Search Results (107)

The Zeta-Minimizer Theorem establishes that the Riemann zeta function $\zeta \left(s\right)$ and the primes arise variationally as unique minimizers of a phase functional defined on a symmetric measure space $\left(X,\mu ,G\right)$ equipped with helical operators. Three fundamental axioms—strict concave entropy maximization (Axiom 1), spectral Gibbs minima with non-vanishing ground states (Axiom 2), and irreducible bounded oscillations with flux conservation (Axiom 3)—allow for the selection of the non-proper Archimedean conical helix as the sole topology satisfying all constraints. Primes emerge as indivisible minimal cycles in the associated representation graph $\Gamma$ (via Hilbert irreducibility and Maschke’s theorem), while the Euler product is recovered through the spectral Dirichlet mapping of the helical eigenvalues. The partial zeta product, $Z\left(s\right)=\prod _j{\displaystyle \frac{1}{1-p_j^{-s}}},s\in \mathbb{R}\left\{0\right\},$ constitutes the exact grand partition function of any finite subsystem. Numerical inversion of this product directly recovers the mixture frequency $s$ from any experimental compressibility factor $Z_{\mathrm{m}\mathrm{i}\mathrm{x}}$. Mole fractions $x_i\left(s\right)$, interaction parameters $\Delta \left(x_i\right)$, and the Lyapunov spectrum $\lambda \left(x_i\right)$ then follow deductively via the helical transfer matrix and the closed-form linear ODE for $\Delta$. Occupation numbers $N\left(x_i\right)$ attain sharp maxima precisely at Fibonacci ratios $F_r/F_{r+1}$, leading to the molecular prime-ID rule. For twelve representative purely binary (irreducible) systems spanning atomic noble gases, simple diatomics, polar molecules, and an aromatic ring, the residuals satisfy $|Z\left(s\right)-Z_{\mathrm{m}\mathrm{i}\mathrm{x}}|<1.5\times {10}^{-8}$. The resulting $\lambda \left(x_i\right)$ curves accurately reproduce critical points, liquid ranges, and thermodynamic anomalies with zero adjustable parameters. The Riemann Hypothesis follows rigorously as a theorem: the unique fixed point of the duality functor $s\mapsto 1-s$ that preserves the orthogonality condition $\sum {\mathrm{c}\mathrm{o}\mathrm{s}}^2{\theta }^k=1$ is $\mathrm{R}\mathrm{e}\left(s\right)=1/2$, enforced by Axiom 1 concavity and Axiom 3 irreducibility. The framework is fully deductive and parameter-free and extends naturally to arbitrary mixtures and multiplicities through the helical representation graph. It provides a variational unification of analytic number theory, spectral geometry, thermodynamic phase behavior, and the Riemann Hypothesis from first principles. Full article

Scientific publishing is currently constrained by an unstructured narrative bottleneck paradigm, which increasingly diverges from the scale, complexity, and computational nature of modern research. Despite rapid advancements in data generation and analysis, scientific knowledge is predominantly disseminated as static narrative artifacts, thereby limiting reproducibility, machine accessibility, and cumulative integration. This study explores how scientific communication can be restructured to facilitate scalable validation and reliable knowledge accumulation. We propose the Object-Oriented Scientific Information paradigm, wherein scientific contributions are represented as executable, machine-interpretable objects that integrate structured data, reproducible methodologies, and formally encoded semantic claims. To operationalize this paradigm, we delineate the architecture of an Autonomous Knowledge Engine, a modular neuro-symbolic system that combines domain-specialized Mixture-of-Experts routing, formal verification of claims, and an information-theoretic filter based on marginal information gain. This architecture enables continuous validation, redundancy control, and the integration of scientific contributions within an active knowledge graph. The analysis demonstrates that Object-Oriented Scientific Information (OOSI) and Autonomous Knowledge Engine (AKE) fundamentally differ from existing document-based, executable, and semantic publishing models by shifting epistemic control from narrative evaluation to computational verification. We conclude that transitioning toward a computable scientific record is essential for sustaining reliable and self-correcting science in the context of accelerating knowledge production. Full article

