Search Results (218)

Let $G=(V,E)$ be a simple graph with the vertex set V and the edge set E$\left(\left|V\right|=n,\left|E\right|=m\right)$. An example of a vertex-decorated graph $DG$ is a vertex-quadrangulated graph $QG$. The vertex quadrangulation $QG$ of 4-regular graph G visually looks like a graph whose vertices are depicted as empty squares, and the connecting edges are attached to the corners of the squares. If we contract each quadrangle of $QG$ to a point that takes over the incidence of the four edges that were previously joined to this quadrangle, then we can again get the original graph G. Any connected graph H that provides (some of) its vertices for external connections can play the role of a decorating graph, and any graph G with vertices of valency no greater than the number of contact vertices in H can be decorated with it. Herein, we consider the case when G is a regular graph. Since the decoration also depends on the way the edges are attached to the decorating graph, we clearly stipulate it. We show that all similarly decorated regular graphs $DG$ that meet our conditions have at least $\left|V\right(H\left)\right|$ predicted common eigenvalues. A number of related results are proven. As possible applications of these results in chemistry, cases of simplified findings of eigenvalues of a molecular graph even in the absence of the usual symmetry of the molecule may be of interest. This, in particular, can somewhat expand the possibilities of applying the simple Hückel method for large molecules. Full article

Let $A_{ex}\left(\mathcal{G}\right)$ be the extended adjacency matrix of G. The eigenvalues of $A_{ex}\left(\mathcal{G}\right)$ are called extended adjacency eigenvalues of $\mathcal{G}$. The sum of the absolute values of eigenvalues of the $A_{ex}$-matrix is called the extended adjacency energy ${\mathcal{E}}_{ex}\left(\mathcal{G}\right)$ of $\mathcal{G}$. In this paper, we obtain the $A_{ex}$-spectrum of the joined union of regular graphs in terms of their adjacency spectrum and the eigenvalues of an auxiliary matrix. Consequently, we derive the $A_{ex}$-spectrum of the join of two regular graphs, the lexicographic product of regular graphs, and the $A_{ex}$-spectrum of various families of graphs. Further, as applications of our results, we construct infinite classes of infinite families of extended adjacency equienergetic graphs. We show that the $A_{ex}$-energy of the join of two regular graphs is greater than or equal to their energy. We also determine the $A_{ex}$-eigenvalues of the power graph of finite abelian groups. Full article

Cyber defense has evolved into an algorithmically intensive discipline where mathematical rigor and adaptive computation underpin the robustness and continuity of digital infrastructures. This review consolidates the algorithmic spectrum that supports modern cyber defense, from cryptographic primitives that ensure confidentiality and integrity to behavioral intelligence algorithms that provide predictive security. Classical symmetric and asymmetric schemes such as AES, ChaCha20, RSA, and ECC define the computational backbone of confidentiality and authentication in current systems. Intrusion and anomaly detection mechanisms range from deterministic pattern matchers exemplified by Aho-Corasick and Boyer-Moore to probabilistic inference models such as Markov Chains and HMMs, as well as deep architectures such as CNNs, RNNs, and Autoencoders. Malware forensics combines graph theory, entropy metrics, and symbolic reasoning into a unified diagnostic framework, while network defense employs graph-theoretic algorithms for routing, flow control, and intrusion propagation. Behavioral paradigms such as reinforcement learning, evolutionary computation, and swarm intelligence transform cyber defense from reactive automation to adaptive cognition. Hybrid architectures now merge deterministic computation with distributed learning and explainable inference to create systems that act, reason, and adapt. This review identifies and contextualizes over 50 foundational algorithms, ranging from AES and RSA to LSTMs, graph-based models, and post-quantum cryptography, and redefines them not as passive utilities, but as the cognitive genome of cyber defense: entities that shape, sustain, and evolve resilience within adversarial environments. Full article

As the Internet of Things (IoT) expands and spectrum resources become increasingly scarce, Automatic Modulation Classification (AMC) has become critical for enabling dynamic spectrum access, interference mitigation, and spectrum monitoring without coordination or prior signaling. Most deep learning-based AMC methods (e.g., CNNs, LSTMs, Transformers) operate in Euclidean spaces and therefore overlook the non-Euclidean relationships inherent in modulated signals. We propose KGNN, a graph-based AMC architecture that couples a KNN-driven graph representation with GraphSAGE convolutions for neighborhood aggregation. In the KNN stage, each feature vector is connected to its nearest neighbors, transforming temporal signals into structured graphs, while GraphSAGE extracts relational information across nodes and edges for classification. On the RML2016.10b dataset, KGNN attains an overall accuracy of 64.72%, outperforming strong baselines (including MCLDNN) while using only one-eighth the number of parameters used by MCLDNN and preserving fast inference. These results highlight the effectiveness of graph convolutional modeling for AMC under practical resource constraints and motivate further exploration of graph-centric designs for robust wireless intelligence. Full article

