{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T04:40:02Z","timestamp":1744605602909,"version":"3.40.4"},"reference-count":91,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T00:00:00Z","timestamp":1742601600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T00:00:00Z","timestamp":1742601600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-17-EURE-0002","ANR-21-CE45-0025-01"],"award-info":[{"award-number":["ANR-17-EURE-0002","ANR-21-CE45-0025-01"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011773","name":"Region Bourgogne Franche-Comte","doi-asserted-by":"crossref","award":["2022-7-13828"],"award-info":[{"award-number":["2022-7-13828"]}],"id":[{"id":"10.13039\/501100011773","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s40314-025-03146-6","type":"journal-article","created":{"date-parts":[[2025,3,23]],"date-time":"2025-03-23T03:00:27Z","timestamp":1742698827000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Numerical approaches for non-local transport-dominated PDE models with applications to biology"],"prefix":"10.1007","volume":"44","author":[{"given":"Johan","family":"Marguet","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9726-1498","authenticated-orcid":false,"given":"Raluca","family":"Eftimie","sequence":"additional","affiliation":[]},{"given":"Alexei","family":"Lozinski","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,22]]},"reference":[{"issue":"9","key":"3146_CR1","doi-asserted-by":"publisher","first-page":"17446","DOI":"10.3934\/mbe.2023776","volume":"20","author":"OE Adebayo","year":"2023","unstructured":"Adebayo OE, Urcun S, Rolin G, Bordas SPA, Trucu D, Eftimie R (2023) Mathematical investigation of normal and abnormal wound healing dynamics: local and non-local model. Math Biosci Eng 20(9):17446\u201317498. https:\/\/doi.org\/10.3934\/mbe.2023776","journal-title":"Math Biosci Eng"},{"key":"3146_CR2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719154","volume-title":"Introduction to numerical continuation methods","author":"EL Allgower","year":"1990","unstructured":"Allgower EL, Georg K (1990) Introduction to numerical continuation methods. SIAM, Philadelphia. https:\/\/doi.org\/10.1137\/1.9780898719154"},{"issue":"4","key":"3146_CR3","doi-asserted-by":"publisher","first-page":"3720","DOI":"10.3934\/mbe.2022171","volume":"19","author":"M Alwuthaynani","year":"2022","unstructured":"Alwuthaynani M, Eftimie R, Trucu D (2022) Inverse problem approaches for mutation laws in heterogeneous tumours with local and nonlocal dynamics. Math Biosci Eng 19(4):3720\u20133747. https:\/\/doi.org\/10.3934\/mbe.2022171","journal-title":"Math Biosci Eng"},{"issue":"1","key":"3146_CR4","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1016\/j.jtbi.2006.05.030","volume":"243","author":"NJ Armstrong","year":"2006","unstructured":"Armstrong NJ, Painter KJ, Sherratt JA (2006) A continuum approach to modelling cell-cell adhesion. J Theor Biol 243(1):98\u2013113. https:\/\/doi.org\/10.1016\/j.jtbi.2006.05.030","journal-title":"J Theor Biol"},{"issue":"13","key":"3146_CR5","doi-asserted-by":"publisher","first-page":"2487","DOI":"10.1142\/S0218202520500487","volume":"30","author":"R Bailo","year":"2020","unstructured":"Bailo R, Carrillo JA, Murakawa H, Schmidtchen M (2020) Convergence of a fully discrete and energy-dissipating finite-volume scheme for aggregation-diffusion equations. Math Model Methods Appl Sci 30(13):2487\u20132522. https:\/\/doi.org\/10.1142\/S0218202520500487","journal-title":"Math Model Methods Appl Sci"},{"key":"3146_CR6","doi-asserted-by":"publisher","DOI":"10.1017\/9781108981361.006","volume-title":"Human stigmergic problem solving","author":"RK Baltzersen","year":"2022","unstructured":"Baltzersen RK (2022) Human stigmergic problem solving. Cambridge University Press, Cambridge. https:\/\/doi.org\/10.1017\/9781108981361.006"},{"key":"3146_CR7","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/s00607-008-0003-x","volume":"82","author":"P Bastian","year":"2008","unstructured":"Bastian P, Blatt M, Dedner A, Engwer C, Kl\u00f6fkorn R, Ohlberger M, Sander O (2008) A generic grid interface for parallel and adaptive scientific computing. Part i: abstract framework. Computing 82:103\u2013119. https:\/\/doi.org\/10.1007\/s00607-008-0003-x","journal-title":"Computing"},{"key":"3146_CR8","unstructured":"Bengtsson J (2008) Aggregation in non-social insects. V\u00e4xtskyddsbiologi, Sveriges lantbruksuniversitet. Alnarp, Sweden, pp 1\u201318"},{"key":"3146_CR9","doi-asserted-by":"publisher","first-page":"20170009","DOI":"10.1098\/rstb.2017.0009","volume":"373","author":"A Berdahl","year":"2018","unstructured":"Berdahl A, Kao A, Flack A, Westley