{"type":"journal_article","citation":{"short":"N. Kalinin, A. Guzmán Sáenz, Y. Prieto, M. Shkolnikov, V. Kalinina, E. Lupercio, PNAS: Proceedings of the National Academy of Sciences of the United States of America 115 (2018) E8135–E8142.","ista":"Kalinin N, Guzmán Sáenz A, Prieto Y, Shkolnikov M, Kalinina V, Lupercio E. 2018. Self-organized criticality and pattern emergence through the lens of tropical geometry. PNAS: Proceedings of the National Academy of Sciences of the United States of America. 115(35), E8135–E8142.","ama":"Kalinin N, Guzmán Sáenz A, Prieto Y, Shkolnikov M, Kalinina V, Lupercio E. Self-organized criticality and pattern emergence through the lens of tropical geometry. <i>PNAS: Proceedings of the National Academy of Sciences of the United States of America</i>. 2018;115(35):E8135-E8142. doi:<a href=\"https://doi.org/10.1073/pnas.1805847115\">10.1073/pnas.1805847115</a>","ieee":"N. Kalinin, A. Guzmán Sáenz, Y. Prieto, M. Shkolnikov, V. Kalinina, and E. Lupercio, “Self-organized criticality and pattern emergence through the lens of tropical geometry,” <i>PNAS: Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 115, no. 35. National Academy of Sciences, pp. E8135–E8142, 2018.","mla":"Kalinin, Nikita, et al. “Self-Organized Criticality and Pattern Emergence through the Lens of Tropical Geometry.” <i>PNAS: Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 115, no. 35, National Academy of Sciences, 2018, pp. E8135–42, doi:<a href=\"https://doi.org/10.1073/pnas.1805847115\">10.1073/pnas.1805847115</a>.","chicago":"Kalinin, Nikita, Aldo Guzmán Sáenz, Y Prieto, Mikhail Shkolnikov, V Kalinina, and Ernesto Lupercio. “Self-Organized Criticality and Pattern Emergence through the Lens of Tropical Geometry.” <i>PNAS: Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences, 2018. <a href=\"https://doi.org/10.1073/pnas.1805847115\">https://doi.org/10.1073/pnas.1805847115</a>.","apa":"Kalinin, N., Guzmán Sáenz, A., Prieto, Y., Shkolnikov, M., Kalinina, V., &#38; Lupercio, E. (2018). Self-organized criticality and pattern emergence through the lens of tropical geometry. <i>PNAS: Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.1805847115\">https://doi.org/10.1073/pnas.1805847115</a>"},"date_created":"2018-12-11T11:44:26Z","scopus_import":"1","article_processing_charge":"No","isi":1,"month":"08","date_updated":"2023-09-18T08:41:16Z","title":"Self-organized criticality and pattern emergence through the lens of tropical geometry","publication_identifier":{"issn":["00278424"]},"abstract":[{"text":"Tropical geometry, an established field in pure mathematics, is a place where string theory, mirror symmetry, computational algebra, auction theory, and so forth meet and influence one another. In this paper, we report on our discovery of a tropical model with self-organized criticality (SOC) behavior. Our model is continuous, in contrast to all known models of SOC, and is a certain scaling limit of the sandpile model, the first and archetypical model of SOC. We describe how our model is related to pattern formation and proportional growth phenomena and discuss the dichotomy between continuous and discrete models in several contexts. Our aim in this context is to present an idealized tropical toy model (cf. Turing reaction-diffusion model), requiring further investigation.","lang":"eng"}],"year":"2018","issue":"35","publisher":"National Academy of Sciences","article_type":"original","ec_funded":1,"status":"public","department":[{"_id":"TaHa"}],"oa_version":"Preprint","publication_status":"published","day":"28","publication":"PNAS: Proceedings of the National Academy of Sciences of the United States of America","date_published":"2018-08-28T00:00:00Z","project":[{"grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"external_id":{"isi":["000442861600009"],"arxiv":["1806.09153"]},"_id":"64","volume":115,"author":[{"first_name":"Nikita","full_name":"Kalinin, Nikita","last_name":"Kalinin"},{"first_name":"Aldo","last_name":"Guzmán Sáenz","full_name":"Guzmán Sáenz, Aldo"},{"first_name":"Y","full_name":"Prieto, Y","last_name":"Prieto"},{"last_name":"Shkolnikov","full_name":"Shkolnikov, Mikhail","id":"35084A62-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4310-178X","first_name":"Mikhail"},{"first_name":"V","last_name":"Kalinina","full_name":"Kalinina, V"},{"first_name":"Ernesto","full_name":"Lupercio, Ernesto","last_name":"Lupercio"}],"doi":"10.1073/pnas.1805847115","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1806.09153"}],"oa":1,"publist_id":"7990","language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":"       115","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","page":"E8135 - E8142"}