{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T13:11:35Z","timestamp":1790082695440,"version":"4.0.1"},"reference-count":79,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T00:00:00Z","timestamp":1790035200000},"content-version":"vor","delay-in-days":21,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"COSMIC European Training Network"},{"name":"European Union\u2019s Horizon 2020 research and innovation program","award":["765158"],"award-info":[{"award-number":["765158"]}]},{"DOI":"10.13039\/501100001711","name":"Swiss National Science Foundation","doi-asserted-by":"publisher","award":["Sinergia CRSII5 193832"],"award-info":[{"award-number":["Sinergia CRSII5 193832"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Discrete stochastic processes are widespread across physics, chemistry, ecology, and beyond. In computational biology and epidemiology, however, most simulators still assume Markovian kinetics with memoryless dynamics, despite growing evidence for history-dependent effects in gene regulation, RNA transcription, cell differentiation, and infection. This reliance on Markovian models limits the routine use and comparison of more realistic, memory-aware descriptions. Here, we develop and benchmark a unified framework for simulating non-Markovian reaction networks using Gillespie-based algorithms. We implement multiple algorithmic classes, including exact, rejection-based, delay-based, and hybrid Markovian\/non-Markovian schemes, and compare them across representative biological models. Across three case studies, we show that non-Markovian waiting times can qualitatively change population-level predictions, and that delay-based approximations can break down when intrinsic system timescales approach the imposed delays. We further show how population-level measurements can be used to infer otherwise inaccessible waiting-time distributions, and how non-Markovian structure can be leveraged for sensitivity analysis and statistical inference. To support broad use of these approaches, we release NoMaSS (Non-Markovian Stochastic Simulations), an open-source Python library that provides a unified interface to a wide range of non-Markovian Gillespie algorithms and enables hybrid Markovian\/non-Markovian models (https:\/\/github.com\/AI-SysBio\/NoMaSS).<\/jats:p>","DOI":"10.1093\/bib\/bbag486","type":"journal-article","created":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T11:51:13Z","timestamp":1787140273000},"source":"Crossref","is-referenced-by-count":0,"title":["Gillespie-based simulation and inference for non-Markovian stochastic reaction networks"],"prefix":"10.1093","volume":"27","author":[{"given":"Aur\u00e9lien","family":"P\u00e9lissier","sequence":"first","affiliation":[{"name":"IBM Research Europe , S\u00e4umerstrasse 4, 8803 R\u00fcschlikon ,","place":["Switzerland"]},{"name":"Department of Biosystems Science and Engineering, ETH Zurich , Mattenstrasse 26, 4058 Basel ,","place":["Switzerland"]},{"name":"Institute of Computational Life Sciences, Z\u00fcrich University of Applied Sciences (ZHAW) , Schloss 1, 8820 W\u00e4denswil ,","place":["Switzerland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miroslav","family":"Phan","sequence":"additional","affiliation":[{"name":"IBM Research Europe , S\u00e4umerstrasse 4, 8803 R\u00fcschlikon ,","place":["Switzerland"]},{"name":"Department of Biosystems Science and Engineering, ETH Zurich , Mattenstrasse 26, 4058 Basel ,","place":["Switzerland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Niko","family":"Beerenwinkel","sequence":"additional","affiliation":[{"name":"Department of Biosystems Science and Engineering, ETH Zurich , Mattenstrasse 26, 4058 Basel ,","place":["Switzerland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mar\u00eda","family":"Rodr\u00edguez Mart\u00ednez","sequence":"additional","affiliation":[{"name":"IBM Research Europe , S\u00e4umerstrasse 4, 8803 R\u00fcschlikon ,","place":["Switzerland"]},{"name":"Department of Biomedical Informatics and Data Science , Yale School of Medicine, 101 College Street, New Haven, CT 06510 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,9,22]]},"reference":[{"key":"2026092208241115100_ref1","volume-title":"Stochastic