOI":"10.3233\/ISB-210226","article-title":"Reverse engineering of a mechanistic model of gene expression using metastability and temporal dynamics","volume":"14","author":"E Ventre","year":"2021","journal-title":"In Silico Biol"},{"issue":"1","key":"pcbi.1014838.ref036","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1012752","article-title":"Trajectory inference from single-cell genomics data with a process time model","volume":"21","author":"M Fang","year":"2025","journal-title":"PLoS Comput Biol"},{"issue":"2","key":"pcbi.1014838.ref037","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1006\/tpbi.1995.1027","article-title":"Markovian Modeling of Gene-Product Synthesis","volume":"48","author":"J Peccoud","year":"1995","journal-title":"Theoretical Population Biology"},{"key":"pcbi.1014838.ref038","doi-asserted-by":"crossref","first-page":"910","DOI":"10.12688\/f1000research.164530.1","article-title":"Inferring and simulating a gene regulatory network for the sympathoadrenal differentiation from single-cell transcriptomics in human","volume":"14","author":"O Gandrillon","year":"2025","journal-title":"F1000 Research"},{"issue":"5","key":"pcbi.1014838.ref039","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1038\/s41588-021-00818-x","article-title":"Single-cell transcriptomics of human embryos identifies multiple sympathoblast lineages with potential implications for neuroblastoma origin","volume":"53","author":"P Kameneva","year":"2021","journal-title":"Nat Genet"},{"issue":"7356","key":"pcbi.1014838.ref040","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1038\/nature10315","article-title":"Central dogma at the single-molecule level in living cells","volume":"475","author":"G-W Li","year":"2011","journal-title":"Nature"},{"key":"pcbi.1014838.ref041","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1146\/annurev-biochem-011520-105250","article-title":"Transcription in Living Cells: Molecular Mechanisms of Bursting","volume":"89","author":"J Rodriguez","year":"2020","journal-title":"Annu Rev Biochem"},{"issue":"6028","key":"pcbi.1014838.ref042","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1126\/science.1198817","article-title":"Mammalian genes are transcribed with widely different bursting kinetics","volume":"332","author":"DM Suter","year":"2011","journal-title":"Science"},{"issue":"6","key":"pcbi.1014838.ref043","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1038\/nmeth.2930","article-title":"Validation of noise models for single-cell transcriptomics","volume":"11","author":"D Gr\u00fcn","year":"2014","journal-title":"Nat Methods"},{"issue":"5","key":"pcbi.1014838.ref044","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/s00285-021-01684-1","article-title":"Reduction of a stochastic model of gene expression: Lagrangian dynamics gives access to basins of attraction as cell types and metastabilty","volume":"83","author":"E Ventre","year":"2021","journal-title":"J Math Biol"},{"issue":"1","key":"pcbi.1014838.ref045","doi-asserted-by":"crossref","first-page":"3222","DOI":"10.1038\/s41467-021-23518-w","article-title":"Generative modeling of single-cell time series with PRESCIENT enables prediction of cell trajectories with interventions","volume":"12","author":"GHT Yeo","year":"2021","journal-title":"Nat Commun"},{"issue":"3","key":"pcbi.1014838.ref046","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1038\/s41592-025-02855-4","article-title":"STORIES: learning cell fate landscapes from spatial transcriptomics using optimal transport","volume":"23","author":"G-J Huizing","year":"2026","journal-title":"Nat Methods"},{"key":"pcbi.1014838.ref047","doi-asserted-by":"crossref","unstructured":"Herbach U. Harissa: stochastic simulation and inference of gene regulatory networks based on transcriptional bursting. In: International Conference on Computational Methods in Systems Biology. 2023. 97\u2013105.","DOI":"10.1007\/978-3-031-42697-1_7"},{"issue":"7","key":"pcbi.1014838.ref048","doi-asserted-by":"crossref","DOI":"10.1016\/j.cell.2019.05.031","article-title":"Comprehensive Integration of Single-Cell Data","volume":"177","author":"T Stuart","year":"2019","journal-title":"Cell"},{"issue":"2","key":"pcbi.1014838.ref049","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1093\/bioinformatics\/btx575","article-title":"SINCERITIES: inferring gene regulatory networks from time-stamped single cell transcriptional expression profiles","volume":"34","author":"N Papili Gao","year":"2018","journal-title":"Bioinformatics"},{"issue":"3","key":"pcbi.1014838.ref050","article-title":"Gene Regulatory Network Inference from Single-Cell Data Using Multivariate Information Measures","volume":"5","author":"TE Chan","year":"2017","journal-title":"Cell Syst"},{"issue":"18","key":"pcbi.1014838.ref051","article-title":"Maximum entropy determination of mammalian proteome dynamics","volume":"121","author":"AJ Dear","year":"2024","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"7347","key":"pcbi.1014838.ref052","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1038\/nature10098","article-title":"Global quantification of mammalian gene expression control","volume":"473","author":"B