Related papers: Melody and Variation Generation Through KAM Theory
We present a model for capturing musical features and creating novel sequences of music, called the Convolutional Variational Recurrent Neural Network. To generate sequential data, the model uses an encoder-decoder architecture with latent…
We develop a quantitative mathematical theory that offers new perspectives on nonlinear harmonic generation in plasmonic structures arising from symmetry breaking. Focusing on second harmonic generation--the most fundamental process and the…
This announcement considers the following problem. We produce a bounded mean oscillation theorem for small distorted diffeomorphisms from $\mathbb R^D$ to $\mathbb R^D$. A revision of this announcement is in the memoir preprint:…
In this paper we introduce a novel feature augmentation approach for generating structured musical compositions comprising melodies and harmonies. The proposed method augments a connectionist generation model with count-down to song…
In this review, we compare different descriptions of photon-number statistics in harmonic generation processes within quantum, classical and semiclassical approaches. First, we study the exact quantum evolution of the harmonic generation by…
We develop KAM theory close to an elliptic fixed point for quasi-linear Hamiltonian perturbations of the dispersive Degasperis-Procesi equation on the circle. The overall strategy in KAM theory for quasi-linear PDEs is based on Nash-Moser…
In this paper, we prove a KAM theorem in a-posteriori format, using the parameterization method to look invariant tori in non-autonomous Hamiltonian systems with $n$ degrees of freedom that depend periodically or quasi-periodically (QP) on…
Recent advancements in generative models have shown remarkable progress in music generation. However, most existing methods focus on generating monophonic or homophonic music, while the generation of polyphonic and multi-track music with…
In this paper, we give a new proof of the classical KAM theorem which avoids small divisors and relies on two basic principles of Diophantine approximation: Dirichlet's box and Khintchine transference principles.
We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. Main results provide fractional…
In music-driven dance motion generation, most existing methods use hand-crafted features and neglect that music foundation models have profoundly impacted cross-modal content generation. To bridge this gap, we propose a diffusion-based…
Musical source separation methods exploit source-specific spectral characteristics to facilitate the decomposition process. Kernel Additive Modelling (KAM) models a source applying robust statistics to time-frequency bins as specified by a…
An algorithmic approach towards the formulation of non-relativistic diffeomorphism invariance has been developed which involves both matter and gauge fields. A step by step procedure has been provided which can accommodate all types of…
We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. Applying our methods to several field theories such as abelian BF, Chern-Simons and 2-dimensional…
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…
We present an abstract KAM theorem, adapted to space-multidimensional hamiltonian PDEs with smoothing non-linearities. The main novelties of this theorem are that: $\bullet$ the integrable part of the hamiltonian may contain a hyperbolic…
In this article, the enumeration of partial chord diagrams is discussed via matrix model techniques. In addition to the basic data such as the number of backbones and chords, we also consider the Euler characteristic, the backbone spectrum,…
A quantum computing algorithm for rhythm generation is presented, which aims to expand and explore quantum computing applications in the arts, particularly in music. The algorithm maps quantum random walk trajectories onto a rhythmspace --…
The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…
Music accompaniment generation is a crucial aspect in the composition process. Deep neural networks have made significant strides in this field, but it remains a challenge for AI to effectively incorporate human emotions to create beautiful…