Processes","author":"Ross","year":"1996"},{"key":"2026092208241115100_ref2"},{"key":"2026092208241115100_ref3","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/S0076-6879(08)03805-6","article-title":"Discrete stochastic simulation methods for chemically reacting systems","volume":"454","author":"Cao","year":"2009","journal-title":"Methods Enzymol"},{"key":"2026092208241115100_ref4","volume-title":"Mathematical Epidemiology"},{"key":"2026092208241115100_ref5"},{"key":"2026092208241115100_ref6","doi-asserted-by":"publisher","first-page":"134246","DOI":"10.1016\/j.scitotenv.2019.134246","article-title":"Forecasting the seasonal pollen index by using a hidden Markov model combining meteorological and biological factors","volume":"698","author":"Tseng","year":"2020","journal-title":"Sci Total Environ"},{"key":"2026092208241115100_ref7","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/0021-9991(76)90041-3","article-title":"A general method for numerically simulating the stochastic time evolution of coupled chemical reactions","volume":"22","author":"Gillespie","year":"1976","journal-title":"J Comput Phys"},{"key":"2026092208241115100_ref8","doi-asserted-by":"crossref","first-page":"2340","DOI":"10.1021\/j100540a008","article-title":"Exact stochastic simulation of coupled chemical reactions","volume":"81","author":"Gillespie","year":"1977","journal-title":"J Phys Chem"},{"key":"2026092208241115100_ref9","doi-asserted-by":"publisher","first-page":"e95150","DOI":"10.1371\/journal.pone.0095150","article-title":"Comparing stochastic differential equations and agent-based modelling and simulation for early-stage cancer","volume":"9","author":"Figueredo","year":"2014","journal-title":"PLoS One"},{"key":"2026092208241115100_ref10","doi-asserted-by":"crossref","first-page":"1633","DOI":"10.1093\/genetics\/149.4.1633","article-title":"Stochastic kinetic analysis of developmental pathway bifurcation in phage $\\lambda$-infected Escherichia coli cells","volume":"149","author":"Arkin","year":"1998","journal-title":"Genetics"},{"key":"2026092208241115100_ref11","doi-asserted-by":"publisher","first-page":"031924","DOI":"10.1103\/PhysRevE.81.031924","article-title":"Messenger RNA fluctuations and regulatory RNAs shape the dynamics of a negative feedback loop","volume":"81","author":"Martinez","year":"2010","journal-title":"Phys Rev E"},{"key":"2026092208241115100_ref12","doi-asserted-by":"publisher","first-page":"689","DOI":"10.3389\/fimmu.2019.00689","article-title":"A probabilistic model of the germinal center reaction","volume":"10","author":"Thomas","year":"2019","journal-title":"Front Immunol"},{"key":"2026092208241115100_ref13","doi-asserted-by":"publisher","first-page":"1448","DOI":"10.3390\/cells9061448","article-title":"Computational model reveals a stochastic mechanism behind germinal center clonal bursts","volume":"9","author":"P\u00e9lissier","year":"2020","journal-title":"Cells"},{"key":"2026092208241115100_ref14","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1371\/journal.pcbi.1004579","article-title":"Temporal Gillespie algorithm: fast simulation of contagion processes on time-varying networks","volume":"11","author":"Vestergaard","year":"2015","journal-title":"PLoS Comput Biol"},{"key":"2026092208241115100_ref15","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1093\/molbev\/msz199","article-title":"Stochastic gene expression influences the selection of antibiotic resistance mutations","volume":"37","author":"Sun","year":"2020","journal-title":"Mol Biol Evol"},{"key":"2026092208241115100_ref16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41467-020-20113-3","article-title":"Demonstration of non-Markovian process characterisation and control on a quantum processor","volume":"11","author":"White","year":"2020","journal-title":"Nat Commun"},{"key":"2026092208241115100_ref17","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1038\/nchem.1378","article-title":"Non-Markovian polymer reaction kinetics","volume":"4","author":"Gu\u00e9rin","year":"2012","journal-title":"Nat Chem"},{"key":"2026092208241115100_ref18","doi-asserted-by":"publisher","first-page":"e2023856118","DOI":"10.1073\/pnas.2023856118","article-title":"Non-Markovian modeling of protein