Re-thinking noise-induced tipping

2021 ◽  
Author(s):  
Julian Newman ◽  
Peter Ashwin
Keyword(s):  
Early Warning ◽  
Gaussian White Noise ◽  
External Noise ◽  
Critical Slowing Down ◽  
Critical Threshold ◽  
Geophysical Fluid Dynamics ◽  
Internal Dynamics ◽  
Slowing Down ◽  
The Earth ◽  
Joint Dynamics

<p>When modelling potential tipping elements of the earth system, one conventionally distinguishes "bifurcation-induced" and "noise-induced" tipping. The former occurs when an internal system parameter slowly crosses a critical threshold and external noise is negligible. The latter arises from forcing by noise well before a critical threshold for the internal dynamics is reached. The former comes with early warning signals, due to "critical slowing down" in the internal dynamics; but the latter occurs randomly without warning. However, these descriptions typically assume that the noise is Gaussian white noise, which arises as a limit of fast-timescale chaotic driving. We will instead consider, through a simple discrete-time prototype, finite-timescale bounded chaotic driving; this is a more suitable description of the subgrid forcing of turbulent geophysical fluid dynamics than uncorrelated noise. We will see that the phenomenon previously known as "noise-induced tipping" now corresponds to a deterministic bifurcation-induced tipping of the joint dynamics of the tipping element and the driving. Although "critical slowing down" does not occur in this bifurcation, early warning and near-exact prediction of the tipping event may still be possible. We also discuss the phenomenon of "noise-induced" prevention or delay of a tipping event, which cannot occur under conventional memoryless noise.</p>

scholarly journals Early warning signals of malaria resurgence in Kericho, Kenya

2020 ◽  
Vol 16 (3) ◽  
pp. 20190713 ◽  
Author(s):  
Mallory J. Harris ◽  
Simon I. Hay ◽  
John M. Drake
Keyword(s):  
Early Warning ◽  
Disease Transmission ◽  
Empirical Test ◽  
Disease Incidence ◽  
Critical Slowing Down ◽  
Summary Statistics ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Slowing Down ◽  
Imported Case

Campaigns to eliminate infectious diseases could be greatly aided by methods for providing early warning signals of resurgence. Theory predicts that as a disease transmission system undergoes a transition from stability at the disease-free equilibrium to sustained transmission, it will exhibit characteristic behaviours known as critical slowing down, referring to the speed at which fluctuations in the number of cases are dampened, for instance the extinction of a local transmission chain after infection from an imported case. These phenomena include increases in several summary statistics, including lag-1 autocorrelation, variance and the first difference of variance. Here, we report the first empirical test of this prediction during the resurgence of malaria in Kericho, Kenya. For 10 summary statistics, we measured the approach to criticality in a rolling window to quantify the size of effect and directions. Nine of the statistics increased as predicted and variance, the first difference of variance, autocovariance, lag-1 autocorrelation and decay time returned early warning signals of critical slowing down based on permutation tests. These results show that time series of disease incidence collected through ordinary surveillance activities may exhibit characteristic signatures prior to an outbreak, a phenomenon that may be quite general among infectious disease systems.

scholarly journals Transient indicators of tipping points in infectious diseases

2020 ◽  
Vol 17 (170) ◽  
pp. 20200094
Author(s):  
Suzanne M. O’Regan ◽  
Eamon B. O’Dea ◽  
Pejman Rohani ◽  
John M. Drake
Keyword(s):  
Infectious Diseases ◽  
Vaccine Uptake ◽  
Critical Slowing Down ◽  
Critical Threshold ◽  
Continuous Systems ◽  
Dominant Eigenvalue ◽  
Tipping Points ◽  
Critical Transition ◽  
Slowing Down ◽  
Critical Transitions

The majority of known early warning indicators of critical transitions rely on asymptotic resilience and critical slowing down. In continuous systems, critical slowing down is mathematically described by a decrease in magnitude of the dominant eigenvalue of the Jacobian matrix on the approach to a critical transition. Here, we show that measures of transient dynamics, specifically, reactivity and the maximum of the amplification envelope, also change systematically as a bifurcation is approached in an important class of models for epidemics of infectious diseases. Furthermore, we introduce indicators designed to detect trends in these measures and find that they reliably classify time series of case notifications simulated from stochastic models according to levels of vaccine uptake. Greater attention should be focused on the potential for systems to exhibit transient amplification of perturbations as a critical threshold is approached, and should be considered when searching for generic leading indicators of tipping points. Awareness of this phenomenon will enrich understanding of the dynamics of complex systems on the verge of a critical transition.

scholarly journals Anticipating critical transitions in epithelial-hybrid-mesenchymal cell-fate determination