Schwanh\u00e4usser","year":"2011","journal-title":"Nature"},{"issue":"1","key":"pcbi.1014838.ref053","doi-asserted-by":"crossref","first-page":"6778","DOI":"10.1038\/s41467-021-26842-3","article-title":"An atlas of protein turnover rates in mouse tissues","volume":"12","author":"Z Rolfs","year":"2021","journal-title":"Nat Commun"},{"issue":"4","key":"pcbi.1014838.ref054","article-title":"Topological and statistical analyses of gene regulatory networks reveal unifying yet quantitatively different emergent properties","volume":"14","author":"WZ Ouma","year":"2018","journal-title":"PLoS Comput Biol"},{"issue":"1","key":"pcbi.1014838.ref055","doi-asserted-by":"crossref","first-page":"4940","DOI":"10.1038\/s41467-021-25133-1","article-title":"LineageOT is a unified framework for lineage tracing and trajectory inference","volume":"12","author":"A Forrow","year":"2021","journal-title":"Nat Commun"},{"issue":"12","key":"pcbi.1014838.ref056","doi-asserted-by":"crossref","first-page":"1482","DOI":"10.1038\/s41587-019-0336-3","article-title":"Visualizing structure and transitions in high-dimensional biological data","volume":"37","author":"KR Moon","year":"2019","journal-title":"Nat Biotechnol"},{"issue":"1","key":"pcbi.1014838.ref057","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1101\/gad.947102","article-title":"DNA methylation patterns and epigenetic memory","volume":"16","author":"A Bird","year":"2002","journal-title":"Genes Dev"},{"issue":"12","key":"pcbi.1014838.ref058","doi-asserted-by":"crossref","first-page":"966","DOI":"10.1038\/nmeth.4077","article-title":"OmniPath: guidelines and gateway for literature-curated signaling pathway resources","volume":"13","author":"D T\u00fcrei","year":"2016","journal-title":"Nat Methods"},{"issue":"9","key":"pcbi.1014838.ref059","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1013300","article-title":"NeKo: A tool for automatic network construction from prior knowledge","volume":"21","author":"M Ruscone","year":"2025","journal-title":"PLoS Comput Biol"},{"issue":"5","key":"pcbi.1014838.ref060","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1012476","article-title":"Optimal transport reveals dynamic gene regulatory networks via gene velocity estimation","volume":"21","author":"W Zhao","year":"2025","journal-title":"PLoS Comput Biol"},{"issue":"2","key":"pcbi.1014838.ref061","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/S0955-0674(02)00314-9","article-title":"Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability","volume":"14","author":"JE Ferrell","year":"2002","journal-title":"Curr Opin Cell Biol"},{"issue":"4","key":"pcbi.1014838.ref062","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1007\/s13538-025-01785-y","article-title":"Two-State Stochastic Model of In Vivo Observations of Transcriptional Bursts","volume":"55","author":"LGS da Silva","year":"2025","journal-title":"Braz J Phys"},{"issue":"43","key":"pcbi.1014838.ref063","doi-asserted-by":"crossref","first-page":"17454","DOI":"10.1073\/pnas.1213530109","article-title":"Transcriptional burst frequency and burst size are equally modulated across the human genome","volume":"109","author":"RD Dar","year":"2012","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi.1014838.ref064","unstructured":"Belgacem I. Exploring Logistic Functions as Robust Alternatives to Hill Functions in Genetic Network Modeling. arXiv preprint arXiv:2512.14325. 2025."},{"key":"pcbi.1014838.ref065","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.100623.4","article-title":"Deep learning linking mechanistic models to single-cell transcriptomics data reveals transcriptional bursting in response to DNA damage","volume":"13","author":"Z Huang","year":"2026","journal-title":"Elife"},{"issue":"5","key":"pcbi.1014838.ref066","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/s00285-026-02375-5","article-title":"Trajectory inference for a branching SDE model of cell differentiation via lineage tracing","volume":"92","author":"E Ventre","year":"2026","journal-title":"J Math Biol"},{"issue":"314","key":"pcbi.1014838.ref067","doi-asserted-by":"crossref","first-page":"2563","DOI":"10.1090\/mcom\/3303","article-title":"Scaling algorithms for unbalanced optimal transport problems","volume":"87","author":"L Chizat","year":"2018","journal-title":"Math Comp"},{"issue":"5","key":"pcbi.1014838.ref068","first-page":"1297","article-title":"Convergence of the Sinkhorn algorithm when the Schr\u00f6dinger problem has no solution","volume":"33","author":"A Baradat","year":"2025","journal-title":"Annales de la Facult\u00e9 des sciences de Toulouse: Math\u00e9matiques"}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1014838","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T17:44:50Z","timestamp":1791308690000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1014838"}},"subtitle":[],"editor":[{"given":"James","family":"Gallo","sequence":"first","affiliation":[{"name":"University at Buffalo - The State University of New York","place":["UNITED STATES OF AMERICA"]}],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2026,10,6]]},"references-count":68,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2026,10,6]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1014838","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,6]]}}}