folding","volume":"118","author":"Ayaz","year":"2021","journal-title":"Proc Natl Acad Sci"},{"key":"2026092208241115100_ref19","doi-asserted-by":"publisher","first-page":"e2117586119","DOI":"10.1073\/pnas.2117586119","article-title":"Likelihood-based non-Markovian models from molecular dynamics","volume":"119","author":"Vroylandt","year":"2022","journal-title":"Proc Natl Acad Sci"},{"key":"2026092208241115100_ref20","doi-asserted-by":"crossref","first-page":"244112","DOI":"10.1063\/5.0031979","article-title":"Modeling non-Markovian data using Markov state and Langevin models","volume":"153","author":"Lickert","year":"2020","journal-title":"J Chem Phys"},{"key":"2026092208241115100_ref21","doi-asserted-by":"publisher","first-page":"14593","DOI":"10.1073\/pnas.0503858102","article-title":"Delay-induced stochastic oscillations in gene regulation","volume":"102","author":"Bratsun","year":"2005","journal-title":"Proc Natl Acad Sci"},{"key":"2026092208241115100_ref22","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1016\/j.cels.2017.08.009","article-title":"Stem cell differentiation as a non-Markov stochastic process","volume":"5","author":"Stumpf","year":"2017","journal-title":"Cell Syst"},{"key":"2026092208241115100_ref23","doi-asserted-by":"crossref","first-page":"4682","DOI":"10.1073\/pnas.1910888117","article-title":"Analytical distributions for detailed models of stochastic gene expression in eukaryotic cells","volume":"117","author":"Cao","year":"2020","journal-title":"Proc Natl Acad Sci"},{"key":"2026092208241115100_ref24","doi-asserted-by":"publisher","first-page":"1775","DOI":"10.1098\/rspb.1997.0246","article-title":"Responses of neurons in primary and inferior temporal visual cortices to natural scenes","volume":"264","author":"Baddeley","year":"1997","journal-title":"Proc R Soc Lond Ser B Biol Sci"},{"key":"2026092208241115100_ref25","doi-asserted-by":"publisher","first-page":"1600","DOI":"10.1073\/pnas.1220433110","article-title":"Calling patterns in human communication dynamics","volume":"110","author":"Jiang","year":"2013","journal-title":"Proc Natl Acad Sci"},{"key":"2026092208241115100_ref26","doi-asserted-by":"crossref","first-page":"101","DOI":"10.3389\/fphys.2011.00101","article-title":"Social interactions model and adaptability of human behavior","volume":"2","author":"Zhao","year":"2011","journal-title":"Front Physiol"},{"key":"2026092208241115100_ref27","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1038\/nature03459","article-title":"The origin of bursts and heavy tails in human dynamics","volume":"435","author":"Barabasi","year":"2005","journal-title":"Nature"},{"key":"2026092208241115100_ref28","doi-asserted-by":"crossref","first-page":"108501","DOI":"10.1103\/PhysRevLett.92.108501","article-title":"Long-term clustering, scaling, and universality in the temporal occurrence of earthquakes","volume":"92","author":"Corral","year":"2004","journal-title":"Phys Rev Lett"},{"key":"2026092208241115100_ref29","doi-asserted-by":"crossref","first-page":"23542","DOI":"10.1073\/pnas.1913926116","article-title":"Markovian approaches to modeling intracellular reaction processes with molecular memory","volume":"116","author":"Zhang","year":"2019","journal-title":"Proc Natl Acad Sci"},{"key":"2026092208241115100_ref30","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/MASSP.1986.1165342","article-title":"An introduction to hidden Markov models","volume":"3","author":"Rabiner","year":"1986","journal-title":"IEEE ASSP Mag"},{"key":"2026092208241115100_ref31","doi-asserted-by":"crossref","first-page":"402","DOI":"10.2174\/138920209789177575","article-title":"Hidden Markov models and their applications in biological sequence analysis","volume":"10","author":"Yoon","year":"2009","journal-title":"Curr Genomics"},{"key":"2026092208241115100_ref32","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1137\/16M1055876","article-title":"A Gillespie algorithm for non-Markovian stochastic processes","volume":"60","author":"Masuda","year":"2018","journal-title":"SIAM Rev"},{"key":"2026092208241115100_ref33","doi-asserted-by":"publisher","first-page":"042108","DOI":"10.1103\/PhysRevE.90.042108","article-title":"Simulating non-Markovian stochastic