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This paper is the continuation of the study on discrete harmonic analysis related to Jacobi expansions initiated in [1]. Considering the operator $\mathcal{J}^{(\alpha,\beta)}=J^{(\alpha,\beta)}-I$, where $J^{(\alpha,\beta)}$ is the…
Symbolic music analysis tasks are often performed by models originally developed for Natural Language Processing, such as Transformers. Such models require the input data to be represented as sequences, which is achieved through a process…
Although stochastic resonance phenomena are ubiquitous across various complex systems, the influence mechanisms of higher-order interactions remain elusive. Here, we address this gap by investigating stochastic resonance in coupled phase…
Some quantal systems require only a small part of the full quantum theory for their analysis in classical terms. In such understanding we review some recent literature on semiclassical treatments. An analysis of it allows one to see that…
The three-manifold topological invariants $\hat Z$ capture the half-index of the three-dimensional theory with ${\mathcal{N}}=2$ supersymmetry obtained by compactifying the M5 brane theory on the closed three-manifold. In 2019, surprising…
Geometric representations provide a principled framework for structuring the description of latent constructs and clarifying sources of uncertainty in their dimensional characterisation. We introduce a novel geometric representation of…
An important problem in physics concerns the analysis of audio time series generated by transduced acoustic phenomena. Here, we develop a new method to quantify the scaling properties of the local variance of nonstationary time series. We…
Audio embeddings enable large scale comparisons of the similarity of audio files for applications such as search and recommendation. Due to the subjectivity of audio similarity, it can be desirable to design systems that answer not only…
We classify three-tone and four-tone chords based on subgroups of the symmetric group acting on chords contained within a twelve-tone scale. The actions are inversion, major-minor duality, and augmented-diminished duality. These actions…
Tensor models are measures for random tensors. They generalise matrix models and were developed to study random geometry in arbitrary dimension. Moreover, they are strongly connected to quantum gravity theories as additionally to the…
Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to…
Harmonic inversion techniques have been shown to be a powerful tool for the semiclassical quantization and analysis of quantum spectra of both classically integrable and chaotic dynamical systems. Various computational procedures have been…
Compositional generalization is a basic and essential intellective capability of human beings, which allows us to recombine known parts readily. However, existing neural network based models have been proven to be extremely deficient in…
The models for the internal structure of the newly found four-quark charmonium-like resonance $Z_c(3900)$ are discussed: the molecular model as well as the hadro-charmonium and tetraquark schemes. It is argued that it would be possible to…
Multimodal models are critical for music understanding tasks, as they capture the complex interplay between audio and lyrics. However, as these models become more prevalent, the need for explainability grows-understanding how these systems…
Music is a form of expression that often requires interaction between players. If one wishes to interact in such a musical way with a computer, it is necessary for the machine to be able to interpret the input given by the human to find its…
We define a new monoidal category on collections (shuffle composition). Monoids in this category (shuffle operads) turn out to bring a new insight in the theory of symmetric operads. For this category, we develop the machinery of Gr\"obner…
To train a machine learning model is necessary to take numerous decisions about many options for each process involved, in the field of sequence generation and more specifically of music composition, the nature of the problem helps to…
Existing approaches for generating multitrack music with transformer models have been limited in terms of the number of instruments, the length of the music segments and slow inference. This is partly due to the memory requirements of the…
A robust energy transfer mechanism is found in nonlinear wave systems, which favours transfers towards modes interacting via triads with nonzero frequency mismatch, applicable in meteorology, nonlinear optics and plasma wave turbulence. We…