Sebastien Bubeck of OpenAI says “yes, nonsofic groups exist”—as an example of “many new beautiful results” from Astra, next major OpenAI model. OpenAI published a page and PDF detailing ten advances ...

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Combinatorial structures such as set systems, hypergraphs and families of finite objects form a unifying framework for extremal problems that probe how local intersection constraints govern global ...

In 2019, mathematicians finally solved one of the hardest math problems—one that had stumped them for decades. It’s called a Diophantine Equation, and it’s sometimes known as the “summing of three ...

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Joyal’s proof was published here: André Joyal, Une théorie combinatoire des séries formelles. Advances in Mathematics 42 (1981), 1–82. (I try not to link to Elsevier, as I’m permanently furious with ...

Integrated Information Theory is one of the leading models of consciousness. It aims to describe both the quality and quantity of the conscious experience of a physical system, such as the brain, in a ...

Abstract: A cutset is a concept of importance in both graph theory and many engineering problems. In this paper, cutset properties are studied and applied to transient stability problems in power ...

ABSTRACT: A set is a dominating set of G if every vertex of is adjacent to at least one vertex of S. The cardinality of the smallest dominating set of G is called the domination number of G. The ...

ABSTRACT: If G is a connected graph, the distance d (u,v) between two vertices u,v ∈ V(G) is the length of a shortest path between them. Let W = {w1, w2, ..., wk} be an ordered set of vertices of G ...