Anomalous diffusion as a stochastic component in the dynamics of complex processes

Multifractal spectral features enhance classification of anomalous diffusion

Anomalous diffusion processes, characterized by their nonstandard scaling of the mean-squared displacement, pose a unique challenge in classification and characterization. In a previous study [Mangalam et al., Phys. Rev. Res. 5, 023144 (2023)2643-156410.1103/PhysRevResearch.5.023144], we established a comprehensive framework for understanding anomalous diffusion using multifractal formalism. The present study delves into the potential of multifractal spectral features for effectively distinguishing anomalous diffusion trajectories from five widely used models: fractional Brownian motion, scaled Brownian motion, continuous-time random walk, annealed transient time motion, and Lévy walk. We generate extensive datasets comprising 10^{6} trajectories from these five anomalous diffusion models and extract multiple multifractal spectra from each trajectory to accomplish this. Our investigation entails a thorough analysis of neural network performance, encompassing features derived from varying numbers of spectra. We also explore the integration of multifractal spectra into traditional feature datasets, enabling us to assess their impact comprehensively. To ensure a statistically meaningful comparison, we categorize features into concept groups and train neural networks using features from each designated group. Notably, several feature groups demonstrate similar levels of accuracy, with the highest performance observed in groups utilizing moving-window characteristics and p varation features. Multifractal spectral features, particularly those derived from three spectra involving different timescales and cutoffs, closely follow, highlighting their robust discriminatory potential. Remarkably, a neural network exclusively trained on features from a single multifractal spectrum exhibits commendable performance, surpassing other feature groups. In summary, our findings underscore the diverse and potent efficacy of multifractal spectral features in enhancing the predictive capacity of machine learning to classify anomalous diffusion processes.

Analysis of EEG signal by flicker-noise spectroscopy: identification of right-/left-hand movement imagination

Flicker-noise spectroscopy (FNS) is a general phenomenological approach to analyzing dynamics of complex nonlinear systems by extracting information contained in chaotic signals. The main idea of FNS is to describe an information hidden in correlation links, which are present in the chaotic component of the signal, by a set of parameters. In the paper, FNS is used for the analysis of electroencephalography signal related to the hand movement imagination. The signal has been parametrized in accordance with the FNS method, and significant changes in the FNS parameters have been observed, at the time when the subject imagines the movement. For the right-hand movement imagination, abrupt changes (visible as a peak) of the parameters, calculated for the data recorded from the left hemisphere, appear at the time corresponding to the initial moment of the imagination. In contrary, for the left-hand movement imagination, the meaningful changes in the parameters are observed for the data recorded from the right hemisphere. As the motor cortex is activated mainly contralaterally to the hand, the analysis of the FNS parameters allows to distinguish between the imagination of the right- and left-hand movement. This opens its potential application in the brain–computer interface.