相关论文: Melody and Variation Generation Through KAM Theory

We propose a novel approach for the generation of polyphonic music based on LSTMs. We generate music in two steps. First, a chord LSTM predicts a chord progression based on a chord embedding. A second LSTM then generates polyphonic music…

The KAM iterative scheme turns out to be effective in many problems arising in perturbation theory. I propose an abstract version of the KAM theorem to gather these different results.

Melody reduction, as an abstract representation of musical compositions, serves not only as a tool for music analysis but also as an intermediate representation for structured music generation. Prior computational theories, such as the…

Music generation with the aid of computers has been recently grabbed the attention of many scientists in the area of artificial intelligence. Deep learning techniques have evolved sequence production methods for this purpose. Yet, a…

Automatic melody generation for pop music has been a long-time aspiration for both AI researchers and musicians. However, learning to generate euphonious melody has turned out to be highly challenging due to a number of factors.…

Perturbations due to round-off errors in computer modeling are discontinuous and therefore one cannot use results like KAM theory about smooth perturbations of twist maps. We elaborate a special approximation scheme to construct two smooth…

Human usually composes music by organizing elements according to the musical form to express music ideas. However, for neural network-based music generation, it is difficult to do so due to the lack of labelled data on musical form. In this…

The creation of long melody sequences requires effective expression of coherent musical structure. However, there is no clear representation of musical structure. Recent works on music generation have suggested various approaches to deal…

We present a method for the generation of Midi files of piano music. The method models the right and left hands using two networks, where the left hand is conditioned on the right hand. This way, the melody is generated before the harmony.…

We apply KAM theory to the equation of the forced relativistic pendulum to prove that all the solutions have bounded momentum. Subsequently, we detect the existence of quasiperiodic solutions in a generalized sense. This is achieved using a…

We propose a scenario for particle-mass generation, assuming the existence of a physical regime where, firstly, physical particles can be considered as point-like objects moving in a background space-time and, secondly, their mere presence…

Music that is generated by recurrent neural networks often lacks a sense of direction and coherence. We therefore propose a two-stage LSTM-based model for lead sheet generation, in which the harmonic and rhythmic templates of the song are…

We prove a version of the Mayer-Vietoris sequence for De Rham differential forms in diffeological spaces. It is based on the notion of a generating family instead of that of a covering by open subsets.

We present a novel approach for deriving KAM-type linearization theorems directly -- and almost immediately -- from the existence of the stable foliation for a renormalization operator. We give a few illustrations in dynamics in one and…

We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the…

Creativity, or the ability to produce new useful ideas, is commonly associated to the human being; but there are many other examples in nature where this phenomenon can be observed. Inspired by this fact, in engineering and particularly in…

A method for successive synthesis of a Weyl matrix (or Dirichlet-to-Neumann map) of an arbitrary quantum tree is proposed. It allows one, starting from one boundary edge, to compute the Weyl matrix of a whole quantum graph by adding on new…

A method via the KAM technique is introduced to study the existence of invariant tori and quasiperiodic solutions for impulsive Duffing-type equations with time period 1. Basing on several planar symplectic homeomorphisms and some estimates…

In this paper, we study the persistence and remaining regularity of KAM invariant torus under sufficiently small perturbations of a Hamiltonian function together with its derivatives, in sense of finite smoothness with modulus of…

Our understanding of the mechanisms governing the structure and secular evolution galaxies assume nearly integrable Hamiltonians with regular orbits; our perturbation theories are founded on the averaging theorem for isolated resonances. On…