2019 ◽  
Author(s):  
Sukanta Sarkar ◽  
Sudipta Kumar Sinha ◽  
Herbert Levine ◽  
Mohit Kumar Jolly ◽  
Partha Sharathi Dutta
Keyword(s):  
Drug Resistance ◽  
Cell Fate ◽  
Early Warning ◽  
Cancer Metastasis ◽  
Critical Slowing Down ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Slowing Down ◽  
Tumor Relapse ◽  
Critical Transitions

AbstractIn the vicinity of a tipping point, critical transitions occur when small changes in an input condition causes sudden, large and often irreversible changes in the state of a system. Many natural systems ranging from ecosystems to molecular biosystems are known to exhibit critical transitions in their response to stochastic perturbations. In diseases, an early prediction of upcoming critical transitions from a healthy to a disease state by using early warning signals is of prime interest due to potential application in forecasting disease onset. Here, we analyze cell-fate transitions between different phenotypes (epithelial, hybrid epithelial/mesenchymal (E/M) and mesenchymal states) that are implicated in cancer metastasis and chemoresistance. These transitions are mediated by a mutually inhibitory feedback loop microRNA-200/ZEB driven by the levels of transcription factor SNAIL. We find that the proximity to tipping points enabling these transitions among different phenotypes can be captured by critical slowing down based early warning signals, calculated from the trajectory of ZEB mRNA level. Further, the basin stability analysis reveals the unexpectedly large basin of attraction for a hybrid E/M phenotype. Finally, we identified mechanisms that can potentially elude the transition to a hybrid E/M phenotype. Overall, our results unravel the early warning signals that can be used to anticipate upcoming epithelial-hybrid-mesenchymal transitions. With the emerging evidence about the hybrid E/M phenotype being a key driver of metastasis, drug resistance, and tumor relapse; our results suggest ways to potentially evade these transitions, reducing the fitness of cancer cells and restricting tumor aggressiveness.Significance StatementEpithelial-hybrid-mesenchymal transitions play critical roles in cancer metastasis, drug resistance, and tumor relapse. Recent studies have proposed that cells in a hybrid epithelial/mesenchymal phenotype may be more aggressive than those on either end of the spectrum. However, no biomarker to predict upcoming transitions has been identified. Here, we show that critical slowing down based early warning signals can detect sudden transitions among epithelial, hybrid E/M, and mesenchymal phenotypes. Importantly, our results highlight how stable a hybrid E/M phenotype can be, and how can a transition to this state be avoided. Thus, our study provides valuable insights into restricting cellular plasticity en route metastasis.

scholarly journals Overlapping Time Scales Obscure Early Warning Signals for the Second COVID-19 Wave

2021 ◽  
Author(s):  
Fabian Dablander ◽  
Hans Heesterbeek ◽  
Denny Borsboom ◽  
John M. Drake
Keyword(s):  
Time Scales ◽  
Early Warning ◽  
Critical Slowing Down ◽  
Multiple Time Scales ◽  
Unexpected Finding ◽  
Multiple Time ◽  
Slowing Down ◽  
Early Warning Indicators ◽  
Second Wave ◽  
Warning Indicators

Early warning indicators based on critical slowing down have been suggested as a model-independent and low-cost tool to anticipate the (re)emergence of infectious diseases. We studied whether such indicators could reliably have anticipated the second COVID-19 wave in European countries. Contrary to theoretical predictions, we found that characteristic early warning indicators generally decreased rather than increased prior to the second wave. A model explains this unexpected finding as a result of transient dynamics and the multiple time scales of relaxation during a non-stationary epidemic. Particularly, if an epidemic that seems initially contained after a first wave does not fully settle to its new quasi-equilibrium prior to changing circumstances or conditions that force a second wave, then indicators will show a decreasing rather than an increasing trend as a result of the persistent transient trajectory of the first wave. Our simulations show that this lack of time scale separation was to be expected during the second European epidemic wave of COVID-19. Overall, our results emphasize that the theory of critical slowing down applies only when the external forcing of the system across a critical point is slow relative to the internal system dynamics.

scholarly journals Early warning of climate tipping points from critical slowing down: comparing methods to improve robustness

2012 ◽  
Vol 370 (1962) ◽  
pp. 1185-1204 ◽  
Author(s):  
T. M. Lenton ◽  
V. N. Livina ◽  
V. Dakos ◽  
E. H. van Nes ◽  
M. Scheffer
Keyword(s):  
Early Warning ◽  
Thermohaline Circulation ◽  
Critical Slowing Down ◽  
Ice Age ◽  
Fluctuation Analysis ◽  
Test Bed ◽  
Slowing Down ◽  
Last Ice Age ◽  
Atlantic Thermohaline Circulation ◽  
Early Warnings

