Related papers: Group theory approach to combination tones
Compositional generalization is the capacity to recognize and imagine a large amount of novel combinations from known components. It is a key in human intelligence, but current neural networks generally lack such ability. This report…
A combination of three or more tones played together is called a chord. In the chromatic scale, chords which are consonant are of particular interest and can be divided into several groups, two main ones being the major and minor chords.…
We present a compositional theory of nonlinear audio signal processing based on a categorification of the Volterra series. We begin by augmenting the classical definition of the Volterra series so that it is functorial with respect to a…
Many first-order equational theories, such as the theory of groups or boolean algebras, can be presented by a smaller set of axioms than the original one. Recent studies showed that a homological approach to equational theories gives us…
Tone is a prosodic feature used to distinguish words in many languages, some of which are endangered and scarcely documented. In this work, we use unsupervised representation learning to identify probable clusters of syllables that share…
Hybrid aeroacoustic methods seek for computational efficiency and robust noise prediction. Using already existing aeroacoustic wave equations, we propose a general hybrid aeroacoustic method, based on compressible source data. The main…
A new theory of mammalian hearing is presented, which accounts for the auditory image in the midbrain (inferior colliculus) of objects in the acoustical environment of the listener. It is shown that the ear is a temporal imaging system that…
Quantum decoherence can arise due to classical fluctuations in the parameters which define the dynamics of the system. In this case decoherence, and complementary noise, is manifest when data from repeated measurement trials are combined.…
In classical music and in any genre of contemporary music, the tonal elements or notes used for playing are the same. The numerous possibilities of chords for a given instance in a piece make the playing, in general, very intricate, and…
This work reviews the human auditory system, elucidating some of the specialized mechanisms and non-linear pathways along the chain of events between physical sound and its perception. Customary relationships between frequency, time, and…
Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…
Group synchronization refers to estimating a collection of group elements from the noisy pairwise measurements. Such a nonconvex problem has received much attention from numerous scientific fields including computer vision, robotics, and…
Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…
The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional…
Harmonic and Intermodulation distortions occur when a physical system is excited with a single or several frequencies and when the relationship between the input and output is non-linear. Working with non-linearities in the Frequency domain…
A detailed study of the anharmonicity-induced resonances caused by the coupling of center-of-mass and relative motion is presented for a system of two ultracold atoms in single-well potentials. As has been confirmed experimentally, these…
Arbitrary high order numerical methods for time-harmonic acoustic scattering problems originally defined on unbounded domains are constructed. This is done by coupling recently developed high order local absorbing boundary conditions (ABCs)…
Compositional Explanations is a method for identifying logical formulas of concepts that approximate the neurons' behavior. However, these explanations are linked to the small spectrum of neuron activations (i.e., the highest ones) used to…
The classification and characterization of topological phases of matter is well understood for ground states of gapped Hamiltonians that are well isolated from the environment. However, decoherence due to interactions with the environment…
We describe a coupled cluster framework for coupled systems of electrons and phonons. Neutral and charged excitations are accessed via the equation-of-motion version of the theory. Benchmarks on the Hubbard-Holstein model allow us to assess…