We present a new benchmarking study comparing a boundary-constrained Ehrenpreis--Palamodov Gaussian Process (B-EPGP) surrogate with a classical finite element method combined with Crank--Nicolson time stepping (CN-FEM) for solving the two-dimensional wave equation with homogeneous Dirichlet boundary conditions. The B-EPGP construction leverages exponential-polynomial bases derived from the characteristic variety to enforce the PDE and boundary conditions exactly and employs penalized least squares to estimate the coefficients. To ensure fairness across paradigms, we introduce a degrees-of-freedom (DoF) matching protocol. Under matched DoF, B-EPGP consistently attains lower space-time $L^2$-error and maximum-in-time $L^{2}$-error in space than CN-FEM, improving accuracy by roughly two orders of magnitude.

Sliding window-factor graph optimization (SW-FGO) has gained more and more attention in navigation research due to its robust approximation to non-Gaussian noises and nonlinearity of measuring models. There are lots of works focusing on its application performance compared to extended Kalman filter (EKF) but there is still a myth at the theoretical relationship between the SW-FGO and EKF. In this paper, we find the necessarily fair condition to connect SW-FGO and Kalman filter variants (KFV) (e.g., EKF, iterative EKF (IEKF), robust EKF (REKF) and robust iterative EKF (RIEKF)). Based on the conditions, we propose a recursive FGO (Re-FGO) framework to represent KFV under SW-FGO formulation. Under explicit conditions (Markov assumption, Gaussian noise with L2 loss, and a one-state window), Re-FGO regenerates exactly to EKF/IEKF/REKF/RIEKF, while SW-FGO shows measurable benefits in nonlinear, non-Gaussian regimes at a predictable compute cost. Finally, after clarifying the connection between them, we highlight the unique advantages of SW-FGO in practical phases, especially on numerical estimation and deep learning integration. The code and data used in this work is open sourced at https://github.com/Baoshan-Song/KFV-FGO-Comparison.

This survey paper explores the transformative role of Machine Learning (ML) and Artificial Intelligence (AI) in Cardiopulmonary Resuscitation (CPR). It examines the evolution from traditional CPR methods to innovative ML-driven approaches, highlighting the impact of predictive modeling, AI-enhanced devices, and real-time data analysis in improving resuscitation outcomes. The paper provides a comprehensive overview, classification, and critical analysis of current applications, challenges, and future directions in this emerging field.

To address the challenge of limited experimental materials data, extensive physical property databases are being developed based on high-throughput computational experiments, such as molecular dynamics simulations. Previous studies have shown that fine-tuning a predictor pretrained on a computational database to a real system can result in models with outstanding generalization capabilities compared to learning from scratch. This study demonstrates the scaling law of simulation-to-real (Sim2Real) transfer learning for several machine learning tasks in materials science. Case studies of three prediction tasks for polymers and inorganic materials reveal that the prediction error on real systems decreases according to a power-law as the size of the computational data increases. Observing the scaling behavior offers various insights for database development, such as determining the sample size necessary to achieve a desired performance, identifying equivalent sample sizes for physical and computational experiments, and guiding the design of data production protocols for downstream real-world tasks.

Model averaging is a widely adopted technique in federated learning (FL) that aggregates multiple client models to obtain a global model. Remarkably, model averaging in FL can yield a superior global model, even when client models are trained with non-convex objective functions and on heterogeneous local datasets. However, the rationale behind its success remains poorly understood. To shed light on this issue, we first visualize the loss landscape of FL over client and global models to illustrate their geometric properties. The visualization shows that the client models encompass the global model within a common basin, and interestingly, the global model may deviate from the bottom of the basin while still outperforming the client models. To gain further insights into model averaging in FL, we decompose the expected loss of the global model into five factors related to the client models. Specifically, our analysis reveals that the loss of the global model after early training mainly arises from \textit{i)} the client model's loss on non-overlapping data between client datasets and the global dataset and \textit{ii)} the maximum distance between the global and client models. Based on these findings from our loss landscape visualization and loss decomposition, we propose utilizing iterative moving averaging (IMA) on the global model at the late training phase to reduce its deviation from the expected minimum, while constraining client exploration to limit the maximum distance between the global and client models. Our experiments demonstrate that incorporating IMA into existing FL methods significantly improves their accuracy and training speed on various heterogeneous data setups of benchmark datasets.

