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 ...

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 ...

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 ...

The DNA sequences containing multifarious novel symmetrical structure frequently play crucial role in how genomes work. Here we present a new scheme for understanding the structural features and ...

The human genome is just over 6 feet 8 inches long, which is 2 inches taller than the average NBA basketball player and in total, a lot of nucleotides! But what if the amount of sequence diversity ...

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 multi-institutional ...

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 ...