Although knowledge graph can enhance the efficiency of knowledge understanding and application, its inherent accuracy and completeness problems make knowledge graph complementation a current research focus. In this paper, the Trans H algorithm is improved by fusing semantic information, simplifying the triad by constructing an information hyperplane, and introducing BERT word vectors, which effectively improves the training efficiency. Adopting the attention mechanism proposed by previous researchers, the semantic information and the parameter vectors of the original model are fused and inputted into the Attention structure, and the attention scores of the semantic information of the triad are calculated. In order to evaluate the performance of the joint model SI-KGC, the dataset and experimental environment are constructed, hyperparameters are set, and the evaluation results are obtained after experiments such as ternary classification. The SI-KGC model constructed in this paper improves the accuracy by 3.12% compared to TransD. Meanwhile, it has high accuracy in the ternary group classification task, with an average accuracy of 83.8% and 74.75% on the two datasets, respectively, with higher classification accuracy and superior performance. Comparing the performance of TransE and SI-KGC on the FB15K dataset, the performance gap between the two models is between 0.003 and 0.011, and SI-KGC has a complete modeling capability, which has the effect of improving the model performance.

This paper addresses the stability and stabilization problems of rolling mill main drive systems with time delay. The complete stability problem with respect to the delay parameter is investigated for linearized systems with and without control. The systems are first formulated in the characteristic function form, and the corresponding complete stability problem is introduced. By employing the frequency-sweeping approach, the complete stability properties are systematically analyzed. As a result, several analytical properties related to the local asymptotic behavior of critical imaginary roots are derived. Finally, numerical examples demonstrate that the whole stability set with respect to delay can be accurately determined.

Image restoration under adverse weather conditions has attracted increasing attention because of its importance for both human perception and downstream vision applications. Existing methods, however, are often designed for a single degradation type. We present WeatherMAR, a multi-weather restoration framework that formulates adverse-weather restoration as a paired-domain completion problem in a shared continuous token space. Specifically, WeatherMAR concatenates degraded and clean token sequences into a joint paired-domain sequence and performs restoration through masked autoregressive modeling, in which self-attention enables direct cross-domain interaction. To strengthen conditional learning while avoiding trivial paired correspondences, we introduce complementary bidirectional masking together with an optional reverse objective used only during training to encourage degradation-aware representations. WeatherMAR further employs a conditional diffusion objective for continuous token prediction and adopts a progress-to-step schedule to improve inference efficiency. Extensive experiments on standard multi-weather benchmarks, including Snow100K, Outdoor-Rain, and RainDrop, show that WeatherMAR achieves the best PSNR/SSIM on Snow100K-S (38.14/0.9684), the best SSIM on Outdoor-Rain (0.9396), and the best PSNR on Snow100K-L (32.58) and RainDrop (33.12). These results demonstrate that paired-domain token completion provides an effective solution for adverse-weather restoration.

Physics-informed graph neural network for carbon emission flow analysis in power systems