Graph Neural Networks (GNNs) have emerged as the standard for learning representations from graph-structured data. While traditional architectures relying on message-passing mechanisms excel in homophilic settings, they essentially function as fixed low-pass filters. However, this smoothing operation limits their ability to generalize to heterophilic graphs, where connected nodes often exhibit dissimilar labels and high-frequency signals are crucial for discrimination. Furthermore, existing Mixture-of-Experts (MoE) methods for graphs often suffer from local-view routing, failing to capture global structural context during expert selection. To address these challenges, this paper proposes SS-AdaMoE, a novel Spatio-Spectral Adaptive Mixture of Experts framework designed for robust node classification across diverse graph patterns. Specifically, a Dual-Domain Expert System is constructed, integrating heterogeneous spatial aggregators with learnable spectral filters based on Bernstein polynomials. This allows the model to adaptively capture arbitrary frequency responses—including high-pass and band-pass signals—which are overlooked by standard GNNs. To resolve the locality bias, a Hierarchical Global-Prior Gating Network augmented by a Linear Graph Transformer is introduced, ensuring that expert selection is guided by both local node features and global topological awareness. Extensive experiments are conducted on five benchmark datasets spanning both homophilic and heterophilic networks. The results demonstrate that SS-AdaMoE consistently outperforms baselines, achieving accuracy improvements of up to 2.65% on Chameleon and 1.41% on Roman-empire over the strongest MoE baseline, while surpassing traditional GCN architectures by margins exceeding 28% on heterophilic datasets such as Texas. These findings validate that the synergy of learnable spectral priors and global gating effectively bridges the gap between spatial aggregation and spectral filtering. Full article

Retrieval-Augmented Generation (RAG) is widely used for long-text summarization due to its efficiency and scalability. However, standard RAG methods flatten documents into independent chunks, disrupting sequential flow and thematic structure, resulting in significant loss of contextual information. This paper presents MOEGAT, a novel graph-enhanced retrieval framework that addresses this limitation by explicitly modeling document structure. MOEGAT constructs an Orthogonal Context Graph to capture sequential discourse and global semantic relationships—long-range dependencies between non-adjacent text spans that reflect topical similarity and logical associations beyond local context. It then employs a query-aware Mixture-of-Experts Graph Attention Network to dynamically activate specialized reasoning pathways. Experiments conducted on three public long-text summarization datasets demonstrate that MOEGAT achieves state-of-the-art performance. Notably, on the WCEP dataset, it outperforms the previous state-of-the-art Graph of Records (GOR) baseline by 14.9%, 18.1%, and 18.4% on ROUGE-L, ROUGE-1, and ROUGE-2, respectively. These substantial gains, especially the 14.9% improvement in ROUGE-L, reflect significantly better capture of long-range coherence and thematic integrity in summaries. Ablation studies confirm the effectiveness of the orthogonal graph and Mixture-of-Experts components. Overall, this work introduces a novel structure-aware approach to RAG that explicitly models and leverages document structure through an orthogonal graph representation and query-aware Mixture-of-Experts reasoning. Full article

This paper introduces Graph-Propagated Multi-Scale Hashing with Contrastive Learning (GPMCL), a novel unsupervised cross-modal hashing framework designed to address the semantic deficiency in large-scale unlabeled multimodal data. GPMCL first constructs an initial similarity matrix via cross-modal graph propagation, effectively capturing potential inter-modal relationships. A multi-scale enhancement strategy is then employed to integrate both local and global similarities, resulting in a more informative and robust similarity representation. To adaptively distinguish sample relationships, a Gaussian Mixture Model (GMM) is utilized to determine dynamic thresholds. Additionally, contrastive learning is incorporated in the feature space to enhance intra-class compactness and inter-class separability. Extensive experiments conducted on three public benchmark datasets demonstrate that GPMCL consistently outperforms existing state-of-the-art unsupervised cross-modal hashing methods in terms of retrieval performance. These results validate the effectiveness and generalization capability of the proposed method, highlighting its potential for practical cross-modal retrieval applications. Full article

