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 ...

For non-planar graphs, such solutions are computationally intractable," explained the researchers. The algorithm relies on the Kac-Ward formalism, a mathematical method that allows exact computation ...

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 ...

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 ...

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and ...

The Phillips curve essentially describes the relationship between wage inflation and unemployment as an inverse one, suggesting that reduced inflation accompanies rising unemployment. This principle ...