Accurately solving high-dimensional partial differential equations (PDEs) remains a central challenge in computational mathematics. Traditional numerical methods, while effective in low-dimensional settings or on coarse grids, often struggle to deliver the precision required in practical applications. Recent machine learning-based approaches offer flexibility but frequently fall short in terms of accuracy and reliability, particularly in industrial contexts. In this work, we explore a quantum-inspired method based on quantized tensor trains (QTT), enabling efficient and accurate solutions to PDEs in a variety of challenging scenarios. Through several representative examples, we demonstrate that the QTT approach can achieve logarithmic scaling in both memory and computational cost for linear and nonlinear PDEs. Additionally, we introduce a novel technique for data-driven learning within the quantum-inspired framework, combining the adaptability of neural networks with enhanced accuracy and reduced training time.

With the growing adoption of autonomous driving, the advancement of sensor technology is crucial for ensuring safety and reliable operation. Sensor fusion techniques that combine multiple sensors such as LiDAR, radar, and cameras have proven effective, but the integration of multiple devices increases both hardware complexity and cost. Therefore, developing a single sensor capable of performing multiple roles is highly desirable for cost-efficient and scalable autonomous driving systems. Event cameras have emerged as a promising solution due to their unique characteristics, including high dynamic range, low latency, and high temporal resolution. These features enable them to perform well in challenging lighting conditions, such as low-light or backlit environments. Moreover, their ability to detect fine-grained motion events makes them suitable for applications like pedestrian detection and vehicle-to-infrastructure communication via visible light. In this study, we present a method for distance estimation using a monocular event camera and a roadside LED bar. By applying a phase-only correlation technique to the event data, we achieve sub-pixel precision in detecting the spatial shift between two light sources. This enables accurate triangulation-based distance estimation without requiring stereo vision. Field experiments conducted in outdoor driving scenarios demonstrated that the proposed approach achieves over 90% success rate with less than 0.5-meter error for distances ranging from 20 to 60 meters. Future work includes extending this method to full position estimation by leveraging infrastructure such as smart poles equipped with LEDs, enabling event-camera-based vehicles to determine their own position in real time. This advancement could significantly enhance navigation accuracy, route optimization, and integration into intelligent transportation systems.

Data fusion--the process of combining observational and exp erimental data--can enable the identification of causal effects that would otherwise rem ain non-identifiable. Although identification algorithms have been developed for specific s cenarios, do-calculus remains the only general-purpose tool for causal data fusion, particul arly when variables are present in some data sources but not others. However, approaches based on do-calculus may encounter computational challenges as the number of variables increa ses and the causal graph grows in complexity. Consequently, there exists a need to reduce t he size of such models while preserving the essential features. For this purpose, we pro pose pruning (removing unnecessary variables) and clustering (combining variables) as pr eprocessing operations for causal data fusion. We generalize earlier results on a single data s ource and derive conditions for applying pruning and clustering in the case of multiple data sources. We give sufficient conditions for inferring the identifiability or non-identi fiability of a causal effect in a larger graph based on a smaller graph and show how to obtain the corre sponding identifying functional for identifiable causal effects. Examples from ep idemiology and social science demonstrate the use of the results.

To overcome the limitation of existing indoor odometry technologies which often cannot simultaneously meet requirements for accuracy cost-effectiveness, and robustness-this paper proposes a novel magnetometer array-aided inertial odometry approach, MSCEKF-MIO (Multi-State Constraint Extended Kalman Filter-based Magnetic-Inertial Odometry). We construct a magnetic field model by fitting measurements from the magnetometer array and then use temporal variations in this model-extracted from continuous observations-to estimate the carrier's absolute velocity. Furthermore, we implement the MSCEKF framework to fuse observed magnetic field variations with position and attitude estimates from inertial navigation system (INS) integration, thereby enabling autonomous, high-precision indoor relative positioning. Experimental results demonstrate that the proposed algorithm achieves superior velocity estimation accuracy and horizontal positioning precision relative to state-of-the-art magnetic array-aided INS algorithms (MAINS). On datasets with trajectory lengths of 150-250m, the proposed method yields an average horizontal position RMSE of approximately 2.5m. In areas with distinctive magnetic features, the magneto-inertial odometry achieves a velocity estimation accuracy of 0.07m/s. Consequently, the proposed method offers a novel positioning solution characterized by low power consumption, cost-effectiveness, and high reliability in complex indoor environments.

