Search Results (1,276)

A novel method for three-dimensional (3D) wave reconstruction based on stereo vision is proposed to overcome the challenges of measuring water surfaces under laboratory conditions. Traditional methods, such as adding seed particles or projecting artificial textures, can solve the image problem caused by the optical properties of the water surface. However, these methods can be costly and complicated to operate. In this paper, the proposed method uses affine consistency as matching invariants, bypassing the need for artificial textures. The method presents new data and smoothness terms within the graph cuts framework to achieve robust wave reconstruction. In a laboratory tank experiment, the wave point clouds were successfully reconstructed using a binocular camera. The accuracy of the method was verified by comparing the reconstruction with theoretical values and the sequences of the wave probe. Full article

Cytosine and its derivatives are an important research topic in the fields of bioorganic chemistry, molecular biology and medicine due to their key role in the structure and function of nucleic acids. The article provides a detailed overview of the natural occurrence of cytosine, its biosynthetic and degradation pathways in living organisms, as well as its physicochemical and chemical properties. Particular attention was paid to the biological activity and therapeutic applications of cytosine derivatives, including their use in cancer, antiviral and epigenetic therapy. The analytical section describes high-performance liquid chromatography techniques as a major tool for identifying and determining cytosine and its derivatives in biological samples. Examples of separation conditions, column selection, mobile phases and detection parameters for these compounds are presented. The article also provides chemical structures, graphs, comparative tables and an up-to-date review of the scientific literature, presenting a comprehensive overview of the topic, including biological, chemical and analytical aspects. Full article

This paper develops extension theory for Brown functors in directed graph homotopy theory. We establish a systematic method for extending Brown functors from finite directed graphs to arbitrary directed graphs using inverse limits over finite subdigraphs. We prove that this extension is well-defined and preserves essential functorial properties. Additionally, we provide an alternative characterization of this extension through the Yoneda lemma, demonstrating how extended Brown functors can be naturally identified with sets of natural transformations from representable functors. This categorical perspective offers deeper theoretical insight into the structure of extended Brown functors and establishes important connections with classical representability theory, providing the technical foundation for Brown representability in directed graph theory. Full article

In this paper, we introduce the concept of the “graph primal,” which serves as the dual structure to the “graph grill”. We present several results associated with graph primal operations. Moreover, we introduce two new graph-local functions on graph adjacency topological spaces (graph ATSs). We then explore the basic properties of the proposed graph-local functions and describe a method for generating two new graph ATSs from existing ones via graph primals. In addition, we examine several fundamental properties and connections of the resulting topologies, supported by some counterexamples. Furthermore, we characterize the nature of the open sets of these new topologies in terms of closure operators. Finally, we assess the compatibility of graph ATSs with the graph primal concept. Full article

The Collatz conjecture is a famous unsolved problem in mathematics, known for its deceptively simple rules that generate complex, unpredictable behaviour. It can be efficiently modelled using a Petri net that represents its inverse graph, where each place corresponds to an integer and each transition encodes an inverse rule. The net, constructed up to a bound n, reveals the tree-like structure of predecessors and highlights properties such as recurrence, reachability, and liveness. Token flows simulate possible trajectories towards 1. This formal approach enables the investigation of the problem through discrete event systems theory and opens perspectives for parametric or inductive extensions beyond the bounded domain. The model proposed provides a structured framework for visualising and analysing the inverse dynamics of the conjecture. Some key numerical results highlight the challenges of working within a finite domain: for $n_{max}=1000$, the constructed Petri net comprises 1000 places and 667 transitions, including 417 source nodes (no predecessors), 333 sink nodes (no successors), and 218 isolated orphans, i.e., nodes only reachable via $\mathrm{Div}2$ transitions with no incoming $3n+1$ edge. Full article

