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

Reaction networks are commonly used within the mathematical biology andmathematical chemistry communities to model the dynamics of interactingspecies. These models differ from the typical graphs found in random graphtheory since their vertices are constructed from elementary building blocks,i.e., the species. In this paper, we consider these networks in an Erd\Hos-R\'enyi framework and, under suitable assumptions, derive a thresholdfunction for the network to have a deficiency of zero, which is a property ofgreat interest in the reaction network community. Specifically, if the numberof species is denoted by $n$ and if the edge probability is denote by $p_n$,then we prove that the probability of a random binary network being deficiencyzero converges to 1 if $\frac{p_n}{r(n)}\to 0$, as $n \to \infty$, andconverges to 0 if $\frac{p_n}{r(n)}\to \infty$, as $n \to \infty$, where$r(n)=\frac{1}{n^3}$.

Prevalence of deficiency zero reaction networks in an Erdos-Renyi framework