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

Thomson problem is a classical problem in physics to study how $n$ number ofcharged particles distribute themselves on the surface of a sphere of $k$dimensions. When $k=2$, i.e. a 2-sphere (a circle), the particles appear atequally spaced points. Such a configuration can be computed analytically.However, for higher dimensions such as $k \ge 3$, i.e. the case of 3-sphere(standard sphere), there is not much that is understood analytically. Findingglobal minimum of the problem under these settings is particularly tough sincethe optimization problem becomes increasingly computationally intensive withlarger values of $k$ and $n$. In this work, we explore a wide variety ofnumerical optimization methods to solve the Thomson problem. In our empiricalstudy, we find stochastic gradient based methods (SGD) to be a compellingchoice for this problem as it scales well with the number of points.

Optimization on the Surface of the (Hyper)-Sphere