A D-decomposition of a directed graph G is a collection of arc-disjoint subgraphs of G, each isomorphic to D, such that every arc of G belongs to exactly one subgraph. The $\lambda$-fold spectrum problem for a directed graph D asks for the set of all integers v such that the $\lambda$-fold complete symmetric directed graph ${\phantom{K^{*}}}^{\lambda }{K}_v^{*}$ admits a D-decomposition. A five-cycle (pentagon) has 4 non-isomorphic orientations. The $\lambda$-fold spectrum problem has been solved for one of these oriented pentagons. In this paper, we provide a complete solution for each of the remaining three orientations, proving that the necessary and sufficient condition is $5\mid \lambda v(v-1)$ in all cases. Full article

Efficient spectrum allocation and telecom traffic steering in densified heterogeneous maritime communication networks remains a critical challenge due to user mobility, dynamic interference, and congestion across terrestrial, aerial, and sea-based transmitters. This paper introduces the Moving Colorable Graph (MCG) framework, a dynamic graph-theoretical representation of interferences that extends conventional graph coloring to capture the spatiotemporal evolution of heterogeneous wireless links under varying channel and traffic conditions. The formulated spectrum allocation problem is inherently non-convex, as it involves discrete frequency assignments, mobility-induced dependencies, and interference coupling among multiple transmitters and users, thus requiring suboptimal yet computationally efficient solvers. The proposed approach models resource assignment as a time-dependent coloring problem, targeting to optimally support users’ diverse demands in dense port-area networks. Considering a realistic port-area network with coastal, sea and Unmanned Aerial Vehicle (UAV) radio coverage, we design and evaluate three MCG-based algorithm variants that dynamically update frequency assignments, highlighting their adaptability to fluctuating demands and heterogeneous coverage domains. Simulation results demonstrate that the selective reuse-enabled MCG scheme significantly decreases network outage and improves user demand satisfaction, compared with static, greedy and heuristic baselines. Overall, the MCG framework may act as a flexible scheme for mobility-aware and congestion-resilient resource management in densified and heterogeneous maritime networks. Full article

Background: Autism spectrum disorder (ASD) is a highly heterogeneous neurodevelopmental condition for which accurate and automated diagnosis is crucial to enable timely intervention. Resting-state functional magnetic resonance imaging (rs-fMRI) serves as one of the key modalities for diagnosing ASD and elucidating its underlying mechanisms. Numerous existing studies using rs-fMRI data have achieved accurate diagnostic performance. However, these methods often rely on a single brain atlas for constructing brain networks and overlook the data heterogeneity caused by variations in imaging devices, acquisition parameters, and processing pipelines across multiple centers. Methods: To address these limitations, this paper proposes a multi-view, low-rank subspace graph structure learning method to integrate multi-atlas and multi-center data for automated ASD diagnosis, termed M³ASD. The proposed framework first constructs functional connectivity matrices from multi-center neuroimaging data using multiple brain atlases. Edge weight filtering is then applied to build multiple brain networks with diverse topological properties, forming several complementary views. Samples from different classes are separately projected into low-rank subspaces within each view to mitigate data heterogeneity. Multi-view consistency regularization is further incorporated to extract more consistent and discriminative features from the low-rank subspaces across views. Results: Experimental results on the ABIDE-I dataset demonstrate that our model achieves an accuracy of 83.21%, outperforming most existing methods and confirming its effectiveness. Conclusions: The proposed method was validated using the publicly available Autism Brain Imaging Data Exchange (ABIDE) dataset. Experimental results demonstrate that the M³ASD method not only improves ASD diagnostic accuracy but also identifies common functional brain connections across atlases, thereby enhancing the interpretability of the method. Full article

Artificial intelligence (AI) and machine learning (ML), especially deep learning, have profoundly transformed biology by enabling precise interpretation of complex genomic and proteomic data. This review presents a comprehensive overview of cutting-edge AI methodologies spanning from foundational neural networks to advanced transformer architectures and large language models (LLMs). These tools have revolutionized our ability to predict gene function, identify genetic variants, and accurately determine protein structures and interactions, exemplified by landmark milestones such as AlphaFold and DeepBind. We elaborate on the synergistic integration of genomics and protein structure prediction through AI, highlighting recent breakthroughs in generative models capable of designing novel proteins and genomic sequences at unprecedented scale and accuracy. Furthermore, the fusion of multi-omics data using graph neural networks and hybrid AI frameworks has provided nuanced insights into cellular heterogeneity and disease mechanisms, propelling personalized medicine and drug discovery. This review also discusses ongoing challenges including data quality, model interpretability, ethical concerns, and computational demands. By synthesizing current progress and emerging frontiers, we provide insights to guide researchers in harnessing AI’s transformative power across the biological spectrum from genes to functional proteins. Full article