processes","volume":"90","author":"Bogun\u00e1","year":"2014","journal-title":"Phys Rev E"},{"key":"2026092208241115100_ref34","doi-asserted-by":"publisher","volume":"17","journal-title":"Nat Commun","DOI":"10.1038\/s41467-026-69817-y"},{"key":"2026092208241115100_ref35","doi-asserted-by":"publisher","first-page":"e117","DOI":"10.1371\/journal.pcbi.0020117","article-title":"Oscillatory regulation of Hes1: discrete stochastic delay modelling and simulation","volume":"2","author":"Barrio","year":"2006","journal-title":"PLoS Comput Biol"},{"key":"2026092208241115100_ref36","first-page":"12","article-title":"Exact stochastic simulation of coupled chemical reactions with delays","volume":"126","author":"Cai","year":"2007","journal-title":"J Chem Phys"},{"key":"2026092208241115100_ref37","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1063\/1.2799998","article-title":"A modified next reaction method for simulating chemical systems with time dependent propensities and delays","volume":"127","author":"Anderson","year":"2007","journal-title":"J Chem Phys"},{"key":"2026092208241115100_ref38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1063\/1.3521496","article-title":"A partial-propensity formulation of the stochastic simulation algorithm for chemical reaction networks with delays","volume":"134","author":"Ramaswamy","year":"2011","journal-title":"J Chem Phys"},{"key":"2026092208241115100_ref39","doi-asserted-by":"publisher","first-page":"4243","DOI":"10.1093\/bioinformatics\/btac472","article-title":"DelaySSAToolkit. Jl: stochastic simulation of reaction systems with time delays in Julia","volume":"38","author":"Xiaoming","year":"2022","journal-title":"Bioinformatics"},{"key":"2026092208241115100_ref40","doi-asserted-by":"publisher","first-page":"15912","DOI":"10.1073\/pnas.1403232111","article-title":"Scaling laws governing stochastic growth and division of single bacterial cells","volume":"111","author":"Iyer-Biswas","year":"2014","journal-title":"Proc Natl Acad Sci"},{"key":"2026092208241115100_ref41","doi-asserted-by":"crossref","first-page":"822","DOI":"10.1038\/nrmicro2202","article-title":"Metabolism, cell growth and the bacterial cell cycle","volume":"7","author":"Wang","year":"2009","journal-title":"Nat Rev Microbiol"},{"key":"2026092208241115100_ref42","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1128\/JB.01240-09","article-title":"Global regulation of gene expression and cell differentiation in Caulobacter crescentus in response to nutrient availability","volume":"192","author":"England","year":"2010","journal-title":"J Bacteriol"},{"key":"2026092208241115100_ref43","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/j.cell.2014.02.041","article-title":"Rethinking differentiation: stem cells, regeneration, and plasticity","volume":"157","author":"Alvarado","year":"2014","journal-title":"Cell"},{"key":"2026092208241115100_ref44","doi-asserted-by":"publisher","first-page":"1230","DOI":"10.1038\/nature06403","article-title":"Nanog safeguards pluripotency and mediates germline development","volume":"450","author":"Chambers","year":"2007","journal-title":"Nature"},{"key":"2026092208241115100_ref45","doi-asserted-by":"publisher","first-page":"1183","DOI":"10.1126\/science.1070919","article-title":"Stochastic gene expression in a single cell","volume":"297","author":"Elowitz","year":"2002","journal-title":"Science"},{"key":"2026092208241115100_ref46","doi-asserted-by":"crossref","first-page":"17256","DOI":"10.1073\/pnas.0803850105","article-title":"Analytical distributions for stochastic gene expression","volume":"105","author":"Shahrezaei","year":"2008","journal-title":"Proc Natl Acad Sci"},{"key":"2026092208241115100_ref47","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1126\/science.1198817","article-title":"Mammalian genes are transcribed with widely different bursting kinetics","volume":"332","author":"Suter","year":"2011","journal-title":"Science"},{"key":"2026092208241115100_ref48","doi-asserted-by":"crossref","first-page":"031911","DOI":"10.1103\/PhysRevE.79.031911","article-title":"Stochasticity of gene products from transcriptional pulsing","volume":"79","author":"Iyer-Biswas","year":"2009","journal-title":"Phys Rev