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

Calabi-Yau four-folds may be constructed as hypersurfaces in weightedprojective spaces of complex dimension 5 defined via weight systems of 6weights. In this work, neural networks were implemented to learn the Calabi-YauHodge numbers from the weight systems, where gradient saliency and symbolicregression then inspired a truncation of the Landau-Ginzburg model formula forthe Hodge numbers of any dimensional Calabi-Yau constructed in this way. Theapproximation always provides a tight lower bound, is shown to be dramaticallyquicker to compute (with compute times reduced by up to four orders ofmagnitude), and gives remarkably accurate results for systems with largeweights. Additionally, complementary datasets of weight systems satisfying thenecessary but insufficient conditions for transversality were constructed,including considerations of the IP, reflexivity, and intradivisibilityproperties. Overall producing a classification of this weight system landscape,further confirmed with machine learning methods. Using the knowledge of thisclassification, and the properties of the presented approximation, a noveldataset of transverse weight systems consisting of 7 weights was generated fora sum of weights $\leq 200$; producing a new database of Calabi-Yau five-folds,with their respective topological properties computed. Further to this anequivalent database of candidate Calabi-Yau six-folds was generated withapproximated Hodge numbers.

Calabi-Yau Four/Five/Six-folds as $\mathbb{P}^n_\textbf{w}$ Hypersurfaces: Machine Learning, Approximation, and Generation