P, Codling E, Couzin I, Dell A, Biro D (2018) Collective animal navigation and migratory culture: from theoretical models to empirical evidence. Philos Trans R Soc B Biol Sci 373:20170009. https:\/\/doi.org\/10.1098\/rstb.2017.0009","journal-title":"Philos Trans R Soc B Biol Sci"},{"issue":"9","key":"3146_CR10","doi-asserted-by":"publisher","first-page":"917","DOI":"10.1070\/PU1999v042n09ABEH000564","volume":"42","author":"FS Berezovskaya","year":"1999","unstructured":"Berezovskaya FS, Karev GP (1999) Bifurcations of travelling waves in population taxis models. Phys Uspekhi 42(9):917. https:\/\/doi.org\/10.1070\/PU1999v042n09ABEH000564","journal-title":"Phys Uspekhi"},{"issue":"4","key":"3146_CR11","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1137\/130925669","volume":"55","author":"AJ Bernoff","year":"2013","unstructured":"Bernoff AJ, Topaz CM (2013) Nonlocal aggregation models: a primer of swarm equilibria. SIAM Rev 55(4):709\u2013747. https:\/\/doi.org\/10.1137\/130925669","journal-title":"SIAM Rev"},{"key":"3146_CR12","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1007\/s13592-016-0428-8","volume":"47","author":"H Bhagavan","year":"2016","unstructured":"Bhagavan H, Muthmann O, Brockmann A (2016) Structural and temporal dynamics of the bee curtain in the open-nesting honey bee species, apis florea. Apidologie 47:749\u2013758. https:\/\/doi.org\/10.1007\/s13592-016-0428-8","journal-title":"Apidologie"},{"issue":"10","key":"3146_CR13","doi-asserted-by":"publisher","first-page":"2600","DOI":"10.1007\/s11538-018-0477-4","volume":"80","author":"V Bitsouni","year":"2018","unstructured":"Bitsouni V, Eftimie R (2018) Non-local parabolic and hyperbolic models for cell polarisation in heterogeneous cancer cell populations. Bull Math Biol 80(10):2600\u20132632. https:\/\/doi.org\/10.1007\/s11538-018-0477-4","journal-title":"Bull Math Biol"},{"issue":"10","key":"3146_CR14","doi-asserted-by":"publisher","first-page":"1929","DOI":"10.1142\/S021820251750035X","volume":"27","author":"V Bitsouni","year":"2017","unstructured":"Bitsouni V, Chaplain MAJ, Eftimie R (2017) Mathematical modelling of cancer invasion: the multiple roles of TGF-$$\\beta $$ pathway on tumour proliferation and cell adhesion. Math Models Methods Appl Sci 27(10):1929\u20131962. https:\/\/doi.org\/10.1142\/S021820251750035X","journal-title":"Math Models Methods Appl Sci"},{"issue":"4","key":"3146_CR15","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1093\/imammb\/dqx019","volume":"35","author":"V Bitsouni","year":"2018","unstructured":"Bitsouni V, Trucu D, Chaplain MAJ, Eftimie R (2018) Aggregation and travelling wave dynamics in a two-population model of cancer cell growth and invasion. Math Med Biol J IMA 35(4):541\u2013577. https:\/\/doi.org\/10.1093\/imammb\/dqx019","journal-title":"Math Med Biol J IMA"},{"key":"3146_CR16","doi-asserted-by":"publisher","first-page":"103895","DOI":"10.1016\/j.ijnonlinmec.2021.103895","volume":"140","author":"EC Braun","year":"2022","unstructured":"Braun EC, Bretti G, Natalini R (2022) Parameter estimation techniques for a chemotaxis model inspired by cancer-on-chip (coc) experiments. Int J Nonlinear Mech 140:103895. https:\/\/doi.org\/10.1016\/j.ijnonlinmec.2021.103895","journal-title":"Int J Nonlinear Mech"},{"key":"3146_CR17","doi-asserted-by":"publisher","unstructured":"Buono P-L, Eftimie R, Kovacic M. Veen L (2019) Kinetic models for pattern formation in animal aggregations: a symmetry and bifurcation approach. Active particles, volume 2: advances in theory, models, and applications, pp 39\u201364. https:\/\/doi.org\/10.1007\/978-3-030-20297-2_2","DOI":"10.1007\/978-3-030-20297-2_2"},{"issue":"3","key":"3146_CR18","doi-asserted-by":"publisher","first-page":"939","DOI":"10.1016\/j.nonrwa.2006.04.002","volume":"8","author":"M Burger","year":"2007","unstructured":"Burger M, Capasso V, Morale D (2007) On an aggregation model with long and short range interactions. Nonlinear Anal Real World Appl 8(3):939\u2013958. https:\/\/doi.org\/10.1016\/j.nonrwa.2006.04.002","journal-title":"Nonlinear Anal Real World Appl"},{"issue":"13","key":"3146_CR19","doi-asserted-by":"publisher","first-page":"2663","DOI":"10.1142\/S021820251450033X","volume":"24","author":"E Burman","year":"2014","unstructured":"Burman E (2014) Robust error estimates in weak norms for advection dominated transport problems with rough data. Math Models Methods Appl Sci 24(13):2663\u20132684. https:\/\/doi.org\/10.1142\/S021820251450033X","journal-title":"Math Models Methods Appl Sci"},{"issue":"3","key":"3146_CR20","doi-asserted-by":"publisher","first-page":"346","DOI":"10.2307\/1374834","volume":"24","author":"WH Burt","year":"1943","unstructured":"Burt