{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T17:34:51Z","timestamp":1770140091247,"version":"3.49.0"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"32","license":[{"start":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T00:00:00Z","timestamp":1643760000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T00:00:00Z","timestamp":1643760000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100013077","name":"National Science and Technology Planning Project","doi-asserted-by":"publisher","award":["61773271"],"award-info":[{"award-number":["61773271"]}],"id":[{"id":"10.13039\/501100013077","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key scientific technological innovation research project by Ministry of Education"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2023,11]]},"DOI":"10.1007\/s00521-021-06039-x","type":"journal-article","created":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T02:02:31Z","timestamp":1643767351000},"page":"23465-23476","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Grid cell modeling with mapping representation of self-motion for path integration"],"prefix":"10.1007","volume":"35","author":[{"given":"Jiru","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Yan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huajin","family":"Tang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,2,2]]},"reference":[{"issue":"7705","key":"6039_CR1","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1038\/s41586-018-0102-6","volume":"557","author":"A Banino","year":"2018","unstructured":"Banino A, Barry C, Uria B, Blundell C, Lillicrap T, Mirowski P, Pritzel A et al (2018) Vector-based navigation using grid-like representations in artificial agents. Nature 557(7705):429\u2013433","journal-title":"Nature"},{"issue":"8","key":"6039_CR2","doi-asserted-by":"publisher","first-page":"R330","DOI":"10.1016\/j.cub.2014.02.049","volume":"24","author":"C Barry","year":"2014","unstructured":"Barry C, Burgess N (2014) Neural mechanisms of self-location. Curr Biol 24(8):R330-339","journal-title":"Curr Biol"},{"issue":"2","key":"6039_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1371\/journal.pcbi.1000291","volume":"5","author":"Y Burak","year":"2009","unstructured":"Burak Y, Fiete IR (2009) Accurate path integration in continuous attractor network models of grid cells. PLOS Comput Biol 5(2):1\u201316","journal-title":"PLOS Comput Biol"},{"issue":"9","key":"6039_CR4","doi-asserted-by":"publisher","first-page":"801","DOI":"10.1002\/hipo.20327","volume":"17","author":"N Burgess","year":"2010","unstructured":"Burgess N, Barry C, O\u2019Keefe J (2010) An oscillatory interference model of grid cell firing. Hippocampus 17(9):801\u2013812","journal-title":"Hippocampus"},{"issue":"14","key":"6039_CR5","doi-asserted-by":"publisher","first-page":"5065","DOI":"10.1523\/JNEUROSCI.4017-13.2014","volume":"34","author":"D Bush","year":"2014","unstructured":"Bush D, Burgess N (2014) A hybrid oscillatory interference\/continuous attractor network model of grid cell firing. J Neurosci 34(14):5065\u20135079","journal-title":"J Neurosci"},{"key":"6039_CR6","unstructured":"Cueva CJ, Wei XX (2018) Emergence of grid-like representations by training recurrent neural networks to perform spatial localization. In: International conference on learning representations"},{"issue":"3","key":"6039_CR7","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1016\/j.neuron.2015.07.006","volume":"87","author":"B Daniel","year":"2015","unstructured":"Daniel B, Caswell B, Daniel M, Neil B (2015) Using grid cells for navigation. Neuron 87(3):507\u2013520","journal-title":"Neuron"},{"issue":"23","key":"6039_CR8","doi-asserted-by":"publisher","first-page":"7504","DOI":"10.1523\/JNEUROSCI.6048-08.2009","volume":"29","author":"L de Almeida","year":"2009","unstructured":"de Almeida L, Idiart M, Lisman JE (2009) The input-output transformation of the hippocampal granule cells: from grid cells to place fields. J Neurosci 29(23):7504\u20137512","journal-title":"J Neurosci"},{"key":"6039_CR9","doi-asserted-by":"crossref","unstructured":"Federico S, Alessandro T (2015) The self-organization of grid cells in 3d. eLife 4","DOI":"10.7554\/eLife.05913"},{"issue":"27","key":"6039_CR10","doi-asserted-by":"publisher","first-page":"6858","DOI":"10.1523\/JNEUROSCI.5684-07.2008","volume":"28","author":"IR Fiete","year":"2008","unstructured":"Fiete IR, Burak Y, Brookings T (2008) What grid cells convey about rat location. J Neurosci 28(27):6858\u20136871","journal-title":"J Neurosci"},{"issue":"16","key":"6039_CR11","doi-asserted-by":"publisher","first-page":"4266","DOI":"10.1523\/JNEUROSCI.4353-05.2006","volume":"26","author":"MC