Stephen Shing-Toung Yau

Chang Liu, Wenhan Cao, Zeju Sun et al.

Bayesian filtering is a cornerstone of state estimation in complex systems such as aerospace systems, yet exact solutions are available only for linear Gaussian models. In practice,nonlinear systems are handled through tractable approximations,with Gaussian filters such as the extended and unscented Kalman filters being among the most widely used methods. This tutorial revisits Gaussian filtering from an information-geometric perspective, viewing the prediction and measurement update steps as inference procedures over state distributions. Within this framework, we introduce a geometry-aware Gaussian filtering approach that leverages natural gradient descent on the statistical manifold of Gaussian distributions. The resulting Natural Gradient Gaussian Approximation (NANO) filter iteratively refines the posterior mean and covariance while respecting the intrinsic geometry of the Gaussian family and preserving the positive definiteness of the covariance matrix. We further highlight fundamental connections to the classical Kalman filtering, showing that a single natural-gradient step exactly recovers the Kalman measurement update in the linear-Gaussian case. The practical implications of the proposed framework are illustrated through case studies in representative nonlinear estimation problems,including satellite attitude estimation, simultaneous localization and mapping, and state estimation for robotic systems including quadruped and humanoid robots.

Songlin Zhou, Tao Zhou, Xin Li et al.

Purpose: Thyroid cancer has been a common cancer. Papillary thyroid cancer and follicular thyroid cancer are the two most common types of thyroid cancer. Follicular thyroid cancer lacks distinctive ultrasound signs and is more difficult to diagnose preoperatively than the more prevalent papillary thyroid cancer, and the clinical studies associated with it are less well established. We aimed to analyze the clinical data of follicular thyroid cancer based on a novel data mining tool to identify some clinical indications that may help in preoperative diagnosis. Methods: We performed a retrospective analysis based on case data collected by the Department of General Surgery of Peking University Third Hospital between 2010 and 2023. Unlike traditional statistical methods, we improved the association rule mining, a classical data mining method, and proposed new analytical metrics reflecting the malignant association between clinical indications and cancer with the help of the idea of SHAP method in interpretable machine learning. Results: The dataset was preprocessed to contain 1673 cases (in terms of nodes rather than patients), of which 1414 were benign and 259 were malignant nodes. Our analysis pointed out that in addition to some common indicators (e.g., irregular or lobulated nodal margins, uneven thickness halo, hypoechogenicity), there were also some indicators with strong malignant associations, such as nodule-in-nodule pattern, trabecular pattern, and low TSH scores. In addition, our results suggest that the combination of Hashimoto's thyroiditis may also have a strong malignant association. Conclusion: In the preoperative diagnosis of nodules suspected of follicular thyroid cancer, multiple clinical indications should be considered for a more accurate diagnosis. The diverse malignant associations identified in our study may serve as a reference for clinicians in related fields.