WH (1943) Territoriality and home range concepts as applied to mammals. J Mammal 24(3):346\u2013352. https:\/\/doi.org\/10.2307\/1374834","journal-title":"J Mammal"},{"key":"3146_CR21","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1101\/093617","volume":"76","author":"A Buttensch\u00f6n","year":"2018","unstructured":"Buttensch\u00f6n A, Hillen T, Gerisch A, Painter KJ (2018) A space-jump derivation for non-local models of cell\u2013cell adhesion and non-local chemotaxis. J Math Biol 76:429\u2013456. https:\/\/doi.org\/10.1101\/093617","journal-title":"J Math Biol"},{"key":"3146_CR22","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/s11538-018-0518-z","volume":"81","author":"E Campillo-Funollet","year":"2019","unstructured":"Campillo-Funollet E, Madzvamuse A, Venkataraman C (2019) Bayesian parameter identification for turing systems on stationary and evolving domains. Bull Math Biol 81:81\u2013104. https:\/\/doi.org\/10.1007\/s11538-018-0518-z","journal-title":"Bull Math Biol"},{"issue":"327","key":"3146_CR23","doi-asserted-by":"publisher","first-page":"103","DOI":"10.48550\/arXiv.1804.07796","volume":"90","author":"JA Carrillo","year":"2021","unstructured":"Carrillo JA, Fjordholm U, Solem S (2021) A second-order numerical method for the aggregation equations. Math Comput 90(327):103\u2013139. https:\/\/doi.org\/10.48550\/arXiv.1804.07796","journal-title":"Math Comput"},{"key":"3146_CR24","doi-asserted-by":"crossref","unstructured":"Carrillo JA, Estrada-Rodriguez G, Mikolas L, Tang S (2024) Sparse identification of nonlocal interaction kernels in nonlinear gradient flow equations via partial inversion. arXiv preprint arXiv:2402.06355","DOI":"10.1142\/S0218202525500137"},{"issue":"26","key":"3146_CR25","doi-asserted-by":"publisher","first-page":"11865","DOI":"10.1073\/pnas.1005766107","volume":"107","author":"A Cavagna","year":"2010","unstructured":"Cavagna A, Cimarelli A, Giardina I, Parisi G, Santagati R, Stefanini F, Viale M (2010) Scale-free correlations in starling flocks. Proc Natl Acad Sci 107(26):11865\u201311870. https:\/\/doi.org\/10.1073\/pnas.1005766107","journal-title":"Proc Natl Acad Sci"},{"key":"3146_CR26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.92.012705","author":"A Cavagna","year":"2014","unstructured":"Cavagna A, Castello L, Dey S, Giardina I, Melillo S, Parisi L, Viale M (2014) Short-range interaction vs long-range correlation in bird flocks. Phys Rev E. https:\/\/doi.org\/10.1103\/PhysRevE.92.012705","journal-title":"Phys Rev E"},{"key":"3146_CR27","doi-asserted-by":"publisher","first-page":"15239","DOI":"10.1038\/s41598-023-42440-3","volume":"13","author":"K Chang","year":"2023","unstructured":"Chang K, Zhang Z, Liang G (2023) Dynamics analysis of a nonlocal diffusion dengue model. Sci Rep 13:15239. https:\/\/doi.org\/10.1038\/s41598-023-42440-3","journal-title":"Sci Rep"},{"issue":"1807","key":"3146_CR28","doi-asserted-by":"publisher","first-page":"20190379","DOI":"10.1098\/rstb.2019.0379","volume":"375","author":"L Chen","year":"2020","unstructured":"Chen L, Painter K, Surulescu C, Zhigun A (2020) Mathematical models for cell migration: a non-local perspective. Philos Trans R Soc B 375(1807):20190379. https:\/\/doi.org\/10.1098\/rstb.2019.0379","journal-title":"Philos Trans R Soc B"},{"key":"3146_CR29","doi-asserted-by":"publisher","DOI":"10.21105\/joss.01848","author":"FR Cooper","year":"2020","unstructured":"Cooper FR, Baker RE, Bernabeu MO, Bordas R, Bowler L, Bueno-Orovio A, Byrne HM, Carapella V, Cardone-Noott L, Jonatha C et al (2020) Chaste: cancer, heart and soft tissue environment. J Open Sour Softw. https:\/\/doi.org\/10.21105\/joss.01848","journal-title":"J Open Sour Softw"},{"key":"3146_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/jtbi.2002.3065","volume":"218","author":"ID Couzin","year":"2002","unstructured":"Couzin ID, Krause J, James R, Ruxton GD, Franks NR (2002) Collective memory and spatial sorting in animal groups. J Theor Biol 218:1\u201311. https:\/\/doi.org\/10.1006\/jtbi.2002.3065","journal-title":"J Theor Biol"},{"key":"3146_CR31","doi-asserted-by":"publisher","first-page":"217","DOI":"10.5802\/ahl.30","volume":"3","author":"F Delarue","year":"2020","unstructured":"Delarue F, Lagout\u00ec\u00e8re F, Vauchelet N (2020) Convergence analysis of upwind type schemes for the aggregation equation with pointy potential. Ann Henri Lebesgue 3:217\u2013260. https:\/\/doi.org\/10.5802\/ahl.30","journal-title":"Ann Henri Lebesgue"},{"issue":"sup1","key":"3146_CR32","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1080\/17513758.2012.755572","volume":"7","author":"J Dyson","year":"2013","unstructured":"Dyson J, Gourley