Related papers: Scale invariant growth processes in expanding spac…
Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments…
We investigate the statistical properties of translation invariant random fields (including point processes) on Euclidean spaces (or lattices) under constraints on their spectrum or structure function. An important class of models that…
This paper is concerned mainly with the macroscopic fractal behavior of various random sets that arise in modern and classical probability theory. Among other things, it is shown here that the macroscopic behavior of Boolean coverage…
We investigate the conditions under which cosmological variations in physical `constants' and scalar fields are detectable on the surface of local gravitationally-bound systems, such as planets, in non-spherically symmetric background…
There is evidence of a scale-invariant matter distribution up to scales over 10 Megaparsecs. We review scaling (fractal or multifractal) models of large scale structure and their observational evidence. We conclude that the dynamics of…
We study the fluctuations of the area $A=\int_0^T x(t) dt$ under a one-dimensional Brownian motion $x(t)$ in a trapping potential $\sim |x|$, at long times $T\to\infty$. We find that typical fluctuations of $A$ follow a Gaussian…
Studies of a class of infinite one dimensional self-gravitating systems have highlighted that, on the one hand, the spatial clustering which develops may have scale invariant (fractal) properties, and, on the other, that they display…
The properties of scale-free random trees are investigated using both preconditioning on non-extinction and fixed size averages, in order to study the thermodynamic limit. The scaling form of volume probability is found, the connectivity…
The concepts of scale invariance, self-similarity and scaling have been fruitfully applied to the study of price fluctuations in financial markets. After a brief review of the properties of stable Levy distributions and their applications…
We study, both with numerical simulations and theoretical methods, a cellular automata model for continuum equations describing growth processes in the presence of an external flux of particles. As a result of local instabilities we find a…
We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves…
We develop a scale-invariant truncated L\'evy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits L\'evy stability for the probability density, and hence shows scaling…
We develop the formalism to investigate the relation between the evolution of the large-scale (quasi) linear structure and that of the small-scale nonlinear structure in Newtonian cosmology within the Lagrangian framework. In doing so, we…
Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance…
In this lecture we present an overview of the physics of irreversible fractal growth process, with particular emphasis on a class of models characterized by {\em quenched disorder}. These models exhibit self-organization, with critical…
The dependence of the scaling properties of the structure factor on space dimensionality, range of interaction, initial and final conditions, presence or absence of a conservation law is analysed in the framework of the large-N model for…
We study various solution behaviors of scale equations which are recently proposed in \cite{Kim}. On the contrary to conventional mathematical tools, scale equations are capable to accommodate various behaviors at different scale levels…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
Recent deep learning models increasingly rely on depth without structural guarantees on the validity of intermediate representations, rendering early stopping and adaptive computation ill-posed. We address this limitation by formulating a…
It is shown that density fluctuations obey a scaling law in an open Friedmann universe. In a flat universe, the fluctuations are not scale-invariant. We compute the growth rate of adiabatic scale-invariant density fluctuations in flat, open…