Quilombola communities in the Brazilian Amazon face persistent social and territorial inequities that shape health outcomes and access to care. Geographic isolation, limited transportation, centralization of specialized services, and socioeconomic disadvantages contribute to unequal opportunities for timely diagnosis and treatment. Understanding how these determinants interact with patterns of multimorbidity is essential for guiding equiTable health policies and strengthening primary care in remote territories. A cross-sectional epidemiological study was conducted with 518 adults from nine quilombola communities in Santarém, Pará. Data were collected through household surveys addressing sociodemographics, self-reported diseases, service utilization and resolvability. Geographic coordinates of communities and health services were mapped to classify accessibility as high, medium or low. Diseases were converted into a binary matrix to estimate prevalence and identify multimorbidity (≥2 conditions). Statistical analyses included chi-square tests, ANOVA, Spearman correlations and heatmap visualization. A Composite Access Index (CAI) integrating geographic distance, epidemiological burden and service-use indicators was developed. A Random Forest model was used to identify conditions most strongly associated with multimorbidity. Communities showed marked territorial heterogeneity. Pérola do Maicá had the highest accessibility, while Ituqui, Tiningu and Murumuru presented substantial geographic and logistical barriers. Service utilization ranged from 42.9% to 95.0%, and most communities relied on care outside their territory (70-95%). Complete problem resolution was reported by 72.5% of participants, though with variation among communities. The CAI identified Ituqui (0.550), Tiningu (0.480) and Murumurutuba (0.331) as the most vulnerable territories. The Random Forest model achieved 93.6% accuracy, with hypertension, diabetes, musculoskeletal diseases, arthritis/rheumatism and heart disease emerging as key predictors of multimorbidity. Findings indicate that social and territorial determinants are strongly associated with inequities in access to health services, continuity of care, and disease burden across quilombola communities. Geographic barriers and the distribution of health services are associated with distinct patterns of multimorbidity and health service access among quilombola populations. Strengthening primary care, transportation, and diagnostic support may help mitigate inequities and improve health conditions in remote Amazonian territories.

Collaborative filtering (CF) over ordinal feedback is naturally organized as a problem of matrix completion, where the input consists of a partially observed user-item interaction matrix. Maximum Margin Matrix Factorization (MMMF) has achieved widespread popularity for effectively completing such partially observed ordinal matrices from its inception. Geometrically, MMMF embeds items as points and users as linear hyperplanes, separating items with similar ratings from others. The all-threshold hinge loss function ensures that the user hyperplane maximizes the margin between distinct classes of rated items. However, the restriction that the user hyperplane be linear limits the performance of MMMF substantially, as user features are often intricate and do not exhibit linear patterns. To address this, we have proposed a deep variant of maximum margin matrix factorization that can easily predict user-item interactions by accommodating complex, non-linear user tastes and item feature representations. We have experimentally shown over the three benchmark datasets that the proposed deep variant of MMMF outperforms various state-of-the-art CF methods in terms of the Normalized Mean Absolute Error (NMAE) metric.

Abstract The H - Coloring problem is a well-known generalization of the classical -complete problem k - Coloring where the task is to determine whether an input graph admits a homomorphism to the template graph H . This problem has been the subject of intense theoretical research and in this article we study the complexity of H - Coloring with respect to the parameters clique-width and the more recent component twin-width , which describe desirable computational properties of graphs. We give two surprising linear bounds between these parameters, thus improving the previously known exponential and double exponential bounds. Our constructive proof naturally extends to related parameters and as a showcase we prove that total twin-width and linear clique-width can be related via a tight quadratic bound. These bounds naturally lead to algorithmic applications. The linear bounds between component twin-width and clique-width entail natural approximations of component twin-width, by making use of the results known for clique-width. As for computational aspects of graph coloring, we target the richer problem of counting the number of homomorphisms to H (# H - Coloring ). The first algorithm that we propose uses a contraction sequence of the input graph G parameterized by the component twin-width of G . This leads to a positive result for the counting version. The second uses a contraction sequence of the template graph H and here we instead measure the complexity with respect to the number of vertices in the input graph. Using our linear bounds we show that our algorithms are always at least as fast as the previously best # H -Coloring algorithms (based on clique-width) and for several interesting classes of graphs (e.g., cographs, cycles of length $$\varvec{\ge 7}$$ ≥ 7 , or distance-hereditary graphs) are in fact strictly faster.

