Related papers: Characterization of strongly non-linear and singul…
In this paper, we investigate the role of scalar field potentials in the dynamical evolution of the Universe. A gravity theory with a non-minimally coupled scalar field with torsion in the geometrical action simulating effective dark energy…
The literature on time series of functional data has focused on processes of which the probabilistic law is either constant over time or constant up to its second-order structure. Especially for long stretches of data it is desirable to be…
The nonlinear, cubic Schrodinger (NLS) equation has numerous physical applications, but in general is very difficult to solve. Nonetheless, under certain circumstances parameters quantifying the width, momentum and energy of the…
We investigate the use of models from the theory of regularity structures as features in machine learning tasks. A model is a polynomial function of a space-time signal designed to well-approximate solutions to partial differential…
We introduce a notion of fractional (noninteger order) derivative on an arbitrary nonempty closed subset of the real numbers (on a time scale). Main properties of the new operator are proved and several illustrative examples given.
The steady state reached by a system of particles sliding down a fluctuating surface has interesting properties. Particle clusters form and break rapidly, leading to a broad distribution of sizes and large fluctuations. The density-density…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
We present results of direct numerical simulations of passive scalar advection and diffusion in turbulent rotating flows. Scaling laws and the development of anisotropy are studied in spectral space, and in real space using an axisymmetric…
Large assemblies of nonlinear dynamical units driven by a long-wave fluctuating external field are found to generate strong turbulence with scaling properties. This type of turbulence is so robust that it persists over a finite parameter…
We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
We study samples of natural images for which a set of statistical characteristics is computed and scale-invariant properties of samples are demonstrated computationally. Computations of the power spectrum are carried out and a power-law…
Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time-ordered data, with applications in many disciplines such as physics, biology, finance, and engineering. Measured time-series data, however, are…
Modeling phenomena from experimental data, always begin with a \emph{choice of hypothesis} on the observed dynamics such as \emph{determinism}, \emph{randomness}, \emph{derivability} etc. Depending on these choices, different behaviors can…
The interpretation proposed in quant-ph/9812011 is extended to the general case of a non-relativistic particle moving in an arbitrary external potential. It is shown that, even in this general case, "particle" solutions exist which do not…
In this paper we study two types of means of the entries of a nonnegative matrix: the \emph{permanental mean}, which is defined using permanents, and the \emph{scaling mean}, which is defined in terms of an optimization problem. We explore…
We consider the set of power functions defined on the set of positive real number, and their linear combinations. After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative…
The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to…
Neural scaling laws describe how the performance of deep neural networks scales with key factors such as training data size, model complexity, and training time, often following power-law behaviors over multiple orders of magnitude. Despite…
We study, using numerical simulations, the dynamical evolution of self-gravitating point particles in static euclidean space, starting from a simple class of infinite ``shuffled lattice'' initial conditions. These are obtained by applying…