Related papers: Characterization of strongly non-linear and singul…
Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics has been recently proposed able to generate high velocity gradients…
In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral…
The hypothesis of a discrete fabric of the universe--the "Planck scale"--is always on stage, since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for…
In machine learning, the scaling law describes how the model performance improves with the model and data size scaling up. From a learning theory perspective, this class of results establishes upper and lower generalization bounds for a…
This paper discusses the use of absolutely one-homogeneous regularization functionals in a variational, scale space, and inverse scale space setting to define a nonlinear spectral decomposition of input data. We present several theoretical…
Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a…
We study the dispersive properties of a linear equation in one spatial dimension which is inspired by models in peridynamics. The interplay between nonlocality and dispersion is analyzed in detail through the study of the asymptotics at low…
Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in…
The assumption that wave function collapse is a real occurrence has very interesting consequences - both experimental and theoretical. Besides predicting observable deviations from linear evolution, it implies that these deviations must…
A large deviation function mathematically characterizes the statistical property of atypical events. Recently, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the…
We give a brief summary of the formalism of invariants in general scalar-tensor and multiscalar-tensor gravities without derivative couplings. By rescaling of the metric and reparametrization of the scalar fields, the theory can be…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…
A two-dimensional lattice system of non-interacting electrons in a homogeneous magnetic field with half a flux quantum per plaquette and a random potential is considered. For the large scale behavior a supersymmetric theory with collective…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a…
Within the framework of scalar-non-metricity gravity, we introduce a steep potential together with a power-law coupling function and investigate whether the acceleration phases of the universe can be consistently described by this model. In…
We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…
Elastic waves of short wavelength propagating through the upper layer of the Earth appear to move faster at large separations of source and receiver than at short separations. This scale dependent velocity is a manifestation of Fermat's…
Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…