Implements a doubly connected edge list (DCEL) in C#. From Wikipedia: The doubly connected edge list (DCEL), also known as half-edge data structure, is a data structure to represent an embedding of a ...

Fullerenes are hollow carbon molecules where each atom is connected to exactly three other atoms, arranged in pentagonal and hexagonal rings. Mathematically, they can be combinatorially modeled as ...

While retrieval-augmented generation is effective for simpler queries, advanced reasoning questions require deeper connections between information that exist across documents. They require a knowledge ...

The original version of this story appeared in Quanta Magazine. Much of mathematics is driven by intuition, by a deep-rooted sense of what should be true. But sometimes instinct can lead a ...

I know that for chordal graphs, Sage has a function to recognize a perfect elimination ordering. This problem is somewhat similar, identifying chordal bipartite graphs. The following theorem is ...

Lennard J. Davis does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond ...

JD Vance has climbed to his current position as former President Donald Trump’s running mate, in part, by selling himself as a hillbilly, calling on his Appalachian background to bolster his ...

Abstract: A new method is proposed to synthesize arbitrary-tiled arrays fitting multiple, generally conflicting, requirements for multiantenna systems operating beyond 100 GHz. The array structure is ...