相关论文: Motivic Rhythms
Understanding the structural characteristics of harmony is essential for an effective use of music as a communication medium. Of the three expressive axes of music (melody, rhythm, harmony), harmony is the foundation on which the emotional…
The main goal of this paper is to study relative versions of the category of modules over the isotropic motivic Brown-Peterson spectrum, with a particular emphasis on their cellular subcategories. Using techniques developed by Levine, we…
We construct motivic power operations on the mod-$p$ motivic cohomology of $\Fb_p$-schemes using a motivic refinement of Nizio{\l}'s theorem. The key input is a purity theorem for motivic cohomology established by Levine. Our operations…
Using the theory of framed correspondences developed by Voevodsky, we introduce and study framed motives of algebraic varieties. They are the major computational tool for constructing an explicit quasi-fibrant motivic replacement of the…
In this work we present an algorithm for composing monophonic melodies similar in style to those of a given, phrase annotated, sample of melodies. For implementation, a hybrid approach incorporating parametric Markov models of higher order…
We present an algebraic construction of music notes and show how to associate them inseveral ways to construct music ranges. Then a family of ranges emerge with a fixed number of notes: two, three, five, seven, twelve, seventeen, etc. A…
This is an overview and a preview of the theory of "mixed motives of level 1" explaining some results, projects, ideas and indicating a bunch of problems.
We compute the motivic nearby cycles of functions obtained by composition with a polynomial which is non-degenerate with respect to its Newton polyhedron. Our result involves new convolution operators and generalized nearby cycles.
Transformer architectures offer significant advantages regarding the generation of symbolic music; their capabilities for incorporating user preferences toward what they generate is being studied under many aspects. This paper studies the…
We define the categories of log motives and log mixed motives. The latter gives a new formulation for the category of mixed motives. We prove that the former is a semisimple abelian category if and only if the numerical equivalence and…
Creativity, or the ability to produce new useful ideas, is commonly associated to the human being; but there are many other examples in nature where this phenomenon can be observed. Inspired by this fact, in engineering and particularly in…
Theory of motivic superpolynomials is developed, including its extension to algebraic links colored by rows, relations to $L$-functions of plane curve singularities, the justification of the motivic versions of Weak Riemann Hypothesis, and…
In the domain of algorithmic music composition, machine learning-driven systems eliminate the need for carefully hand-crafting rules for composition. In particular, the capability of recurrent neural networks to learn complex temporal…
We investigate high-order harmonic generation in inhomogeneous media for reduced dimensionality models. We perform a phase-space analysis, in which we identify specific features caused by the field inhomogeneity. We compute high-order…
Music comprises of a set of complex simultaneous events organized in time. In this paper we introduce a novel framework that we call Deep Musical Information Dynamics, which combines two parallel streams - a low rate latent representation…
We give an explicit formula for the motivic integrals related to the Milnor number over spaces of parametrised arcs on the plane with fixed tangency orders with the axis. These integrals are rational functions of the parameters and the…
In addressing the challenge of interpretability and generalizability of artificial music intelligence, this paper introduces a novel symbolic representation that amalgamates both explicit and implicit musical information across diverse…
Many applications, including rank aggregation and crowd-labeling, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and columns. We consider the problem of estimating such a matrix based on…
Given two smooth projective varieties X and Y over a field, we say that X motivates Y if the (suitably defined) motive of Y is contained in the category generated from X by taking sums, summands and products. This notion has appeared…
In this note we will illustrate a method for computing the $\pi_0$ of the effective log motive of a smooth and proper variety over a perfect field $k$ and show that it is $\mathbf{A}^1$-invariant. We will apply this to compute the first…