Objective: Exploit accelerometry data for an automatic, reliable, and prompt detection of spontaneous circulation during cardiac arrest, as this is both vital for patient survival and practically challenging. Methods: We developed a machine learning algorithm to automatically predict the circulatory state during cardiopulmonary resuscitation from 4-second-long snippets of accelerometry and electrocardiogram (ECG) data from pauses of chest compressions of real-world defibrillator records. The algorithm was trained based on 422 cases from the German Resuscitation Registry, for which ground truth labels were created by a manual annotation of physicians. It uses a kernelized Support Vector Machine classifier based on 49 features, which partially reflect the correlation between accelerometry and electrocardiogram data. Results: Evaluating 50 different test-training data splits, the proposed algorithm exhibits a balanced accuracy of 81.2%, a sensitivity of 80.6%, and a specificity of 81.8%, whereas using only ECG leads to a balanced accuracy of 76.5%, a sensitivity of 80.2%, and a specificity of 72.8%. Conclusion: The first method employing accelerometry for pulse/no-pulse decision yields a significant increase in performance compared to single ECG-signal usage. Significance: This shows that accelerometry provides relevant information for pulse/no-pulse decisions. In application, such an algorithm may be used to simplify retrospective annotation for quality management and, moreover, to support clinicians to assess circulatory state during cardiac arrest treatment.

The Mat\'ern covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Mat\'ern class is that it is possible to get precise control over the degree of differentiability of the process realizations. However, the Mat\'ern class possesses exponentially decaying tails, and thus may not be suitable for modeling long range dependence. This problem can be remedied using polynomial covariances; however one loses control over the degree of differentiability of the process realizations, in that the realizations using polynomial covariances are either infinitely differentiable or not differentiable at all. We construct a new family of covariance functions using a scale mixture representation of the Mat\'ern class where one obtains the benefits of both Mat\'ern and polynomial covariances. The resultant covariance contains two parameters: one controls the degree of differentiability near the origin and the other controls the tail heaviness, independently of each other. Using a spectral representation, we derive theoretical properties of this new covariance including equivalence measures and asymptotic behavior of the maximum likelihood estimators under infill asymptotics. The improved theoretical properties in predictive performance of this new covariance class are verified via extensive simulations. Application using NASA's Orbiting Carbon Observatory-2 satellite data confirms the advantage of this new covariance class over the Mat\'ern class, especially in extrapolative settings.

CHELMSFORD, MASSACHUSETTS - The U.S. Army is looking for a few good robots. Not to fight -- not yet, at least -- but to help the men and women who do. These robots aren't taking up arms, but the companies making them have waged a different kind of battle. At stake is a contract worth almost half a billion dollars for 3,000 backpack-sized robots that can defuse bombs and scout enemy positions. Competition for the work has spilled over into Congress and federal court.

The U.S. Department of Defense will soon spend about $1 billion to deploy robot soldiers in the field, alongside -- and eventually in place of -- human troops. "Within five years, I have no doubt there will be robots in every Army formation," said Bryan McVeigh, the Army's project manager for force protection, as quoted in an article published by Bloomberg. McVeigh reported that there have been about 800 robots put into military service within the last 18 months. "This is an exciting time to be working on robots with the Army." The American branch of the British-based science and technology conglomerate QinetiQ and the Chelmsford, Massachusetts-based Endeavor Robotics have received the lion's share of the contracts to develop the robot warriors.

Binary Decision Diagram (BDD) based set bounds propagation is a powerful approach to solving set-constraint satisfaction problems. However, prior BDD based techniques in- cur the significant overhead of constructing and manipulating graphs during search. We present a set-constraint solver which combines BDD-based set-bounds propagators with the learning abilities of a modern SAT solver. Together with a number of improvements beyond the basic algorithm, this solver is highly competitive with existing propagation based set constraint solvers.