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The emergence of scale-free fires in Australia. iScience 2023; 26:106181. [PMID: 36895645 PMCID: PMC9988665 DOI: 10.1016/j.isci.2023.106181] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2022] [Revised: 11/15/2022] [Accepted: 02/07/2023] [Indexed: 02/16/2023] Open
Abstract
Between 2019 and 2020, during the country's hottest and driest year on record, Australia experienced a dramatic bushfire season, with catastrophic ecological and environmental consequences. Several studies highlighted how such abrupt changes in fire regimes may have been in large part a consequence of climate change and other anthropogenic transformations. Here, we analyze the monthly evolution of the burned area in Australia from 2000 to 2020, obtained via satellite imaging through the MODIS platform. We find that the 2019-2020 peak is associated with signatures typically found near critical points. We introduce a modeling framework based on forest-fire models to study the properties of these emergent fire outbreaks, showing that the behavior observed during the 2019-2020 fire season matches the one of a percolation transition, where system-size outbreaks appear. Our model also highlights the existence of an absorbing phase transition that might be eventually crossed, after which the vegetation cannot recover.
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Agrawal V, Chakraborty S, Knöpfel T, Shew WL. Scale-Change Symmetry in the Rules Governing Neural Systems. iScience 2019; 12:121-131. [PMID: 30682624 PMCID: PMC6352707 DOI: 10.1016/j.isci.2019.01.009] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2018] [Revised: 12/05/2018] [Accepted: 01/04/2019] [Indexed: 11/16/2022] Open
Abstract
Similar universal phenomena can emerge in different complex systems when those systems share a common symmetry in their governing laws. In physical systems operating near a critical phase transition, the governing physical laws obey a fractal symmetry; they are the same whether considered at fine or coarse scales. This scale-change symmetry is responsible for universal critical phenomena found across diverse systems. Experiments suggest that the cerebral cortex can also operate near a critical phase transition. Thus we hypothesize that the laws governing cortical dynamics may obey scale-change symmetry. Here we develop a practical approach to test this hypothesis. We confirm, using two different computational models, that neural dynamical laws exhibit scale-change symmetry near a dynamical phase transition. Moreover, we show that as a mouse awakens from anesthesia, scale-change symmetry emerges. Scale-change symmetry of the rules governing cortical dynamics may explain observations of similar critical phenomena across diverse neural systems.
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Affiliation(s)
- Vidit Agrawal
- Department of Physics, University of Arkansas, Fayetteville, AR 72701, USA
| | - Srimoy Chakraborty
- Department of Physics, University of Arkansas, Fayetteville, AR 72701, USA
| | - Thomas Knöpfel
- Laboratory for Neuronal Circuit Dynamics, Faculty of Medicine Imperial College London, London W12 0NN, UK; Centre for Neurotechnology, Institute of Biomedical Engineering, Imperial College London, London SW7 2AZ, UK
| | - Woodrow L Shew
- Department of Physics, University of Arkansas, Fayetteville, AR 72701, USA.
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Milne BT, Gupta VK, Restrepo C. A scale invariant coupling of plants, water, energy, and terrain. ECOSCIENCE 2016. [DOI: 10.1080/11956860.2002.11682705] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Lansdell B, Ford K, Kutz JN. A reaction-diffusion model of cholinergic retinal waves. PLoS Comput Biol 2014; 10:e1003953. [PMID: 25474327 PMCID: PMC4256014 DOI: 10.1371/journal.pcbi.1003953] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2014] [Accepted: 10/01/2014] [Indexed: 01/21/2023] Open
Abstract
Prior to receiving visual stimuli, spontaneous, correlated activity in the retina, called retinal waves, drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then propagates this activity laterally. Their inter-wave interval and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In addition to simulation, we are thus able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how parameters such as the spontaneous activation rate and sAHP refractory period contribute to critical wave size variability.
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Affiliation(s)
- Benjamin Lansdell
- Department of Applied Mathematics, University of Washington, Seattle, Washington, United States of America
| | - Kevin Ford
- Department of Biochemistry and Biophysics, University of California San Francisco, San Francisco, California, United States of America
| | - J. Nathan Kutz
- Department of Applied Mathematics, University of Washington, Seattle, Washington, United States of America
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Power laws reveal phase transitions in landscape controls of fire regimes. Nat Commun 2012; 3:726. [DOI: 10.1038/ncomms1731] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2011] [Accepted: 02/06/2012] [Indexed: 11/08/2022] Open
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Nagy V, Ott E. Dynamics of the one-dimensional self-organized forest-fire model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:021113. [PMID: 18850792 DOI: 10.1103/physreve.78.021113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2008] [Indexed: 05/26/2023]
Abstract
We examine the dynamical evolution of the one-dimensional self-organized forest-fire model (FFM), when the system is far from its statistically steady state. In particular, we investigate situations in which conditions change on a time scale that is faster than, or of the order of the typical time needed for relaxation. An analytical approach is introduced based on a hierarchy of first-order nonlinear differential equations. This hierarchy can be closed at any level, yielding a sequence of successively more accurate descriptions of the dynamics. It is found that our approximate description can yield a faithful description of the FFM dynamics, even when a low order truncation is used. Employing both full simulations of the FFM and our approximate descriptions, we examine the time scales and cluster-size-dependent dynamics of relaxation to the statistical equilibrium. As an example of changing external conditions in a natural forest, the effects of a time-dependent lightning frequency are considered.
