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/

Zendy Plus

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

Zendy Tools

Zendy Open

We consider a space of sparse Boolean matrices of size $n \times n$, whichhave finite co-rank over $GF(2)$ with high probability. In particular, theprobability such a matrix has full rank, and is thus invertible, is a positiveconstant with value about $0.2574$ for large $n$.  The matrices arise as the vertex-edge incidence matrix of 1-out 3-uniformhypergraphs The result that the null space is finite, can be contrasted withresults for the usual models of sparse Boolean matrices, based on thevertex-edge incidence matrix of random $k$-uniform hypergraphs. For this lattermodel, the expected co-rank is linear in the number of vertices $n$,\cite{ACO}, \cite{CFP}.  For fields of higher order, the co-rank is typically Poisson distributed.

Rank of the vertex-edge incidence matrix of $r$-out hypergraphs