Engineering bound states in continuum via nonlinearity induced extra dimension

Bound states in continuum (BICs) are localized states of a system possessing significantly large life times with applications across various branches of science. In this work, we propose an expedient protocol to engineer BICs which involves the use of Kerr nonlinearities in the system. The generation of BICs is a direct artifact of the nonlinearity and the associated expansion in the dimensionality of the system. In particular, we consider single and two mode anharmonic systems and provide a number of solutions apposite for the creation of BICs. In close vicinity to the BIC, the steady state response of the system is immensely sensitive to perturbations in natural frequencies of the system and we illustrate its propitious sensing potential in the context of experimentally realizable setups for both optical and magnetic nonlinearities.Comment: 7 pages, 4 figure

Contrastive Graph Pooling for Explainable Classification of Brain Networks

Functional magnetic resonance imaging (fMRI) is a commonly used technique to measure neural activation. Its application has been particularly important in identifying underlying neurodegenerative conditions such as Parkinson's, Alzheimer's, and Autism. Recent analysis of fMRI data models the brain as a graph and extracts features by graph neural networks (GNNs). However, the unique characteristics of fMRI data require a special design of GNN. Tailoring GNN to generate effective and domain-explainable features remains challenging. In this paper, we propose a contrastive dual-attention block and a differentiable graph pooling method called ContrastPool to better utilize GNN for brain networks, meeting fMRI-specific requirements. We apply our method to 5 resting-state fMRI brain network datasets of 3 diseases and demonstrate its superiority over state-of-the-art baselines. Our case study confirms that the patterns extracted by our method match the domain knowledge in neuroscience literature, and disclose direct and interesting insights. Our contributions underscore the potential of ContrastPool for advancing the understanding of brain networks and neurodegenerative conditions