Manifold learning is a significant computer vision task used to describe high-dimensional visual data in lower-dimensional manifolds without sacrificing the intrinsic structural properties required for 3D reconstruction. Isomap, Locally Linear Embedding (LLE), Laplacian Eigenmaps, and t-SNE are helpful in data topology preservation but are typically indifferent to the intrinsic differential geometric characteristics of the manifolds, thus leading to deformation of spatial relations and reconstruction accuracy loss. This research proposes an Optimization of Manifold Learning using Differential Geometry Framework (OML-DGF) to overcome the drawbacks of current manifold learning techniques in 3D reconstruction. The framework employs intrinsic geometric properties—like curvature preservation, geodesic coherence, and local–global structure correspondence—to produce structurally correct and topologically consistent low-dimensional embeddings. The model utilizes a Riemannian metric-based neighborhood graph, approximations of geodesic distances with shortest path algorithms, and curvature-sensitive embedding from second-order derivatives in local tangent spaces. A curvature-regularized objective function is derived to steer the embedding toward facilitating improved geometric coherence. Principal Component Analysis (PCA) reduces initial dimensionality and modifies LLE with curvature weighting. Experiments on the ModelNet40 dataset show an impressive improvement in reconstruction quality, with accuracy gains of up to 17% and better structure preservation than traditional methods. These findings confirm the advantage of employing intrinsic geometry as an embedding to improve the accuracy of 3D reconstruction. The suggested approach is computationally light and scalable and can be utilized in real-time contexts such as robotic navigation, medical image diagnosis, digital heritage reconstruction, and augmented/virtual reality systems in which strong 3D modeling is a critical need. Full article

Background: Enhancing adipose tissue functionality is a promising cellular-level approach to combating obesity. White adipose tissue (WAT) can acquire beige or brown adipose tissue (BAT)-like properties, characterized by increased thermogenesis and energy dissipation. While the SIRT1-SRSF10–Lipin-1 axis has been identified in hepatocytes, where Lipin-1 regulates triglyceride metabolism, its role in adipocytes remains unclear. This study aimed to investigate the function of Lipin-1 in 3T3-L1 preadipocytes and its interaction with SIRT1, SRSF10, and PPARγ in promoting browning-like transcriptional responses. Methods: Mouse 3T3-L1 preadipocytes were treated during differentiation with either rosiglitazone (RGZ), the SIRT1 activator SRT1720, or the SIRT1 inhibitor EX527. Gene expression was assessed by real-time PCR, and protein levels were measured using the Simple Western blot system. Data were compared with untreated controls and analyzed using GraphPad Prism. Results: Lipin-1 expression was significantly upregulated by RGZ treatment, alongside increased transcription of Sirt1 and Srsf10, supporting the presence of this regulatory axis in adipocytes. Elevated Srsf10 favored the production of the Lipin-1b isoform, whereas SIRT1 inhibition reversed these effects, confirming its upstream role. Pathway activation further enhanced the expression of browning markers, including Ucp1, Pgc1a, PRDM16, and CIDEA. Conclusions: These findings demonstrate that Lipin-1 interacts with the SIRT1–PPARγ–SRSF10 axis in adipocytes and contributes to the acquisition of beige/brown-like characteristics in WAT. This regulatory pathway may represent a potential target for improving lipid metabolism and metabolic health. Full article

The internal structure of hyperedges has become central to understanding collective dynamics in hypernetworks. This study investigates the impact of hyperedge overlap on network synchronization when hyperedge structures are explicitly considered. We propose a modified hyper-adjacency matrix that captures the internal organization of the hyperedges while preserving the higher-order properties. Using this framework, we examine how non-complete connections within hyperedges influence synchronization as the overlap increases. Our findings reveal clear differences from fully connected hyperedge models. Furthermore, spectral graph theory and numerical simulations confirm that the structural variations induced by overlaps significantly regulate global synchronization. This work extends the theoretical framework of hypernetwork synchronization and highlights the critical role of hyperedge overlaps in shaping the internal hyperedge structure. Full article

