相关论文: Composing (with) automorphisms in the colored Cube…
When $\pi:\widetilde{\Sigma}\rightarrow D^2$ is a cover of the disc branched over $n$ marked points, the braid group $B_n$ acts on the disc by homeomorphisms fixing the marked points setwise. A braid $\beta$ \textit{lifts} if there is a…
Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum…
The polyphonic nature of music makes the application of deep learning to music modelling a challenging task. On the other hand, the Transformer architecture seems to be a good fit for this kind of data. In this work, we present Calliope, a…
The automorphism group of the composition of graphs $G \circ H$ contains the wreath product $Aut(H) \wr Aut(G)$ of the automorphism groups of the corresponding graphs. The classical problem considered by Sabidussi and Hemminger was under…
Although audio-visual representation has been proved to be applicable in many downstream tasks, the representation of dancing videos, which is more specific and always accompanied by music with complex auditory contents, remains challenging…
We show that the map obtained by viewing a geometric (ie. representative) braid as a string link induces an isomorphism of the n-strand braid group onto the group of units of the n-strand string link monoid.
We introduce in a general setting a dynamic programming method for solving reconfiguration problems. Our method is based on contracted solution graphs, which are obtained from solution graphs by performing an appropriate series of edge…
Every n-edge colored n-regular graph G naturally gives rise to a simple abstract n-polytope, the colorful polytope of G, whose 1-skeleton is isomorphic to G. The paper describes colorful polytope versions of the associahedron and…
When S is a discrete subsemigroup of a discrete group G such that G = S^{-1} S, it is possible to extend circle-valued multipliers from S to G; to dilate (projective) isometric representations of S to (projective) unitary representations of…
Singularities arise in diverse disciplines and play a key role in both exploring fundamental laws of physics and making highly-sensitive sensors. Higher-order (>3) singularities, with further improved performance, however, usually require…
We describe polynomial time algorithms for determining whether an undirected graph may be embedded in a distance-preserving way into the hexagonal tiling of the plane, the diamond structure in three dimensions, or analogous structures in…
Several prior works have proposed various methods for the task of automatic melody harmonization, in which a model aims to generate a sequence of chords to serve as the harmonic accompaniment of a given multiple-bar melody sequence. In this…
A song's backbone is its chord progressions, a series of chords that improve the harmony and add to the overall composition. For individuals ranging from beginners to creative artists, comprehending and implementing music theory grammar for…
This article studies automorphism groups of graph products of arbitrary groups. We completely characterise automorphisms that preserve the set of conjugacy classes of vertex groups as those automorphisms that can be decomposed as a product…
Shuffle operads were introduced to forget the symmetric group actions on symmetric operads while preserving all possible operadic compositions. Rewriting methods were then applied to symmetric operads via shuffle operads: in particular, a…
This paper explores the modeling method of polyphonic music sequence. Due to the great potential of Transformer models in music generation, controllable music generation is receiving more attention. In the task of polyphonic music, current…
Metrically homogeneous graphs are connected graphs which, when endowed with the path metric, are homogeneous as metric spaces. In this paper we introduce the concept of twisted automorphisms, a notion of isomorphism up to a permutation of…
We formally introduce a systematic (de/re)-composition approach, based on the algebraic formalism of "Multi-Dimensional Homomorphisms (MDHs)". Our approach is designed as general enough to be applicable to a wide range of data-parallel…
Multi-modal embeddings form the foundation for vision-language models, such as CLIP embeddings, the most widely used text-image embeddings. However, these embeddings are vulnerable to subtle misalignment of cross-modal features, resulting…
We determine the structure of automorphism groups of finite graphs of bounded Hadwiger number. Our proof includes a structural analysis of finite edge-transitive graphs. In particular, we show that for connected, $K_{h+1}$-minor-free,…