E"},{"key":"2026092208241115100_ref49","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1038\/s41586-018-0836-1","article-title":"Genomic encoding of transcriptional burst kinetics","volume":"565","author":"Larsson","year":"2019","journal-title":"Nature"},{"key":"2026092208241115100_ref50","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/gb-2013-14-1-r7","article-title":"Inferring the kinetics of stochastic gene expression from single-cell RNA-sequencing data","volume":"14","author":"Kim","year":"2013","journal-title":"Genome Biol"},{"key":"2026092208241115100_ref51","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1038\/s41467-017-02737-0","article-title":"The chemical fluctuation theorem governing gene expression","volume":"9","author":"Park","year":"2018","journal-title":"Nat Commun"},{"key":"2026092208241115100_ref52","doi-asserted-by":"publisher","first-page":"5860","DOI":"10.1073\/pnas.092538799","article-title":"Precision and functional specificity in mRNA decay","volume":"99","author":"Wang","year":"2002","journal-title":"Proc Natl Acad Sci"},{"key":"2026092208241115100_ref53","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1038\/msb.2011.62","article-title":"Coupled pre-mRNA and mRNA dynamics unveil operational strategies underlying transcriptional responses to stimuli","volume":"7","author":"Zeisel","year":"2011","journal-title":"Mol Syst Biol"},{"key":"2026092208241115100_ref54","doi-asserted-by":"publisher","first-page":"20563","DOI":"10.1073\/pnas.1312310110","article-title":"Stimulus-induced modulation of transcriptional bursting in a single mammalian gene","volume":"110","author":"Molina","year":"2013","journal-title":"Proc Natl Acad Sci"},{"key":"2026092208241115100_ref55","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/S0378-4754(00)00270-6","article-title":"Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates","volume":"55","author":"Sobol","year":"2001","journal-title":"Math Comput Simul"},{"key":"2026092208241115100_ref56","doi-asserted-by":"crossref","first-page":"052406","DOI":"10.1103\/PhysRevE.101.052406","article-title":"Analytical results for non-Markovian models of bursty gene expression","volume":"101","author":"Wang","year":"2020","journal-title":"Phys Rev E"},{"key":"2026092208241115100_ref57","volume":"112","journal-title":"J Geophys Res Solid Earth"},{"key":"2026092208241115100_ref58","doi-asserted-by":"publisher","first-page":"158702","DOI":"10.1103\/PhysRevLett.98.158702","article-title":"Impact of non-Poissonian activity patterns on spreading processes","volume":"98","author":"Vazquez","year":"2007","journal-title":"Phys Rev Lett"},{"key":"2026092208241115100_ref59","doi-asserted-by":"publisher","first-page":"7311","DOI":"10.1038\/s41467-023-42868-1","article-title":"Constructing temporal networks with bursty activity patterns","volume":"14","author":"Sheng","year":"2023","journal-title":"Nat Commun"},{"key":"2026092208241115100_ref60","doi-asserted-by":"crossref","first-page":"036115","DOI":"10.1103\/PhysRevE.84.036115","article-title":"Voter model with non-Poissonian interevent intervals","volume":"84","author":"Takaguchi","year":"2011","journal-title":"Phys Rev E Stat Nonlin Soft Matter Phys"},{"key":"2026092208241115100_ref61","doi-asserted-by":"crossref","first-page":"08B609_1","DOI":"10.1063\/1.4928635","article-title":"Constant-complexity stochastic simulation algorithm with optimal binning","volume":"143","author":"Sanft","year":"2015","journal-title":"J Chem Phys"},{"key":"2026092208241115100_ref62","doi-asserted-by":"crossref","first-page":"5","DOI":"10.35784\/acs-2022-25","article-title":"Application of Gillespie algorithm for simulating evolution of fitness of microbial population","volume":"18","author":"Gil","year":"2022","journal-title":"Appl Comput Sci"},{"key":"2026092208241115100_ref63","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s12918-017-0487-0","article-title":"Inferring gene regulatory networks from single-cell data: a mechanistic approach","volume":"11","author":"Herbach","year":"2017","journal-title":"BMC Syst Biol"},{"key":"2026092208241115100_ref64","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0269964805050011","article-title":"On\/off storage systems with state-dependent input, output, and switching