Let $\mathfrak{R}$ be a commutative ring with identity $1\ne 0$. The weakly zero-divisor graph of $\mathfrak{R}$, denoted $W_{\Gamma }(\mathfrak{R})$, is the simple undirected graph whose vertex set consists of the nonzero zero-divisors of $\mathfrak{R}$, where two distinct vertices $\mathfrak{a}$ and $\mathfrak{b}$ are adjacent if and only if there exist $r\in \mathrm{ann}(\mathfrak{a})$ and $s\in \mathrm{ann}(\mathfrak{b})$ such that $rs=0$. In this paper, we study the signless Laplacian spectrum of $W_{\Gamma }({\mathbb{Z}}_n)$ for several composite forms of n, including $n=p^2{q}^2$, $n=p^{2}qr$, $n=p^m{q}^m$ and $n=p^{m}qr$, where $p, q, r$ are distinct primes and $m\ge 2$. By using generalized join decomposition and quotient matrix methods, we obtain explicit eigenvalue formulas for each case, along with structural bounds, spectral integrality conditions and Nordhaus–Gaddum-type inequalities. Illustrative examples with computed spectra are provided to validate the theoretical results, demonstrating the interplay between the algebraic structure of ${\mathbb{Z}}_n$ and the spectral properties of its weakly zero-divisor graph. Full article

The Angular Bisector Insertion Constructive Heuristic Algorithm (ABIA), though effective for small-scale TSPs, suffers from reduced solution quality and high computational complexity in larger instances due to the degradation of its geometric properties. To address this, two enhanced variants—k-ABIA and k-ABIA-3opt—are proposed. k-ABIA employs k-means clustering to decompose large-scale problems into subgroups, each solved via ABIA, with designed inter-cluster connections to reduce global search cost. k-ABIA-3opt further integrates 3-opt local search and ATSP-specific refinement strategies to avoid local optima. Both algorithms were benchmarked against GA, AACO-LST, and the original ABIA on instances ranging from 100 to 1200 nodes, considering solution quality, stability, runtime, and ATSP performance. k-ABIA-3opt achieved the best overall solution quality, with a total deviation of 28.75%, outperforming AACO-LST (44.86%) and ABIA (144.93%). Meanwhile, k-ABIA, with its O(n²) complexity and low constant overhead, was the fastest, solving 1000-node problems within seconds on standard hardware. Both variants exhibit strong robustness due to minimal stochasticity. For ATSP, k-ABIA-3opt further incorporates directed graph-specific optimization strategies, yielding the best solution quality among all tested algorithms. In summary, k-ABIA-3opt is well-suited for scenarios demanding high-quality solutions within tight time constraints, while k-ABIA provides an efficient option for rapid large-scale TSP solving. Together, they offer scalable and effective solutions for both symmetric and asymmetric TSP instances. Full article

Accurate transformer–customer relationships are crucial for the efficient operation and high-quality service of the low-voltage distribution grid (LVDG). This paper proposes a novel two-stage transformer–customer relationship identification strategy for LVDG using physics-guided graph attention network (PGAT). First, considering both transient and steady-state voltage fluctuations, a modified piecewise aggregate approximation (MPAA) algorithm is developed to preprocess raw measurement data through compression and denoising while preserving key voltage correlation features. Second, electrical similarity among customers is explored using the Modified Piecewise Aggregate Approximation K-means (MPAA-K-means) algorithm, enabling preliminary identification of transformer–customer relationships. Then, a training paradigm based on PGAT is introduced to characterize node features constrained by grid topology and electrical properties, achieving refined identification of transformer–customer relationships. Finally, testing results on real LVDG demonstrate the effectiveness and accuracy of the proposed two-stage identification strategy, providing new insights for transformer–customer relationship identification. Full article

Knowledge Graph Reasoning (KGR) aims to deduce missing or novel knowledge by learning structured information and semantic relationships within Knowledge Graphs (KGs). Despite significant advances achieved by deep neural networks in recent years, existing models typically extract non-linear representations from explicit features in a relatively simplistic manner and fail to fully exploit semantic heterogeneity of relation types and entity co-occurrence frequencies. Consequently, these models struggle to capture critical predictive cues embedded in various entities and relations. To address these limitations, this paper proposes a relation aware spectral decoupling attention network for KGR (RASD). First, a spectral decoupling attention network module projects joint embeddings of entities and relations into the frequency domain, extracting features across different frequency bands and adaptively allocating attention at the global level to model frequency specific information. Next, a relation-aware learning module employs relation aware filters and an augmentation mechanism to preserve distinct relational properties and suppress redundant features, thereby enhancing representation of heterogeneous relations. Experimental results demonstrate that RASD achieves significant and consistent improvements over multiple leading baseline models on link prediction tasks across five public benchmark datasets. Full article

