Related papers: Melody and Variation Generation Through KAM Theory
In recent years, machine learning, and in particular generative adversarial neural networks (GANs) and attention-based neural networks (transformers), have been successfully used to compose and generate music, both melodies and polyphonic…
We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral…
Beyond H\"{o}lder's type, this paper mainly concerns the persistence and remaining regularity of an individual frequency-preserving KAM torus in a finitely differentiable Hamiltonian system, even allows the non-integrable part being…
Holland's (1975) genetic algorithm is a minimal computer model of natural selection that made it possible to investigate the effect of manipulating specific parameters on the evolutionary process. If culture is, like biology, a form of…
I will discuss three related unconventional ways to generate neutrino oscillations (1)Equivalence principle violation by the string dilaton field (i2)Violation of Lorentz Invariance and (3) Equivalence principle violation through a…
A homology theory is developed for set-theoretic Yang-Baxter equations, and knot invariants are constructed by generalized colorings by biquandles and Yang-Baxter cocycles.
We present a quantum deformation theory of the Airy curve and use it to establish a version of mirror symmetry of a point.
It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the behavior of the power spectrum of the excitation energy fluctuations, which is…
We give some general criteria of being a homeomorphism for continuous mappings of topological manifolds, as well as criteria of being a diffeomorphism for smooth mappings of smooth manifolds. As an illustration, we apply these criteria to…
The theory of quandle (co)homology and cocycle knot invariants is rapidly being developed. We begin with a summary of these recent advances. One such advance is the notion of a dynamical cocycle. We show how dynamical cocycles can be used…
The representation theory of non-centrally extended Lie algebras of Noether symmetries, including spacetime diffeomorphisms and reparametrizations of the observer's trajectory, has recently been developped. It naturally solves some…
This paper explores the idea of utilising Long Short-Term Memory neural networks (LSTMNN) for the generation of musical sequences in ABC notation. The proposed approach takes ABC notations from the Nottingham dataset and encodes it to be…
We obtain results on the growth sequences of the differential for iterations of circle diffeomorphisms without periodic points.
This paper presents NetWorks (NW), an interactive music generation system that uses a hierarchically clustered scale free network to generate music that ranges from orderly to chaotic. NW was inspired by the Honing Theory of creativity,…
Using a construction closely related to Waldhausen's $S_\bullet$-construction, we produce a spectrum $K(\mathbf{Var}_{/k})$ whose components model the Grothendieck ring of varieties (over a field $k$) $K_0 (\mathbf{Var}_{/k})$. We then…
Previous studies on music style transfer have mainly focused on one-to-one style conversion, which is relatively limited. When considering the conversion between multiple styles, previous methods required designing multiple modes to…
In this paper, we give a new proof of the classical KAM theorem on the persistence of an invariant quasi-periodic torus, whose frequency vector satisfies the Bruno-R\"ussmann condition, in real-analytic non-degenerate Hamiltonian systems…
In a diffeomorphism invariant theory, symmetry breaking may be a mask for coordinate choice.
We construct time quasi-periodic vortex patch solutions with one hole for the planar Euler equations. These structures are captured close to any annulus provided that its modulus belongs to a massive Borel set. The proof is based on…
A formalism in terms of Hertz potentials is presented describing sum-frequency generation in a uniaxial non-linear crystal. A scheme is proposed consisting in aligning the side-walk propagation of extraordinary waves in combination with…