Mechanisms of pelvic floor muscle function and the effect on the urethra during a cough

Background: Current measurement tools have difficulty identifying the automaticphysiologic processes maintaining continence, and many questions still remainabout pelvic floor muscle (PFM) function during automatic events.Objective: To perform a feasibility study to characterise the displacement, velocity,and acceleration of the PFM and the urethra during a cough.Design, setting, and participants: A volunteer convenience sample of 23 continentwomen and 9 women with stress urinary incontinence (SUI) from the generalcommunity of San Francisco Bay Area was studied.Measurements: Methods included perineal ultrasound imaging, motion trackingof the urogenital structures, and digital vaginal examination. Statistical analysisused one-tailed unpaired student t tests, and Welch’s correction was applied whenvariances were unequal.Results and limitations: The cough reflex activated the PFM of continent women tocompress the urogenital structures towards the pubic symphysis, which wasabsent in women with SUI. The maximum accelerations that acted on the PFMduring a cough were generally more similar than the velocities and displacements.The urethras of women with SUI were exposed to uncontrolled transverse accelerationand were displaced more than twice as far ( p = 0.0002), with almost twicethe velocity ( p = 0.0015) of the urethras of continent women. Caution regardingthe generalisability of this study is warranted due to the small number of women inthe SUI group and the significant difference in parity between groups.Conclusions: During a cough, normal PFM function produces timely compressionof the pelvic floor and additional external support to the urethra, reducing displacement,velocity, and acceleration. In women with SUI, who have weakerurethral attachments, this shortening contraction does not occur; consequently,the urethras of women with SUI move further and faster for a longer duratio

Node Embedding from Neural Hamiltonian Orbits in Graph Neural Networks

In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit over time. Since the Hamiltonian orbits generalize the exponential maps, this approach allows us to learn the underlying manifold of the graph in training, in contrast to most of the existing literature that assumes a fixed graph embedding manifold with a closed exponential map solution. Our proposed node embedding strategy can automatically learn, without extensive tuning, the underlying geometry of any given graph dataset even if it has diverse geometries. We test Hamiltonian functions of different forms and verify the performance of our approach on two graph node embedding downstream tasks: node classification and link prediction. Numerical experiments demonstrate that our approach adapts better to different types of graph datasets than popular state-of-the-art graph node embedding GNNs. The code is available at \url{https://github.com/zknus/Hamiltonian-GNN}

On the Robustness of Graph Neural Diffusion to Topology Perturbations

Neural diffusion on graphs is a novel class of graph neural networks that has attracted increasing attention recently. The capability of graph neural partial differential equations (PDEs) in addressing common hurdles of graph neural networks (GNNs), such as the problems of over-smoothing and bottlenecks, has been investigated but not their robustness to adversarial attacks. In this work, we explore the robustness properties of graph neural PDEs. We empirically demonstrate that graph neural PDEs are intrinsically more robust against topology perturbation as compared to other GNNs. We provide insights into this phenomenon by exploiting the stability of the heat semigroup under graph topology perturbations. We discuss various graph diffusion operators and relate them to existing graph neural PDEs. Furthermore, we propose a general graph neural PDE framework based on which a new class of robust GNNs can be defined. We verify that the new model achieves comparable state-of-the-art performance on several benchmark datasets

Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approach

Graph neural networks (GNNs) are vulnerable to adversarial perturbations, including those that affect both node features and graph topology. This paper investigates GNNs derived from diverse neural flows, concentrating on their connection to various stability notions such as BIBO stability, Lyapunov stability, structural stability, and conservative stability. We argue that Lyapunov stability, despite its common use, does not necessarily ensure adversarial robustness. Inspired by physics principles, we advocate for the use of conservative Hamiltonian neural flows to construct GNNs that are robust to adversarial attacks. The adversarial robustness of different neural flow GNNs is empirically compared on several benchmark datasets under a variety of adversarial attacks. Extensive numerical experiments demonstrate that GNNs leveraging conservative Hamiltonian flows with Lyapunov stability substantially improve robustness against adversarial perturbations. The implementation code of experiments is available at https://github.com/zknus/NeurIPS-2023-HANG-Robustness.Comment: Accepted by Advances in Neural Information Processing Systems (NeurIPS), New Orleans, USA, Dec. 2023, spotligh

Graph Neural Convection-Diffusion with Heterophily

Graph neural networks (GNNs) have shown promising results across various graph learning tasks, but they often assume homophily, which can result in poor performance on heterophilic graphs. The connected nodes are likely to be from different classes or have dissimilar features on heterophilic graphs. In this paper, we propose a novel GNN that incorporates the principle of heterophily by modeling the flow of information on nodes using the convection-diffusion equation (CDE). This allows the CDE to take into account both the diffusion of information due to homophily and the ``convection'' of information due to heterophily. We conduct extensive experiments, which suggest that our framework can achieve competitive performance on node classification tasks for heterophilic graphs, compared to the state-of-the-art methods. The code is available at \url{https://github.com/zknus/Graph-Diffusion-CDE}.Comment: Proc. International Joint Conference on Artificial Intelligence (IJCAI), Macao, China, Aug. 202