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This manuscript derives locally weighted ensemble Kalman methods from the point of view of ensemble-based function approximation. This is done by using pointwise evaluations to build up a local linear or quadratic approximation of a function, tapering off the effect of distant particles via local weighting. This introduces a candidate method (the locally weighted Ensemble Kalman method for inversion) with the motivation of combining some of the strengths of the particle filter (ability to cope with nonlinear maps and non-Gaussian distributions) and the Ensemble Kalman filter (no filter degeneracy).

This paper contributes to the study of optimal experimental design for Bayesian inverse problems governed by partial differential equations (PDEs). We derive estimates for the parametric regularity of multivariate double integration problems over high-dimensional parameter and data domains arising in Bayesian optimal design problems. We provide a detailed analysis for these double integration problems using two approaches: a full tensor product and a sparse tensor product combination of quasi-Monte Carlo (QMC) cubature rules over the parameter and data domains. Specifically, we show that the latter approach significantly improves the convergence rate, exhibiting performance comparable to that of QMC integration of a single high-dimensional integral. Furthermore, we numerically verify the predicted convergence rates for an elliptic PDE problem with an unknown diffusion coefficient in two spatial dimensions, offering empirical evidence supporting the theoretical results and highlighting practical applicability.

This paper introduces a novel approach to enhance the performance of pre-trained neural networks in medical image segmentation using Neural Architecture Search (NAS) methods, specifically Differentiable Architecture Search (DARTS). We present the concept of Implantable Adaptive Cell (IAC), small but powerful modules identified through Partially-Connected DARTS, designed to be injected into the skip connections of an existing and already trained U-shaped model. Our strategy allows for the seamless integration of the IAC into the pre-existing architecture, thereby enhancing its performance without necessitating a complete retraining from scratch. The empirical studies, focusing on medical image segmentation tasks, demonstrate the efficacy of this method. The integration of specialized IAC cells into various configurations of the U-Net model increases segmentation accuracy by almost 2\% points on average for the validation dataset and over 3\% points for the training dataset. The findings of this study not only offer a cost-effective alternative to the complete overhaul of complex models for performance upgrades but also indicate the potential applicability of our method to other architectures and problem domains.

This paper explores how deep learning techniques can improve visual-based SLAM performance in challenging environments. By combining deep feature extraction and deep matching methods, we introduce a versatile hybrid visual SLAM system designed to enhance adaptability in challenging scenarios, such as low-light conditions, dynamic lighting, weak-texture areas, and severe jitter. Our system supports multiple modes, including monocular, stereo, monocular-inertial, and stereo-inertial configurations. We also perform analysis how to combine visual SLAM with deep learning methods to enlighten other researches. Through extensive experiments on both public datasets and self-sampled data, we demonstrate the superiority of the SL-SLAM system over traditional approaches. The experimental results show that SL-SLAM outperforms state-of-the-art SLAM algorithms in terms of localization accuracy and tracking robustness. For the benefit of community, we make public the source code at //github.com/zzzzxxxx111/SLslam.

Challenges to reproducibility and replicability have gained widespread attention, driven by large replication projects with lukewarm success rates. A nascent work has emerged developing algorithms to estimate the replicability of published findings. The current study explores ways in which AI-enabled signals of confidence in research might be integrated into the literature search. We interview 17 PhD researchers about their current processes for literature search and ask them to provide feedback on a replicability estimation tool. Our findings suggest that participants tend to confuse replicability with generalizability and related concepts. Information about replicability can support researchers throughout the research design processes. However, the use of AI estimation is debatable due to the lack of explainability and transparency. The ethical implications of AI-enabled confidence assessment must be further studied before such tools could be widely accepted. We discuss implications for the design of technological tools to support scholarly activities and advance replicability.

We propose an abstract conceptual framework for analysing complex security systems using a new notion of modes and mode transitions. A mode is an independent component of a system with its own objectives, monitoring data, algorithms, and scope and limits. The behaviour of a mode, including its transitions to other modes, is determined by interpretations of the mode's monitoring data in the light of its objectives and capabilities -- these interpretations we call beliefs. We formalise the conceptual framework mathematically and, by quantifying and visualising beliefs in higher-dimensional geometric spaces, we argue our models may help both design, analyse and explain systems. The mathematical models are based on simplicial complexes.

Matching on a low dimensional vector of scalar covariates consists of constructing groups of individuals in which each individual in a group is within a pre-specified distance from an individual in another group. However, matching in high dimensional spaces is more challenging because the distance can be sensitive to implementation details, caliper width, and measurement error of observations. To partially address these problems, we propose to use extensive sensitivity analyses and identify the main sources of variation and bias. We illustrate these concepts by examining the racial disparity in all-cause mortality in the US using the National Health and Nutrition Examination Survey (NHANES 2003-2006). In particular, we match African Americans to Caucasian Americans on age, gender, BMI and objectively measured physical activity (PA). PA is measured every minute using accelerometers for up to seven days and then transformed into an empirical distribution of all of the minute-level observations. The Wasserstein metric is used as the measure of distance between these participant-specific distributions.

We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to concentration in general metric spaces.

In the past few years, the emergence of pre-training models has brought uni-modal fields such as computer vision (CV) and natural language processing (NLP) to a new era. Substantial works have shown they are beneficial for downstream uni-modal tasks and avoid training a new model from scratch. So can such pre-trained models be applied to multi-modal tasks? Researchers have explored this problem and made significant progress. This paper surveys recent advances and new frontiers in vision-language pre-training (VLP), including image-text and video-text pre-training. To give readers a better overall grasp of VLP, we first review its recent advances from five aspects: feature extraction, model architecture, pre-training objectives, pre-training datasets, and downstream tasks. Then, we summarize the specific VLP models in detail. Finally, we discuss the new frontiers in VLP. To the best of our knowledge, this is the first survey on VLP. We hope that this survey can shed light on future research in the VLP field.