Intra-tumor heterogeneity (ITH) is a compounding factor for cancer prognoses and treatment. Single-cell DNA sequencing (scDNA-seq) provides cellular resolution of the variations in a cell and has been widely used to study cancer progression and the responses to drugs and treatments. While low-coverage scDNA-seq technologies typically provide a large number of cells, accurate cell clustering is essential for effectively characterizing the ITH. The existing cell clustering methods are typically based on either single-nucleotide variations (SNV) or copy number alterations (CNA), without leveraging both signals together. Since both SNVs and CNAs are indicative of cell subclonality, in this paper, we designed a robust cell-clustering tool that integrates both signals using a graph autoencoder. Our model co-trains the graph autoencoder and a graph convolutional network (GCN) to guarantee meaningful clustering results and to prevent all cells from collapsing into a single cluster. Given the low-dimensional embedding generated by the autoencoder, we adopted a Gaussian mixture model (GMM) to further cluster the cells. We evaluated our method on eight simulated datasets and a real cancer sample. Our results demonstrate that our method consistently achieved higher V-measure scores compared to SBMClone, an SNV-based method, and a K-means method that relies solely on CNA signals. These findings highlight the advantage of integrating both SNV and CNA signals within a graph autoencoder framework for accurate cell clustering. Full article

Accurate state estimation is essential for the real-time operation and control of modern distribution systems characterized by high renewable energy penetration, bidirectional power flows, and volatile loads. Conventional model-driven approaches such as the Weighted Least Squares (WLS) exhibit limited robustness under noisy and sparse measurements, while existing data-driven methods often neglect critical physical constraints inherent to power systems. To address these limitations, this paper proposes a physics-constrained Graph Attention Network (GAT) framework for distribution system state estimation (DSSE) that synergistically integrates data-driven learning with physical domain knowledge. The proposed method comprises three key components: (1) a Gaussian Mixture Model (GMM)-based data augmentation strategy that captures the stochastic characteristics of loads and distributed generation to generate synthetic samples consistent with actual operating distributions; (2) a GAT-based feature extractor with topology-aware admittance matrix embedding that effectively learns spatial dependencies and structural relationships among network nodes; and (3) a physics-constrained loss function that incorporates nodal power and voltage limit penalties to enforce operational feasibility. Comprehensive evaluations on the real-world 141-bus test system demonstrate that the proposed method achieves mean absolute error (MAE) reductions of 52.4% and 45.5% for voltage magnitude and angle estimation, respectively, compared to conventional Graph Convolutional Network (GCN)-based approaches. These results validate the superior accuracy, robustness, and adaptability of the proposed framework under challenging measurement conditions. Full article

Tree-Augmented Naive Bayes (TAN) is an interpretable graphical structure model. However, its structure learning for continuous attributes depends on the class-conditional mutual information, which is sensitive to one-dimensional or two-dimensional density estimation. Accurate estimation is challenging under complex distributions such as multi-peak, long-tailed and heteroscedastic cases. To address this issue, we propose a structure learning method for TAN based on Fast Generative Bootstrap Maximum Likelihood Estimation (TAN-FGBMLE). FGBMLE consists of two stages of work. In the first stage, resampling weights and random noise are input into a network generator to rapidly produce candidate parameters, efficiently covering the latent density space without repeated independent optimization. In the second stage, optimal mixture weights are estimated by maximum likelihood estimation, assigning appropriate contributions to each candidate component. This design enables fast and accurate complex density estimation for both single and joint attributes, providing reliable computation of class-conditional mutual information. The TAN structure is then constructed using Prim’s maximum spanning tree algorithm. Experiments show that our estimation method attains higher fitting accuracy and lower runtime compared with traditional nonparametric estimators. By using open-source datasets, the TAN-FGBMLE achieves superior accuracy and recall compared to classic methods, demonstrating good robustness and interpretability. On publicly available real air quality data, it has a high classification result and produces graph structures that more accurately capture dependencies among continuous attributes. Full article

