The behavior of the network and its stability are governed by both dynamics of the individual nodes, as well as their topological interconnections. The attention mechanism as an integral part of neural network models was initially designed for natural language processing (NLP) and, so far, has shown excellent performance in combining the dynamics of individual nodes and the coupling strengths between them within a network. Despite the undoubted impact of the attention mechanism, it is not yet clear why some nodes of a network obtain higher attention weights. To come up with more explainable solutions, we tried to look at the problem from a stability perspective. Based on stability theory, negative connections in a network can create feedback loops or other complex structures by allowing information to flow in the opposite direction. These structures play a critical role in the dynamics of a complex system and can contribute to abnormal synchronization, amplification, or suppression. We hypothesized that those nodes that are involved in organizing such structures could push the entire network into instability modes and therefore need more attention during analysis. To test this hypothesis, the attention mechanism, along with spectral and topological stability analyses, was performed on a real-world numerical problem, i.e., a linear Multi-Input Multi-Output state-space model of a piezoelectric tube actuator. The findings of our study suggest that the attention should be directed toward the collective behavior of imbalanced structures and polarity-driven structural instabilities within the network. The results demonstrated that the nodes receiving more attention cause more instability in the system. Our study provides a proof of concept to understand why perturbing some nodes of a network may cause dramatic changes in the network dynamics.

Deep brain stimulation (DBS) is widely used as a treatment option for patients with movement disorders. In addition to its clinical impact, DBS has been utilized in the field of cognitive neuroscience wherein the answers to several fundamental questions underpinning the mechanisms of neuromodulation in decision making rely on how a burst of DBS pulses, usually delivered at clinical frequency, i.e., 130 Hz, perturb participants' choices. It was observed that neural activities recorded during DBS were contaminated with stereotype large artifacts, which lasts for a few milliseconds, as well as a low-frequency (slow) signal (~1-2 Hz) that can persist for hundreds of milliseconds. While the focus of the most of methods for removing DBS artifact was on the former, the artifact removal of the slow signal has not been addressed. In this work, we propose a new method based on combining singular value decomposition (SVD) and normalized adaptive filtering to remove both large (fast) and slow artifacts in local field potentials recorded during a cognitive task in which bursts of DBS were utilized. Using synthetic data, we show that our proposed algorithm outperforms four commonly used techniques in the literature, namely, (1) Normalized least mean square adaptive filtering, (2) Optimal FIR Wiener filtering, (3) Gaussian model matching, and (4) Moving average. The algorithm's capabilities are further demonstrated by its ability to effectively remove DBS artifacts in local field potentials recorded from the subthalamic nucleus during a verbal Stroop task, highlighting its utility in real-world applications.