Introduction Problem solving is a central competence in STEM education, yet many secondary school students struggle to coordinate the multiple skills required for successful problem solving. Early assessment of problem-solving skills can support individual feedback during this pivotal phase of schooling. However, existing assessment approaches focus mainly on complete problem solutions, which are resource-intensive and cannot adequately capture skills of students who fail in early phases of the problem-solving process. Methods To address this gap, the atomized problem-solving test (APST) was developed as a digital instrument that independently assesses four problem-solving subprocesses: Representation, Planning, Execution, and Evaluation. The APST was evaluated in two consecutive studies with a total of 800 German secondary school students within a web-based learning environment on energy conservation. Multidimensional item response theory (MIRT) was used to examine item quality and dimensional structure, complemented by supplemental assessments of conceptual knowledge, school grades, and rubric-based analyses of written problem solutions. Results The analyses supported a four-dimensional structure aligned with the theoretical design of the APST. The items showed acceptable model fit and reliable measurement of the intended subprocesses. All APST dimensions were moderately associated with conceptual knowledge of energy and with school grades in physics and mathematics, while no meaningful correlations were found with gender or native language. Evaluation emerged as a distinctive subprocess, showing strong associations with other subprocesses–particularly Execution–alongside evaluation-specific skills. Discussion The results indicate that the APST enables valid and reliable assessment of problem-solving subprocess skills in secondary physics education. At the same time, the findings underscore limitations of atomized assessments for measuring general problem-solving competence, as independent decision making is not assessed. The prominent role of Evaluation highlights its integrative function within the problem-solving process and points to important implications for both assessment design and future research.

This paper is devoted to the study of complexity of finding a special covering for a set, as well as to obtaining some important applications of special decomposition. We formulate the problem of existence of a special covering as a decision problem. To determine the complexity class in which this problem is located, we study the relationship between this problem and the Boolean satisfiability problem, treating them as formal languages. We prove that these problems are polynomially equivalent, which means that the problem of existence of a special covering for a set is an -complete problem. In this article we also introduce a new concept ‘Replaceable Subsets’. The properties of such subsets are used to fill in the missing elements needed to obtain a special set covering. It is proved that when searching for missing elements to fill a special covering, the order in which these elements are considered does not matter. This result is of great importance in the search for satisfiability of Boolean functions.

Alternating Linearized Proximal Algorithm for the Low Tucker Rank Tensor Completion Problem

Accurate mapping of localization error distribution is essential for assessing passive sensor systems and guiding sensor placement. However, conventional analytical methods like the Geometrical Dilution of Precision (GDOP) rely on idealized error models, failing to capture the complex, heterogeneous error distributions typical of real-world environments. To overcome this challenge, we propose a novel data-driven framework that reconstructs high-fidelity localization error maps from sparse observations in TDOA-based systems. Specifically, we model the error distribution as a tensor and formulate the reconstruction as a tensor completion problem. A key innovation is our physics-informed regularization strategy, which incorporates prior knowledge from the analytical error covariance matrix into the tensor factorization process. This allows for robust recovery of the complete error map even from highly incomplete data. Experiments on a real-world dataset validate the superiority of our approach, showing an accuracy improvement of at least 27.96% over state-of-the-art methods.

The problem of robust matrix completion-the recovery of a low-rank matrix and a sparse matrix from a sampling of their superposition-has been addressed extensively in prior literature. Yet, much of this work has focused exclusively on the case in which the matrix sampling is done at random, as this scenario is amenable to theoretical analysis. In contrast, sampling with an arbitrary deterministic pattern is often more accommodating to hardware implementation; consequently, the problem of robust matrix completion under deterministic sampling is considered. To this end, a restricted approximate isometry property is proposed and used, along with a modified golfing scheme and a slightly strengthened incoherence condition, to prove that the latent low-rank and sparse matrices are uniquely recoverable via convex optimization with asymptotically high probability, providing the first exact-recovery theory for robust matrix completion with arbitrary deterministic sampling. A corresponding convex-optimization algorithm, driven by a traditional nuclear norm, is developed and then subsequently generalized by substituting a convolutional nuclear norm in order to cover a broader range of application scenarios. Empirical experiments on synthetic data verify the proposed theory while a battery of results on real-world images demonstrate the practical efficacy of the generalized algorithm for robust matrix recovery.

