English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A general, variational approach to derive low-order reduced systems ispresented. The approach is based on the concept of optimal parameterizingmanifold (OPM) that substitutes the more classical notions of invariant or slowmanifold when breakdown of "slaving" occurs, i.e. when the unresolved variablescannot be expressed as an exact functional of the resolved ones anymore. TheOPM provides, within a given class of parameterizations of the unresolvedvariables, the manifold that averages out optimally these variables asconditioned on the resolved ones.  The class of parameterizations retained here is that of continuousdeformations of parameterizations rigorously valid near the onset ofinstability. These deformations are produced through integration of auxiliarybackward-forward (BF) systems built from the model's equations and lead toanalytic formulas for parameterizations. In this modus operandi, the backwardintegration time is the key parameter to select per scale/variable toparameterize in order to derive the relevant parameterizations which are doomedto be no longer exact, away from instability onset, due to breakdown of slavingtypically encountered e.g. for chaotic regimes. The selection criterion is thenmade through data-informed minimization of a least-square parameterizationdefect. It is thus shown, through optimization of the backward integration timeper scale/variable to parameterize, that skilled OPM reduced systems can bederived for predicting with accuracy higher-order critical transitions orcatastrophic tipping phenomena, while training our parameterization formulasfor regimes prior to these transitions take place.

Optimal Parameterizing Manifolds for Anticipating Tipping Points and Higher-order Critical Transitions