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

Discovering the mechanism underlying the ubiquity of $"1/f^{\alpha}"$ noisehas been a long--standing problem. The wide range of systems in which thefluctuations show the implied long--time correlations suggests the existence ofsome simple and general mechanism that is independent of the details of anyspecific system. We argue here that a {\it memoryless nonlinear response}suffices to explain the observed non--trivial values of $\alpha$: a randominput noisy signal $S(t)$ with a power spectrum varying as $1/f^{\alpha'}$,when fed to an element with such a response function $R$ gives an output$R(S(t))$ that can have a power spectrum $1/f^{\alpha}$ with $\alpha <\alpha'$. As an illustrative example, we show that an input Brownian noise($\alpha'=2$) acting on a device with a sigmoidal response function $R(S)=\sgn(S)|S|^x$, with $x<1$, produces an output with $\alpha = 3/2 +x$, for $0\leq x \leq 1/2$. Our discussion is easily extended to more general types ofinput noise as well as more general response functions.

Memoryless nonlinear response: A simple mechanism for the 1/f noise