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 ...

Say you’re at a party with nine other people and everyone shakes everyone else’s hand exactly once. How many handshakes take place? This is the “handshake problem,” and it’s one of my favorites. As 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 ...

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 ...

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 ...

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 ...