Urban Network Security Games (UNSGs), which model the strategic allocation of limited security resources on city road networks, are critical for urban safety. However, finding a Nash Equilibrium (NE) in large-scale UNSGs is challenging due to their massive and combinatorial action spaces. One common approach to addressing these games is the Policy-Space Response Oracle (PSRO) framework, which requires computing best responses (BR) at each iteration. However, precisely computing exact BRs is impractical in large-scale games, and employing reinforcement learning to approximate BRs inevitably introduces errors that limit the overall effectiveness of the PSRO methods. Recent advancements in leveraging non-convex stochastic optimization to approximate an NE offer a promising alternative to the burdensome BR computation. However, utilizing existing stochastic optimization techniques with an unbiased loss function for UNSGs remains challenging because the action spaces are too vast to be effectively represented by neural networks. To address these issues, we introduce Tree-based Stochastic Optimization (TSO), a framework that bridges the gap between the stochastic optimization paradigm for NE-finding and the demands of UNSGs. Specifically, we employ the tree-based action representation that maps the whole action space onto a tree structure, addressing the challenge faced by neural networks in representing actions when the action space cannot be enumerated. We then incorporate this representation into the loss function and theoretically demonstrate its equivalence to the unbiased loss function. To further enhance the quality of the converged solution, we introduce a sample-and-prune mechanism that reduces the risk of being trapped in suboptimal local optima. Extensive experimental results indicate the superiority of TSO over other baseline algorithms in addressing the UNSGs.

Vascular segmentation is a critical task in clinical medical image processing and a prerequisite for accurately diagnosing vascular-related diseases. The development of automated segmentation methods is challenged by internal variability in vessel representations. Recently, topology guidance has shown potential for capturing semantically consistent representations. However, current topology-guided methods lack modeling of global-to-local dependencies. This limitation forces latent representations subject to a trade-off between learning global topology and local geometries within the vascular network. In this paper, we propose a Bayesian-based topology-guided (BayeTopo) learning approach to capture global-to-local dependencies. It introduces a prior that explicitly models local geometry as a probability conditioned on global topology within topology-sensitive regions of the vascular network. We further implement a topology-guided diffusion model to optimize the conditional probability. It gradually infers local geometry from the restored global topology with multi-scale noise, enabling rich global-to-local representations. Then, an inhomogeneous diffusion process is involved, where noise initially accumulates in topology-sensitive regions before achieving uniformity. It ensures an orderly degradation of information from global topology to local geometry, thereby enabling effective global-to-local supervision. Extensive experiments on six datasets, involving three types of vascular networks under four imaging modalities, demonstrate the superior performance and generalization capability of our method compared to previous topology-guided learning and diffusion-based models. A series of case studies further validates the effectiveness of our designs in enhancing semantic consistency within local vascular regions, thereby improving topological accuracy.

Motion estimation of left ventricle myocardium on the cardiac image sequence is crucial for assessing cardiac function. However, the intensity variation of cardiac image sequences brings the challenge of uncertain interference to myocardial motion estimation. Such imaging-related uncertain interference appears in different cardiac imaging modalities. We propose adaptive sequential Bayesian iterative learning to overcome the challenge. Specifically, our method applies the adaptive structural inference to state transition and observation to cope with a complex myocardial motion under uncertain setting. In state transition, adaptive structural inference establishes a hierarchical structure recurrence to obtain the complex latent representation of cardiac image sequences. In state observation, the adaptive structural inference forms a chain structure mapping to correlate the latent representation of the cardiac image sequence with that of the motion. Extensive experiments on US, CMR, and TMR datasets concerning 1270 patients (650 patients for CMR, 500 patients for US and 120 patients for TMR) have shown the effectiveness of our method, as well as the superiority to eight state-of-the-art motion estimation methods.