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We present a novel method, Fractal Space-Curve Analysis (FSCA), which combines Space-Filling Curve (SFC) mapping for dimensionality reduction with fractal Detrended Fluctuation Analysis (DFA). The method is suitable for multidimensional…
We present a tool for batch generation of input scripts and multi-type Fourier analysis from simulation results for the micromagnetic software MuMax3. The introduction of graphical user interface and parameter-sweeping functionality…
Two-Dimensional (2D) Discrete Fourier Transform (DFT) is a basic and computationally intensive algorithm, with a vast variety of applications. 2D images are, in general, non-periodic, but are assumed to be periodic while calculating their…
Source wavelet estimation is the key in seismic signal processing for resolving subsurface structural properties. Homomorphic deconvolution using cepstrum analysis has been an effective method for wavelet estimation for decades. In general,…
With the growing demand for non-Euclidean data analysis, graph signal processing (GSP) has gained significant attention for its capability to handle complex time-varying data. This paper introduces a novel sampling method based on the joint…
Frequency domain representation of time series feature offers a concise representation for handling real-world time series data with inherent complexity and dynamic nature. However, current frequency-based methods with complex operations…
We introduce a multi-windowed graph Fourier transform (MWGFT) for the joint vertex-frequency analysis of signals defined on graphs. Building on generalized translation and modulation induced by the graph Laplacian, the proposed framework…
In this paper, we study long-term correlations and multifractal properties elaborated from time series of three-phase current signals coming from an industrial electric arc furnace plant. Implicit sinusoidal trends are suitably detected by…
Feature Transformation is crucial for classic machine learning that aims to generate feature combinations to enhance the performance of downstream tasks from a data-centric perspective. Current methodologies, such as manual expert-driven…
Transformer-based models, despite their promise for long-term time series forecasting (LTSF), suffer from an inherent low-pass filtering effect that limits their effectiveness. This issue arises due to undifferentiated propagation of…
Machine fault diagnosis (FD) is a critical task for predictive maintenance, enabling early fault detection and preventing unexpected failures. Despite its importance, existing FD models are operation-specific with limited generalization…
With diverse presentation forgery methods emerging continually, detecting the authenticity of images has drawn growing attention. Although existing methods have achieved impressive accuracy in training dataset detection, they still perform…
The logical structure and the basic theorems of time-dependent current density functional theory (TDCDFT) are analyzed and reconsidered from the point of view of recently proposed time-dependent deformation functional theory (TDDefFT). It…
The current generation of all-sky surveys is rapidly expanding our ability to study variable and transient sources. These surveys, with a variety of sensitivities, cadences, and fields of view, probe many ranges of timescale and magnitude.…
Asynchronous Time Series is a multivariate time series where all the channels are observed asynchronously-independently, making the time series extremely sparse when aligning them. We often observe this effect in applications with complex…
Material Flow Analysis (MFA) is used to quantify and understand the life cycles of materials from production to end of use, which enables environmental, social and economic impacts and interventions. MFA is challenging as available data is…
We examine the scaling regime for the detrended fluctuation analysis (DFA) - the most popular method used to detect the presence of long memory in data and the fractal structure of time series. First, the scaling range for DFA is studied…
In Refs. [1,2] we have shown how a combination of modern linear-scaling DFT, together with a subsequent use of large, effective tight-binding Hamiltonians, allows to compute multifractal wave functions yielding the critical properties of…
Time series analysis plays a vital role in fields such as finance, healthcare, industry, and meteorology, underpinning key tasks including classification, forecasting, and anomaly detection. Although deep learning models have achieved…
Based on the well-known Detrended Fluctuation Analysis (DFA) for time series, in this work we describe a DFA for continuous real variable functions. Under certain conditions, DFA accurately predicts the long-term auto-correlation of the…