Related papers: Multifractal nonlinearity as a robust estimator of…
Datagaps are ubiquitous in real world observational data. Quantifying nonlinearity in data having gaps can be challenging. Reported research points out that interpolation can affect nonlinear quantifiers adversely, artificially introducing…
Although stochastic optimization is central to modern machine learning, the precise mechanisms underlying its success, and in particular, the precise role of the stochasticity, still remain unclear. Modelling stochastic optimization…
We perform a systematic investigation on the components of the empirical multifractality of financial returns using the daily data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. The temporal structure and…
The system size dependence of the multifractal spectrum $f(\alpha)$ and its singularity strength $\alpha$ is investigated numerically. We focus on one-dimensional (1D) and 2D disordered systems with long-range random hopping amplitudes in…
Probability distributions which emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems. In this paper we unite modeling of such distributions with the model of widespread 1/f noise. We…
We introduce a particular construction of an autocorrelation matrix of a time series and its analysis based on the random-matrix theory ideas that is capable of unveiling the type of correlations information which is inaccessible to the…
Improvement in time resolution sometimes introduces short-range random noises into temporal data sequences. These noises affect the results of power-spectrum analyses and the Detrended Fluctuation Analysis (DFA). The DFA is one of useful…
Multivariate Time Series Anomaly Detection (MTSAD) is critical for real-world monitoring scenarios such as industrial control and aerospace systems. Mainstream reconstruction-based anomaly detection methods suffer from two key limitations:…
Let $M_{\gamma}$ be a subcritical Gaussian multiplicative chaos measure associated with a general log-correlated Gaussian field defined on a bounded domain $D \subset \mathbb{R}^d$, $d \geq 1$. We find an explicit formula for its…
Multifractal detrended fluctuation analysis (MFDFA) has become a central method to characterise the variability and uncertainty in empiric time series. Extracting the fluctuations on different temporal scales allows quantifying the strength…
The crucial aspect of this demonstration is the discovery of renewal events, hidden in the computed dynamics of a multifractal metronome, which enables the replacement of the phenomenon of strong anticipation with a time delayed…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
We demonstrate analytically and numerically the possibility that the fractal property of a scale-free network cannot be characterized by a unique fractal dimension and the network takes a multifractal structure. It is found that the mass…
A hallmark of far-from-equilibrium systems is the emergence of a spectral cascade, where energy is transferred across length-scales following a simple power law. The universal nature of this phenomenon has led to advances in a range of…
We consider the "multi-frequency" periodogram, in which the putative signal is modelled as a sum of two or more sinusoidal harmonics with idependent frequencies. It is useful in the cases when the data may contain several periodic…
Multifractal analysis is a forecasting technique used to study the scaling regularity properties of financial returns, to analyze the long-term memory and predictability of financial markets. In this paper, we propose a novel structural…
Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires…
Information from frequency bands in biomedical time series provides useful summaries of the observed signal. Many existing methods consider summaries of the time series obtained over a few well-known, pre-defined frequency bands of…
For many complex systems the interaction of different scales is among the most interesting and challenging features. It seems not very successful to extract the physical properties in different scale regimes by the existing approaches, such…
Modern cellular systems rely increasingly on simultaneous communication in multiple discontinuous bands for macro-diversity and increased bandwidth. Multi-frequency communication is particularly crucial in the millimeter wave (mmWave) and…