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

We generalize the belief-propagation algorithm to sparse random networks witharbitrary distributions of motifs (triangles, loops, etc.). Each vertex inthese networks belongs to a given set of motifs (generalization of theconfiguration model). These networks can be treated as sparse uncorrelatedhypergraphs in which hyperedges represent motifs. Here a hypergraph is ageneralization of a graph, where a hyperedge can connect any number ofvertices. These uncorrelated hypergraphs are tree-like (hypertrees), whichcrucially simplify the problem and allow us to apply the belief-propagationalgorithm to these loopy networks with arbitrary motifs. As natural examples,we consider motifs in the form of finite loops and cliques. We apply thebelief-propagation algorithm to the ferromagnetic Ising model on the resultingrandom networks. We obtain an exact solution of this model on networks withfinite loops or cliques as motifs. We find an exact critical temperature of theferromagnetic phase transition and demonstrate that with increasing theclustering coefficient and the loop size, the critical temperature increasescompared to ordinary tree-like complex networks. Our solution also gives thebirth point of the giant connected component in these loopy networks.

Belief-propagation algorithm and the Ising model on networks with arbitrary distributions of motifs