Time series modeling and analysis has become critical in various domains. Conventional methods such as RNNs and Transformers, while effective for discrete-time and regularly sampled data, face significant challenges in capturing the continuous dynamics and irregular sampling patterns inherent in real-world scenarios. Neural Differential Equations (NDEs) represent a paradigm shift by combining the flexibility of neural networks with the mathematical rigor of differential equations. This paper presents a comprehensive review of NDE-based methods for time series analysis, including neural ordinary differential equations, neural controlled differential equations, and neural stochastic differential equations. We provide a detailed discussion of their mathematical formulations, numerical methods, and applications, highlighting their ability to model continuous-time dynamics. Furthermore, we address key challenges and future research directions. This survey serves as a foundation for researchers and practitioners seeking to leverage NDEs for advanced time series analysis.

-- Translation of fully automated deep learning based medical image segmentation technologies to clinical workflows face two main algorithmic challenges. The first, is the collection and archival of large quantities of manually annotated ground truth data for both training and validation. The second is the relative inability of the majority of deep learning based segmentation techniques to alert physicians to a likely segmentation failure. Here we propose a novel algorithm, named'Eigenrank' which addresses both of these challenges. Eigenrank can select for manual labeling, a subset of medical images from a large database, such that a U-Net trained on this subset is superior to one trained on a randomly selected subset of the same size. Eigenrank can also be used to pick out, cases in a large database, where deep learning segmentation will fail. We present our algorithm, followed by results and a discussion of how Eigenrank exploits the V on Neumann information to perform both data subset selection and failure prediction for medical image segmentation using deep learning. I. INTRODUCTION A. Significance Deep learning methods have become the mainstay of fully automatic medical image segmentation. These methods play a key role in the development of quantitative imaging biomarkers for a number of pathologies. However, training and deploying deep learning segmentation in practice is beset by a number of challenges. Failure Prediction (FP) - the ability to predict on which cases a deep learning based segmentation model will fail. Both problems are significant in medical image segmentation, more than natural image segmentation. This is because, availability of expert annotated data for training medical image segmentation models is severely constrained.