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 ...

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 ...

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 ...

This is a preview. Log in through your library . Abstract C. H. Gibbons, M. R. S. Kulenovic and G. Ladas [1] have posed the following problem: Is there a solution of the difference equation: ${x_{n + ...

A linear-recursive-sequence (LRS) generator produces binary sequences using a shift register and feedback through an exclusive-OR gate. The sequence length equals 2 N ­1, where N represents the number ...

One of the biggest surprises in molecular biology was the discovery in 1977 that coding information in genes is interrupted by non-coding sequences known as introns. Much has since been learned about ...

It’s wild to think that a math puzzle from the 1200s is now helping power AI, encryption, and the digital world we live in.

Arabic numerals to Europe in 1202. His famous number sequence began as a simple rabbit puzzle. Centuries later, this sequence ...