rates","volume":"19","author":"Boxma","year":"2005","journal-title":"Probab Eng Inf Sci"},{"key":"2026092208241115100_ref65","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1239\/aap\/1282924062","article-title":"Fluid limit theorems for stochastic hybrid systems with application to neuron models","volume":"42","author":"Pakdaman","year":"2010","journal-title":"Adv Appl Probab"},{"key":"2026092208241115100_ref66","doi-asserted-by":"publisher","first-page":"3067","DOI":"10.1093\/bioinformatics\/btl485","article-title":"COPASI\u2014a complex pathway simulator","volume":"22","author":"Hoops","year":"2006","journal-title":"Bioinformatics"},{"key":"2026092208241115100_ref67","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.physrep.2012.03.001","article-title":"Temporal networks","volume":"519","author":"Holme","year":"2012","journal-title":"Phys Rep"},{"key":"2026092208241115100_ref68","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1038\/srep00469","article-title":"Activity driven modeling of time varying networks","volume":"2","author":"Perra","year":"2012","journal-title":"Sci Rep"},{"key":"2026092208241115100_ref69","doi-asserted-by":"crossref","first-page":"e1013490","DOI":"10.1371\/journal.pcbi.1013490","article-title":"Fast and exact stochastic simulations of epidemics on static and temporal networks","volume":"21","author":"Cure","year":"2025","journal-title":"PLOS Comput Biol"},{"key":"2026092208241115100_ref70","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1090\/S0002-9904-1946-08672-3","article-title":"Representation of ${e}^{-{x}^{\\lambda }}$ as a Laplace integral","volume":"52","author":"Pollard","year":"1946","journal-title":"Bull Am Math Soc"},{"key":"2026092208241115100_ref71","volume":"3","journal-title":"Ann Probab"},{"key":"2026092208241115100_ref72","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.entcs.2009.10.006","article-title":"The Kantorovich metric in computer science: a brief survey","volume":"253","author":"Deng","year":"2009","journal-title":"Electronic Notes in Theoretical Computer Science"},{"key":"2026092208241115100_ref73","volume-title":"Sixth International Conference on Computer Vision (IEEE Cat. No. 98CH36271)"},{"key":"2026092208241115100_ref74","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2070781.2024192","article-title":"Displacement interpolation using Lagrangian mass transport","volume":"30","author":"Bonneel","year":"2011","journal-title":"ACM Trans Graph"},{"key":"2026092208241115100_ref75","volume-title":"IEEE 12th International Conference on Computer Vision,"},{"key":"2026092208241115100_ref76","article-title":"A global optimization algorithm worth using","author":"Davis","year":"2017","journal-title":"dlib C++ library"},{"key":"2026092208241115100_ref77","volume":"25","journal-title":"Adv Neural Inf Process Syst"},{"key":"2026092208241115100_ref78","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1080\/01621459.1991.10475041","article-title":"Transformations in density estimation","volume":"86","author":"Wand","year":"1991","journal-title":"J Am Stat Assoc"},{"key":"2026092208241115100_ref79","doi-asserted-by":"crossref","first-page":"97","DOI":"10.21105\/joss.00097","article-title":"SALib: an open-source python library for sensitivity analysis","volume":"2","author":"Herman","year":"2017","journal-title":"J Open Source Softw"}],"container-title":["Briefings in Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bib\/article-pdf\/27\/5\/bbag486\/71311969\/bbag486.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bib\/article-pdf\/27\/5\/bbag486\/71311969\/bbag486.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T12:24:24Z","timestamp":1790079864000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bib\/article\/doi\/10.1093\/bib\/bbag486\/8827746"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,1]]},"references-count":79,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2026,9,1]]}},"URL":"https:\/\/doi.org\/10.1093\/bib\/bbag486","relation":{},"ISSN":["1467-5463","1477-4054"],"issn-type":[{"value":"1467-5463","type":"print"},{"value":"1477-4054","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,9]]},"published":{"date-parts":[[2026,9,1]]},"article-number":"bbag486"}}