Self-organized criticality and pattern emergence through the lens of tropical geometry

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.


Journal Article | Published | English
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Abstract
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.
Publishing Year
Date Published
2018-08-28
Journal Title
PNAS: Proceedings of the National Academy of Sciences of the United States of America
Volume
115
Issue
35
Page
E8135 - E8142
ISSN
IST-REx-ID

Cite this

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. PNAS: Proceedings of the National Academy of Sciences of the United States of America. 2018;115(35):E8135-E8142. doi:10.1073/pnas.1805847115
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. https://doi.org/10.1073/pnas.1805847115
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.” PNAS: Proceedings of the National Academy of Sciences of the United States of America 115, no. 35 (2018): E8135–42. https://doi.org/10.1073/pnas.1805847115.
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,” PNAS: Proceedings of the National Academy of Sciences of the United States of America, vol. 115, no. 35, pp. E8135–E8142, 2018.
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.
Kalinin, Nikita, et al. “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, vol. 115, no. 35, National Academy of Sciences, 2018, pp. E8135–42, doi:10.1073/pnas.1805847115.

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