Related papers: Model selection for identifying power-law scaling
It has long been conjectured that, in three dimensional turbulence, velocity modes at scales larger than the forcing scale follow equilibrium dynamics. Recent numerical and experimental evidence show that such modes share the same mean…
We present an empirical study in the geometric task of learning interatomic potentials, which shows equivariance matters even more at larger scales; we show a clear power-law scaling behaviour with respect to data, parameters and compute…
In general, the power-law degree distribution has profound influence on various dynamical processes defined on scale-free networks. In this paper, we will show that power-law degree distribution alone does not suffice to characterize the…
We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for…
In this paper, we provide a simple, ``generic'' interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as observed…
Over the last decades, impressive progresses have been made in many experimental domains, e.g. microscopic techniques such as single-particle tracking, leading to plethoric amounts of data. In a large variety of systems, from natural to…
It is ubiquitous in natural and social sciences that two variables, recorded temporally or spatially in a complex system, are cross-correlated and possess multifractal features. We propose a new method called multifractal detrended…
The spatial distribution of people exhibits clustering across a wide range of scales, from household ($\sim 10^{-2}$ km) to continental ($\sim 10^4$ km) scales. Empirical data indicates simple power-law scalings for the size distribution of…
We develop a framework to track the structure of temporal networks with a signal processing approach. The method is based on the duality between networks and signals using a multidimensional scaling technique. This enables a study of the…
In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically…
Deep Neural Networks (DNNs) rely on inherent fluctuations in their internal parameters (weights and biases) to effectively navigate the complex optimization landscape and achieve robust performance. While these fluctuations are recognized…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
We propose a new approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface-growth problem. In this framework, the fluctuation sampling time interval…
We propose a novel algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that constitutes a consistent extension of the Detrended Cross-Correlation Analysis (DCCA) and is able to properly identify and quantify subtle characteristics…
In a spatially embedded network, that is a network where nodes can be uniquely determined in a system of coordinates, links' weights might be affected by metric distances coupling every pair of nodes (dyads). In order to assess to what…
We propose a new method of statistical analysis of nucleotide sequences yielding the true scaling without requiring any form of de-trending. With the help of artificial sequences that are proved to be statistically equivalent to the real…
We investigate the relationship of resting-state fMRI functional connectivity estimated over long periods of time with time-varying functional connectivity estimated over shorter time intervals. We show that using Pearson's correlation to…
Diffusion noise is a major source of spectral line broadening in liquid state nano-scale nuclear magnetic resonance with shallow nitrogen-vacancy centres, whose main consequence is a limited spectral resolution. This limitation arises by…
Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these large-scale fluctuations have many degrees of freedom and are…
Several studies have investigated the scaling behavior in naturally occurring biological and physical processes using techniques such as detrended fluctuation analysis (DFA). Data acquisition is an inherent part of these studies and maps…