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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study properties of an attractive-repulsive energy functional based onpower-kernels, which can be used for halftoning of images. In the first part ofthis work, using a variational framework for probability measures, we examineexistence and behavior of minimizers to the functional and to a regularizationof it by a total variation term. Moreover, we introduce particle approximationsto the functional and to its regularized version and prove their consistency interms of Gamma-convergence, which we additionally illustrate by numericalexamples. In the second part, we consider the gradient flow of the functionalin the 2-Wasserstein space and prove statements about its asymptotic behaviorfor large times, for which we employ the pseudo-inverse technique forprobability measures in 1D. Depending on the parameter range, this includesexistence of a subsequence converging to a steady state or even convergence ofthe whole trajectory to a limit which we can specify explicitly. For both partsof the work, a key ingredient is the generalized Fourier transform, whichallows us to verify the conditional positive definiteness of the interactionkernel for coinciding attractive and repulsive exponents.

Minimizers and Gradient Flows of Attraction-Repulsion Functionals with Power Kernels and Their Total Variation Regularization