Advanced Persistent Threats (APTs) pose significant cybersecurity challenges due to their multi-stage complexity. Knowledge graphs (KGs) effectively model APT attack processes through node-link architectures; however, the scarcity of high-quality, annotated datasets limits research progress. The primary challenge lies in balancing annotation cost and quality, particularly due to the lack of quality assessment methods for graph annotation data. This study addresses these issues by extending existing APT ontology definitions and developing a dynamic, trustworthy annotation framework for APT knowledge graphs. The framework introduces a self-verification mechanism utilizing large language model (LLM) annotation consistency and establishes a comprehensive graph data metric system for problem localization in annotated data. This metric system, based on structural properties, logical consistency, and APT attack chain characteristics, comprehensively evaluates annotation quality across representation, syntax semantics, and topological structure. Experimental results show that this framework significantly reduces annotation costs while maintaining quality. Using this framework, we constructed LAPTKG, a reliable dataset containing over 10,000 entities and relations. Baseline evaluations show substantial improvements in entity and relation extraction performance after metric correction, validating the framework’s effectiveness in reliable APT knowledge graph dataset construction. Full article

Traditional educational assessment systems suffer from inefficient question selection strategies that fail to optimally probe student knowledge while requiring extensive testing time. We present a novel hierarchical probabilistic neural framework that integrates Bayesian inference with symmetric deep neural architectures to enable adaptive, efficient knowledge assessment. Our method models student knowledge as latent representations within a graph-structured concept dependency network, where probabilistic mastery states, updated through variational inference, are encoded by symmetric graph properties and symmetric concept representations that preserve structural equivalences across similar knowledge configurations. The system employs a symmetric dual-network architecture: a concept embedding network that learns scale-invariant hierarchical knowledge representations from assessment data and a question selection network that optimizes symmetric information gain through deep reinforcement learning with symmetric reward structures. We introduce a novel uncertainty-aware objective function that leverages symmetric uncertainty measures to balance exploration of uncertain knowledge regions with exploitation of informative question patterns. The hierarchical structure captures both fine-grained concept mastery and broader domain understanding through multi-scale graph convolutions that preserve local graph symmetries and global structural invariances. Our symmetric information-theoretic method ensures balanced assessment strategies that maintain diagnostic equivalence across isomorphic concept subgraphs. Experimental validation on large-scale educational datasets demonstrates that our method achieves 76.3% diagnostic accuracy while reducing the question count by 35.1% compared to traditional assessments. The learned concept embeddings reveal interpretable knowledge structures with symmetric dependency patterns that align with pedagogical theory. Our work generalizes across domains and student populations through symmetric transfer learning mechanisms, providing a principled framework for intelligent tutoring systems and adaptive testing platforms. The integration of probabilistic reasoning with symmetric neural pattern recognition offers a robust solution to the fundamental trade-off between assessment efficiency and diagnostic precision in educational technology. Full article

Biodegradable polyesters have gained attention due to their sustainability benefits, considering the escalating environmental challenges posed by synthetic polymers. Advances in artificial intelligence (AI), including machine learning (ML) and deep learning (DL), are expected to significantly accelerate research in polymer science. This review article explores “bio” polymer informatics by harnessing insights from the AI techniques used to predict structure–property relationships and to optimize the synthesis of bioplastics. This review also discusses PolyID, a machine learning-based tool that employs message-passing graph neural networks to provide a framework capable of accelerating the discovery of bioplastics. An extensive literature review is conducted on explainable AI (XAI) and generative AI techniques, as well as on benchmarking data repositories in polymer science. The current state-of-the art in ML methods for ring-opening polymerizations and the synthesizability of biodegradable polyesters is also presented. This review offers an in-depth insight and comprehensive knowledge of current AI-based models for polymerizations, molecular descriptors, structure–property relationships, predictive modeling, and open-source benchmarked datasets for sustainable polymers. This study serves as a reference and provides critical insights into the capabilities of AI for the accelerated design and discovery of green polymers aimed at achieving a sustainable future. Full article