String Quartets In Binary

The (non-)existence of perfect codes in Lucas cubes

A Fibonacci string of length $n$ is a binary string $b = b_1b_2ldots b_n$ in which for every $1 leq i < n$, $b_icdot b_{i+1} = 0$. In other words, a Fibonacci string is a binary string without 11 as a substring. Similarly, a Lucas string is a Fibonacci string $b_1b_2ldots b_n$ that $b_1cdot b_n = 0$. For a natural number $ngeq1$, a Fibonacci cube of dimension $n$ is denoted by $Gamma_n$ and i...

Feature-Based Analysis of Haydn String Quartets

When listening to multi-movement works, amateur listeners have almost certainly asked the following situation: Am I still listening to the same movement? If not, which movement is being played now? Is this still the same work? These questions motivate the key questions in this study. First, is it possible to distinguish between different movements of the same multimovement work? Further, can on...

British string quartets of the twentieth century

Computing Rooted and Unrooted Maximum Consistent Supertrees

A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary trees on four leaves. We give exact algorithms constructing rooted and unrooted maximum consistent supertrees in time O(2nm log m) for a set of m triplets (qua...

Optimal feedback correction in string quartet synchronization

Control of relative timing is critical in ensemble music performance. We hypothesize that players respond to and correct asynchronies in tone onsets that arise from fluctuations in their individual tempos. We propose a first-order linear phase correction model and demonstrate that optimal performance that minimizes asynchrony variance predicts a specific value for the correction gain. In two se...