Related papers: Detecting Long-range Correlations with Detrended F…
We investigate how various linear and nonlinear transformations affect the scaling properties of a signal, using the detrended fluctuation analysis (DFA). Specifically, we study the effect of three types of transforms: linear, nonlinear…
In order to interpret and explain the physiological signal behaviors, it can be interesting to find some constants among the fluctuations of these data during all the effort or during different stages of the race (which can be detected…
The imperative of user privacy protection and regulatory compliance necessitates sensitive data removal in model training, yet this process often induces distributional shifts that undermine model performance-particularly in…
Techniques for detecting critical phenomena -- phase transitions where correlation length diverges and small perturbations have large effects -- have been developed across multiple fields over nine decades. We survey between six and twelve…
This paper introduces a multiscale analysis based on optimal piecewise linear approximations of time series. An optimality criterion is formulated and on its base a computationally effective algorithm is constructed for decomposition of a…
We use some fractal analysis methods to study river flow fluctuations. The result of the Multifractal Detrended Fluctuation Analysis (MF-DFA) shows that there are two crossover timescales at $s_{1\times}\sim12$ and $s_{2\times}\sim130$…
Canonical correlation analysis (CCA) is a classic statistical method for discovering latent co-variation that underpins two or more observed random vectors. Several extensions and variations of CCA have been proposed that have strengthened…
We consider several transitions between narrow lines that have an enhanced sensitivity to a possible variation of the fine structure constant, alpha. This enhancement may allow a search to be performed with an effective suppression of the…
The scaling function $F(s)$ in detrended fluctuation analysis (DFA) scales as $F(s)\sim s^{H}$ for stochastic processes with Hurst exponents $H$. We prove this scaling law for both stationary stochastic processes with $0<H<1$, and…
This paper investigates the problem of dim frequency line detection and recovery in the so-called lofargram. Theoretically, time integration long enough can always enhance the detection characteristic. But this does not hold for irregularly…
We propose a fluctuation analysis to quantify spatial correlations in complex networks. The approach considers the sequences of degrees along shortest paths in the networks and quantifies the fluctuations in analogy to time series. In this…
Multivariate time series in domains such as finance, climate science, and healthcare often exhibit long-term trends, seasonal patterns, and short-term fluctuations, complicating causal inference under non-stationarity and autocorrelation.…
We describe an algorithm for simulating ultrasound propagation in random one-dimensional media, mimicking different microstructures by choosing physical properties such as domain sizes and mass densities from probability distributions. By…
Disentanglement is a highly desirable property of representation due to its similarity with human's understanding and reasoning. This improves interpretability, enables the performance of down-stream tasks, and enables controllable…
We present a statistical analysis of music scores from different composers using detrended fluctuation analysis. We find different fluctuation profiles that correspond to distinct auto-correlation structures of the musical pieces. Further,…
As edge devices become increasingly powerful, data analytics are gradually moving from a centralized to a decentralized regime where edge compute resources are exploited to process more of the data locally. This regime of analytics is…
This paper looks into the analysis of the long-range auto-correlations and cross-correlations in bond market. Based on Detrended Moving Average (DMA) method, empirical results present a clear evidence of long-range persistence that exists…
Certain instrumental effects and data reduction anomalies introduce systematic errors in photometric time-series. Detrending algorithms such as the Trend Filtering Algorithm (TFA) (Kov\'{a}cs et al. 2004) have played a key role in…
We present an optimal detrended fluctuation analysis (DFA) and applied it to evaluate the local roughness exponent in non-equilibrium surface growth models with mounded morphology. Our method consists in analyzing the height fluctuations…
Canonical Correlation Analysis (CCA) is a widespread technique for discovering linear relationships between two sets of variables $X \in \mathbb{R}^{n \times p}$ and $Y \in \mathbb{R}^{n \times q}$. In high dimensions however, standard…