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We first apply the WT-MFDFA, MFDFA, and WTMM multifractal methods to binomial multifractal time series of three different binomial parameters and find that the WTMM method indicates an enhanced difference between the fractal components than…
In this study, we challenge the traditional approach of frequency analysis on directed graphs, which typically relies on a single measure of signal variation such as total variation. We argue that the inherent directionality in directed…
An analytical formula for the contributions of the trend leftovers in DFA method is presented, based upon which the crossovers in DFA are investigated in detail. This general formula can explain the calculated results with DFA method for…
We illustrate the efficacy of a discrete wavelet based approach to characterize fluctuations in non-stationary time series. The present approach complements the multi-fractal detrended fluctuation analysis (MF-DFA) method and is quite…
To understand methodological features of the detrended fluctuation analysis (DFA) using a higher-order polynomial fitting, we establish the direct connection between DFA and Fourier analysis. Based on an exact calculation of the…
Canonical correlation analysis is a statistical technique that is used to find relations between two sets of variables. An important extension in pattern analysis is to consider more than two sets of variables. This problem can be expressed…
Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, controlling the roughness of the extracted…
Cross-frequency coupling (CFC) has been proposed to coordinate neural dynamics across spatial and temporal scales. Despite its potential relevance for understanding healthy and pathological brain function, the standard CFC analysis and…
Rank-Ordered Multifractal Analysis (ROMA), a recently developed technique that combines the ideas of parametric rank ordering and one parameter scaling of monofractals, has the capabilities of deciphering the multifractal characteristics of…
We develop a Non-Crossing Approximation (NCA) for the effective cluster problem of the recently developed Dynamical Cluster Approximation (DCA). The DCA technique includes short-ranged correlations by mapping the lattice problem onto a…
A powerful study design in the fields of genomics and metabolomics is the 'replicated time course experiment' where individual time series are observed for a sample of biological units, such as human patients, termed replicates. Standard…
Complex networks have been studied in recent years due to their relevance in biological, social and technical real systems, such as the world wide web, social networks and biochemical interactions. One of the most current features of…
Multivariate time series forecasting is widely used in various fields. Reasonable prediction results can assist people in planning and decision-making, generate benefits and avoid risks. Normally, there are two characteristics of time…
Multivariate time series (MTS) forecasting has been extensively applied across diverse domains, such as weather prediction and energy consumption. However, current studies still rely on the vanilla point-wise self-attention mechanism to…
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…
In this work, the concept of Braced Fourier Continuation and Regression (BFCR) is introduced. BFCR is a novel and computationally efficient means of finding nonlinear regressions or trend lines in arbitrary one-dimensional data sets. The…
Dynamic conditional correlation (DCC) is a method that estimates the correlation between two time series across time. Although used primarily in finance so far, DCC has been proposed recently as a model-based estimation method for…
Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or…
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…
Multilinear Principal Component Analysis (MPCA) is a widely utilized method for the dimension reduction of tensor data. However, the integration of MPCA into federated learning remains unexplored in existing research. To tackle this gap,…