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Affiliation(s)
- Viktor Nagy
- University of Maryland, College Park, Maryland 20742, USA
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Freeman MP, Watkins NW, Riley DJ. Power law distributions of burst duration and interburst interval in the solar wind: turbulence or dissipative self-organized criticality? PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:8794-8797. [PMID: 11138184 DOI: 10.1103/physreve.62.8794] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2000] [Revised: 06/27/2000] [Indexed: 05/23/2023]
Abstract
We calculate the probability density functions P of burst energy e, duration T, and interburst interval tau for a known turbulent system in nature. Bursts in the Earth-Sun component of the Poynting flux at 1 AU in the solar wind were measured using the MFI and SWE experiments on the NASA WIND spacecraft. We find P(e) and P(T) to be power laws, consistent with self-organized criticality (SOC). We find also a power-law form for P(tau) that distinguishes this turbulent cascade from the exponential P(tau) of ideal SOC, but not from some other SOC-like sandpile models. We discuss the implications for the relation between SOC and turbulence.
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Affiliation(s)
- MP Freeman
- British Antarctic Survey, High Cross, Madingley Road, Cambridge, CB3 0ET, United Kingdom
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Moreno Y, Gómez JB, Pacheco AF. Modified renormalization strategy for sandpile models. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:7565-8. [PMID: 11970710 DOI: 10.1103/physreve.60.7565] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/1999] [Indexed: 11/07/2022]
Abstract
Following the renormalization-group scheme recently developed by Pietronero et al. [Phys. Rev. Lett. 72, 1690 (1994)] we introduce a simplifying strategy for the renormalization of the relaxation dynamics of sandpile models. In our scheme, five subcells at a generic scale b form the renormalized cell at the next larger scale. Now the fixed point has a unique nonzero dynamical component that allows for a great simplification in the computation of the critical exponent z. The values obtained are in good agreement with both numerical and theoretical results previously reported.
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Affiliation(s)
- Y Moreno
- Departamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain
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Ivashkevich EV, Povolotsky AM, Vespignani A, Zapperi S. Dynamical real space renormalization group applied to sandpile models. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:1239-51. [PMID: 11969882 DOI: 10.1103/physreve.60.1239] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/1997] [Indexed: 04/18/2023]
Abstract
A general framework for the renormalization group analysis of self-organized critical sandpile models is formulated. The usual real space renormalization scheme for lattice models when applied to nonequilibrium dynamical models must be supplemented by feedback relations coming from the stationarity conditions. On the basis of these ideas the dynamically driven renormalization group is applied to describe the boundary and bulk critical behavior of sandpile models. A detailed description of the branching nature of sandpile avalanches is given in terms of the generating functions of the underlying branching process.
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Affiliation(s)
- E V Ivashkevich
- Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna 141980, Russia
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Abstract
We show how ideas and models which were originally introduced to gain an understanding of critical phenomena can be used to interpret the dynamics of epidemics of communicable disease in real populations. Specifically, we present an analysis of the dynamics of disease outbreaks for three common communicable infections from a small isolated island population. The strongly fluctuating nature of the temporal incidence of disease is captured by the model, and comparisons between exponents calculated from the data and from simulations are made. A forest-fire model with sparks is used to classify the observed scaling dynamics of the epidemics and provides a unified picture of the epidemiology which conventional epidemiological analysis is unable to reproduce. This study suggests that power-law scaling can emerge in natural systems when they are driven on widely separated time-scales, in accordance with recent analytic renormalization group calculations.
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Affiliation(s)
- C J Rhodes
- Wellcome Trust Centre for the Epidemiology of Infectious Disease, Department of Zoology, University of Oxford, UK.
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Rhodes CJ, Anderson RM. A scaling analysis of measles epidemics in a small population. Philos Trans R Soc Lond B Biol Sci 1996; 351:1679-88. [PMID: 9004320 DOI: 10.1098/rstb.1996.0150] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
We present a detailed analysis of the pattern of measles outbreaks in the small isolated community of the Faroe Islands. Measles outbreaks in this population are characterized by frequent fade-out of infection resulting in long intervals when the disease is absent from the islands. Using an analysis of the distribution of epidemic sizes and epidemic durations we propose that the dynamical structure observed in the measles case returns reflects the existence of an underlying scaling mechanism. Consequently the dynamics are not as purely stochastic as is usually thought for epidemiological systems of this sort. We use a lattice-based epidemic model to provide a theoretical estimate of the scaling exponents and show that a conventional compartmental SEIR model is unable to reproduce this result. The methods discussed in this paper are general and represent a novel way to consider the dynamics of any other communicable disease where there is frequent fade-out in the case returns.
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Affiliation(s)
- C J Rhodes
- Department of Zoology, University of Oxford, U.K
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Vespignani A, Zapperi S, Loreto V. Renormalization of Nonequilibrium Systems with Critical Stationary States. PHYSICAL REVIEW LETTERS 1996; 77:4560-4563. [PMID: 10062569 DOI: 10.1103/physrevlett.77.4560] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Zapperi S, Stanley HE. Self-organized branching processes: Avalanche models with dissipation. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:2483-2488. [PMID: 9965358 DOI: 10.1103/physreve.54.2483] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Bauer W, Pratt S. Word processors with line wrap: Cascading, self-organized criticality, random walks, diffusion, and predictability. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:R1009-R1012. [PMID: 9965310 DOI: 10.1103/physreve.54.r1009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Kutnjak-Urbanc B, Zapperi S, Milosevic S, Stanley HE. Sandpile model on the Sierpinski gasket fractal. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:272-277. [PMID: 9965069 DOI: 10.1103/physreve.54.272] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Ivashkevich EV. Critical behavior of the sandpile model as a self-organized branching process. PHYSICAL REVIEW LETTERS 1996; 76:3368-3371. [PMID: 10060949 DOI: 10.1103/physrevlett.76.3368] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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