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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We define an activity dependent branching ratio that allows comparison ofdifferent time series $X_{t}$. The branching ratio $b_x$ is defined as $b_x=E[\xi_x/x]$. The random variable $\xi_x$ is the value of the next signal giventhat the previous one is equal to $x$, so $\xi_x=\{X_{t+1}|X_t=x\}$. If$b_x>1$, the process is on average supercritical when the signal is equal to$x$, while if $b_x<1$, it is subcritical. For stock prices we find $b_x=1$within statistical uncertainty, for all $x$, consistent with an ``efficientmarket hypothesis''. For stock volumes, solar X-ray flux intensities, and theBak-Tang-Wiesenfeld (BTW) sandpile model, $b_x$ is supercritical for smallvalues of activity and subcritical for the largest ones, indicating a tendencyto return to a typical value. For stock volumes this tendency has anapproximate power law behavior. For solar X-ray flux and the BTW model, thereis a broad regime of activity where $b_x \simeq 1$, which we interpret as anindicator of critical behavior. This is true despite different underlyingprobability distributions for $X_t$, and for $\xi_x$. For the BTW model thedistribution of $\xi_x$ is Gaussian, for $x$ sufficiently larger than one, andits variance grows linearly with $x$. Hence, the activity in the BTW modelobeys a central limit theorem when sampling over past histories. The broadregion of activity where $b_x$ is close to one disappears once bulk dissipationis introduced in the BTW model -- supporting our hypothesis that it is anindicator of criticality.

Activity Dependent Branching Ratios in Stocks, Solar X-ray Flux, and the Bak-Tang-Wiesenfeld Sandpile Model