Related papers: Euclidean rhythm with palindromic rests
In this work, we present new constructions for topological subsystem codes using semi-regular Euclidean and hyperbolic tessellations. They give us new families of codes, and we also provide a new family of codes obtained through an already…
In the framework of Clifford analysis, a chain of harmonic and monogenic potentials is constructed in the upper half of Euclidean space $\mR^{m+1}$, including a higher dimensional generalization of the complex logarithmic function. Their…
We define and investigate a new three-parameter family of graphs that further generalizes the Fibonacci and metallic cubes. Namely, the number of vertices in this family of graphs satisfies Horadam recurrence, a linear recurrence of second…
Neural networks and deep learning are often deployed for the sake of the most comprehensive music generation with as little involvement as possible from the human musician. Implementations in aid of, or being a tool for, music practitioners…
In this article, a framework for defining and analysing a family of graphs or networks from symbolic music information is discussed. Such graphs concern different types of elements, such as pitches, chords and rhythms, and the relations…
In this paper, we study convolutional codes with a specific cyclic structure. By definition, these codes are left ideals in a certain skew polynomial ring. Using that the skew polynomial ring is isomorphic to a matrix ring we can describe…
Elasticity ellipses or central ellipses have been long used in graphic statics to capture the elastic behaviour of structural elements. The paper gives a generalisation the concept both in dimensions and in the possibility of degenerate…
In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of Euclidean space R^{m+1} was constructed recently, including a higher dimensional analogue of the logarithmic function in the complex…
We introduce the notion of Riemannian twistorial structure and we show that it provides new natural constructions of harmonic maps.
Definitive embeddings remain a fundamental challenge of computational musicology for symbolic music in deep learning today. Analogous to natural language, music can be modeled as a sequence of tokens. This motivates the majority of existing…
The structure of the hadron resonances attracts much attention, in association with the recent observations of various exotic hadrons which do not fit well in the conventional picture. These findings urge us to consider various new…
We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed…
Cycle polytopes of matroids have been introduced in combinatorial optimization as a generalization of important classes of polyhedral objects like cut polytopes and Eulerian subgraph polytopes associated to graphs. Here we start an…
Dynamic systems have found their use in sound synthesis as well as score synthesis. These levels can be integrated in monolithic autonomous systems in a novel approach to algorithmic composition that shares certain aesthetic motivations…
Disclinations are ubiquitous lattice defects existing in almost all crystalline materials. In two-dimensional nanomaterials, disclinations lead to the warping and deformation of the hosting material, yielding non-Euclidean geometries.…
For large ranks, there is no good algorithm that decides whether a given lattice has an orthonormal basis. But when the lattice is given with enough symmetry, we can construct a provably deterministic polynomial-time algorithm to accomplish…
By studying the structures of clusters bound by a model potential that favours polytetrahedral order, we find a previously unknown series of `magic numbers' (i.e. sizes of special stability) whose polytetrahedral structures are…
``Quasi-elliptic'' functions can be given a ring structure in two different ways, using either ordinary multiplication, or convolution. The map between the corresponding standard bases is calculated. A related structure has appeared…
We consider the billiard map inside a polyhedron. We give a condition for the stability of the periodic trajectories. We apply this result to the case of the tetrahedron. We deduce the existence of an open set of tetrahedra which have a…
Music comprises two core structural components, melody and rhythm, that vary widely across cultures. Whether these components coevolve in a coupled way or follow independent trajectories remains unclear. We introduce a novel computational…