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

A solution to a 3-satisfiability (3-SAT) formula can be expanded into acluster, all other solutions of which are reachable from this one through asequence of single-spin flips. Some variables in the solution cluster arefrozen to the same spin values by one of two different mechanisms: frozen-coreformation and long-range frustrations. While frozen cores are identified by alocal whitening algorithm, long-range frustrations are very difficult to trace,and they make an entropic belief-propagation (BP) algorithm fail to converge.For BP to reach a fixed point the spin values of a tiny fraction of variables(chosen according to the whitening algorithm) are externally fixed during theiteration. From the calculated entropy values, we infer that, for a largerandom 3-SAT formula with constraint density close to the satisfiabilitythreshold, the solutions obtained by the survey-propagation or the walksatalgorithm belong neither to the most dominating clusters of the formula nor tothe most abundant clusters. This work indicates that a single solution clusterof a random 3-SAT formula may have further community structures.

From one solution of a 3-satisfiability formula to a solution cluster: Frozen variables and entropy