相关论文: Configurations, Tessellations and Tone Networks

A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…

This paper presents an approach to model melodies (and music pieces in general) as networks. Notes of a melody can be seen as nodes of a network that are connected whenever these are played in sequence. This creates a directed graph. By…

We enumerate the state diagrams of the twist knot shadow which consist of the disjoint union of two trivial knots. The result coincides with the maximal number of regions into which the plane is divided by a given number of circles. We then…

Consider two horizontal lines in the plane. A pair of a point on the top line and an interval on the bottom line defines a triangle between two lines. The intersection graph of such triangles is called a simple-triangle graph. This paper…

We determine the number of labelled chordal planar graphs with $n$ vertices, which is asymptotically $c_1\cdot n^{-5/2} \gamma^n n!$ for a constant $c_1>0$ and $\gamma \approx 11.89235$. We also determine the number of rooted simple chordal…

Tensor diagrams are a handy way to depict complicated relationships between objects in projective geometry. One of the simpler ones takes two copies of a $3\times 3$ matrix and computes its adjugate. In this paper, we give a geometric…

Music is inherently complex, with structures and interactions that unfold across multiple layers. Complex networks have emerged as powerful structures for the quantitative analysis of Western classical music, revealing significant features…

The vast amount of data and increase of computational capacity have allowed the analysis of texts from several perspectives, including the representation of texts as complex networks. Nodes of the network represent the words, and edges…

Motivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangulations (whose edges can be partitioned into two trees). Our…

We study the enumeration of alternating links and tangles, considered up to topological (flype) equivalences. A weight $n$ is given to each connected component, and in particular the limit $n\to 0$ yields information about (alternating)…

Given the Hamiltonian realisation of a topological (3+1)d gauge theory with finite group $G$, we consider a family of tensor network representations of its ground state subspace. This family is indexed by gapped boundary conditions encoded…

A connected graph is 4-connected if it contains at least five vertices and removing any three of them does not disconnect it. A frequent preprocessing step in graph drawing is to decompose a plane graph into its 4-connected components and…

Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…

In this paper, first we introduce the notions of 3-tri-Leibniz algebras and embedding tensors on 3-Leibniz algebras. We show that an embedding tensor gives rise to a 3-tri-Leibniz algebra. Conversely, a 3-tri-Leibniz algebra gives rise to a…

Consider a graph G with n vertices. In this paper we study geometric conditions for an n-tuple of points in R^d to admit a tensegrity with underlying graph G. We introduce and investigate a natural stratification, depending on G, of the…

How do different musical traditions achieve tonal coherence? Most computational measures to date have analysed tonal coherence in terms of a single dimension, whereas a multi-dimensional analyses have not been sufficiently explored. We…

An $(n_k)$-configuration is a set of $n$ points and $n$ lines in the projective plane such that their point-line incidence graph is $k$-regular. The configuration is geometric, topological, or combinatorial depending on whether lines are…

The purpose of this paper is to outline a generalised model for representing hybrids of relational-categorical, symbolic, perceptual-sensory and perceptual-latent data, so as to embody, in the same architectural data layer, representations…

This paper introduces a geometric representation of hypergraphs by representing hyperedges as simplices. Building on this framework, we employ homotopy groups to analyze the topological structure of hypergraphs embedded in high-dimensional…

An L-shape is the union of a horizontal and a vertical segment with a common endpoint. These come in four rotations: L, \Gamma, LE{} and \eeG. A $k$-bend path is a simple path in the plane, whose direction changes $k$ times from horizontal…