Related papers: Characterization of strongly non-linear and singul…
Physical ageing phenomena far from equilibrium naturally lead to dynamical scaling. It has been proposed to consider the consequences of an extension to a larger Lie algebra of local scale-transformation. The best-tested applications of…
The aim of the present article is to give physical meaning to the ingredients of standard gauge field theory in the framework of the scale relativity theory. Owing to the principle of the relativity of scales, the scale-space is not…
Dynamical theories of speech use computational models of articulatory control to generate quantitative predictions and advance understanding of speech dynamics. The addition of a nonlinear restoring force to task dynamic models is a…
The Herglotz problem is a generalization of the fundamental problem of the calculus of variations. In this paper, we consider a class of non-differentiable functions, where the dynamics is described by a scale derivative. Necessary…
Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality.…
In this paper we study scalar perturbations of the metric for nonlinear $f(R)$ models. We consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. We investigate the astrophysical approach in the case…
Particle segregation is common in natural and industrial processes involving flowing granular materials. Complex, and seemingly contradictory, segregation phenomena have been observed for different boundary conditions and forcing. Using…
Machine learning is rapidly making its path into natural sciences, including high-energy physics. We present the first study that infers, directly from experimental data, a functional form of fragmentation functions. The latter represent a…
We present and analyze stochastic nonlinear differential equations generating signals with the power-law distributions of the signal intensity, 1/f^b noise, power-law autocorrelations and second order structural (height-height correlation)…
On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…
In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…
Scale-space energy density function, $E(\mathbf{x}, \mathbf{r})$, is defined as the derivative of the two-point velocity correlation. The function E describes the turbulent kinetic energy density of scale r at a location x and can be…
The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…
Collapse models possibly suggest the need for a better understanding of the structure of space-time. We argue that physical space, and space-time, are emergent features of the Universe, which arise as a result of dynamical collapse of the…
The turbulent dynamics of nearby and extragalactic gas structures can be studied with the column density power spectrum, which is often described by a broken power-law.In an extragalactic context, the breaks in the power spectra have been…
This paper introduces a scale-invariant methodology employing \textit{Fractal Geometry} to analyze and explain the nonlinear dynamics of complex connectionist systems. By leveraging architectural self-similarity in Deep Neural Networks…
Random fields are commonly used for modeling of spatially (or timely) dependent stochastic processes. In this study, we provide a characterization of the intrinsic complexity of a random field in terms of its second order statistics, e.g.,…
We consider a scale invariant model which includes a $R^{2}$ term in action and show that a stable "emerging universe" scenario is possible. The model belongs to the general class of theories, where an integration measure independent of the…
We study the large time behavior of solutions to the semilinear wave equation with space-dependent damping and absorbing nonlinearity in the whole space or exterior domains. Our result shows how the amplitude of the damping coefficient, the…
The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small…