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1.
Chaos ; 34(7)2024 Jul 01.
Artículo en Inglés | MEDLINE | ID: mdl-38985968

RESUMEN

Phase space reconstruction (PSR) methods allow for the analysis of low-dimensional data with methods from dynamical systems theory, but their application to prediction models, such as those from machine learning (ML), is limited. Therefore, we here present a model adaptive phase space reconstruction (MAPSR) method that unifies the process of PSR with the modeling of the dynamical system. MAPSR is a differentiable PSR based on time-delay embedding and enables ML methods for modeling. The quality of the reconstruction is evaluated by the prediction loss. The discrete-time signal is converted into a continuous-time signal to achieve a loss function, which is differentiable with respect to the embedding delays. The delay vector, which stores all potential embedding delays, is updated along with the trainable parameters of the model to minimize prediction loss. Thus, MAPSR does not rely on any threshold or statistical criterion for determining the dimension and the set of delay values for the embedding process. We apply the MAPSR method to uni- and multivariate time series stemming from chaotic dynamical systems and a turbulent combustor. We find that for the Lorenz system, the model trained with the MAPSR method is able to predict chaotic time series for nearly seven to eight Lyapunov time scales, which is found to be much better compared to other PSR methods [AMI-FNN (average mutual information-false nearest neighbor) and PECUZAL (Pecora-Uzal) methods]. For the univariate time series from the turbulent combustor, the long-term cumulative prediction error of the MAPSR method for the regime of chaos stays between other methods, and for the regime of intermittency, MAPSR outperforms other PSR methods.

2.
Chaos ; 30(2): 023111, 2020 Feb.
Artículo en Inglés | MEDLINE | ID: mdl-32113225

RESUMEN

The development of new approaches to detect motor-related brain activity is key in many aspects of science, especially in brain-computer interface applications. Even though some well-known features of motor-related electroencephalograms have been revealed using traditionally applied methods, they still lack a robust classification of motor-related patterns. Here, we introduce new features of motor-related brain activity and uncover hidden mechanisms of the underlying neuronal dynamics by considering event-related desynchronization (ERD) of µ-rhythm in the sensorimotor cortex, i.e., tracking the decrease of the power spectral density in the corresponding frequency band. We hypothesize that motor-related ERD is associated with the suppression of random fluctuations of µ-band neuronal activity. This is due to the lowering of the number of active neuronal populations involved in the corresponding oscillation mode. In this case, we expect more regular dynamics and a decrease in complexity of the EEG signal recorded over the sensorimotor cortex. In order to support this, we apply measures of signal complexity by means of recurrence quantification analysis (RQA). In particular, we demonstrate that certain RQA quantifiers are very useful to detect the moment of movement onset and, therefore, are able to classify the laterality of executed movements.


Asunto(s)
Electroencefalografía , Actividad Motora/fisiología , Adolescente , Adulto , Femenino , Humanos , Masculino , Procesamiento de Señales Asistido por Computador , Factores de Tiempo , Adulto Joven
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