AI governance mechanisms today are predominantly procedural. Documentation standards, audits, and risk assessments improve transparency but do not constrain runtime behavior. As AI systems evolve into autonomous, distributed platforms that invoke tools, spawn sub-agents, and operate across services, governance violations manifest as execution events rather than documentation failures. This structural mismatch prevents existing approaches from providing enforceable guarantees. We introduce Governance-in-the-Loop (GiL), a runtime architecture that embeds non-bypassable policy enforcement directly into AI execution primitives. GiL integrates Governance Enforcement Points (GEPs) into schedulers, model invocation paths, and inter-service communication layers. Policies support three outcomes: permit, deny, and modify – unlike deny, which cascades into workflow failure, modify preserves system availability by transforming the action into a policy-compliant alternative before execution. Each decision is bound to a verifiable audit artifact. We formalize governance as a complete mediation problem over distributed execution traces, define enforcement invariants, formally argue two core safety properties, and demonstrate differentiation from existing policy enforcement systems. The central argument is that enforceable AI governance requires architectural embedding, not procedural overlay.

ABSTRACT The field generated by a time‐harmonic pure irrotational current distributed in a finite region of free space is derived analytically. Only an electric field is produced and is nonzero even merely within the finite interior of the current distribution, though the problem space itself is infinite. To consider the obtained field solution nonphysical according to our current physical concepts, however, lacks evidence or reasoning. It satisfies the original first‐order Maxwell's equations (MEs) and the related continuity conditions exactly, hence cannot be rejected mathematically. It is also shown that a conceptual denial of such a different kind of solution based on physical interpretations of other known solutions of the same MEs is logically not acceptable. A direct experiment study is necessary to conclude convincingly whether or not the above solution is physical. The completeness problem of MEs and their consistency with the Lorentz force law and the equation of motion are discussed. Free space MEs are incomplete or underdetermined due to the absence of a curl equation for the current density. If the solution is nonphysical, ME‐based electromagnetic (EM) theory is not self‐consistent. On the other hand, if it is physical, this type of inconsistency within the frame of the ME‐based EM theory disappears, yet it is inconsistent with the Lorentz force law and the equation of motion in this case.

Matrix completion (MC) is fundamental for predicting missing data with a wide range of applications in personalized healthcare, e-commerce, recommendation systems, and social network analysis. Traditional MC approaches typically assume centralized data storage, which raises challenges in terms of computational efficiency, scalability, and user privacy. In this article, we address the problem of federated MC, focusing on scenarios where user-specific data is distributed across multiple clients, and privacy constraints are uncompromising. Federated learning (FL) provides a promising framework to address these challenges by enabling collaborative learning across distributed datasets without sharing raw data. We propose FedMC-ADMM for solving federated MC problems, a novel algorithmic framework that combines the alternating direction method of multipliers (ADMM) with a randomized block-coordinate strategy and alternating proximal gradient steps. Unlike existing federated approaches, FedMC-ADMM effectively handles multiblock nonconvex and nonsmooth optimization problems, allowing efficient computation while preserving user privacy. We analyze the theoretical properties of our algorithm, demonstrating subsequential convergence and establishing a convergence rate of $\mathcal {O}(K^{-1/2})$ , leading to a communication complexity of $\mathcal {O}(\epsilon ^{-2})$ for reaching an $\epsilon $ -stationary point. This work is the first to establish these theoretical guarantees for federated MC in the presence of multiblock variables. To validate our approach, we conduct extensive experiments on real-world datasets, including MovieLens 1M, 10M, and Netflix. The results demonstrate that FedMC-ADMM outperforms existing methods in terms of convergence speed and testing accuracy.