Fuhs","year":"2006","unstructured":"Fuhs MC, Touretzky DS (2006) A spin glass model of path integration in rat medial entorhinal cortex. J Neurosci 26(16):4266\u20134276","journal-title":"J Neurosci"},{"issue":"5688","key":"6039_CR12","doi-asserted-by":"publisher","first-page":"1258","DOI":"10.1126\/science.1099901","volume":"305","author":"M Fyhn","year":"2004","unstructured":"Fyhn M, Molden S, Witter MP, Moser EI, Moser MB (2004) Spatial representation in the entorhinal cortex. Science 305(5688):1258\u20131264","journal-title":"Science"},{"key":"6039_CR13","unstructured":"Gao R, Xie J, Zhu SC, Wu YN (2019) Learning grid cells as vector representation of self-position coupled with matrix representation of self-motion. In: International conference on learning representations, https:\/\/openreview.net\/forum?id=Syx0Mh05YQ"},{"issue":"1","key":"6039_CR14","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1038\/s41593-017-0039-3","volume":"21","author":"M Gil","year":"2018","unstructured":"Gil M, Ancau M, Schlesiger MI, Neitz A, Allen K, De Marco RJ, Monyer H (2018) Impaired path integration in mice with disrupted grid cell firing. Nat Neurosci 21(1):81\u201391. https:\/\/doi.org\/10.1038\/s41593-017-0039-3","journal-title":"Nat Neurosci"},{"issue":"3","key":"6039_CR15","doi-asserted-by":"publisher","first-page":"736","DOI":"10.1016\/j.cell.2018.08.066","volume":"175","author":"Y Gu","year":"2018","unstructured":"Gu Y, Lewallen S, Kinkhabwala AA, Domnisoru C, Yoon K, Gauthier JL, Fiete IR, Tank DW (2018) A map-like micro-organization of grid cells in the medial entorhinal cortex. Cell 175(3):736-750.e30","journal-title":"Cell"},{"issue":"4","key":"6039_CR16","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1142\/s0129065707001093","volume":"17","author":"A Guanella","year":"2007","unstructured":"Guanella A, Kiper D, Verschure P (2007) A model of grid cells based on a twisted torus topology. Int J Neural Syst 17(4):231\u2013240. https:\/\/doi.org\/10.1142\/s0129065707001093","journal-title":"Int J Neural Syst"},{"key":"6039_CR17","doi-asserted-by":"publisher","first-page":"801","DOI":"10.1038\/nature03721","volume":"436","author":"T Hafting","year":"2005","unstructured":"Hafting T, Fyhn M, Molden S, Moser MB, Moser EI (2005) Microstructure of a spatial map in the entorhinal cortex. Nature 436:801\u2013806","journal-title":"Nature"},{"issue":"17","key":"6039_CR18","doi-asserted-by":"publisher","first-page":"R1043","DOI":"10.1016\/j.cub.2018.04.058","volume":"28","author":"S Heinze","year":"2018","unstructured":"Heinze S, Narendra A, Cheung A (2018) Principles of insect path integration. Curr Biol 28(17):R1043-1058. https:\/\/doi.org\/10.1016\/j.cub.2018.04.058","journal-title":"Curr Biol"},{"issue":"9","key":"6039_CR19","doi-asserted-by":"publisher","first-page":"1188","DOI":"10.1038\/nn.3466","volume":"16","author":"J Jacobs","year":"2013","unstructured":"Jacobs J, Weidemann CT, Miller JF, Solway A et al (2013) Direct recordings of grid-like neuronal activity in human spatial navigation. Nat Neurosci 16(9):1188","journal-title":"Nat Neurosci"},{"key":"6039_CR20","unstructured":"Mai G, Janowicz K, Yan B, Zhu R, Cai L, Lao N (2020) Multi-scale representation learning for spatial feature distributions using grid cells. In: International conference on learning representations, https:\/\/openreview.net\/forum?id=rJljdh4KDH"},{"issue":"9","key":"6039_CR21","doi-asserted-by":"publisher","first-page":"2280","DOI":"10.1162\/neco_a_00319","volume":"24","author":"A Mathis","year":"2012","unstructured":"Mathis A, Herz AVM, Stemmler M (2012) Optimal population codes for space: grid cells outperform place cells. Neural Comput 24(9):2280\u20132317. https:\/\/doi.org\/10.1162\/neco_a_00319","journal-title":"Neural Comput"},{"key":"6039_CR22","doi-asserted-by":"publisher","first-page":"e05979","DOI":"10.7554\/eLife.05979","volume":"4","author":"A Mathis","year":"2015","unstructured":"Mathis A, Stemmler MB, Herz AV (2015) Probable nature of higher-dimensional symmetries underlying mammalian grid-cell activity patterns. eLife 4:e05979","journal-title":"eLife"},{"key":"6039_CR23","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1038\/nrn1932","volume":"7","author":"BL McNaughton","year":"2006","unstructured":"McNaughton BL, Battaglia FP, Jensen O, Moser EI, Moser MB (2006) Path integration and the neural basis of the cognitive map. Nat Rev Neurosci 7:663\u2013678","journal-title":"Nat Rev Neurosci"},{"key":"6039_CR24","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1016\/j.neuroimage.2018.11.041","volume":"186","author":"K Misun","year":"2019","unstructured":"Misun K, Maguire EA (2019) Can we study 3d grid codes non-invasively in the human brain? methodological considerations and fmri findings. NeuroImage 186:667\u2013678","journal-title":"NeuroImage"},{"key":"6039_CR25","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1146\/annurev.neuro.31.061307.090723","volume":"31","author":"EI Moser","year":"2008","unstructured":"Moser EI, Kropff E, Moser MB (2008) Place cells, grid cells, and the brain\u2019s spatial representation system. Ann Rev Neurosci 31:69\u201389","journal-title":"Ann Rev Neurosci"},{"issue":"2","key":"6039_CR26","doi-asserted-by":"publisher","first-page":"a021808","DOI":"10.1101\/cshperspect.a021808","volume":"7","author":"MB Moser","year":"2015","unstructured":"Moser MB, Rowland DC, Moser EI (2015) Place cells, grid cells, and memory. Cold Spring Harb Perspect Biol 7(2):a021808","journal-title":"Cold Spring Harb Perspect Biol"},{"issue":"9","key":"6039_CR27","doi-asserted-by":"publisher","first-page":"170954","DOI":"10.1098\/rsos.170954","volume":"4","author":"H Murakami","year":"2017","unstructured":"Murakami H, Tomaru T, Gunji YP (2017) Interaction between path integration and visual orientation during the homing run of fiddler crabs. R Soc Open Sci 4(9):170954. https:\/\/doi.org\/10.1098\/rsos.170954","journal-title":"R Soc Open Sci"},{"key":"6039_CR28","unstructured":"Sorscher B, Mel G, Ganguli S, Ocko S (2019) A unified theory for the origin of grid cells through the lens of pattern formation. In: Advances in neural information processing systems, vol\u00a032, pp 10003\u201310013, https:\/\/proceedings.neurips.cc\/paper\/2019\/file\/6e7d5d259be7bf56ed79029c4e621f44-Paper.pdf"},{"issue":"7427","key":"6039_CR29","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1038\/nature11649","volume":"492","author":"H Stensola","year":"2012","unstructured":"Stensola H, Stensola T, Solstad T, Fraland K, Moser MB, Moser EI (2012) The entorhinal grid map is discretized. Nature 492(7427):72\u201378","journal-title":"Nature"},{"issue":"5","key":"6039_CR30","doi-asserted-by":"publisher","first-page":"1313","DOI":"10.1016\/j.celrep.2018.01.005","volume":"22","author":"SA Tennant","year":"2018","unstructured":"Tennant SA, Fischer L, Garden DL, Gerlei KZ, Martinez-Gonzalez C, McClure C, Wood ER, Nolan MF (2018) Stellate cells in the medial entorhinal cortex are required for spatial learning. Cell Rep 22(5):1313\u20131324. https:\/\/doi.org\/10.1016\/j.celrep.2018.01.005","journal-title":"Cell Rep"},{"key":"6039_CR31","doi-asserted-by":"publisher","first-page":"e08362","DOI":"10.7554\/eLife.08362","volume":"4","author":"XX Wei","year":"2015","unstructured":"Wei XX, Prentice J, Balasubramanian V (2015) A principle of economy predicts the functional architecture of grid cells. eLife 4:e08362. https:\/\/doi.org\/10.7554\/eLife.08362","journal-title":"eLife"},{"issue":"12","key":"6039_CR32","doi-asserted-by":"publisher","first-page":"1283","DOI":"10.1002\/hipo.20519","volume":"18","author":"PE Welinder","year":"2010","unstructured":"Welinder PE, Burak Y, Fiete IR (2010) Grid cells: the position code, neural network models of activity, and the problem of learning. Hippocampus 18(12):1283\u20131300","journal-title":"Hippocampus"},{"key":"6039_CR33","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1038\/nature10583","volume":"479","author":"MM Yartsev","year":"2011","unstructured":"Yartsev MM, Witter MP, Ulanovsky N (2011) Grid cells without theta oscillations in the entorhinal cortex of bats. Nature 479:103\u2013107","journal-title":"Nature"},{"key":"6039_CR34","doi-asserted-by":"crossref","unstructured":"Zhang SJ, Ye J, Miao C, Tsao A, Cerniauskas I, Ledergerber D, Moser MB, Moser EI (2013) Optogenetic dissection of entorhinal-hippocampal functional connectivity. Science 340(6128)","DOI":"10.1126\/science.1232627"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-021-06039-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-021-06039-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-021-06039-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,17]],"date-time":"2023-10-17T18:15:18Z","timestamp":1697566518000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-021-06039-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,2]]},"references-count":34,"journal-issue":{"issue":"32","published-print":{"date-parts":[[2023,11]]}},"alternative-id":["6039"],"URL":"https:\/\/doi.org\/10.1007\/s00521-021-06039-x","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,2]]},"assertion":[{"value":"28 November 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 April 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 February 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}