English
Related papers

Related papers: Generation of musical patterns through operads

200 papers

Pattern formation of sound is predicted in a driven resonator where subharmonic generation takes place. A model allowing for diffraction of the fields (large-aspect ratio limit) is derived by means of the multiple scale expansions…

Pattern Formation and Solitons · Physics 2009-11-11 Isabel Perez-Arjona , Victor J. Sanchez-Morcillo

Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…

Category Theory · Mathematics 2025-05-12 John H. Selby , Maria E. Stasinou , Matt Wilson , Bob Coecke

The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…

Logic in Computer Science · Computer Science 2015-02-18 Mikołaj Bojańczyk

A new hierarchy of operads over the linear spans of $\delta$-cliffs, which are some words of integers, is introduced. These operads are intended to be analogues of the operad of permutations, also known as the associative symmetric operad.…

Combinatorics · Mathematics 2022-10-24 Camille Combe , Samuele Giraudo

The theory of operads (May, cyclic, modular, PROPs, etc) is extended to include higher dimensional phenomena, i.e. operations between operations, mimicking the algebraic structure on varieties of arbitrary dimensions, having marked…

Quantum Algebra · Mathematics 2010-12-16 Dennis Borisov

We develop a self-dual, bivariant extension of the concept of an operadic category, its associated operads and their algebras. Our new theory covers, besides all classical subjects, also generalized traces and bivariant versions of…

Category Theory · Mathematics 2024-03-27 Martin Markl

This study proposes a system designed to enumerate the process of collaborative composition among humans, using automatic music composition technology. By integrating multiple Recurrent Neural Network (RNN) models, the system provides an…

Sound · Computer Science 2024-03-07 So Hirawata , Noriko Otani

We present a hybrid neural network and rule-based system that generates pop music. Music produced by pure rule-based systems often sounds mechanical. Music produced by machine learning sounds better, but still lacks hierarchical temporal…

Sound · Computer Science 2017-10-09 Yifei Teng , An Zhao , Camille Goudeseune

Operads may be represented as symmetric monoidal functors on a small symmetric monoidal category. We discuss the axioms which must be imposed on a symmetric monoidal functor in order that it give rise to a theory similar to the theory of…

Category Theory · Mathematics 2018-01-16 Ezra Getzler

The ability to continually learn, retain and deploy skills to accomplish goals is a key feature of intelligent and efficient behavior. However, the neural mechanisms facilitating the continual learning and flexible (re-)composition of…

Machine Learning · Computer Science 2025-10-24 Haozhe Shan , Sun Minni , Lea Duncker

Graphs can be leveraged to model polyphonic multitrack symbolic music, where notes, chords and entire sections may be linked at different levels of the musical hierarchy by tonal and rhythmic relationships. Nonetheless, there is a lack of…

Sound · Computer Science 2023-07-28 Emanuele Cosenza , Andrea Valenti , Davide Bacciu

Modelling musical structure is vital yet challenging for artificial intelligence systems that generate symbolic music compositions. This literature review dissects the evolution of techniques for incorporating coherent structure, from…

Sound · Computer Science 2024-03-14 Keshav Bhandari , Simon Colton

Networks can be combined in various ways, such as overlaying one on top of another or setting two side by side. We introduce "network models" to encode these ways of combining networks. Different network models describe different kinds of…

Category Theory · Mathematics 2020-07-22 John C. Baez , John Foley , Joe Moeller , Blake S. Pollard

Automatic music generation systems have gained in popularity and sophistication as advances in cloud computing have enabled large-scale complex computations such as deep models and optimization algorithms on personal devices. Yet, they…

Sound · Computer Science 2018-12-13 Dorien Herremans , Elaine Chew

We use Giraudo's construction of combinatorial operads from monoids to offer a conceptual explanation of the origins of Hoffbeck's path sequences of shuffle trees, and use it to define new monomial orders of shuffle trees. One such order is…

Category Theory · Mathematics 2020-10-15 Vladimir Dotsenko

The purpose of this dissertation is to set up a theory of generalized operads and multicategories, and to use it as a language in which to propose a definition of weak n-category. Included is a full explanation of why the proposed…

Category Theory · Mathematics 2007-05-23 Tom Leinster

We introduce anticipation: a method for constructing a controllable generative model of a temporal point process (the event process) conditioned asynchronously on realizations of a second, correlated process (the control process). We…

Sound · Computer Science 2024-07-29 John Thickstun , David Hall , Chris Donahue , Percy Liang

We give an explicit construction of the generating set of a colored operad that implements theta theory in the mathematical model of Minimalism in generative linguistics, in the form of a coloring algorithm for syntactic objects. We show…

Computation and Language · Computer Science 2025-03-11 Matilde Marcolli , Richard K. Larson

Musical Metacreation tries to obtain creative behaviors from computers algorithms composing music. In this paper I briefly analyze how this field evolved from algorithmic composition to be focused on the search for creativity, and I point…

Sound · Computer Science 2022-09-01 Filippo Carnovalini

In this paper, we study averaging operators from an algebraic and combinatorial point of view. We first construct free averaging algebras in terms of a class of bracketed words called averaging words. We next apply this construction to…

Rings and Algebras · Mathematics 2015-10-15 Li Guo , Jun Pei