Videos contain multi-modal content, and exploring multi-branch cross-modal interactions with natural language queries can be of benefit to the text-video retrieval task (TVR). However, recent methods applying the large-scale pre-trained CLIP model for TVR only focus on visual cues in videos. Furthermore, traditional methods of simply concatenating multimodal features do not exploit fine-grained cross-modal information in videos. In this paper, we propose a multi-branch multi-modal hybrid fusion (M2HF) network to hierarchically explore interaction between text queries and other modality content in videos. Specifically, M2HF first fuses visual features extracted by CLIP with audio and motion features extracted from videos to obtain fused audio-visual features and motion-visual features respectively. The multi-modal completion problem is also considered and solved in this process. Then, visual features, audio-visual features, motion-visual features, and text extracted from the video are used to establish cross-modal relationships with caption text queries using a multibranch approach. The retrieval outputs from all branches are then fused to obtain the final text-video retrieval results. Our framework provides two kinds of training strategies, using an ensemble approach and an end-to-end approach. Moreover, a novel multi-modal loss function is proposed to balance the contributions of each modality for efficient end-to-end training. M2HF allows us to obtain state-of-the-art results on various benchmarks: Rank@1 of 66.0%, 68.6%, 33.9%, 57.4%, and 57.3% on MSR-VTT, MSVD, LSMDC, DiDeMo, and ActivityNet, respectively.

In the field of spectrum situation monitoring, space-based spectrum mapping can overcome the limitations of ground-based monitoring, such as restricted coverage, environmental constraints, and difficulties in equipment deployment. However, current research on radio map reconstruction methods based on space-based satellite data is insufficient. Traditional methods mostly set missing patterns based on the type of data collected on the ground, such as random sampling or strip sampling. These methods can meet the needs of generating spectrum maps for local spectrum monitoring on the ground, but they are hardly adaptable to the task of space-based global spectrum mapping. To address this challenge, we have designed a tensor reconstruction method for radio maps based on local low-rankness. Before conducting global completion, we first identify local regions in the map with more prominent low-rank characteristics for completion. This enables the method to handle radio map reconstruction in the context of space-based wide-area coverage. During the reconstruction phase, targeting the two-dimensional spatial completion problem of space-based spectrum maps, we extend the autoregressive process from the temporal dimension in classical spatiotemporal models to the spatial domain, proposing a low-rank tensor completion model based on dual autoregression (LRTCDAR). By incorporating a dual autoregressive structure to capture spatial correlations and combining it with the inherent low-rank property of radio maps, the model achieves high-precision reconstruction of incomplete radio maps. Extensive experimental results demonstrate that, compared to state-of-the-art methods, the proposed approach effectively reconstructs radio maps under various conditional backgrounds. Notably, LRTCDAR exhibits greater advantages when applied to satellite data acquisition scenarios.

ABSTRACT The low‐rank tensor completion problem is about recovering a tensor from partially observed entries. We consider this problem in the tensor train format and extend the preconditioned metric from the matrix case to the tensor case. The first‐order and second‐order quotient geometry of the manifold of fixed tensor train rank tensors under this metric is studied in detail. Algorithms, including Riemannian gradient descent, Riemannian conjugate gradient, and Riemannian Gauss–Newton, have been proposed for the tensor completion problem based on the quotient geometry. It has also been shown that the Riemannian Gauss–Newton method on the quotient geometry is equivalent to the Riemannian Gauss–Newton method on the embedded geometry with a specific retraction. Empirical evaluations on random instances as well as on function‐related tensors show that the proposed algorithms are competitive with other existing algorithms in terms of recovery ability, convergence performance, and reconstruction quality.

This study employs a novel combination of eye-tracking technology and matrix completion problems to investigate some of the sources of individual differences in problem-solving skills among 67 children aged 7–8 years. Our study provides physiological evidence that children who are better problem solvers examine the matrix areas of matrix completion problems longer than response-choice areas; a finding that suggests they are most likely adopting a constructive matching approach for solving problems. In contrast, poor problem solvers examine the response-choice areas longer than better problem solvers. They also examine the matrices for a considerable amount of time after viewing the response choices. These findings suggest that poor problem solvers are more likely to adopt a response-elimination approach for solving problems than better problem solvers. Finally, our study shows that children who are better problem solvers systematically study the rows and columns in the matrices more frequently than poor problem solvers. This latter finding suggests that better problem solvers intentionally try to extract the underlying structural features of the matrix completion problems.

Some results on completion problems of upper triangular operator matrices