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

We obtain an optimal deviation from the mean upper bound \begin{equation}D(x)\=\sup_{f\in \F}\mu\{f-\E_{\mu} f\geq x\},\qquad\ \text{for}\x\in\R\label{abstr} \end{equation} where $\F$ is the class of the integrable,Lipschitz functions on probability metric (product) spaces. As corollaries weget exact solutions of $\eqref{abstr}$ for Euclidean unit sphere $S^{n-1}$ witha geodesic distance and a normalized Haar measure, for $\R^n$ equipped with aGaussian measure and for the multidimensional cube, rectangle, torus or Diamondgraph equipped with uniform measure and Hamming distance. We also prove that ingeneral probability metric spaces the $\sup$ in $\eqref{abstr}$ is achieved ona family of distance functions.

Extremal Lipschitz functions in the deviation inequalities from the mean