Graph Neural Networks (GNNs) have achieved remarkable progress in community detection, which is an essential topic in network analysis with the aim of dividing a network into multiple subgraphs to mine potential information. However, most existing GNN-based community detection approaches adopt static loss function weights during the training process. In this paper, we propose an unsupervised end-to-end community detection framework and define an adaptive loss weighting layer within this framework, named QALW, which is capable of learning an optimal combination of loss weights during model training to balance reconstruction loss and clustering loss. Experimental results obtained based on three real-world benchmark datasets (Cora, Citeseer, and Pubmed) demonstrate that QALW achieves effective and stable community detection performance compared with eight representative baseline methods. In particular, QALW improves ACC by 5.7% over the strongest baseline on the Cora dataset, and achieves ACC values of 64.9%, 61.7%, and 63.9% on Cora, Citeseer, and Pubmed, respectively. Furthermore, the results verify that the proposed dynamic scheduling mechanism effectively alleviates gradient conflicts and enables more stable optimization than fixed-weight strategies. Overall, QALW demonstrates promising competitiveness and good robustness for unsupervised community detection in attributed networks.

Accurate viral protein function annotation is essential for genomic surveillance, yet conventional retrieval-augmented generation (RAG) pipelines often fragment biological evidence into fixed-length text chunks, disrupting relationships among ORFs, annotations, structural domains, sequence motifs, residue mappings, and model-derived attention evidence. We propose ViroBioTree, a tree-structured biological evidence retrieval framework for downstream viral protein evidence review rather than a new primary annotation classifier. Built as an evidence organization layer on ViralMultiNet-derived ORF-level predictions and annotations, ViroBioTree converts sequence, annotation, structure, and attention evidence into typed biological nodes and traceable edges, then performs deterministic multi-channel recall, evidence-aware reranking, balanced TopK selection, rule-based verification, and node-cited report generation. In a demo benchmark, ViroBioTree achieved its strongest deterministic proxy performance on structure-explanation tasks, with Precision@K = 1.0, Recall@K = 1.0, and diversity = 0.52; these values reflect expected node-type and tag agreement rather than independent biological correctness. A bounded full-scale SARS-CoV-2 index contained 39,800 ORF rows, 80,000 attention records, 199,418 nodes, and 495,886 edges. In a stratified full20k diagnostic evaluation, ViroBioTree showed task-dependent advantages over LlamaIndex vector retrieval for conflict detection, evidence retrieval, and structure explanation, while LlamaIndex remained competitive or stronger for annotation-rich function annotation. A cross-family Influenza A Virus (IAV) diagnostic audit showed that the schema can represent IAV evidence namespaces while explicitly exposing missing formal ORF inputs, missing attention evidence, and unavailable residue/PDB assertions. Supplementary robustness, external sanity-check, diversity-risk, expert-evaluation, domain-tool positioning, and cross-family audit analyses supported traceability, report quality, and conservative evidence handling, but also showed that stable Precision@K under query perturbation does not necessarily imply stable retrieved evidence sets. ViroBioTree operates offline and deterministically, but does not address raw-read assembly, base calling, primary ORF prediction, or wet-lab validation. Its results should be interpreted as proxy and expert-reviewed evidence for traceable viral protein evidence retrieval and report generation rather than as direct validation of biological function annotation.

Let G be a connected simple graph with the vertex set $V\left(G\right)=\{v_1,v_2,\dots ,v_n\}$, where the distance $d_G(v_i,v_j)$ is the length of a shortest path between $v_i$ and $v_j$, and the distance matrix $D\left(G\right)=\left(d_{ij}\right)n\times n$ is defined by $d_{ij}=d_G(v_i,v_j)$. Being real symmetric and non-negative, $D\left(G\right)$ has real eigenvalues ${\lambda }_1\left(G\right)\ge {\lambda }_2\left(G\right)\ge \dots \ge {\lambda }_n\left(G\right)$, with ${\lambda }_n\left(G\right)$ referred to as the least distance eigenvalue of G. In this paper, we give the maximum value of the least distance eigenvalue, and determine the unique extremal graph with two pendant vertices whose complements attain the value.

Chaotic systems serve as fundamental pseudo-random sequence generators in encryption algorithms and play a vital role in communication security. However, most current research still focus on the classical Logistic chaotic map, making it vulnerable to targeted attacks. To address this issue, this paper proposes a general construction method for a class of cubic chaotic maps over the real number field and proves the existence of chaos based on the robust chaos criterion for S-unimodal maps. Furthermore, by integrating the proposed cubic chaotic map with the infinite folding map, a new one-dimensional discrete chaotic map is developed. Dynamical analysis demonstrates that, compared with the infinite folding map and the Logistic map, the newly constructed map exhibits stronger chaotic behavior and more stable complexity, showing superior potential for practical applications in secure communications.