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Self-organized criticality and pattern emergence through the lens of tropical geometry. / Kalinin, N.; Guzmán-Sáenz, A.; Prieto, Y.; Shkolnikov, M.; Kalinina, V.; Lupercio, E.

в: Proceedings of the National Academy of Sciences of the United States of America, Том 115, № 35, 01.01.2018, стр. E8135-E8142.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

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', Proceedings of the National Academy of Sciences of the United States of America, Том. 115, № 35, стр. E8135-E8142. https://doi.org/10.1073/pnas.1805847115

APA

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. Proceedings of the National Academy of Sciences of the United States of America, 115(35), E8135-E8142. https://doi.org/10.1073/pnas.1805847115

Vancouver

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. Proceedings of the National Academy of Sciences of the United States of America. 2018 Янв. 1;115(35):E8135-E8142. https://doi.org/10.1073/pnas.1805847115

Author

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. в: Proceedings of the National Academy of Sciences of the United States of America. 2018 ; Том 115, № 35. стр. E8135-E8142.

BibTeX

@article{7276be2468cf4f1b87e84f01807a27b4,
title = "Self-organized criticality and pattern emergence through the lens of tropical geometry",
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.",
keywords = "Pattern formation, Power laws, Proportional growth, Self-organized criticality, Tropical geometry",
author = "N. Kalinin and A. Guzm{\'a}n-S{\'a}enz and Y. Prieto and M. Shkolnikov and V. Kalinina and E. Lupercio",
year = "2018",
month = jan,
day = "1",
doi = "10.1073/pnas.1805847115",
language = "English",
volume = "115",
pages = "E8135--E8142",
journal = "Proceedings of the National Academy of Sciences of the United States of America",
issn = "0027-8424",
publisher = "National Academy of Sciences",
number = "35",

}

RIS

TY - JOUR

T1 - Self-organized criticality and pattern emergence through the lens of tropical geometry

AU - Kalinin, N.

AU - Guzmán-Sáenz, A.

AU - Prieto, Y.

AU - Shkolnikov, M.

AU - Kalinina, V.

AU - Lupercio, E.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Pattern formation

KW - Power laws

KW - Proportional growth

KW - Self-organized criticality

KW - Tropical geometry

UR - http://www.scopus.com/inward/record.url?scp=85053640117&partnerID=8YFLogxK

U2 - 10.1073/pnas.1805847115

DO - 10.1073/pnas.1805847115

M3 - Article

C2 - 30111541

AN - SCOPUS:85053640117

VL - 115

SP - E8135-E8142

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 35

ER -

ID: 48791400