Related papers: ROMA (Rank-Ordered Multifractal Analysis) for inte…
The detrending moving average (DMA) algorithm is a widely used technique to quantify the long-term correlations of non-stationary time series and the long-range correlations of fractal surfaces, which contains a parameter $\theta$…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
This paper demonstrates that intermittent magnetic field fluctuations in the plasma sheet exhibit transitory, localized, and multi-scale features. We propose a multifractal based algorithm, which quantifies intermittence on the basis of the…
We introduce a novel way to extract information from turbulent datasets by applying an ARMA statistical analysis. Such analysis goes well beyond the analysis of the mean flow and of the fluctuations and links the behavior of the recorded…
Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…
Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within…
Reduced-order models (ROMs) allow for the simulation of blood flow in patient-specific vasculatures without the high computational cost and wait time associated with traditional computational fluid dynamics (CFD) models. Unfortunately, due…
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,…
An approach is suggested for treating multiscale fluctuations in macromolecular systems. The emphasis is on the statistical properties of such fluctuations. The approach is illustrated by a macromolecular system with mesoscopic fluctuations…
Multivariate time-series have become abundant in recent years, as many data-acquisition systems record information through multiple sensors simultaneously. In this paper, we assume the variables pertain to some geometry and present an…
We introduce ROMAN (ROuting Multiscale representAtioN), a deterministic operator for time series that maps temporal scale and coarse temporal position into an explicit channel structure while reducing sequence length. ROMAN builds an…
The presence of multifractality in a time series shows different correlations for different time scales as well as intermittent behaviour that cannot be captured by a single scaling exponent. The identification of a multifractal nature…
Reduced order models (ROMs) play a critical role in fluid mechanics by providing low-cost predictions, making them an attractive tool for engineering applications. However, for ROMs to be widely applicable, they must not only generalise…
We study the multifractal temporal scaling properties of river discharge and precipitation records. We compare the results for the multifractal detrended fluctuation analysis method with the results for the wavelet transform modulus maxima…
An efficient method of exploring the effects of anisotropy in the fractal properties of 2D surfaces and images is proposed. It can be viewed as a direction-sensitive generalization of the multifractal detrended fluctuation analysis (MFDFA)…
Virtual cell modeling predicts molecular state changes under genetic perturbations in silico, which is essential for biological mechanism studies. However, existing approaches suffer from unconstrained reasoning, uninterpretable…
We propose convenient inferential methods for potentially nonstationary multivariate unobserved components models with fractional integration and cointegration. Based on finite-order ARMA approximations in the state space representation,…
Random matrix theory (RMT) provides a framework to study the spectral fluctuations in physical systems. RMT is capable of making predictions for the fluctuations only after the removal of the secular properties of the spectrum. Spectral…
We perform a comparative study of applicability of the Multifractal Detrended Fluctuation Analysis (MFDFA) and the Wavelet Transform Modulus Maxima (WTMM) method in proper detecting of mono- and multifractal character of data. We quantify…
Topography is the expression of both internal and external processes of a planetary body. Thus hypsometry (the study of topography) is a way to decipher the dynamic of a planet. For that purpose, the statistics of height and slopes may be…