Related papers: Generic Multifractality in Exponentials of Long Me…
The concept of memory is of central importance for characterizing complex systems and phenomena. Presence of long-term memories indicates how their dynamics can be less sensitive to initial conditions compared to the chaotic cases. On the…
We investigate finite size scaling in percolating widthless stick systems with variable aspect ratios in an extensive Monte Carlo simulation study. A generalized scaling function is introduced to describe the scaling behavior of the…
The brain is a system operating on multiple time scales, and characterisation of dynamics across time scales remains a challenge. One framework to study such dynamics is that of fractal geometry. However, currently there exists no…
In this paper we consider the growth, large fluctuations and memory properties of an affine stochastic functional differential equation with an average functional where the contributions of the average and instantaneous terms are…
While quantum multifractality has been widely studied in the physics literature and is by now well understood from the point of view of physics, there is little work on this subject in the mathematical literature. I will report on a proof…
To understand the sample-to-sample fluctuations in disorder-generated multifractal patterns we investigate analytically as well as numerically the statistics of high values of the simplest model - the ideal periodic $1/f$ Gaussian noise. By…
We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition…
We construct fractionally integrated continuous-time GARCH models, which capture the observed long range dependence of squared volatility in high-frequency data. Since the usual Molchan-Golosov and Mandelbrot-van-Ness fractional kernels…
We present here a detailed multifractal scaling study for the electronic transmission resonances with the system size for an infinitely large one dimensional perfect and imperfect quasiperiodic system represented by a sequence of…
We apply the phenomenological renormalization group to resting-state fMRI time series of brain activity in a large population. By recursively coarse-graining the data, we compute scaling exponents for the series variance, log probability of…
Recent fully nonlinear, kinetic three-dimensional simulations of magnetic reconnection [Daughton et al. 2011] evolve structures and exhibit dynamics on multiple scales, in a manner reminiscent of turbulence. These simulations of…
We consider the structure functions S^(q)(T), i.e. the moments of order q of the increments X(t+T)-X(t) of the Foreign Exchange rate X(t) which give clear evidence of scaling (S^(q)(T)~T^z(q)). We demonstrate that the nonlinearity of the…
Deep ResNets are recognized for achieving state-of-the-art results in complex machine learning tasks. However, the remarkable performance of these architectures relies on a training procedure that needs to be carefully crafted to avoid…
It was shown recently that the anomalous scaling of simultaneous correlation functions in turbulence is intimately related to the breaking of temporal scale invariance, which is equivalent to the appearance of infinitely many times scales…
This article gives a comprehensive description of the fractal geometry of conformally-invariant (CI) scaling curves, in the plane or half-plane. It focuses on deriving critical exponents associated with interacting random paths, by…
Multiplicative processes and multifractals have earned increased popularity in applications ranging from hydrodynamic turbulence to computer network traffic, from image processing to economics. We analyse the multifractality of the recently…
We present results of the numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy tailed probability distribution functions. Assuming that the distribution function of the random fluctuations…
We use multifractal finite-size scaling to perform a high-precision numerical study of the critical properties of the Anderson localization-delocalization transition in the unitary symmetry class, considering the Anderson model including a…
The study of systems with memory requires methods which are different from the methods used in regular dynamics. Systems with power-law memory in many cases can be described by fractional differential equations, which are…
This study makes the first attempt to use the 2/3-order fractional Laplacian modeling of enhanced diffusing movements of random turbulent particle resulting from nonlinear inertial interactions. A combined effect of the inertial…