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

Given integers $n$ and $m=\lfloor\beta n \rfloor$ and a probability measure $Q$ on $\{0, 1,\dots, m\}$, consider the random intersection graph on the vertex set $[n]=\{1,2,\dots, n\}$ where $i,j\in [n]$ are declared adjacent whenever $S(i)\cap S(j)\neq\emptyset$. Here $S(1),\dots, S(n)$ denote the iid random subsets of $[m]$ with the distribution $\bf{P}(S(i)=A)={{m}\choose{|A|}}^{-1}Q(|A|)$, $A\subset [m]$. For sparse random intersection graphs, we establish a first-order asymptotic as $n\to \infty$ for the order of the largest connected component $N_1=n(1-Q(0))\rho+o_P(n)$. Here $\rho$ is the average of nonextinction probabilities of a related multitype Poisson branching process.

The Largest Component in an Inhomogeneous Random Intersection Graph with Clustering