Beyond hard constraint: unified knowledge-embedding physics informed neural networks for multi-domain system.

Implicit relations framework for fixed-point theorems in probabilistic metric spaces

Abstract In a rotating mechanical system, the physical connections among its components provide a natural topological structure for the Graph Neural Network (GNN). The graph model constructed based on these physical connections can transform the operation data of each component into a structured representation, thereby assisting in the extraction and identification of fault features. However, the dynamic correlations among multi-sensor data contain rich information that goes beyond physical connections. These correlations reflect the internal coupling mechanisms and the evolution patterns of faults in the mechanical system. Thus，this paper proposes a small-sample fault diagnosis method based on the mining of implicit relationships among multiple sensors. This method deeply analyses the potential connections among the data of multiple sensors, effectively enhancing the feature extraction efficiency of the Graph Neural Network and significantly improving the accuracy and generalization ability of fault diagnosis. To verify the reliability and practicality of this method, this paper conducts experiments on the PHM2024 dataset and the Southeast University Bearing Dataset (SUFD). The results show that this method improves the ability to extract fault features by mining the implicit relationships among multiple sensors. Especially in scenarios with scarce small-sample data and noisy interference, this method still maintains a high diagnostic accuracy.

Philosophical concepts are an essential component of cultural communication, serving as carriers of a nation’s worldview and intellectual tradition. This study aims to explore the effectiveness of Eugene Nida’s Functional Equivalence Theory in the Chinese-English translation of philosophical concepts. Taking Key Concepts in Chinese Thought and Culture: Philosophy as the case study, this research adopts a qualitative analytical method to examine how lexical and syntactic equivalence are realized in translation practice. The analysis reveals that, at the lexical level, strategies such as word class adjustment, isomorphic substitution, and explanatory translation help overcome cultural and semantic gaps. At the syntactic level, the use of kernel sentence restructuring and function-oriented translation effectively clarifies implicit logical relations in Chinese source texts. These approaches enable target readers to achieve a similar understanding and response as source readers. The study concludes that Functional Equivalence Theory provides a practical and effective framework for translating Chinese philosophical concepts, particularly in enhancing clarity, readability, and cultural transmission. However, limitations remain due to the complexity and interpretive openness of philosophical terms.

This paper investigates fixed point theorems for weakly compatible and occasionally weakly compatible mappings in cone metric spaces and C*-algebra-valued metric spaces. We establish several common fixed-point results under various contractive conditions including rational expressions and integral-type contractions. The study provides a detailed analysis of weak commutativity conditions that are more general than strong commutativity. We prove existence and uniqueness theorems for pairs and families of mappings satisfying implicit relations in both normal and non-normal cone metric spaces. Applications to nonlinear functional equations, including those arising in dynamic programming and iterative functional equations, are presented with illustrative examples. Our results extend and unify several existing fixed point theorems in the literature while providing new insights into the structure of these generalized metric spaces.

We have constructed a generative artificial intelligence model predicting the gravity solutions when the holographic entanglement entropy of the dual quantum field theory is provided as input. The model we utilize is based on the transformer algorithm commonly used in natural language tasks such as text generation, summarization, and translation. The transformer model can understand the implicit relation between input and output sequences by training data. For training, we generate many data sets composed of holographic entanglement entropy and corresponding metric solutions. After training these data, the transformer model predicts the dual geometry from arbitrary test sets of entanglement entropy data. The reconstruction of the dual gravity allows us to get more information on the thermodynamic quantities of thermal systems, which cannot be read directly from entanglement entropy data. In this work, we construct the dual geometry by applying the transformer model. After that, we derive thermodynamic quantities, like temperature and densities of thermal systems, from the entanglement entropy.

Text-to-image person retrieval (TIPR) aims to identify the target person using textual descriptions, facing challenge in modality heterogeneity. Prior works have attempted to address it by developing cross-modal global or local alignment strategies. However, global methods typically overlook fine-grained cross-modal differences, whereas local methods require prior information to explore explicit part alignments. Additionally, current methods are English-centric, restricting their application in multilingual contexts. To alleviate these issues, we pioneer a multilingual TIPR task by developing a multilingual TIPR benchmark, for which we leverage large language models for initial translations and refine them by integrating domain-specific knowledge. Correspondingly, we propose Bi-IRRA: a Bidirectional Implicit Relation Reasoning and Aligning framework to learn alignment across languages and modalities. Within Bi-IRRA, a bidirectional implicit relation reasoning module enables bidirectional prediction of masked image and text, implicitly enhancing the modeling of local relations across languages and modalities, a multi-dimensional global alignment module is integrated to bridge the modality heterogeneity. The proposed method achieves new state-of-the-art results on all multilingual TIPR datasets.

