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 ...

#define _(blk) std::cerr << #blk << " "; start_ = clock(); blk \ std::cerr << (clock()-start_)*1.0/CLOCKS_PER_SEC << "s" << std::endl; "simple_maximal_planar_random ...

A new technical paper titled “Fabrication of graphene field effect transistors on complex non-planar surfaces” was published by researchers at Imperial College London. “Graphene field effect ...

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 ...