Related papers: Sound and motion in the De Generatione Sonorum, a …

A quantum mechanical formulation of de Sitter cosmological spacetimes still eludes string theory. In this paper we conjecture a potentially rigorous framework in which the status of de Sitter space is the same as that of a resonance in a…

It is a deceptively simple question to ask how acoustic disturbances propagate in a non--homogeneous flowing fluid. If the fluid is barotropic and inviscid, and the flow is irrotational (though it may have an arbitrary time dependence),…

The effect of gravity and proper acceleration on the frequency spectrum of an optical resonator - both rigid or deformable - is considered in the framework of general relativity. The optical resonator is modeled either as a rod of matter…

This paper gives an introduction to the theory of orthogonal projection of functions or signals. Several kinds of decomposition are explored: Fourier, Fourier-Legendre, Fourier-Bessel series for 1D signals, and Spherical Harmonic series for…

We propose a novel approach for studying rooted trees by using functions that we will call descent functions. We provide a construction method for rooted trees that allows to study their properties through the use of descent functions.…

Generative diffusion models have emerged as leading models in speech and image generation. However, in order to perform well with a small number of denoising steps, a costly tuning of the set of noise parameters is needed. In this work, we…

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 propose a new representation of human body motion which encodes a full motion in a sequence of latent motion primitives. Recently, task generic motion priors have been introduced and propose a coherent representation of human motion…

In recent years, the field of image generation has been revolutionized by the application of autoregressive transformers and DDPMs. These approaches model the process of image generation as a step-wise probabilistic processes and leverage…

The time in an atomic clock in motion is discussed using the analogy of a sing around sound source. Sing around frequency is modified according to the motion of the sing around sound source, using the Lorentz transformation equation. Thus,…

"How can we animate 3D-characters from a movie script or move robots by simply telling them what we would like them to do?" "How unstructured and complex can we make a sentence and still generate plausible movements from it?" These are…

Noise is widely understood to be something that interferes with a signal or process. Thus, it is generally thought to be destructive, obscuring signals and interfering with function. However, early in the 20th century, mechanical engineers…

We investigate the classical problem of motion of a mathematical pendulum with an oscillating pivot. This simple mechanical setting is frequently used as the prime example of a system exhibiting the parametric resonance phenomenon, which…

The classical walking behaviors of a single atom in an amplitude-modulated standing wave lattice beyond the internal dynamics are investigated. Based on a simple effective model, we identify a diversity of dynamic regimes of atomic motion…

We address two basic issues in the theory of galaxy formation from fluctuations of quantum fields: 1) the nature and origin of noise and fluctuations and 2) the conditions for using a classical stochastic equation for their description. On…

Human motion stylization aims to revise the style of an input motion while keeping its content unaltered. Unlike existing works that operate directly in pose space, we leverage the latent space of pretrained autoencoders as a more…

We study the role of noise on the nature of the transition to collective motion in dry active matter. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a…

We set up a parametrised monadic translation for a class of call-by-value functional languages, and prove a corresponding soundness theorem. We then present a series of concrete instantiations of our translation, demonstrating that a number…

Sonar systems are frequently used to classify objects at a distance by using the structure of the echoes of acoustic waves as a proxy for the object's shape and composition. Traditional synthetic aperture processing is highly effective in…

We discuss the classical motion of a spring of arbitrary mass coupled to two arbitrary massive blocks attached at its ends. A general approach to the problem is presented and some general results are obtained. Examples for which a simple…