S.A, Webb G.F (2013) A non-local evolution equation model of cell\u2013cell adhesion in higher dimensional space. J Biol Dyn 7(sup1):68\u201387. https:\/\/doi.org\/10.1080\/17513758.2012.755572","journal-title":"J Biol Dyn"},{"key":"3146_CR33","doi-asserted-by":"publisher","DOI":"10.3390\/app131910598","author":"E Ellefsen","year":"2023","unstructured":"Ellefsen E, Rodr\u00edguez N (2023) Nonlocal mechanistic models in ecology: numerical methods and parameter inferences. Appl Sci. https:\/\/doi.org\/10.3390\/app131910598","journal-title":"Appl Sci"},{"issue":"8","key":"3146_CR34","doi-asserted-by":"publisher","first-page":"200039","DOI":"10.1098\/rsob.200039","volume":"10","author":"DS Eom","year":"2020","unstructured":"Eom DS (2020) Airinemes: thin cellular protrusions mediate long-distance signalling guided by macrophages. Open Biol 10(8):200039. https:\/\/doi.org\/10.1098\/rsob.200039","journal-title":"Open Biol"},{"key":"3146_CR35","doi-asserted-by":"publisher","first-page":"384","DOI":"10.1051\/proc\/201965384","volume":"65","author":"B Fabr\u00e8ges","year":"2019","unstructured":"Fabr\u00e8ges B, Hivert H, Balc\u2019h KL, Martel S, Delarue F, Lagouti\u00e8re F, Vauchelet N (2019) Numerical schemes for the aggregation equation with pointy potentials. ESAIM Proc Surv 65:384\u2013400. https:\/\/doi.org\/10.1051\/proc\/201965384","journal-title":"ESAIM Proc Surv"},{"key":"3146_CR36","doi-asserted-by":"publisher","first-page":"20230184","DOI":"10.1098\/rsif.2023.0184","volume":"20","author":"C Falco","year":"2023","unstructured":"Falco C, Cohen DJ, Carrillo JA, Baker RE (2023) Quantifying tissue growth, shape and collision via continuum models and bayesian inference. J R Soc Interface 20:20230184. https:\/\/doi.org\/10.1098\/rsif.2023.0184","journal-title":"J R Soc Interface"},{"issue":"8","key":"3146_CR37","doi-asserted-by":"publisher","first-page":"5398","DOI":"10.1002\/mma.6281","volume":"43","author":"K Fellner","year":"2020","unstructured":"Fellner K, Hughes BD (2020) Solutions of a non-local aggregation equation: Universal bounds, concavity changes, and efficient numerical solutions. Math Methods Appl Sci 43(8):5398\u20135429. https:\/\/doi.org\/10.1002\/mma.6281","journal-title":"Math Methods Appl Sci"},{"key":"3146_CR38","doi-asserted-by":"publisher","DOI":"10.1002\/andp.18551700105","author":"A Fick","year":"1855","unstructured":"Fick A (1855) Ueber diffusion. Ann Phys. https:\/\/doi.org\/10.1002\/andp.18551700105","journal-title":"Ann Phys"},{"key":"3146_CR39","doi-asserted-by":"publisher","first-page":"548","DOI":"10.3390\/biophysica2040046","volume":"2","author":"IC Fortunato","year":"2022","unstructured":"Fortunato IC, Sunyer R (2022) The forces behind directed cell migration. Biophysica 2:548\u2013563. https:\/\/doi.org\/10.3390\/biophysica2040046","journal-title":"Biophysica"},{"issue":"5\u20136","key":"3146_CR40","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1387\/ijdb.041810rf","volume":"48","author":"RA Foty","year":"2004","unstructured":"Foty RA, Steinberg MS (2004) Cadherin-mediated cell\u2013cell adhesion and tissue segregation in relation to malignancy. Int J Dev Biol 48(5\u20136):397\u2013409. https:\/\/doi.org\/10.1387\/ijdb.041810rf","journal-title":"Int J Dev Biol"},{"key":"3146_CR41","doi-asserted-by":"publisher","DOI":"10.1038\/nrm2720","author":"P Friedl","year":"2009","unstructured":"Friedl P, Gilmour D (2009) Collective cell migration in morphogenesis, regeneration and cancer. Nat Rev Mol Cell Biol. https:\/\/doi.org\/10.1038\/nrm2720","journal-title":"Nat Rev Mol Cell Biol"},{"issue":"8","key":"3146_CR42","doi-asserted-by":"publisher","first-page":"777","DOI":"10.1038\/ncb2548","volume":"14","author":"P Friedl","year":"2012","unstructured":"Friedl P, Locker J, Sahai E, Segall JE (2012) Classifying collective cancer cell invasion. Nat Cell Biol 14(8):777\u2013783. https:\/\/doi.org\/10.1038\/ncb2548","journal-title":"Nat Cell Biol"},{"issue":"1\u20132","key":"3146_CR43","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.mcm.2004.05.016","volume":"43","author":"A Gerisch","year":"2006","unstructured":"Gerisch A, Chaplain MAJ (2006) Robust numerical methods for taxis-diffusion-reaction systems: applications to biomedical problems. Math Comput Model 43(1\u20132):49\u201375. https:\/\/doi.org\/10.1016\/j.mcm.2004.05.016","journal-title":"Math Comput Model"},{"key":"3146_CR44","doi-asserted-by":"publisher","DOI":"10.1201\/9781420094558-c12","author":"A Gerisch","year":"2010","unstructured":"Gerisch A, Painter KJ (2010) Mathematical modeling of cell adhesion and its applications to developmental biology and cancer invasion. Cell Mech. https:\/\/doi.org\/10.1201\/9781420094558-c12","journal-title":"Cell