Background/Objectives: The overconsumption of animal-derived proteins represents a threat to both the environment and our health. Although there is widespread agreement that reducing meat consumption represents a more sustainable alternative, few studies have explored the implicit relations guiding these food choices. This empirical study explores meat consumption and vegetarianism through the lens of Relational Frame Theory. It is hypothesized that people who eat meat have different relational responses to images of meat and plant-based alternatives than vegetarians. Methods: We used the Implicit Attribute Classification Task (IMPACT) to measure relational responses, testing whether omnivores find plant-based proteins (1) less tasty, (2) less familiar, and (3) more expensive than vegetarians do. We registered the response latencies and calculated D-scores from 110 participants who completed an online test. Results: The study failed to find any statistically significant differences in the IMPACT measures between omnivores and vegetarians, given our specific participants and stimuli. Conclusions: Relational responding measures offer a useful approach to understanding consumer choices. However, they are highly sensitive to the task parameters and could be enhanced by further integration with other consumer behavior models when explaining meat consumption.

Large language models (LLMs) are increasingly used for information extraction, and they often perform well when the target facts are stated plainly. In scientific papers, though, many relationships are only implied: the reader has to connect evidence across sentences, track context, and sometimes make several small inferences before a relation becomes clear. How reliably LLMs handle that kind of reading remains an open question. To study this, we propose an evaluation framework that tests relation extraction under progressively heavier reasoning demands. It relies on three prompt templates that grow more structured and more challenging, and we apply them to a curated perovskite solar cell dataset covering three core categories of scientific informationmaterials, processes, and performance. We then benchmark three representative models. The results show a consistent pattern. When relations are explicit, models extract them with high accuracy. As soon as the task requires deeper inferenceespecially for implicit or multi-hop relations that hinge on nuanced semanticsperformance drops noticeably. The models also fail in different ways: some are comparatively good at maintaining coherent, step-by-step reasoning, while others are more dependable at avoiding hallucinated links or preserving type consistency. Even with these strengths, sizable gaps remain in coverage, reasoning depth, and overall completeness. Taken together, the findings clarify where current LLMs are genuinely useful for scientific information extraction and where they still fall short. They tend to be most reliable in structured extraction settings, while deeper semantic understanding remains the main bottleneck. By quantifying performance across prompt levels, the framework offers a practical yardstick for semantic comprehension and scientific reasoning in relation extraction, and it provides empirical support for downstream applications such as scientific knowledge graph construction.

In accountability-driven educational systems, assessment policies play a central role in regulating English as a Foreign Language (EFL) teachers’ professional practices and institutional responsibilities. Although applied linguistics research has widely addressed assessment practices and their pedagogical effects, there remains a lack of critical inquiry into how assessment policies linguistically construct teacher accountability and shape professional agency. This qualitative study addresses this gap by employing Critical Discourse Analysis (CDA) to investigate the discursive representation of EFL teachers in assessment policy documents and teachers’ interpretations of these representations. Drawing on Fairclough’s three-dimensional framework, the study analyzes a corpus of national and institutional EFL assessment policy texts alongside semi-structured interviews with 8–12 EFL teachers from secondary and higher education contexts. The analysis examines textual features such as modality, evaluative language, and nominalization to uncover implicit power relations embedded in policy discourse. Teachers’ narratives are analyzed to explore how these discourses are appropriated, negotiated, or resisted in classroom assessment practices. At the level of social practice, the study situates these discursive processes within broader accountability regimes in contemporary EFL education. The study is expected to demonstrate that assessment policies predominantly construct teachers as responsible for measurable outcomes, often limiting pedagogical autonomy, while teachers actively negotiate these discourses to maintain professional agency. The findings contribute to applied linguistics by highlighting the role of discourse in shaping assessment-related teacher identities and by offering implications for more equitable and context-sensitive assessment policy development.

