Related papers: Interactions Between Brauer Configuration Algebras…
Bijections between invariants associated to indecomposable projective modules over some suitable Brauer configuration algebras and invariants associated to solutions of the Kronecker problem and the four subspace problem are used to…
Mutations on Brauer configurations are introduced and associated with some suitable automata in order to solve generalizations of the Chicken McNugget problem. Besides, based on marked order polytopes a new class of diophantine equations…
In this paper we introduce a generalization of a Brauer graph algebra which we call a Brauer configuration algebra. As with Brauer graphs and Brauer graph algebras, to each Brauer configuration, there is an associated Brauer configuration…
Using the combinatorial information of a Brauer configuration is possible to compute each entry of the Cartan matrix of the algebra associated to the Brauer configuration.
Beilinson Completion Algebras (BCAs) are generalizations of complete local rings, and have a rich algebraic-analytic structure. These algebras were introduced in my paper "Traces and Differential Operators over Beilinson Completion…
We use coupled hidden Markov models to automatically annotate the 371 Bach chorales in the Riemenschneider edition, a corpus containing approximately 100,000 notes and 20,000 chords. We give three separate analyses that achieve…
Computational models of music, while providing good descriptions of melodic development, still cannot fully grasp the general structure comprised of repetitions, transpositions, and reuse of melodic material. We present a corpus of strongly…
In 2017, Green and Schroll introduced a generalization of Brauer graph algebras which they call Brauer configuration algebras. In the present paper, we further generalize Brauer configuration algebras to fractional Brauer configuration…
Numeric tabular datasets are the dominant data format in scientific practice, yet large language models lack native mechanisms for representing numeric datasets in a meaningful way across heterogeneous feature spaces. Existing approaches…
We propose graph canonical coherence analysis (gCChA), a novel framework that extends canonical correlation analysis to multivariate graph signals in the graph frequency domain. The proposed method addresses challenges posed by the inherent…
Schenkerian Analysis (SchA) is a uniquely expressive method of music analysis, combining elements of melody, harmony, counterpoint, and form to describe the hierarchical structure supporting a work of music. However, despite its powerful…
Algorithmic harmonization - the automated harmonization of a musical piece given its melodic line - is a challenging problem that has garnered much interest from both music theorists and computer scientists. One genre of particular interest…
Canonical correlation analysis (CCA) is a powerful technique for discovering whether or not hidden sources are commonly present in two (or more) datasets. Its well-appreciated merits include dimensionality reduction, clustering,…
The classical Canonical Correlation Analysis (CCA) identifies the correlations between two sets of multivariate variables based on their covariance, which has been widely applied in diverse fields such as computer vision, natural language…
We introduce Block Sparse Canonical Correlation Analysis which estimates multiple pairs of canonical directions (together a "block") at once, resulting in significantly improved orthogonality of the sparse directions which, we demonstrate,…
Canonical Correlation Analysis (CCA) has been widely applied to jointly embed multiple views of data in a maximally correlated latent space. However, the alignment between various data perspectives, which is required by traditional…
In this paper we associate to a dessin d'enfant an associative algebra, called a Brauer configuration algebra. This is an algebra given by quiver and relations induced by the monodromy of the dessin d'enfant. We show that the dimension of…
Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
Music Structure Analysis (MSA) is a Music Information Retrieval task consisting of representing a song in a simplified, organized manner by breaking it down into sections typically corresponding to ``chorus'', ``verse'', ``solo'', etc. In…
h-BCN is an intriguing material system where the bandgap varies considerably depending on the atomic configuration, even at a fixed composition. Exploring stable atomic configurations in this system is crucial for discussing the energetic…