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 ...

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 ...

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 ...

We consider the rational recursive sequence (*) ${x_{n + 1}} - \frac{{a\, + \,\sum\nolimits_{i = 0}^{k - 1} {{b_i}{x_{n - i}}} }} {{{x_{n - k}}}},\,$ n=0, ±1, ±2 ...