Introduction: Fixed point theory is a fundamental area in mathematical analysis with wide-ranging applications. This research aims to extend fixed point results in the framework of neutrosophic metric spaces, which incorporate degrees of membership, non-membership, and indeterminacy. The study focuses on the development of compatible maps to generalize fixed point theorems under more realistic conditions. Methods: We introduce two novel classes of compatible maps—types (α) and (β)—defined via implicit relations in neutrosophic metric spaces. New fixed point theorems are established by using these map types and extending existing theories from fuzzy and intuitionistic fuzzy metric spaces. The work includes formal definitions, interrelations among mappings, and proofs of key results. Results: The newly established theorems offer broader conditions for ensuring the existence of fixed points in neutrosophic metric spaces. These generalizations effectively account for uncertainty, expanding the applicability of fixed point theory to more complex and indeterminate settings. Discussion: The inclusion of implicit relations and compatible maps enhances the theoretical flexibility of fixed point results. To demonstrate the applicability, the proposed theorems are used to solve the Fredholm integral equation under a neutrosophic framework, validating their relevance in handling real-world problems characterized by imprecise information. Conclusion: This study significantly advances fixed point theory by developing and analyzing compatible maps of types (α) and (β) in neutrosophic metric spaces. The findings provide a robust foundation for future mathematical research and practical applications involving uncertainty and incomplete data.

We introduce an ordered implicit relation and obtain related fixed point theorems in rectangular cone $b$-metric space, as an extension of the results on cone metric, rectangular cone metric and cone $b$-metric space. We provide some examples as an explanation of established outcomes. Our theorems universalize many fixed point outcomes in literature(\cite{23}, \cite{k6}). An homotopy result as an application of main theorem is given, which further applied to the human aging process. The obtained fixed point results do not follow from the results proved by Ercan \cite{er}, as the present article deals with nonlinear contractions. The convergence of the sequence generated by Urysohn integral operator is also shown by using fixed point technique.

This paper re-examines the semantic status of the ktvā-suffix within the Pāṇinian grammatical tradition by distinguishing its denotative and suggestive functions. While the sūtras, such as samānakartṛkayoḥ pūrvakāle, appear straightforward in their verbal formulation, a closer study of the Bhāṣya, Vārttikas, and later commentarial literature reveals that the suffix does not directly denote relations like sameness of agent (samānakartṛkatva) or anteriority (pūrvakālikatva). If such meanings were treated as denotative, several attested constructions, such as odanaṃ paktvā ahaṃ bhokṣye and paktvā odano bhujyate, would violate basic kāraka principles concerning agent expression and object placement. To resolve these contradictions, the grammatical tradition maintains a clear separation between the denotative meaning (vācyārtha), which is restricted to the expression of verbal action (bhāva), and the suggestive meaning (dyotyārtha), which encompasses implicit relations such as janya-janakabhāva, sāmānādhikaraṇya, pūrvottarabhāva, and vyāpyatva. Drawing on the vārttika avyayakṛto bhāve and the exposition of these four dyotya-relations in works like the Vaiyākaraṇabhūṣaṇasāra, the study demonstrates that the semantic force of ktvā arises from contextually inferred relations rather than inherent denotation. This layered approach ensures a coherent alignment between the wording of the sūtra, interpretive logic, and actual linguistic usage.

Visualization tools enable the transformation of large datasets into user-friendly graphical representations. This paper presents the development of a graph visualization tool designed to uncover implicit relationships among information entities. We describe a method for identifying such implicit relationships and introduce an interactive graph visualization system that allows users to explore the graph through filtering. The implemented functionality includes a specialized query language for dynamically modifying the appearance of nodes and edges. The proposed method and the developed tool were evaluated on two real-world datasets: (1) detecting potential violations of nuclear non-proliferation commitments and (2) identifying promising areas for scientific collaboration among organizations. The results confirm the practical relevance of the proposed approach.

A simplified kinetic model for the quantitative analysis of a potentiometric, pH-based urea biosensor is presented. The device was an electrolyte–insulator–semiconductor capacitor (EISCAP) with a pH-sensitive Ta2O5 gate functionalized by a polyallylamine hydrochloride (PAH)/urease bilayer. Within the steady-state approximation, the kinetic equations yielded an implicit algebraic relation linking the bulk urea concentration to the local pH at the sensor surface. Numerical solution of this equation, combined with a fitting routine, provides the apparent Michaelis–Menten constant () and the normalized maximum reaction rate (). Validation against the literature data confirmed the reliability of the approach. Experimental results were then analyzed in both phosphate buffer (PBS) and artificial urine (AU), covering urea concentrations of 0.1–50 mM. The fitted parameters showed comparable values of 10.9 mM (PBS) and 32.4 mM (AU), but strongly different values: (PBS) versus (AU). The three-order reduction in AU was attributed to the inhibitory effects inherent to complex biological fluids. These findings highlight the importance of the model-based quantitative analysis of EISCAP biosensors, enabling the accurate characterization of immobilized enzyme layers and guiding optimization for applications in realistic sample matrices.

