Related papers: Motivic Rhythms
The Grothendieck ring of Chow motives admits two natural opposite $\lambda$-ring structures, one of which is a special structure allowing the definition of Adams operations on the ring. In this work I present algorithms which allow an…
The nervous system displays a variety of rhythms in both waking and sleep. These rhythms have been closely associated with different behavioral and cognitive states, but it is still unknown how the nervous system makes use of these rhythms…
Repetition is a basic indicator of musical structure. This study introduces new algorithms for identifying musical phrases based on repetition. Phrases combine to form sections yielding a two-level hierarchical structure. Automatically…
Prosody is usually defined in terms of the three distinct but interacting domains of pitch, intensity and duration patterning, or, more generally, as phonological and phonetic properties of 'suprasegmentals', speech segments which are…
We analyze the distribution of the eigenvalues of the quantum-mechanical rotating harmonic oscillator by means of the Frobenius method. A suitable ansatz leads to a three-term recurrence relation for the expansion coefficients. Truncation…
For the tasks of automatic music emotion recognition, genre recognition, music recommendation it is helpful to be able to extract mode from any section of a musical piece as a perceived amount of major or minor mode (majorness) inside that…
Let $X$ be a variety. In this survey, we study (decompositions of) the motivic class, in the Grothendieck ring of stacks, of the stack $\mathscr{C}oh^n(X)$ of $0$-dimensional coherent sheaves of length $n$ on $X$. To do so, we review the…
This short note is an "elementary'' introduction to the conjectural theory of motives.
We point out the connection of the so-called H\^opital-style rules for monotonicity and oscillation to some well-known properties of concave/convex functions. From this standpoint, we are able to generalize the rules under no…
Mathematicians judge proofs to possess, or lack, a variety of different qualities, including, for example, explanatory power, depth, purity, beauty and fit. Philosophers of mathematical practice have begun to investigate the nature of such…
Some monotone increasing sequences of the lower bounds for the minimum eigenvalue of $M$-matrices are given. It is proved that these sequences are convergent and improve some existing results. Numerical examples show that these sequences…
We propose a design space for data melodification, where standard visualization idioms and fundamental data characteristics map to rhetorical devices of music for a more affective experience of data. Traditional data sonification transforms…
We use the motivic Greenlees spectral sequence from arXiv:2408.00338 to compute Hochschild homology in the stable motivic homotopy category over an algebraically closed field. Our target is $MHH(M\mathbb{Z}/p)/\tau^{p-1}$, where…
Machine learning is the capacity of a computational system to learn structures from datasets in order to make predictions on newly seen data. Such an approach offers a significant advantage in music scenarios in which musicians can teach…
Predictive models for music are studied by researchers of algorithmic composition, the cognitive sciences and machine learning. They serve as base models for composition, can simulate human prediction and provide a multidisciplinary…
The theory of rational motives admits several models, including those of Morel, Beilinson, Ayoub, and Voevodsky. An open question has been the equivalence of Voevodsky's Nisnevich-based $\mathrm{DM}(S, \mathbb{Q})$ with the others, which…
The purpose of this paper is mostly to present conjectures that extend, to the ``triangular partition'' context (partitions ``under any line'' in the terminology of Blaziak-Haiman-Morse-Pun-Seelinger), properties of Frobenius of…
Modeling biological rhythms helps understand the complex principles behind the physical and psychological abnormalities of human bodies, to plan life schedules, and avoid persisting fatigue and mood and sleep alterations due to the…
The collaboration of mathematics in the two musical systems of Pythagorean sounds and of equal sounds is evident and opportune for generating the elements and managing their relationships. The only essential notion for a rational…
We present a rooted hypersequent calculus for modal propositional logic S5. We show that all rules of this calculus are invertible and that the rules of weakening, contraction, and cut are admissible. Soundness and completeness are…