Mech"},{"key":"3146_CR45","doi-asserted-by":"publisher","first-page":"073042","DOI":"10.1088\/1367-2630\/18\/7\/073042","volume":"18","author":"D Gorbonos","year":"2016","unstructured":"Gorbonos D, Ianconesu R, Puckett JG, Ni R, Ouellette NT, Gov NS (2016) Long range acoustic interactions in insect swarms: an adaptive gravity model. New J Phys 18:073042. https:\/\/doi.org\/10.1088\/1367-2630\/18\/7\/073042","journal-title":"New J Phys"},{"issue":"8","key":"3146_CR46","doi-asserted-by":"publisher","first-page":"2664","DOI":"10.1093\/icesjms\/fsab149","volume":"78","author":"AT Greer","year":"2021","unstructured":"Greer AT, Chiaverano LM, Treible LM, Brise\u00f1o-Avena C, Hernandez FJ (2021) From spatial pattern to ecological process through imaging zooplankton interactions. ICES J Mar Sci 78(8):2664\u20132674. https:\/\/doi.org\/10.1093\/icesjms\/fsab149","journal-title":"ICES J Mar Sci"},{"issue":"3\u20134","key":"3146_CR47","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1515\/jnum-2012-0013","volume":"20","author":"F Hecht","year":"2012","unstructured":"Hecht F (2012) New development in freefem++. J Numer Math 20(3\u20134):251\u2013265. https:\/\/doi.org\/10.1515\/jnum-2012-0013","journal-title":"J Numer Math"},{"issue":"6","key":"3146_CR48","doi-asserted-by":"publisher","first-page":"726","DOI":"10.1098\/rsfs.2012.0025","volume":"2","author":"CK Hemelrijk","year":"2012","unstructured":"Hemelrijk CK, Hildenbrandt H (2012) Schools of fish and flocks of birds: their shape and internal structure by self-organization. Interface Focus 2(6):726\u2013737. https:\/\/doi.org\/10.1098\/rsfs.2012.0025","journal-title":"Interface Focus"},{"key":"3146_CR49","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-67111-2","volume-title":"Non-local cell adhesion models: symmetries and bifurcations in 1-D","author":"T Hillen","year":"2021","unstructured":"Hillen T, Buttensch\u00f6n A (2021) Non-local cell adhesion models: symmetries and bifurcations in 1-D. Springer, Berlin. https:\/\/doi.org\/10.1007\/978-3-030-67111-2"},{"issue":"2","key":"3146_CR50","doi-asserted-by":"publisher","first-page":"895","DOI":"10.1137\/140959997","volume":"53","author":"F James","year":"2015","unstructured":"James F, Vauchelet N (2015) Numerical methods for one-dimensional aggregation equations. SIAM J Numer Anal 53(2):895\u2013916. https:\/\/doi.org\/10.1137\/140959997","journal-title":"SIAM J Numer Anal"},{"issue":"1","key":"3146_CR51","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/0169-5347(94)90225-9","volume":"9","author":"OP Judson","year":"1994","unstructured":"Judson OP (1994) The rise of the individual-based model in ecology. Trends Ecol Evol 9(1):9\u201314. https:\/\/doi.org\/10.1016\/0169-5347(94)90225-9","journal-title":"Trends Ecol Evol"},{"key":"3146_CR52","doi-asserted-by":"publisher","first-page":"1251","DOI":"10.1007\/s00285-020-01536-4","volume":"81","author":"M Krasnianski","year":"2020","unstructured":"Krasnianski M, Painter K, Surulescu C, Zhigun A (2020) Nonlocal and local models for taxis in cell migration: a rigorous limit procedure. J Math Biol 81:1251\u20131298. https:\/\/doi.org\/10.1007\/s00285-020-01536-4","journal-title":"J Math Biol"},{"key":"3146_CR53","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0599-9","volume-title":"Numerical analysis","author":"R Kress","year":"2012","unstructured":"Kress R (2012) Numerical analysis. Springer, Berlin. https:\/\/doi.org\/10.1007\/978-1-4612-0599-9"},{"key":"3146_CR54","doi-asserted-by":"publisher","first-page":"656","DOI":"10.1016\/j.amc.2015.05.120","volume":"266","author":"C Kuehn","year":"2015","unstructured":"Kuehn C (2015) Efficient gluing of numerical continuation and a multiple solution method for elliptic pdes. Appl Math Comput 266:656\u2013674. https:\/\/doi.org\/10.1016\/j.amc.2015.05.120","journal-title":"Appl Math Comput"},{"key":"3146_CR55","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1093\/icb\/icn038","volume":"48","author":"R Larkin","year":"2008","unstructured":"Larkin R, Szafoni R (2008) Evidence for widely dispersed birds migrating together at night. Integr Comp Biol 48:40\u20139. https:\/\/doi.org\/10.1093\/icb\/icn038","journal-title":"Integr Comp Biol"},{"key":"3146_CR56","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1016\/j.camwa.2024.06.007","volume":"169","author":"TT Le","year":"2024","unstructured":"Le TT, Eftimie R (2024) Numerical challenges for the understanding of localised solutions with different symmetries in non-local hyperbolic systems. Comput Math Appl 169:112\u2013131. https:\/\/doi.org\/10.1016\/j.camwa.2024.06.007","journal-title":"Comput Math