Discourse markers are fundamental in structuring a text and help to establish meaning relations between its parts.In this study, an analysis of multiword discourse markers and the discourse relations they signal was conducted on a parallel bilingual corpus, composed of different TED Talks in English and their respective translations into European Portuguese.The elaboration of the analysis was based on an annotation scheme created from the ISO 24617-8 standard proposed by Silvano et al.(2022).The results obtained show that the discourse markers used in the translations between the two languages differ in number, although the discourse relations do not change.It was also found that there are discourse relations that predominate in the corpus, namely the relations of expansion and exemplification.Furthermore, it was possible to identify discursive markers capable of signaling more than one discursive relation, as well as the occurrence of cases in which EP translations omit markers, resulting in implicit discourse relations.

This paper presents a generalized fixed-point theorem in fuzzy metric spaces using an implicit relation to unify different contraction types. Based on continuous t-norms, the result extends previous work and includes corollaries demonstrating its generality. The approach simplifies analysis by eliminating separate proofs for each contraction type, while an application to integral equations demonstrates its practical utility, guaranteeing existence and uniqueness of solutions under specific conditions.

Information diffusion prediction is a crucial task for comprehending the dissemination process of information. Although this problem has received significant attention recently, most of the state-of-the-arts primarily focus on the modelling of information cascades, while neglecting the implicit social relations between users in the social network and failing to adequately model the interrelations between the user social network and information cascades. To tackle the aforementioned issues, in this work, we propose a <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</b>ual-<bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</b>tate <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</b>ypergraph <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</b>ontrastive <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</b>earning model (DSHCL). Specifically, we first propose to construct a social hypergraph based on the social network to capture the implicit social relations. Then, for capturing the cascade level correlations among users, we generate the dual-state (i.e., static and dynamic) user representations from the user social hypergraph and information cascades. Finally, we exploit contrastive learning to model the interplay between the social network and information cascades by discriminating the dual-state representations generated from them. We conduct an empirical assessment of DSHCL across four publicly available datasets, and the findings underscore the DSHCL's superiority and the efficacy of its components.

ABSTRACT This research aims to discover the implicit and meaningful relations between the factors that cause accidents by examining the accidents involving offshore vessels utilizing the Association Rule Mining method. In this respect, 374 offshore vessel accident reports are analyzed using the Apriori algorithm. In addition, Logistic Regression analysis is performed to examine the factors affecting accident severity. ‘offshore support vessels’, ‘non-FOC’, ‘vessels over 12 years old’, and ‘serious accident’ were the most frequent items in the formation of rules. Logistic Regression demonstrates that items in association rules have a higher probability of serious accidents in variables such as total loss, vessel age, type, and flag. However, in terms of vessel type, ‘oil exploration and drilling vessels’ and ‘offshore construction vessels’ are determined to be riskier than ‘offshore support vessels’. The results can be helpful for offshore operators and relevant authorities to understand the accidents better and to take preventive measures.

Summary The quantitative interpretation of geological structures relies on multi-parameter models (MPMs) inversion. However, conventional full waveform inversion that matches simulated seismic data to observed seismic data cannot accurately obtain high-resolution MPMs because of the implicit inter-parameter coupling relations in the multi-parameter wave equation. Additionally, conventional supervised deep learning approaches that require a significant number of annotated labels cannot predict precise MPMs, as only a limited number of sophisticated synthetic MPMs are available as labels. To address this issue, we propose a self-supervised multi-parameter inversion (SS-MPI) to provide high-resolution MPMs from the prior first-arrival-based tomography and reflection-based migration image. SS-MPI creates representative MPMs from the prior information as pseudo-labels to pre-train the deep learning algorithm, which then predicts MPMs as feedback to update these training pseudo-labels iteratively. Synthetic examples of elastic and anisotropic models indicate that SS-MPI outperforms the conventional elastic full waveform inversion (EFWI) and delivers highly accurate and high-resolution MPMs.