{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,8]],"date-time":"2024-09-08T23:54:09Z","timestamp":1725839649329},"publisher-location":"Cham","reference-count":17,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319268408"},{"type":"electronic","value":"9783319268415"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-26841-5_11","type":"book-chapter","created":{"date-parts":[[2015,11,30]],"date-time":"2015-11-30T06:53:17Z","timestamp":1448866397000},"page":"137-149","source":"Crossref","is-referenced-by-count":1,"title":["Discrete Geodesics and Cellular Automata"],"prefix":"10.1007","author":[{"given":"Pablo","family":"Arrighi","sequence":"first","affiliation":[]},{"given":"Gilles","family":"Dowek","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,12,1]]},"reference":[{"key":"11_CR1","doi-asserted-by":"publisher","first-page":"1131","DOI":"10.1142\/S0129054112500153","volume":"23","author":"P Arrighi","year":"2012","unstructured":"Arrighi, P., Dowek, G.: The physical Church-Turing thesis and the principles of quantum theory. Int. J. Found. of Comput. Sci. 23, 1131 (2012)","journal-title":"Int. J. Found. of Comput. Sci."},{"key":"11_CR2","unstructured":"Arrighi, P., Dowek, G.: Discrete geodesics. arXiv Pre-print, with program available when downloading source (2015)"},{"key":"11_CR3","unstructured":"Arrighi, P., Facchini, S., Forets, M.: Quantum walks in curved spacetime (2015). Pre-print \n                      arXiv:1505.07023"},{"issue":"9","key":"11_CR4","doi-asserted-by":"publisher","first-page":"1803","DOI":"10.1088\/0264-9381\/10\/9\/021","volume":"10","author":"L Brewin","year":"1993","unstructured":"Brewin, L.: Particle paths in a schwarzschild spacetime via the regge calculus. Class. Quantum Gravity 10(9), 1803 (1993)","journal-title":"Class. Quantum Gravity"},{"issue":"3","key":"11_CR5","doi-asserted-by":"publisher","first-page":"30008","DOI":"10.1209\/0295-5075\/84\/30008","volume":"84","author":"F Cianfrani","year":"2008","unstructured":"Cianfrani, F., Montani, G.: Dirac equations in curved space-time vs. papapetrou spinning particles. EPL (Europhysics Letters) 84(3), 30008 (2008)","journal-title":"EPL (Europhysics Letters)"},{"issue":"4","key":"11_CR6","doi-asserted-by":"publisher","first-page":"042301","DOI":"10.1103\/PhysRevA.88.042301","volume":"88","author":"G Molfetta Di","year":"2013","unstructured":"Di Molfetta, G., Brachet, M., Debbasch, F.: Quantum walks as massless dirac fermions in curved space-time. Phys. Rev. A 88(4), 042301 (2013)","journal-title":"Phys. Rev. A"},{"key":"11_CR7","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1016\/j.physa.2013.11.036","volume":"397","author":"G Molfetta Di","year":"2014","unstructured":"Di Molfetta, G., Brachet, M., Debbasch, F.: Quantum walks in artificial electric and gravitational fields. Phys. A: Stat. Mech. Appl. 397, 157\u2013168 (2014)","journal-title":"Phys. A: Stat. Mech. Appl."},{"key":"11_CR8","volume-title":"Introducing Einstein\u2019s Relatvity","author":"R d\u2019Inverno","year":"1899","unstructured":"d\u2019Inverno, R.: Introducing Einstein\u2019s Relatvity. Oxford University Press, USA (1899)"},{"key":"11_CR9","volume-title":"The Kleene Symposium","author":"R Gandy","year":"1980","unstructured":"Gandy, R.: Church\u2019s thesis and principles for mechanisms. In: Barwise, J., Keisler, H.J., Kunen, K. (eds.) The Kleene Symposium. North-Holland Publishing Company, Amsterdam (1980)"},{"key":"11_CR10","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1007\/978-3-642-22092-0_38","volume-title":"Information Processing in Medical Imaging","author":"M Lorenzi","year":"2011","unstructured":"Lorenzi, M., Ayache, N., Pennec, X.: Schilds ladder for the parallel transport of deformations in time series of images. In: Sz\u00e9kely, G., Hahn, H.K. (eds.) Information Processing in Medical Imaging, pp. 463\u2013474. Springer, Heidelberg (2011)"},{"key":"11_CR11","first-page":"357","volume":"10","author":"JE Marsden","year":"2001","unstructured":"Marsden, J.E., West, M.: Discrete mechanics and variational integrators. Acta Numer. 2001 10, 357\u2013514 (2001)","journal-title":"Acta Numer. 2001"},{"issue":"5","key":"11_CR12","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1016\/j.cag.2005.08.003","volume":"29","author":"D Mart\u00ednez","year":"2005","unstructured":"Mart\u00ednez, D., Velho, L., Carvalho, P.C.: Computing geodesics on triangular meshes. Comput. Graph. 29(5), 667\u2013675 (2005)","journal-title":"Comput. Graph."},{"issue":"4","key":"11_CR13","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1137\/0216045","volume":"16","author":"JSB Mitchell","year":"1987","unstructured":"Mitchell, J.S.B., Mount, D.M., Papadimitriou, C.H.: The discrete geodesic problem. SIAM J. Comput. 16(4), 647\u2013668 (1987)","journal-title":"SIAM J. Comput."},{"issue":"3\u20134","key":"11_CR14","first-page":"197","volume":"5","author":"G Peyr\u00e9","year":"2010","unstructured":"Peyr\u00e9, G., P\u00e9chaud, M., Keriven, R., Cohen, L.D.: Geodesic methods in computer vision and graphics. Found. Trends Comput. Graph. Vis. 5(3\u20134), 197\u2013397 (2010)","journal-title":"Found. Trends Comput. Graph. Vis."},{"key":"11_CR15","doi-asserted-by":"crossref","unstructured":"Polthier, K., Schmies, M.: Straightest geodesics on polyhedral surfaces. In: Discrete Differential Geometry: An Applied Introduction, SIGGRAPH 2006, p. 30 (2006)","DOI":"10.1145\/1185657.1185664"},{"issue":"24","key":"11_CR16","doi-asserted-by":"publisher","first-page":"245005","DOI":"10.1088\/0264-9381\/29\/24\/245005","volume":"29","author":"FH Vincent","year":"2012","unstructured":"Vincent, F.H., Gourgoulhon, E., Novak, J.: 3+1 geodesic equation and images in numerical spacetimes. Class. Quant. Gravity 29(24), 245005 (2012)","journal-title":"Class. Quant. Gravity"},{"issue":"4","key":"11_CR17","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1007\/BF01025469","volume":"13","author":"RM Williams","year":"1981","unstructured":"Williams, R.M., Ellis, G.F.R.: Regge calculus and observations. i. formalism and applications to radial motion and circular orbits. Gen. Relativ. Gravit. 13(4), 361\u2013395 (1981)","journal-title":"Gen. Relativ. Gravit."}],"container-title":["Lecture Notes in Computer Science","Theory and Practice of Natural Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-26841-5_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T19:01:06Z","timestamp":1559329266000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-26841-5_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319268408","9783319268415"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-26841-5_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2015]]}}}