In many machine learning applications on signals and biomedical data, especially electroencephalogram (EEG), one major challenge is the variability of the data across subjects, sessions, and hardware devices. In this work, we propose a new method called Convolutional Monge Mapping Normalization (CMMN), which consists in filtering the signals in order to adapt their power spectrum density (PSD) to a Wasserstein barycenter estimated on training data. CMMN relies on novel closed-form solutions for optimal transport mappings and barycenters and provides individual test time adaptation to new data without needing to retrain a prediction model. Numerical experiments on sleep EEG data show that CMMN leads to significant and consistent performance gains independent from the neural network architecture when adapting between subjects, sessions, and even datasets collected with different hardware. Notably our performance gain is on par with much more numerically intensive Domain Adaptation (DA) methods and can be used in conjunction with those for even better performances.

Markov Condition, are not independent of each other .

B.7 Additional Details on the Running Time In this section, we provide additional details on the running time of the algorithms.

Human hand simulation plays a critical role in digital twin applications, requiring models that balance anatomical fidelity with computational efficiency. We present a complete pipeline for constructing multi-rigid-body approximations of human hands that preserve realistic appearance while enabling real-time physics simulation. Starting from optical motion capture of a specific human hand, we construct a personalized MANO (Multi-Abstracted hand model with Neural Operations) model and convert it to a URDF (Unified Robot Description Format) representation with anatomically consistent joint axes. The key technical challenge is projecting MANO's unconstrained SO(3) joint rotations onto the kinematically constrained joints of the rigid-body model. We derive closed-form solutions for single degree-of-freedom joints and introduce a Baker-Campbell-Hausdorff (BCH)-corrected iterative method for two degree-of-freedom joints that properly handles the non-commutativity of rotations. We validate our approach through digital twin experiments where reinforcement learning policies control the multi-rigid-body hand to replay captured human demonstrations. Quantitative evaluation shows sub-centimeter reconstruction error and successful grasp execution across diverse manipulation tasks.

This article serves as the regression analysis lecture notes in the Intelligent Computing course cluster (including the courses of Artificial Intelligence, Data Mining, Machine Learning, and Pattern Recognition). It aims to provide students -- who are assumed to possess only basic university-level mathematics (i.e., with prerequisite courses in calculus, linear algebra, and probability theory) -- with a comprehensive and self-contained understanding of regression analysis without requiring any additional references. The lecture notes systematically introduce the fundamental concepts, modeling components, and theoretical foundations of regression analysis, covering linear regression, logistic regression, multinomial logistic regression, polynomial regression, basis-function models, kernel-based methods, and neural-network-based nonlinear regression. Core methodological topics include loss-function design, parameter-estimation principles, ordinary least squares, gradient-based optimization algorithms and their variants, as well as regularization techniques such as Ridge and LASSO regression. Through detailed mathematical derivations, illustrative examples, and intuitive visual explanations, the materials help students understand not only how regression models are constructed and optimized, but also how they reveal the underlying relationships between features and response variables. By bridging classical statistical modeling and modern machine-learning practice, these lecture notes aim to equip students with a solid conceptual and technical foundation for further study in advanced artificial intelligence models.

In this letter, we present a closed-form initialization method that recovers the full visual-inertial state without nonlinear optimization. Unlike previous approaches that rely on iterative solvers, our formulation yields analytical, easy-to-implement, and numerically stable solutions for reliable start-up. Our method builds on small-rotation and constant-velocity approximations, which keep the formulation compact while preserving the essential coupling between motion and inertial measurements. We further propose an observability-driven, two-stage initialization scheme that balances accuracy with initialization latency. Extensive experiments on the EuRoC dataset validate our assumptions: our method achieves 10-20% lower initialization error than optimization-based approaches, while using 4x shorter initialization windows and reducing computational cost by 5x.