We address whether robust early warning signals can, in principle, be provided before a climate tipping point is reached, focusing on methods that seek to detect critical slowing down as a precursor of bifurcation. As a test bed, six previously analysed datasets are reconsidered, three palaeoclimate records approaching abrupt transitions at the end of the last ice age and three models of varying complexity forced through a collapse of the Atlantic thermohaline circulation. Approaches based on examining the lag-1 autocorrelation function or on detrended fluctuation analysis are applied together and compared. The effects of aggregating the data, detrending method, sliding window length and filtering bandwidth are examined. Robust indicators of critical slowing down are found prior to the abrupt warming event at the end of the Younger Dryas, but the indicators are less clear prior to the Bølling-Allerød warming, or glacial termination in Antarctica. Early warnings of thermohaline circulation collapse can be masked by inter-annual variability driven by atmospheric dynamics. However, rapidly decaying modes can be successfully filtered out by using a long bandwidth or by aggregating data. The two methods have complementary strengths and weaknesses and we recommend applying them together to improve the robustness of early warnings.

scholarly journals Early-Warning Signals of Drought-Flood State Transition over the Dongting Lake Basin Based on the Critical Slowing Down Theory

Atmosphere ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 1082
Author(s):  
Hao Wu ◽  
Wei Hou ◽  
Dongdong Zuo ◽  
Pengcheng Yan ◽  
Yuxing Zeng
Keyword(s):  
Early Warning ◽  
State Transition ◽  
Dongting Lake ◽  
Critical Slowing Down ◽  
Lake Basin ◽  
Autocorrelation Coefficient ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Technological Support ◽  
Slowing Down

In this study, the standardized precipitation index (SPI) data in Hunan Province from 1961 to 2020 is adopted. Based on the critical slowing down theory, the moving t-test is firstly used to determine the time of drought-flood state transition in the Dongting Lake basin. Afterwards, by means of the variance and autocorrelation coefficient that characterize the phenomenon of critical slowing down, the early-warning signals indicating the drought-flood state in the Dongting Lake basin are explored. The results show that an obvious drought-to-flood (flood-to-drought) event occurred around 1993 (2003) in the Dongting Lake basin in recent 60 years. The critical slowing down phenomena of the increases in the variance and autocorrelation coefficient, which are detected 5–10 years in advance, can be considered as early-warning signals indicating the drought-flood state transition. Through the studies on the drought-flood state and related early-warning signals for the Dongting Lake basin, the reliabilities of the variance and autocorrelation coefficient-based early-warning signals for abrupt changes are demonstrated. It is expected that the wide application of this method could provide important scientific and technological support for disaster prevention and mitigation in the Dongting Lake basin, and even in the middle and lower reaches of the Yangtze River.

scholarly journals Spatial Correlation as an Early Warning Signal of Regime Shifts in a Multiplex Disease-Behaviour Network

2017 ◽  
Author(s):  
Peter C. Jentsch ◽  
Madhur Anand ◽  
Chris T. Bauch
Keyword(s):  
Spatial Correlation ◽  
Early Warning ◽  
Regime Shift ◽  
Tipping Point ◽  
Regime Shifts ◽  
Critical Slowing Down ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Network Layer ◽  
Slowing Down

AbstractEarly warning signals of sudden regime shifts are a widely studied phenomenon for their ability to quantify a system’s proximity to a tipping point to a new and contrasting dynamical regime. However, this effect has been little studied in the context of the complex interactions between disease dynamics and vaccinating behaviour. Our objective was to determine whether critical slowing down (CSD) occurs in a multiplex network that captures opinion propagation on one network layer and disease spread on a second network layer. We parameterized a network simulation model to represent a hypothetical self-limiting, acute, vaccine-preventable infection with shortlived natural immunity. We tested five different network types: random, lattice, small-world, scale-free, and an empirically derived network. For the first four network types, the model exhibits a regime shift as perceived vaccine risk moves beyond a tipping point from full vaccine acceptance and disease elimination to full vaccine refusal and disease endemicity. This regime shift is preceded by an increase in the spatial correlation in non-vaccinator opinions beginning well before the bifurcation point, indicating CSD. The early warning signals occur across a wide range of parameter values. However, the more gradual transition exhibited in the empirically-derived network underscores the need for further research before it can be determined whether trends in spatial correlation in real-world social networks represent critical slowing down. The potential upside of having this monitoring ability suggests that this is a worthwhile area for further research.

Sign in / Sign up

Export Citation Format

Share Document