Related papers: Melody and Variation Generation Through KAM Theory
In this paper we discuss the number of regions in a unit circle after drawing $n$ i.i.d. random chords in the circle according to a particular family of distribution. We find that as $n$ goes to infinity, the distribution of the number of…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider variational wavelet approach for loops,…
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…
Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across…
Regular variation is a continuous-parameter theory; we work in a general setting, containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling theories as special cases. We give sequential versions of the main theorems, that is,…
Analysing music in the field of machine learning is a very difficult problem with numerous constraints to consider. The nature of audio data, with its very high dimensionality and widely varying scales of structure, is one of the primary…
We use a 1-parameter version of gauge theory to investigate the topology of the diffeomorphism group of 4-manifolds. A polynomial invariant, analogous to the Donaldson polynomial, is defined, and is used to show that the diffeomorphism…
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…
We introduce dicodensity monads: a generalisation of pointwise codensity monads generated by functors to monads generated by mixed-variant bifunctors. Our construction is based on the notion of strong dinaturality (also known as Barr…
In this paper we present the first steps towards the creation of a tool which enables artists to create music visualizations using pre-trained, generative, machine learning models. First, we investigate the application of network bending,…
The dichotic method of hearing sound adapts in the region of musical harmony. The algorithm of the separation of the being dissonant voices into several separate groups is proposed. For an increase in the pleasantness of chords the…
Melody extraction is a vital music information retrieval task among music researchers for its potential applications in education pedagogy and the music industry. Melody extraction is a notoriously challenging task due to the presence of…
We study the factorization and monotonicity method for inverse acoustic scattering problems. Firstly, we give a new general functional analysis theorem for the monotonicity method. Comparing with the factorization method, the general…
In this work we show a technique that allows for the musical interpretation of the brightness variations of stars. This method allows composers a lot of freedom to incorporate their own ideas into the score, based on the melodic line…
Mathematics is a far reaching discipline and its tools appear in many applications. In this paper we discuss its role in music and signal processing by revisiting the use of mathematics in algorithms that can extract chord information from…
This is the second part of a project concerning variation of stability and chamber structure for ADHM invariants of curves. Wallcrossing formulas for such invariants are derived using the theory of stack function Ringel-Hall algebras…
Quantum oscillations (QO) describe the periodic variation of physical observables as a function of inverse magnetic field in metals. The Onsager relation connects the basic QO frequencies with the extremal areas of closed Fermi surface…
A new architecture of an artificial neural network that helps to generate longer melodic patterns is introduced alongside with methods for post-generation filtering. The proposed approach called variational autoencoder supported by history…
We reconsider a control theory for Hamiltonian systems, that was introduced on the basis of KAM theory and applied to a model of magnetic field in previous articles. By a combination of Frequency Analysis and of a rigorous (Computer…
Deep generative models allow even novice composers to generate various melodies by sampling latent vectors. However, finding the desired melody is challenging since the latent space is unintuitive and high-dimensional. In this work, we…