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 ...

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 ...

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 ...

In this note a recursive type condition for positivity of the angle between past and future for q-variate stationary sequences is provided. In the case q = 2 it gives a simple different proof of a ...