This paper presents a novel dual-stream framework for multimodal emotion recognition, engineered to address the varying complexity inherent in emotional expressions. The proposed architecture uniquely integrates a graph embedding as an auxiliary modality to explicitly model temporal correlations between utterances, and processes features through two complementary sub-models operating in parallel: a Cross-Attention Transformer Mixture-of-Experts (MoE) model and a Sum-Product Linear MoE model. The former deciphers nuanced and ambiguous emotions, such as ‘fear’ and ‘sadness’, by leveraging a deep cross-attention mechanism to model intricate, bidirectional dependencies between textual and acoustic features. The latter is a lightweight model optimized to efficiently recognize clear and intuitive emotions, like ‘anger’ and ‘happiness’, through simple element-wise operations. The final prediction is derived from an average ensemble of logits from both sub-models, ensuring a robust and balanced classification. Evaluated on the Korean AI-Hub and English IEMOCAP datasets, the framework achieves state-of-the-art accuracy of 0.8071 and demonstrates excellent cross-lingual generalization with an accuracy of 0.7823. Empirical results validate the complementary design, confirming that the specialized models synergistically enhance overall performance. Full article

Background: Mapping anti–HLA class I cross-reactivity from single-antigen bead (SAB) mean fluorescence intensity (MFI) data supports donor selection. However, interpretation is complicated by analytical choices and assay variability. Methods: A total of 4327 SAB assays were analyzed (antigen × test matrix) using an interpretable, distance-based workflow. Antigen profiles were z-scored across tests. Multidimensional scaling (MDS) was used for visualization and hierarchical clustering analysis (HCA) for grouping, and complemented these with a common PCA space for model selection (K-Means via Silhouette; Gaussian Mixture Models via BIC), agglomerative (Ward and average-link on 1–correlation), spectral clustering on correlation-derived affinities, and a graph approach (k-NN ∪ minimum-spanning-tree with modularity-based communities). Non-linear embeddings (t-SNE/UMAP) and density-based HDBSCAN were used only for visual analytics, not for primary inference. Results: The pipeline revealed coherent reactivity neighborhoods that partially overlapped known cross-reactive antigen groups (CREGs) and eplet-based expectations while also highlighting less-documented relationships. Robustness was confirmed through bootstrap resampling, graph modularity, and consensus clustering across methods. Conclusions: This unified, auditable workflow converts descriptive maps into method-robust summaries of antibody reactivity and cross-reactivity. While exploratory and performed on a single dataset without linked outcomes, the approach provides a reproducible structure for comparing cohorts and prioritizing hypotheses that could be prospectively validated for clinical decision support in transplantation. Full article

Amid the increasing frequency and severity of major disasters, the rapid spread of online misinformation poses substantial risks to public safety, effective crisis management, and long-term societal sustainability. Current methods for managing disaster-related rumors rely on static, rule-based approaches that lack scalability, fail to capture nuanced misinformation, and are limited to reactive responses, hindering effective disaster management. To address this gap, this study proposes a novel framework that leverages large language models (LLMs) and event knowledge graphs (EKGs) to facilitate the sustainable agile identification and adaptive control of disaster-related online rumors. The framework follows a multi-stage process, which includes the collection and preprocessing of disaster-related online data, the application of Gaussian Mixture Wasserstein Autoencoders (GMWAEs) for sentiment and rumor analysis, and the development of EKGs to enrich the understanding and reasoning of disaster events. Additionally, an enhanced model for rumor identification and risk control is introduced, utilizing Graph Attention Networks (GATs) to extract node features for accurate rumor detection and prediction of rumor propagation paths. Extensive experimental validation confirms the efficacy of the proposed methodology in improving disaster response. This study contributes novel theoretical insights and presents practical, scalable solutions for rumor control and risk management during crises. Full article

The curing of silicone networks from dimethylsilanediol and methylsilanetriol chainbuilder–crosslinker precursor mixtures is investigated from combined quantum/molecular mechanics simulations. Upon screening different crosslinker content from 5 to 15%, we provide a series of atomic-resolution bulk models all featuring 98–99% curing degree, albeit at rather different arrangement of the chains and nodes, respectively. To elucidate the nm scale alignment of the polymer networks, we bridge scales from atomic simulation cells to graph theory and demonstrate the analyses of 3-dimensional percolation of -O-Si-O- bonds, polydimethylsiloxane branching characteristics and the interpenetration of loops. Our findings are discussed in the context of the available experimental data to relate heat of formation, curing degree and elastic properties to the molecular scale structural details—thus promoting the in-depth understanding of silicone resins. Full article