Underwater imagery exhibits markedly more severe visual degradation than their terrestrial counterparts, manifesting as pronounced color aberration, diminished contrast and luminosity, and spatially non-uniform haze. To surmount these challenges, we propose the graph-aware framework for underwater image enhancement (GA-UIE), integrating specialized modules for color correction and texture restoration, a unified framework that explicitly utilizes the intrinsic graph information of underwater images to achieve high-fidelity color restoration and texture enhancement. The proposed algorithm is architected in three synergistic stages: (1) graph feature generation, which distills color and texture graph feature priors from the underwater image; (2) graph-aware enhancement, performing joint color restoration and texture sharpening under explicit graph priors; and (3) graph-aware fusion, harmoniously aggregating the graph-aware color and texture joint representations to yield the final visually coherent output. Comprehensive quantitative evaluations reveal that the output from our novel framework achieves the significant scores across a broad spectrum of metrics, including PSNR, SSIM, LPIPS, UCIQE, and UIQM on the UIEB and U45 datasets. These results decisively exceed those of all existing benchmark techniques, thereby validating the method’s exceptional efficacy in the enhancement of underwater imagery. Full article

Cayley graphs sit at the intersection of algebra, geometry, and theoretical computer science. Their spectra encode fine structural information about both the underlying group and the graph itself. Building on classical work of Alon–Milman, Dodziuk, Margulis, Lubotzky–Phillips–Sarnak, and many others, we develop a unified representation-theoretic framework that yields several new results. We establish a monotonicity principle showing that the algebraic connectivity never decreases when generators are added. We provide closed-form spectra for canonical 3-regular dihedral Cayley graphs, with exact spectral gaps. We prove a quantitative obstruction demonstrating that bounded-degree Cayley graphs of groups with growing abelian quotients cannot form expander families. In addition, we present two universal comparison theorems: one for quotients and one for direct products of groups. We also derive explicit eigenvalue formulas for class-sum-generating sets together with a Hoffman-type second-moment bound for all Cayley graphs. We also establish an exact relation between the Laplacian spectra of a Cayley graph and its complement, giving a closed-form expression for the complementary spectral gap. These results give new tools for deciding when a given family of Cayley graphs can or cannot expand, sharpening and extending several classical criteria. Full article

Background: Autism spectrum disorder (ASD) is a neurodevelopmental condition characterized by significant neurological plasticity in early childhood, where timely interventions like behavioral therapy, language training, and social skills development can mitigate symptoms. Contributions: We introduce a novel Multi-Atlas Guided Multi-View Contrast Learning (MAMVCL) framework for ASD classification, leveraging functional connectivity (FC) matrices from multiple brain atlases to enhance diagnostic accuracy. Methodology: The MAMVCL framework integrates imaging and phenotypic data through a population graph, where node features derive from imaging data, edge indices are based on similarity scoring matrices, and edge weights reflect phenotypic similarities. Graph convolution extracts global field-of-view features. Concurrently, a Target-aware attention aggregator processes FC matrices to capture high-order brain region dependencies, yielding local field-of-view features. To ensure consistency in subject characteristics, we employ a graph contrastive learning strategy that aligns global and local feature representations. Results: Experimental results on the ABIDE-I dataset demonstrate that our model achieves an accuracy of 85.71%, outperforming most existing methods and confirming its effectiveness. Implications: The proposed model demonstrates superior performance in ASD classification, highlighting the potential of multi-atlas and multi-view learning for improving diagnostic precision and supporting early intervention strategies. Full article

Autism Spectrum Disorder (ASD) is a complex neurodevelopmental condition with diverse behavioral, genetic, and structural characteristics. Due to its heterogeneous nature, early diagnosis of ASD is challenging, and conventional unimodal approaches often fail to capture cross-modal dependencies. To address this, this study introduces an adaptive multimodal fusion framework that integrates behavioral, genetic, and structural MRI (sMRI) data, addressing the limitations of unimodal approaches. Each modality undergoes a dedicated preprocessing and feature optimization phase. For behavioral data, an ensemble of classifiers using a stacking technique and attention mechanism is applied for feature extraction, achieving an accuracy of 95.5%. The genetic data is analyzed using Gradient Boosting, which attained a classification accuracy of 86.6%. For the sMRI data, a Hybrid Convolutional Neural Network–Graph Neural Network (Hybrid-CNN-GNN) architecture is proposed, demonstrating a strong performance with an accuracy of 96.32%, surpassing existing methods. To unify these modalities, fused using an adaptive late fusion strategy implemented with a Multilayer Perceptron (MLP), where adaptive weighting adjusts each modality’s contribution based on validation performance. The integrated framework addresses the limitations of unimodal approaches by creating a unified diagnostic model. The transfer learning framework achieves superior diagnostic accuracy (98.7%) compared to unimodal baselines, demonstrating strong generalization across heterogeneous datasets and offering a promising step toward reliable, multimodal ASD diagnosis. Full article

