Related papers: Multifractal emergent processes: Multiplicative in…
The creativity and emergence of biological and psychological behavior are nonlinear. However, that does not necessarily mean only that the measurements of the behaviors are curvilinear. Furthermore, the linear model might fail to reduce…
Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to…
Multifractal formalisms provide an apt framework to study random cascades in which multifractal spectrum width $\Delta\alpha$ fluctuates depending on the number of estimable power-law relationships. Then again, multifractality without…
Processes occurring in real open systems are far from equilibrium state and they can lead to synergetic effects, which are caused by coordinated behavior of system units. Traditional methods of analysis often just establish such behavior,…
Multiplicative random cascade model naturally reproduces the intermittency or multifractality, which is frequently shown among hierarchical complex systems such as turbulence and financial markets. As described herein, we investigate the…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
Momentum-scalar coupling turbulence, a phenomenon observed in both natural and engineering contexts, involves the intricate interaction between multicomponent scalars and multiscale forces (i.e. multiple coupling mechanisms), resulting in a…
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…
The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves…
We investigate stochastic processes possessing scale invariance properties which we refer to as multifractal processes. The examples of such processes known so far do not go much beyond the original cascade construction of Mandelbrot. We…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
Over the last two decades, network science has greatly advanced our understanding of how the collective behaviors of a complex system emerge from the interactions among its basic units. Multiplex networks, i.e. networks with many layers,…
Complex systems exhibit macroscopic behaviors that emerge from the coordinated interactions of their individual components. Understanding the microscopic origins of these emergent properties remains a significant challenge, especially in…
We study the kinetics of nonlinear irreversible fragmentation. Here fragmentation is induced by interactions/collisions between pairs of particles, and modelled by general classes of interaction kernels, and for several types of breakage…
Multifractal analysis of multiplicative random cascades is revisited within the framework of {\em mixed asymptotics}. In this new framework, statistics are estimated over a sample which size increases as the resolution scale (or the…
Complex system arises as a result of the nonlinear interactions between components. In particular, the evolutionary dynamics of a multivariate system encodes the ways in which different variables interact with each other individually or in…
Multifractal analysis has become a powerful signal processing tool that characterizes signals or images via the fluctuations of their pointwise regularity, quantified theoretically by the so-called multifractal spectrum. The practical…
The n-point statistics of singularity strength variables for multiplicative branching processes is calculated from an analytic expression of the corresponding multivariate generating function. The key ingredient is a branching generating…
In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of…
Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of multifractality in the time series. Series fluctuating according to a qGaussian…