Appl"},{"issue":"6","key":"3146_CR57","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1002\/cm.21661","volume":"78","author":"C Leclech","year":"2021","unstructured":"Leclech C, Barakat AI (2021) Is there a universal mechanism of cell alignment in response to substrate topography? Cytoskeleton 78(6):284\u2013292. https:\/\/doi.org\/10.1002\/cm.21661","journal-title":"Cytoskeleton"},{"issue":"2","key":"3146_CR58","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1006\/jtbi.2000.228","volume":"210","author":"C Lee","year":"2001","unstructured":"Lee C, Hoopes M, Diehl J, Gilliland W, Huxel G, Leaver E, McCann K, Umbanhowar J, Mogilner A (2001) Non-local concepts and models in biology. J Theor Biol 210(2):201\u2013219. https:\/\/doi.org\/10.1006\/jtbi.2000.228","journal-title":"J Theor Biol"},{"key":"3146_CR59","doi-asserted-by":"publisher","first-page":"997","DOI":"10.1038\/s41592-021-01203-6","volume":"18","author":"SM Lewis","year":"2021","unstructured":"Lewis SM, Asselin-Labat M-L, Nguyen Q, Berthelet J, Tan X, Wimmer VC, Merino D, Rogers KL, Naik SH (2021) Spatial omics and multiplexed imaging to explore cancer biology. Nat Methods 18:997\u20131012. https:\/\/doi.org\/10.1038\/s41592-021-01203-6","journal-title":"Nat Methods"},{"key":"3146_CR60","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-23099-8","volume-title":"Automated solution of differential equations by the finite element method: the FEniCS Book","author":"A Logg","year":"2012","unstructured":"Logg A, Mardal K-A, Wells G (2012) Automated solution of differential equations by the finite element method: the FEniCS Book. Springer, Berlin. https:\/\/doi.org\/10.1007\/978-3-642-23099-8"},{"issue":"2","key":"3146_CR61","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1051\/m2an\/2012031","volume":"47","author":"A Lorz","year":"2013","unstructured":"Lorz A, Lorenzi T, Hochberg M.E, Clairambault J, Perthame B (2013) Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies. ESAIM Math Model Numer Anal Mod\u00e9l Math Anal Num\u00e9r 47(2):377\u2013399. https:\/\/doi.org\/10.1051\/m2an\/2012031","journal-title":"ESAIM Math Model Numer Anal Mod\u00e9l Math Anal Num\u00e9r"},{"key":"3146_CR62","doi-asserted-by":"publisher","first-page":"022057","DOI":"10.1088\/1742-6596\/1679\/2\/022057","volume":"1679","author":"I Magomedov","year":"2020","unstructured":"Magomedov I, Khaliev M.S, Elmurzaev A (2020) Application of finite element analysis in medicine. J Phys Conf Ser 1679:022057. https:\/\/doi.org\/10.1088\/1742-6596\/1679\/2\/022057","journal-title":"J Phys Conf Ser"},{"key":"3146_CR63","unstructured":"Mattaini K (2020) Introduction to molecular and cell biology. Creative commons attribution-noncommercial 4.0 International License. Chap. 9"},{"issue":"2","key":"3146_CR64","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1006\/anbe.2003.2047","volume":"65","author":"K McComb","year":"2003","unstructured":"McComb K, Reby D, Baker L, Moss C, Sayialel S (2003) Long-distance communication of acoustic cues to social identity in African elephants. Anim Behav 65(2):317\u2013329. https:\/\/doi.org\/10.1006\/anbe.2003.2047","journal-title":"Anim Behav"},{"key":"3146_CR65","doi-asserted-by":"publisher","DOI":"10.14430\/arctic540","volume-title":"Wolves: behavior, ecology, and conservation","author":"LD Mech","year":"2019","unstructured":"Mech LD, Boitani L (2019) Wolves: behavior, ecology, and conservation. University of Chicago Press, Chicago. https:\/\/doi.org\/10.14430\/arctic540"},{"key":"3146_CR66","doi-asserted-by":"publisher","first-page":"534","DOI":"10.1007\/s002850050158","volume":"38","author":"A Mogilner","year":"1999","unstructured":"Mogilner A, Edelstein-Keshet L (1999) A non-local model for a swarm. J Math Biol 38:534\u2013570. https:\/\/doi.org\/10.1007\/s002850050158","journal-title":"J Math Biol"},{"key":"3146_CR67","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1007\/s00285-003-0209-7","volume":"47","author":"A Mogilner","year":"2003","unstructured":"Mogilner A, Edelstein-Keshet L, Bent L, Spiros A (2003) Mutual interactions, potentials, and individual distances in a social aggregation. J Math Biol 47:353\u2013389. https:\/\/doi.org\/10.1007\/s00285-003-0209-7","journal-title":"J Math Biol"},{"issue":"3","key":"3146_CR68","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1007\/BF00277392","volume":"26","author":"HG Othmer","year":"1988","unstructured":"Othmer HG, Dunbar SR, Alt W (1988) Models of dispersal in biological systems. J Math Biol 26(3):263\u2013298. https:\/\/doi.org\/10.1007\/BF00277392","journal-title":"J Math Biol"},{"issue":"1","key":"3146_CR69","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1142\/S0218202524400025","volume":"34","author":"KJ Painter","year":"2024","unstructured":"Painter KJ, Hillen T, Potts JR (2024) Biological modelling with nonlocal advection diffusion equations. Math Models Methods Appl Sci 34(1):57\u2013107. https:\/\/doi.org\/10.1142\/S0218202524400025","journal-title":"Math Models Methods Appl Sci"},{"key":"3146_CR70","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1111\/j.1749-6632.1971.tb13093.x","volume":"188","author":"R Payne","year":"1971","unstructured":"Payne R, Webb D (1971) Orientation by means of long lange acoustic signaling in baleen whales. Ann N Y Acad Sci 188:110\u2013141. https:\/\/doi.org\/10.1111\/j.1749-6632.1971.tb13093.x","journal-title":"Ann N Y Acad Sci"},{"key":"3146_CR71","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-52462-7","volume-title":"Solving PDEs in Python","author":"LH Petter","year":"2017","unstructured":"Petter LH, Logg A (2017) Solving PDEs in Python. Springer, Berlin. https:\/\/doi.org\/10.1007\/978-3-319-52462-7"},{"key":"3146_CR72","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.jtbi.2015.01.042","volume":"370","author":"M Pineda","year":"2015","unstructured":"Pineda M, Weijer CJ, Eftimie R (2015) Modelling cell movement, cell differentiation, cell sorting and proportion regulation in dictyostelium discoideum aggregations. J Theor Biol 370:135\u2013150. https:\/\/doi.org\/10.1016\/j.jtbi.2015.01.042","journal-title":"J Theor Biol"},{"key":"3146_CR73","doi-asserted-by":"publisher","DOI":"10.1007\/978-88-470-5522-3","volume-title":"Numerical models for differential problems","author":"A Quarteroni","year":"2009","unstructured":"Quarteroni A, Quarteroni S (2009) Numerical models for differential problems. Springer, Berlin. https:\/\/doi.org\/10.1007\/978-88-470-5522-3"},{"key":"3146_CR74","volume-title":"Pliny the Elder: natural history, trans","author":"H Rackham","year":"1961","unstructured":"Rackham H (1961) Pliny the Elder: natural history, trans. Harvard University Press, Cambridge"},{"issue":"12","key":"3146_CR75","doi-asserted-by":"publisher","first-page":"6044","DOI":"10.1529\/biophysj.107.127662","volume":"95","author":"CA Reinhart-King","year":"2008","unstructured":"Reinhart-King CA, Dembo M, Hammer DA (2008) Cell-cell mechanical communication through compliant substrates. Biophys J 95(12):6044\u20136051. https:\/\/doi.org\/10.1529\/biophysj.107.127662","journal-title":"Biophys J"},{"issue":"1","key":"3146_CR76","doi-asserted-by":"publisher","first-page":"20","DOI":"10.4161\/cam.5.1.13491","volume":"5","author":"G Ren","year":"2011","unstructured":"Ren G, Roberts AI, Shi Y (2011) Adhesion molecules: key players in mesenchymal stem cell-mediated immunosuppression. Cell Adhes Migr 5(1):20\u201322. https:\/\/doi.org\/10.4161\/cam.5.1.13491","journal-title":"Cell Adhes Migr"},{"key":"3146_CR77","doi-asserted-by":"publisher","unstructured":"Reynolds CW (1987) Flocks, herds and schools: a distributed behavioural model. In: Proceedings of the 14th annual conference on computer graphics and interactive techniques, 27\u201321 July. Anaheim, CA, pp 27\u2013 21 . https:\/\/doi.org\/10.1145\/37402.37406","DOI":"10.1145\/37402.37406"},{"key":"3146_CR78","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/S0377-0427(00)00428-3","volume":"13","author":"WC Rheinboldt","year":"2000","unstructured":"Rheinboldt WC (2000) Numerical continuation methods: a perspective. J Comput Appl Math 13:103\u2013113. https:\/\/doi.org\/10.1016\/S0377-0427(00)00428-3","journal-title":"J Comput Appl Math"},{"issue":"4","key":"3146_CR79","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1086\/680009","volume":"185","author":"L Riotte-Lambert","year":"2015","unstructured":"Riotte-Lambert L, Benhamou S, Chamaill\u00e9-Jammes S (2015) How memory-based movement leads to nonterritorial spatial segregation. Am Nat 185(4):103\u2013116. https:\/\/doi.org\/10.1086\/680009","journal-title":"Am Nat"},{"key":"3146_CR80","doi-asserted-by":"publisher","DOI":"10.3390\/cancers12040857","author":"C Roehlecke","year":"2020","unstructured":"Roehlecke C, Schmidt MHH (2020) Tunneling nanotubes and tumor microtubes in cancer. Cancers. https:\/\/doi.org\/10.3390\/cancers12040857","journal-title":"Cancers"},{"issue":"2","key":"3146_CR81","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1083\/jcb.201508047","volume":"212","author":"E Scarpa","year":"2016","unstructured":"Scarpa E, Mayor R (2016) Collective cell migration in development. J Cell Biol 212(2):143\u2013155. https:\/\/doi.org\/10.1083\/jcb.201508047","journal-title":"J Cell Biol"},{"issue":"4","key":"3146_CR82","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1016\/j.gde.2007.05.002","volume":"17","author":"MS