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 ...

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 boundedness, the oscillatory behavior and the global stability of the nonnegative solutions of the difference equation ${x_{n + 1}} = \frac{{\alpha + \beta {x_{n ...

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 ...

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 ...