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We undertake a detailed numerical study of the twin phenomena of stochastic and vibrational resonance in a discrete model system in the presence of bichromatic input signal. A two parameter cubic map is used as the model that combines the…

Chaotic Dynamics · Physics 2009-11-13 K. P. Harikrishnan , G. Ambika

We present the characterizations of symbol correspondences for mechanical systems that are symmetric by $SU(3)$, which we refer to as \emph{quark systems}. The quantum quark systems are the unitary irreducible representations of $SU(3)$ of…

Mathematical Physics · Physics 2026-03-26 P. A. S. Alcântara , P. de M. Rios

Extraction of symbolic information from signals is an active field of research enabling numerous applications especially in the Musical Information Retrieval domain. This complex task, that is also related to other topics such as pitch…

We investigate the semiclassical mechanism of tunneling process in non-integrable systems. The significant role of complex-phase-space chaos in the description of the tunneling process is elucidated by studying a simple scattering map…

Chaotic Dynamics · Physics 2009-11-10 T. Onishi , A. Shudo , K. S. Ikeda , K. Takahashi

Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating…

Optimization and Control · Mathematics 2007-07-31 Giordano Pola , Paulo Tabuada

A one dimensional system made up of a compressible fluid and several mechanical oscillators, coupled to the acoustic field in the fluid, is analyzed for different settings of the oscillators array. The dynamical models are formulated in…

Mathematical Physics · Physics 2007-05-23 C. Cacciapuoti , R. Figari , A. Posilicano

In this short paper we discuss how the position - scale half-space of wavelet analysis may be cut into different regions. We discuss conditions under which they are independent in the sense that the T\"oplitz operators associated with their…

funct-an · Mathematics 2008-02-03 Matthias Holschneider

We make some general observations about partial orders on quotient spaces, and explore their use in music theory, in two different contexts. In the first, we show that many of the most familiar chord and scale types in Western music appear…

General Mathematics · Mathematics 2012-11-02 Marcus Pendergrass

We report an approach to obtaining complex networks with diverse topology, here called syntonets, taking into account the consonances and dissonances between notes as defined by scale temperaments. Though the fundamental frequency is…

Sound · Computer Science 2020-12-09 Luciano da Fontoura Costa , Henrique Ferraz de Arruda

We derive a prediction of dynamical tunneling rates from regular to chaotic phase-space regions combining the direct regular-to-chaotic tunneling mechanism in the quantum regime with an improved resonance-assisted tunneling theory in the…

Chaotic Dynamics · Physics 2010-03-18 Steffen Löck , Arnd Bäcker , Roland Ketzmerick , Peter Schlagheck

The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic…

Chaotic Dynamics · Physics 2009-10-31 Diego. A. Wisniacki , Eduardo Vergini

In this paper we present a mathematical way of defining musical modes, we derive a formula for the total number of modes and define the musicality of a mode as the total number of harmonic chords whithin the mode. We also give an algorithm…

Combinatorics · Mathematics 2011-03-04 Mihail Cocos , Shawn Fowers

We analyze the onset of classical field configurations after a phase transition. Firstly, we motivate the problem by means of a toy model in quantum mechanics. Subsequently, we consider a scalar field theory in which the system-field…

High Energy Physics - Phenomenology · Physics 2007-05-23 F. C. Lombardo , R. J. Rivers , F. D. Mazzitelli

A fundamental question in interpretability research is to what extent neural networks, particularly language models, implement reusable functions through subnetworks that can be composed to perform more complex tasks. Recent advances in…

Machine Learning · Computer Science 2025-06-24 Philipp Mondorf , Sondre Wold , Barbara Plank

Discovering and exploring the underlying structure of multi-instrumental music using learning-based approaches remains an open problem. We extend the recent MusicVAE model to represent multitrack polyphonic measures as vectors in a latent…

Machine Learning · Statistics 2018-06-04 Ian Simon , Adam Roberts , Colin Raffel , Jesse Engel , Curtis Hawthorne , Douglas Eck

Polyphonic music files were analyzed using the set of symbols that produced the Minimal Entropy Description which we call the Fundamental Scale. This allowed us to create a novel space to represent music pieces by developing: a) a method to…

Sound · Computer Science 2017-01-13 Gerardo Febres , Klaus Jaffe

Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional modeling approaches suppress this structure.…

Category Theory · Mathematics 2022-11-04 Sophie Libkind , Andrew Baas , Evan Patterson , James Fairbanks

Despite achieving tremendous success, existing deep learning models have exposed limitations in compositional generalization, the capability to learn compositional rules and apply them to unseen cases in a systematic manner. To tackle this…

Machine Learning · Computer Science 2020-10-23 Xinyun Chen , Chen Liang , Adams Wei Yu , Dawn Song , Denny Zhou

We explore the potential of a popular distributional semantics vector space model, word2vec, for capturing meaningful relationships in ecological (complex polyphonic) music. More precisely, the skip-gram version of word2vec is used to model…

Sound · Computer Science 2018-12-03 Ching-Hua Chuan , Kat Agres , Dorien Herremans

Symbolic music is widely used in various deep learning tasks, including generation, transcription, synthesis, and Music Information Retrieval (MIR). It is mostly employed with discrete models like Transformers, which require music to be…

Sound · Computer Science 2023-10-13 Nathan Fradet , Nicolas Gutowski , Fabien Chhel , Jean-Pierre Briot