Steinberg","year":"2007","unstructured":"Steinberg MS (2007) Differential adhesion in morphogenesis: a modern view. Curr Opin Genet Dev 17(4):281\u2013286. https:\/\/doi.org\/10.1016\/j.gde.2007.05.002. (Pattern formation and developmental mechanisms)","journal-title":"Curr Opin Genet Dev"},{"issue":"2","key":"3146_CR83","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1162\/106454699568700","volume":"5","author":"G Theraulaz","year":"1999","unstructured":"Theraulaz G, Bonabeau E (1999) A brief history of stigmergy. Artif Life 5(2):97\u2013116. https:\/\/doi.org\/10.1162\/106454699568700","journal-title":"Artif Life"},{"key":"3146_CR84","doi-asserted-by":"publisher","first-page":"1601","DOI":"10.1007\/s11538-006-9088-6","volume":"68","author":"CM Topaz","year":"2006","unstructured":"Topaz CM, Bertozzi AL, Lewis MA (2006) A nonlocal continuum model for biological aggregation. Bull Math Biol 68:1601\u20131623. https:\/\/doi.org\/10.1007\/s11538-006-9088-6","journal-title":"Bull Math Biol"},{"issue":"6","key":"3146_CR85","doi-asserted-by":"publisher","first-page":"426","DOI":"10.1038\/nphys1269","volume":"5","author":"X Trepat","year":"2009","unstructured":"Trepat X, Wasserman MR, Angelini TE, Millet E, Weitz DA, Butler JP, Fredberg JJ (2009) Physical forces during collective cell migration. Nat Phys 5(6):426\u2013430. https:\/\/doi.org\/10.1038\/nphys1269","journal-title":"Nat Phys"},{"key":"3146_CR86","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1365\/s13291-021-00241-5","volume":"124","author":"H Uecker","year":"2022","unstructured":"Uecker H (2022) Continuation and bifurcation in nonlinear pdes-algorithms, applications, and experiments. Jahresbericht der Deutschen Mathematiker-Vereinigung 124:43\u201380. https:\/\/doi.org\/10.1365\/s13291-021-00241-5","journal-title":"Jahresbericht der Deutschen Mathematiker-Vereinigung"},{"issue":"3\u20134","key":"3146_CR87","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.physrep.2012.03.004","volume":"517","author":"T Vicsek","year":"2012","unstructured":"Vicsek T, Zafeiris A (2012) Collective motion. Phys Rep 517(3\u20134):71\u2013140. https:\/\/doi.org\/10.1016\/j.physrep.2012.03.004","journal-title":"Phys Rep"},{"issue":"5","key":"3146_CR88","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s00285-023-01905-9","volume":"86","author":"H Wang","year":"2023","unstructured":"Wang H, Salmaniw Y (2023) Open problems in pde models for knowledge-based animal movement via nonlocal perception and cognitive mapping. J Math Biol 86(5):71. https:\/\/doi.org\/10.1007\/s00285-023-01905-9","journal-title":"J Math Biol"},{"key":"3146_CR89","doi-asserted-by":"publisher","first-page":"1064","DOI":"10.1126\/science.149.3688.1064","volume":"149","author":"EO Wilson","year":"1965","unstructured":"Wilson EO (1965) Chemical communication in the social insects. Science 149:1064\u20131071. https:\/\/doi.org\/10.1126\/science.149.3688.1064","journal-title":"Science"},{"key":"3146_CR90","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1146\/annurev-cellbio-100617-062932","volume":"34","author":"YM Yamashita","year":"2018","unstructured":"Yamashita YM, Inaba M, Buszczak M (2018) Specialized intercellular communications via cytonemes and nanotubes. Ann Rev Cell Dev Biol 34:59\u201384. https:\/\/doi.org\/10.1146\/annurev-cellbio-100617-062932","journal-title":"Ann Rev Cell Dev Biol"},{"key":"3146_CR91","doi-asserted-by":"publisher","DOI":"10.1093\/cz\/zoad004","author":"X Yan","year":"2023","unstructured":"Yan X, Wang X, Zhao Y, Zhu Q, Yang L, Li Z (2023) Collective decision-making and spatial patterns in orientation of an endemic ungulate on the tibetan plateau. Curr Zool. https:\/\/doi.org\/10.1093\/cz\/zoad004","journal-title":"Curr Zool"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03146-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-025-03146-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03146-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T04:27:00Z","timestamp":1744604820000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-025-03146-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,22]]},"references-count":91,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["3146"],"URL":"https:\/\/doi.org\/10.1007\/s40314-025-03146-6","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2025,3,22]]},"assertion":[{"value":"30 August 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 November 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 February 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 March 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"All authors have no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"199"}}