# life: early warning signals can vanish or amplify; dimensionality in complex systems.

<< Early warning signals (EWS), such as increasing variance and autocorrelation, are widely used to anticipate critical transitions associated with saddle-node bifurcations. However, real-world systems are often high-dimensional and multiscale, potentially altering the classical behavior of EWS. >>

<< Here, (AA) investigate how dimensionality, inertia, and red noise influence the detectability of EWS prior to tipping points. (They) show that when observations are not aligned with the critical direction, stable dynamics in orthogonal directions can mask EWS until very near the bifurcation. >>

<< (AA) further demonstrate that second-order dynamics with damping modify the autocorrelation structure and may either enhance or reduce signatures of critical slowing down. >> 

<< Finally, (AA) study how colored noise influences EWS. (Their) results show that the presence and strength of EWS are not universal properties of tipping systems but depend critically on system geometry and stochastic forcing, implying that the absence of detectable EWS does not necessarily rule out an approaching critical transition. >>

Susanne Ditlevsen, Peter Ditlevsen. Early Warning Signals Can Vanish or Amplify: Dimensionality in Complex Systems. arXiv: 2609.01164v1 [math.DS]. Sep 1, 2026.

https://arxiv.org/abs/2609.01164

Also: noise, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, noise, transitions, early warning signals (EWS), criticality, saddle-node bifurcations, dimensionality, inertia, red noise, colored noise, tipping points, critical slowing down, stochastic forcing.

# gst: early warning skill, extrapolation and tipping for accelerating cascades; if the upstream system crosses a tipping point, this can shorten the timescale of valid extrapolation.

AA << investigate how nonlinear behaviour (both of forcing in time and of the system itself) can affect the skill of early warning signals to predict tipping in (directionally) coupled bistable systems when using measures based on critical slowing down due to the breakdown of extrapolation. (They) quantify the skill of early warnings with a time horizon using a receiver-operator methodology for ensembles where noise realisations and parameters are varied to explore the role of extrapolation and how it can break down. >>

AA << highlight cases where this can occur in an accelerating cascade of tipping elements, where very slow forcing of a slowly evolving ``upstream'' system forces a more rapidly evolving ``downstream'' system. If the upstream system crosses a tipping point, this can shorten the timescale of valid extrapolation. >>

<< In particular, ``downstream-within-upstream'' tipping will typically have warnings only on a timescale comparable to the duration of the upstream tipping process, rather than the timescale of the original forcing. >>

Peter Ashwin, Robbin Bastiaansen, et al. Early warning skill, extrapolation and tipping for accelerating cascades.arXiv: 2506.01981v1 [nlin.CD]. May 16, 2025.

https://arxiv.org/abs/2506.01981

Also: crack, fracture, noise, track changes in noise, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, climate, early warning, tipping prediction, accelerating cascade, crossing a tipping point, multiple tipping points, fragmented tipping, criticality, noise, noise-induced tipping, crack, fracture

# gst: like a bowl of worms, but with two behavioral regimes

AA << have observed strand motion in a polymer melt that contradicts the idea of independent motion. >>️

<< According to the results of new neutron scattering experiments, polymer molecules in plastics move in ways that aren’t captured by commonly used models. >>

<< Melt a plastic, and its constituent molecules, known as polymers, wiggle around. Experts typically describe polymer motion using the so-called tube model, which imagines plastics as a tangle of polymer strands—think a bowlful of worms. The model assumes that each strand moves independently within a virtual tube.  >>️

<< Monitoring the center of mass motion of the short strands, they observed two behavior regimes. For short translational distances, the motion of the short strands slowed as they grew apart. For longer distances, when the center of mass of the strands reached a size on the order of the diameter of the virtual tube, the speed at which the short strands moved stopped slowing down and instead matched that of diffusion. (..) the motions of short strands were tied to those of neighboring strands at short distances, differing from a standard assumption of the tube model. This cooperative motion may come from interactions between the segments, beyond simple local friction. >>️️

Sophia Chen. The Weird Wiggle of Polymers. Physics 14, s56. May 4, 2021.

https://physics.aps.org/articles/v14/s56    

Zamponi M., Kruteva M., et al. Cooperative Chain Dynamics of Tracer Chains in Highly Entangled Polyethylene Melts. Phys. Rev. Lett. 126, 187801. May 4,  2021.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.187801