Recent advances in large language models (LLMs) have intensified efforts to fuse heterogeneous open-source models into a unified system that inherits their complementary strengths. Existing logit-based fusion methods maintain inference efficiency but treat vocabulary dimensions independently, overlooking semantic dependencies encoded by cross-dimension interactions. These dependencies reflect how token types interact under a model's internal reasoning and are essential for aligning models with diverse generation behaviors. To explicitly model these dependencies, we propose \textbf{InfiGFusion}, the first structure-aware fusion framework with a novel \textit{Graph-on-Logits Distillation} (GLD) loss. Specifically, we retain the top-$k$ logits per output and aggregate their outer products across sequence positions to form a global co-activation graph, where nodes represent vocabulary channels and edges quantify their joint activations. To ensure scalability and efficiency, we design a sorting-based closed-form approximation that reduces the original $O(n^4)$ cost of Gromov-Wasserstein distance to $O(n \log n)$, with provable approximation guarantees. Experiments across multiple fusion settings show that GLD consistently improves fusion quality and stability. InfiGFusion outperforms SOTA models and fusion baselines across 11 benchmarks spanning reasoning, coding, and mathematics. It shows particular strength in complex reasoning tasks, with +35.6 improvement on Multistep Arithmetic and +37.06 on Causal Judgement over SFT, demonstrating superior multi-step and relational inference.

Fine-grained economic mapping through urban representation learning has emerged as a crucial tool for evidence-based economic decisions. While existing methods primarily rely on supervised or unsupervised approaches, they often overlook semi-supervised learning in data-scarce scenarios and lack unified multi-task frameworks for comprehensive sectoral economic analysis. To address these gaps, we propose SemiGTX, an explainable semi-supervised graph learning framework for sectoral economic mapping. The framework is designed with dedicated fusion encoding modules for various geospatial data modalities, seamlessly integrating them into a cohesive graph structure. It introduces a semi-information loss function that combines spatial self-supervision with locally masked supervised regression, enabling more informative and effective region representations. Through multi-task learning, SemiGTX concurrently maps GDP across primary, secondary, and tertiary sectors within a unified model. Extensive experiments conducted in the Pearl River Delta region of China demonstrate the model's superior performance compared to existing methods, achieving R2 scores of 0.93, 0.96, and 0.94 for the primary, secondary and tertiary sectors, respectively. Cross-regional experiments in Beijing and Chengdu further illustrate its generality. Systematic analysis reveals how different data modalities influence model predictions, enhancing explainability while providing valuable insights for regional development planning. This representation learning framework advances regional economic monitoring through diverse urban data integration, providing a robust foundation for precise economic forecasting.

