Related papers: Euclidean rhythm with palindromic rests
This paper is devoted to survey composition algebras and some of their applications. After overviewing the classical algebras of quaternions and octonions, both unital composition algebras (or Hurwitz algebras) and symmetric composition…
Classical (maximal) superintegrable systems in $n$ dimensions are Hamiltonian systems with $2n-1$ independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved…
This work is a study of polynomial compositions having a fixed number of terms. We outline a recursive method to describe these characterizations, give some particular results and discuss the general case. In the final sections, some…
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and…
MDS self-dual codes have good algebraic structure, and their parameters are completely determined by the code length. In recent years, the construction of MDS Euclidean self-dual codes with new lengths has become an important issue in…
Algorithmic composition of music has a long history and with the development of powerful deep learning methods, there has recently been increased interest in exploring algorithms and models to create art. We explore the utility of state…
We develop algorithms to turn quotients of rings of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and…
We construct an explicit family of stable proper weak biharmonic maps from the unit ball $B^m$, $m\geq 5$, to Euclidean spheres. To the best of the authors knowledge this is the first example of a stable proper weak biharmonic map from at…
We consider a set of N linearly coupled harmonic oscillators and show that the diagonalization of this problem can be put in geometrical terms. The matrix techniques developed here allowed for solutions in both the classical and quantum…
We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and…
Pattern discovery algorithms in the music domain aim to find meaningful components in musical compositions. Over the years, although many algorithms have been developed for pattern discovery in music data, it remains a challenging task. To…
We provide a natural definition of an elliptic arrangement, extending the classical framework to an elliptic curve E with complex multiplication. We analyse the intersections of elements of the arrangement and their connected components as…
We study complex one-dimensional parameter slices in a three-parameter family of rational maps with two free critical points, obtained by imposing the existence of periodic orbits with prescribed multipliers. Using explicit…
Borrowing inspiration from Marcone and Mont\'{a}lban's one-one correspondence between the class of signed trees and the equimorphism classes of indecomposable scattered linear orders, we find a subclass of signed trees which has an…
This thesis is basically devoted to matroids -- fundamental structure of combinatorial optimization -- though some of our results concern simplicial complexes, or Euclidean spaces. We study old and new problems for these structures, with…
We study polyharmonic (k-harmonic) maps between Riemannian manifolds with finite j-energies (j=1, cdots, 2k-2). We show if the domain is complete and the target is the Euclidean space, then such a map is harmonic.
A method for engineering the behavior of populations of rhythmic elements is presented. The framework, which is based on phase models, allows a nonlinear time-delayed global feedback signal to be constructed which produces an interaction…
Partial orders and directed acyclic graphs are commonly recurring data structures that arise naturally in numerous domains and applications and are used to represent ordered relations between entities in the domains. Examples are task…
Rhythm is ubiquitous in human culture and in nature, but hard to capture in all its complexity. A key dimension of rhythm, integer ratio categories occur when the relationship between temporal intervals can be expressed as small-integer…
The problem of Turing pattern formation has attracted much attention in nonlinear science as well as physics, chemistry and biology. So far all Turing patterns have been observed in stationary and oscillatory media only. In this letter we…