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 consider Boolean functions f:{-1,1}^n->{-1,1} that are close to a sum ofindependent functions on mutually exclusive subsets of the variables. We provethat any such function is close to just a single function on a single subset.  We also consider Boolean functions f:R^n->{-1,1} that are close, with respectto any product distribution over R^n, to a sum of their variables. We provethat any such function is close to one of the variables.  Both our results are independent of the number of variables, but depend onthe variance of f. I.e., if f is \epsilon*Var(f)-close to a sum of independentfunctions or random variables, then it is O(\epsilon)-close to one of theindependent functions or random variables, respectively. We prove that thisdependence on Var(f) is tight.  Our results are a generalization of the Friedgut-Kalai-Naor Theorem [FKN'02],which holds for functions f:{-1,1}^n->{-1,1} that are close to a linearcombination of uniformly distributed Boolean variables.

Boolean functions whose Fourier transform is concentrated on pairwise disjoint subsets of the input