We study the large exceedance probabilities and large exceedance paths of the recursive sequence Vn = Mn Vn−1 + Qn, where {(Mn, Qn)} is an i.i.d. sequence, and M1 is a d × d random matrix and Q1 is a ...

Some strange mathematical sequences are always whole numbers — until they’re not. The puzzling patterns have revealed ties to graph theory and prime numbers, awing mathematicians. Simple, yes, but ...

Recursion -- the computational capacity to embed elements within elements of the same kind -- has been lauded as the intellectual cornerstone of language, tool use and mathematics. A ...

A multi-institutional research team found the cognitive ability to represent recursive sequences occurs in humans and non-human primates across age, education, culture and species. Recursion -- the ...

An aptitude for mentally stringing together related items, often cited as a hallmark of human language, may have deep roots in primate evolution, a new study suggests. But “this work shows that the ...