A novel all-sp³-hybridized superhard carbon allotrope, Ibca-C₆₄, is proposed based on first-principles calculations combined with the RG² (space group and graph theory) structure search method. A systematic investigation of its stability, mechanical properties, and electronic structure is performed. The results indicate that the energy difference between Ibca-C₆₄ and diamond is only 0.295 eV/atom, suggesting its metastability. Detailed analysis of its elastic constants and phonon spectrum confirms both mechanical and dynamical stability. The Ibca-C₆₄ structure demonstrates exceptional mechanical performance, with a Vickers hardness of 83.9 GPa. Furthermore, it possesses a wide direct band gap of 5.58 eV, indicating that Ibca-C₆₄ is a superhard semiconductor material with outstanding mechanical properties. Full article

Background: Accurate and early diagnosis of autism spectrum disorder (ASD) is essential for timely intervention. Structural magnetic resonance imaging (sMRI) and functional magnetic resonance imaging (fMRI) provide complementary insights into brain structure and function. Most deep learning approaches rely on a single modality, limiting their ability to capture cross-modal relationships. Methods: We propose DAGMNet, a dual-branch attention-pruned graph neural network for ASD prediction that integrates sMRI, fMRI, and phenotypic data. The framework employs modality-specific feature extraction to preserve unique structural and functional characteristics, an attention-based cross-modal fusion module to model inter-modality complementarity, and a phenotype-pruned dynamic graph learning module with adaptive graph construction for personalized diagnosis. Results: Evaluated on the ABIDE-I dataset, DAGMNet achieves an accuracy of 91.59% and an AUC of 96.80%, outperforming several state-of-the-art baselines. To validate the method’s generalizability, we also validate it on ADNI datasets from other degenerative diseases and achieve good results. Conclusions: By effectively fusing multimodal neuroimaging and phenotypic information, DAGMNet enhances cross-modal representation learning and improves diagnostic accuracy. To further assist clinical decision making, we conduct biomarker detection analysis to provide region-level explanations of our model’s decisions. Full article

Background: Autism Spectrum Disorder (ASD) is a neurodevelopmental condition characterized by heterogeneous behavioral and neurological patterns, complicating timely and accurate diagnosis. Behavioral datasets are commonly used to diagnose ASD. In clinical practice, it is difficult to identify ASD because of the complexity of the behavioral symptoms, overlap of neurological disorders, and individual heterogeneity. Correct and timely identification is dependent on the presence of skilled professionals to perform thorough neurological examinations. Nevertheless, with developments in deep learning techniques, the diagnostic process can be significantly improved by automatically identifying and automatically classifying patterns of ASD-related behaviors and neuroimaging features. Method: This study introduces a novel multimodal diagnostic paradigm that combines structured behavioral phenotypes and structural magnetic resonance imaging (sMRI) into an interpretable and personalized framework. A Generalized Additive Model with Interactions (GAMI-Net) is used to process behavioral data for transparent embedding of clinical phenotypes. Structural brain characteristics are extracted via a hybrid CNN–GNN model, which retains voxel-level patterns and region-based connectivity through the Harvard–Oxford atlas. The embeddings are then fused using an Autoencoder, compressing cross-modal data into a common latent space. A Hyper Network-based MLP classifier produces subject-specific weights to make the final classification. Results: On the held-out test set drawn from the ABIDE-I dataset, a 20% split with about 247 subjects, the constructed system achieved an accuracy of 99.40%, precision of 100%, recall of 98.84%, an F1-score of 99.42%, and an ROC-AUC of 99.99%. For another test of generalizability, five-fold stratified cross-validation on the entire dataset yielded a mean accuracy of 98.56%, an F1-score of 98.61%, precision of 98.13%, recall of 99.12%, and an ROC-AUC of 99.62%. Conclusions: These results suggest that interpretable and personalized multimodal fusion can be useful in aiding practitioners in performing effective and accurate ASD diagnosis. Nevertheless, as the test was performed on stratified cross-validation and a single held-out split, future research should seek to validate the framework on larger, multi-site datasets and different partitioning schemes to guarantee robustness over heterogeneous populations. Full article