Lotka-Sharpe Neural Operators for Control of Population PDEs

Age-structured predator-prey integro-partial differential equations provide models of interacting populations in ecology, epidemiology, and biotechnology. A key challenge in feedback design for these systems is the scalar $ζ$, defined implicitly by the Lotka-Sharpe nonlinear integral condition, as a mapping from fertility and mortality rates to $ζ$. To solve this challenge with operator learning, we first prove that the Lotka-Sharpe operator is Lipschitz continuous, guaranteeing the existence of arbitrarily accurate neural operator approximations over a compact set of fertility and mortality functions. We then show that the resulting approximate feedback law preserves semi-global practical asymptotic stability under propagation of the operator approximation error through various other nonlinear operators, all the way through to the control input. In the numerical results, not only do we learn ``once-and-for-all'' the canonical Lotka-Sharpe (LS) operator, and thus make it available for future uses in control of other age-structured population interconnections, but we demonstrate the online usage of the neural LS operator under estimation of the fertility and mortality functions.

Bladder Vessel Segmentation using a Hybrid Attention-Convolution Framework

Urinary bladder cancer surveillance requires tracking tumor sites across repeated interventions, yet the deformable and hollow bladder lacks stable landmarks for orientation. While blood vessels visible during endoscopy offer a patient-specific "vascular fingerprint" for navigation, automated segmentation is challenged by imperfect endoscopic data, including sparse labels, artifacts like bubbles or variable lighting, continuous deformation, and mucosal folds that mimic vessels. State-of-the-art vessel segmentation methods often fail to address these domain-specific complexities. We introduce a Hybrid Attention-Convolution (HAC) architecture that combines Transformers to capture global vessel topology prior with a CNN that learns a residual refinement map to precisely recover thin-vessel details. To prioritize structural connectivity, the Transformer is trained on optimized ground truth data that exclude short and terminal branches. Furthermore, to address data scarcity, we employ a physics-aware pretraining, that is a self-supervised strategy using clinically grounded augmentations on unlabeled data. Evaluated on the BlaVeS dataset, consisting of endoscopic video frames, our approach achieves high accuracy (0.94) and superior precision (0.61) and clDice (0.66) compared to state-of-the-art medical segmentation models. Crucially, our method successfully suppresses false positives from mucosal folds that dynamically appear and vanish as the bladder fills and empties during surgery. Hence, HAC provides the reliable structural stability required for clinical navigation.