Data integration approaches are increasingly used to enhance the efficiency and generalizability of studies. However, a key limitation of these methods is the assumption that outcome measures are identical across datasets -- an assumption that often does not hold in practice. Consider the following opioid use disorder (OUD) studies: the XBOT trial and the POAT study, both evaluating the effect of medications for OUD on withdrawal symptom severity (not the primary outcome of either trial). While XBOT measures withdrawal severity using the subjective opiate withdrawal scale, POAT uses the clinical opiate withdrawal scale. We analyze this realistic yet challenging setting where outcome measures differ across studies and where neither study records both types of outcomes. Our paper studies whether and when integrating studies with disparate outcome measures leads to efficiency gains. We introduce three sets of assumptions -- with varying degrees of strength -- linking both outcome measures. Our theoretical and empirical results highlight a cautionary tale: integration can improve asymptotic efficiency only under the strongest assumption linking the outcomes. However, misspecification of this assumption leads to bias. In contrast, a milder assumption may yield finite-sample efficiency gains, yet these benefits diminish as sample size increases. We illustrate these trade-offs via a case study integrating the XBOT and POAT datasets to estimate the comparative effect of two medications for opioid use disorder on withdrawal symptoms. By systematically varying the assumptions linking the SOW and COW scales, we show potential efficiency gains and the risks of bias. Our findings emphasize the need for careful assumption selection when fusing datasets with differing outcome measures, offering guidance for researchers navigating this common challenge in modern data integration.

Multimodal data modeling has emerged as a powerful approach in clinical research, enabling the integration of diverse data types such as imaging, genomics, wearable sensors, and electronic health records. Despite its potential to improve diagnostic accuracy and support personalized care, modeling such heterogeneous data presents significant technical challenges. This systematic review synthesizes findings from 69 studies to identify common obstacles, including missing modalities, limited sample sizes, dimensionality imbalance, interpretability issues, and finding the optimal fusion techniques. We highlight recent methodological advances, such as transfer learning, generative models, attention mechanisms, and neural architecture search that offer promising solutions. By mapping current trends and innovations, this review provides a comprehensive overview of the field and offers practical insights to guide future research and development in multimodal modeling for medical applications.

In battlefield environments, adversaries frequently disrupt GPS signals, requiring alternative localization and navigation methods. Traditional vision-based approaches like Simultaneous Localization and Mapping (SLAM) and Visual Odometry (VO) involve complex sensor fusion and high computational demand, whereas range-free methods like DV-HOP face accuracy and stability challenges in sparse, dynamic networks. This paper proposes LanBLoc-BMM, a navigation approach using landmark-based localization (LanBLoc) combined with a battlefield-specific motion model (BMM) and Extended Kalman Filter (EKF). Its performance is benchmarked against three state-of-the-art visual localization algorithms integrated with BMM and Bayesian filters, evaluated on synthetic and real-imitated trajectory datasets using metrics including Average Displacement Error (ADE), Final Displacement Error (FDE), and a newly introduced Average Weighted Risk Score (AWRS). LanBLoc-BMM (with EKF) demonstrates superior performance in ADE, FDE, and AWRS on real-imitated datasets. Additionally, two safe navigation methods, SafeNav-CHull and SafeNav-Centroid, are introduced by integrating LanBLoc-BMM(EKF) with a novel Risk-Aware RRT* (RAw-RRT*) algorithm for obstacle avoidance and risk exposure minimization. Simulation results in battlefield scenarios indicate SafeNav-Centroid excels in accuracy, risk exposure, and trajectory efficiency, while SafeNav-CHull provides superior computational speed.

Indoor localization faces persistent challenges in achieving high accuracy, particularly in GPS-deprived environments. This study unveils a cutting-edge handheld indoor localization system that integrates 2D LiDAR and IMU sensors, delivering enhanced high-velocity precision mapping, computational efficiency, and real-time adaptability. Unlike 3D LiDAR systems, it excels with rapid processing, low-cost scalability, and robust performance, setting new standards for emergency response, autonomous navigation, and industrial automation. Enhanced with a CNN-driven object detection framework and optimized through Cartographer SLAM (simultaneous localization and mapping ) in ROS, the system significantly reduces Absolute Trajectory Error (ATE) by 21.03%, achieving exceptional precision compared to state-of-the-art approaches like SC-ALOAM, with a mean x-position error of -0.884 meters (1.976 meters). The integration of CNN-based object detection ensures robustness in mapping and localization, even in cluttered or dynamic environments, outperforming existing methods by 26.09%. These advancements establish the system as a reliable, scalable solution for high-precision localization in challenging indoor scenarios