Continuous Dependence on Modeling for Related Cauchy Problems of a Class of Evolution Equations

Continuous dependence results for solutions of the Navier-Stokes equations backward in time

In this paper we are concerned with solutions to the Navier-Stokes equations backward in time on a bounded domain of R3 with “small” data prescribed at time t = 0. The solution of such a problem is compared with that of the analogous linear Stokes problem, and under appropriate constraint restrictions an L2 bound for the difference is obtained.

Comparison of viscous flows backward in time with small data

Order of convergence estimates on the interaction term for a micropolar fluid

Some remarks on ill-posed problems for viscous fluids

Some stability criteria in fluid and solid mechanics

Robot-assisted bimanual training is promising to improve motor function and cortical reorganization for hemiparetic stroke patients. Closing the rehabilitation training loop with neurofeedback can help refine training protocols in time for better engagements and outcomes. However, due to the low signal-to-noise ratio (SNR) and non-stationary properties of neural signals, reliable characterization of bimanual training-induced neural activities from single-trial measurement is challenging. In this study, ten human participants were recruited conducting robot-assisted bimanual cyclical tasks (in-phase, 90° out-of-phase, and anti-phase) when concurrent electroencephalography (EEG) and functional near-infrared spectroscopy (fNIRS) were recorded. A unified EEG-fNIRS bimodal signal processing framework was proposed to characterize neural activities induced by three types of bimanual cyclical tasks. In this framework, novel artifact removal methods were used to improve the SNR and the task-related component analysis (TRCA) was introduced to increase the reproducibility of EEG-fNIRS bimodal features. The optimized features were transformed into low-dimensional indicators to reliably characterize bimanual training-induced neural activation. The SVM classification results of three bimanual cyclical tasks revealed a good discrimination ability of EEG-fNIRS bimodal indicators (90.1%), which was higher than that using EEG (74.8%) or fNIRS (82.2%) alone, supporting the proposed method as a feasible technique to characterize neural activities during robot-assisted bimanual training.

Characterization of Bimanual Cyclical Tasks From Single-Trial EEG-fNIRS Measurements

Bimanual coordination is common in human daily life, whereas current research focused mainly on decoding unimanual movement from electroencephalogram (EEG) signals. Here we developed a brain-computer interface (BCI) paradigm of task-oriented bimanual movements to decode coordinated directions from movement-related cortical potentials (MRCPs) of EEG. Eight healthy subjects participated in the target-reaching task, including (1) performing leftward, midward, and rightward bimanual movements, and (2) performing leftward and rightward unimanual movements. A combined deep learning model of convolution neural network and bidirectional long short-term memory network was proposed to classify movement directions from EEG. Results showed that the average peak classification accuracy for three coordinated directions of bimanual movements reached <inline-formula> <tex-math notation="LaTeX">$73.39~\pm ~6.35$ </tex-math></inline-formula>%. The binary classification accuracies achieved <inline-formula> <tex-math notation="LaTeX">$80.24~\pm ~6.25$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$82.62~\pm ~7.82$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$86.28~\pm ~5.50$ </tex-math></inline-formula>% for leftward versus midward, rightward versus midward and leftward versus rightward, respectively. We also compared the binary classification (leftward versus rightward) of bimanual, left-hand, and right-hand movements, and accuracies achieved <inline-formula> <tex-math notation="LaTeX">$86.28~\pm ~5.50$ </tex-math></inline-formula>%, <inline-formula> <tex-math notation="LaTeX">$75.67~\pm ~7.18$ </tex-math></inline-formula>%, and <inline-formula> <tex-math notation="LaTeX">$77.79~\pm ~5.65$ </tex-math></inline-formula>%, respectively. The results indicated the feasibility of decoding human coordinated directions of task-oriented bimanual movements from EEG.

https://ieeexplore.ieee.org/ielx7/7333/4359219/09943285.pdf

Decoding Coordinated Directions of Bimanual Movements From EEG Signals

While many voluntary movements involve bimanual coordination, few attempts have been made to simultaneously decode the trajectory of bimanual movements from electroencephalogram (EEG) signals. In this study, we proposed a novel bimanual brain-computer interface (BCI) paradigm to reconstruct the continuous trajectory of both hands during coordinated movements from EEG. The protocol required human subjects to complete a bimanual reaching task to the left, middle, or right target while EEG data were collected. A multi-task deep learning model combining the EEGNet and long short-term memory network (LSTM) was proposed to decode bimanual trajectories, including position and velocity. Decoding performance was evaluated in terms of the correlation coefficient (CC) and normalized root mean square error (NRMSE) between decoded and real trajectories. Experimental results from 13 human subjects showed that the grand-averaged combined CC values achieved 0.54 and 0.42 for position and velocity decoding, respectively. The corresponding combined NRMSE values were 0.22 and 0.23. Both CC and NRMSE were significantly superior to the chance level (p<0.05). Comparative experiments also indicated that the proposed model significantly outperformed some other commonly-used methods in terms of CC and NRMSE for continuous trajectory decoding. These findings demonstrated the feasibility of simultaneously decoding bimanual trajectory from EEG, indicating the potential of bimanual control for coordinated tasks.

Continuous Bimanual Trajectory Decoding of Coordinated Movement From EEG Signals

Recent studies revealed that setting motor priming prior to main intervention can improve rehabilitation outcomes. However, existing priming strategies generally take dozens of minutes, leading to reduced effective treatment time and rehabilitation prescription flexibility. Priming individual training trial with a short-term (a few seconds) task may be a promising alternative. The current study focused on investigating short-term priming effects via an electroencephalogram (EEG) study of action observation (AO) on motor imagery (MI). Six healthy adults were recruited to perform MI of left or right elbow flexion-extension primed by AO of the same action. The control condition replaced AO priming with directional arrows indicating different elbows. We employed the event-related desynchronization (ERD) of &#x00B5; rhythm (8-13 Hz) and the classification accuracy of MI to evaluate short-term priming effects. The obtained results revealed that both ERD intensity and classification accuracy of AO-primed MI were greater than those of arrow cue-guided MI, supporting short-term priming as a feasible adjuvant technique to boost the effect of main intervention. 

Jong Chul Song

Papers

Some stability criteria in fluid and solid mechanics

Characterization of Bimanual Cyclical Tasks From Single-Trial EEG-fNIRS Measurements

Decoding Coordinated Directions of Bimanual Movements From EEG Signals

Continuous Bimanual Trajectory Decoding of Coordinated Movement From EEG Signals

Short-term Priming Effects: an EEG Study of Action Observation on Motor Imagery