Knowledge-graph-based recommendation aims to provide personalized recommendation services to users based on their historical interaction information, which is of great significance for shopping transaction rates and other aspects. With the rapid growth of online shopping, the knowledge graph constructed from users’ historical interaction data now incorporates multiattribute information, including timestamps, images, and textual content. The information of multiple modalities is difficult to effectively utilize due to their different representation structures and spaces. The existing methods attempt to utilize the above information through simple embedding representation and aggregation, but ignore targeted representation learning for information with different attributes and learning effective weights for aggregation. In addition, existing methods are not sufficient for effectively modeling temporal information. In this article, we propose MTR, a knowledge graph recommendation framework based on mixture of experts network. To achieve this goal, we use a mixture-of-experts network to learn targeted representations and weights of different product attributes for effective modeling and utilization. In addition, we effectively model the temporal information during the user shopping process. A thorough experimental study on popular benchmarks validates that MTR can achieve competitive results. Full article

In this article, we propose a novel nonlinear cross-diffusion framework to model the distribution of susceptible and infected individuals within their habitat using a reduced SIR model that incorporates saturated incidence and treatment rates. The study investigates solution boundedness through the theory of parabolic partial differential equations, thereby validating the proposed spatio-temporal model. Through the implementation of the suggested cross-diffusion mechanism, the model reveals at least one non-constant positive equilibrium state within the susceptible–infected (SI) system. This work demonstrates the potential coexistence of susceptible and infected populations through cross-diffusion and unveils Turing instability within the system. By analyzing codimension-2 Turing–Hopf bifurcation, the study identifies the Turing space within the spatial context. In addition, we explore the results for Turing–Bogdanov–Takens bifurcation. To account for seasonal disease variations, novel perturbations are introduced. Comprehensive numerical simulations illustrate diverse emerging patterns in the Turing space, including holes, strips, and their mixtures. Additionally, the study identifies non-Turing and Turing–Bogdanov–Takens patterns for specific parameter selections. Spatial series and surfaces are graphed to enhance the clarity of the pattern results. This research provides theoretical insights into the implications of cross-diffusion in epidemic modeling, particularly in contexts characterized by localized mobility, clinically evident infections, and community-driven isolation behaviors. Full article

A solid propellant rocket motor is a propulsion system used in missiles and rockets that burns a propellant, typically composed of a mixture of fuel and an oxidizer, to generate the thrust necessary to propel the vehicle. During both the development and quality assurance phases, static firing tests of rocket motors are conducted to verify whether the system requirements meet the product specifications. These tests aim to produce two main types of graphs, “thrust versus burn time” and “pressure versus burn time,” both generated by the rocket motor during the burn. While thrust and pressure are important parameters in the design of a rocket motor, total impulse is the quantity that incorporates the crucial element of time, measuring how high a rocket can be launched. To ensure greater metrological reliability in static tests of rocket motors, it is important to carefully evaluate the uncertainty levels in the measurement chain of the data acquisition system. This work aims to assess the uncertainty levels expressed in the calculated total impulse values during a static firing test of a rocket motor at the Propulsion Jets Testing Laboratory of the Brazilian Army Technological Center. To estimate the measurement uncertainty of the chain in question, approaches based on combined and expanded uncertainty theories were adopted. These methodologies consider Type A and Type B uncertainties, providing a comprehensive and rigorous analysis. In addition to the uncertainties previously mentioned, the oscillation of the measured signal should also be recognized as a contributing factor to the overall uncertainty in the calculation of total impulse. By incorporating these various sources of uncertainty, we can achieve a more comprehensive and reliable understanding of the uncertainty associated with the measurements obtained from the measurement chain. This analysis yields a measurement uncertainty of 0.24% for thrust and 0.007% for impulse, both calculated at a confidence level of 95.45%. Full article