Bayesian networks play a crucial role in various domains for unsupervised feature extraction and data interpretation. The Poisson gamma belief networks (PGBNs), as a type of Bayesian networks, have shown promise in analyzing high-dimensional count data. However, PGBNs encounter significant challenges when applied to sparse data, particularly in achieving accurate feature extraction and avoiding overfitting during missing value prediction. In this paper, we propose the sparse Poisson gamma belief networks (SPGBNs), a Bayesian network model designed to address these limitations. By incorporating sparse graph-structured priors over the weight matrices between adjacent layers, the proposed SPGBNs effectively capture the inherent sparsity and graph structures of latent features. Meanwhile, SPGBNs demonstrate superior generalization on missing data prediction and enable more stable extraction of meaningful latent features compared to existing approaches. Additionally, we develop an efficient Gibbs sampling algorithm that significantly improves the training stability and computational efficiency of SPGBNs. Extensive experiments on real-world datasets are conducted to validate the effectiveness of our approach.

Effectively modeling multimodal spatial omics data is critical for understanding tissue complexity and underlying biological mechanisms. While spatial transcriptomics, proteomics, and epigenomics capture molecular features, they lack pathological morphological context. Integrating these omics with histopathological images is thus critical for comprehensive disease tissue analysis. However, substantial heterogeneity across omics, imaging, and spatial modalities poses significant challenges. Naive fusion of semantically distinct sources often leads to ambiguous representations. Additionally, the resolution mismatch between high-resolution histology images and lower-resolution sequencing spots complicates spatial alignment. Biological perturbations during sample preparation further distort modality-specific signals, hindering accurate integration. To address these challenges, we propose Graph-guided Representation of Omics and Vision with Expert Regulation for Adaptive Spatial Multi-omics Fusion (GROVER), a novel framework for adaptive integration of spatial multi-omics data. GROVER leverages a Graph Convolutional Network encoder based on Kolmogorov–Arnold Networks to capture the nonlinear dependencies between each modality and its associated spatial structure, thereby producing expressive, modality-specific embeddings. To align these representations, we introduce a spot-feature-pair contrastive learning strategy that explicitly optimizes the correspondence across modalities at each spot. Furthermore, we design a dynamic expert routing mechanism that adaptively selects informative modalities for each spot while suppressing noisy or low-quality inputs. Experiments on real-world spatial omics datasets demonstrate that GROVER outperforms state-of-the-art baselines, providing a robust and reliable solution for multimodal integration.

Spatial multi-modal omics technology, highlighted by Nature Methods as an advanced biological technique in 2023, plays a critical role in resolving biological regulatory processes with spatial context. Recently, graph neural networks based on K-nearest neighbor (KNN) graphs have gained prominence in spatial multi-modal omics methods due to their ability to model semantic relations between sequencing spots. However, the fixed KNN graph fails to capture the latent semantic relations hidden by the inevitable data perturbations during the biological sequencing process, resulting in the loss of semantic information. In addition, the common lack of spot annotation and class number priors in practice further hinders the optimization of spatial multi-modal omics models. Here, we propose a novel spatial multi-modal omics resolved framework, termed Prototype-aware Graph Adaptative Aggregation for Spatial Multi-modal Omics Analysis (PRAGA). PRAGA constructs a dynamic graph to capture latent semantic relations and comprehensively integrate spatial information and feature semantics. The learnable graph structure can also denoise perturbations by learning cross-modal knowledge. Moreover, a dynamic prototype contrastive learning is proposed based on the dynamic adaptability of Bayesian Gaussian Mixture Models to optimize the multi-modal omics representations for unknown biological priors. Quantitative and qualitative experiments on simulated and real datasets with 7 competing methods demonstrate the superior performance of PRAGA.

Predicting gene regulatory relationship is crucial to reveal cancer mechanism and develop targeted therapies. However, current computational methods typically estimate gene-gene associations without regulatory directions and only based on statistical significance, often lacking accuracy after validation by biological experiments. Therefore, we introduce a pipeline named LiGRNet that constructs gene regulatory networks as signed directed graphs using large language models (LLMs) from the literature and predicts potential gene regulatory relationship with magnetic signed graph neural networks (MSGNNs). First, we teach LLM to extract the known gene regulatory relationships proved by biological experiments through prompt. Then, a signed directed graph was constructed and learnt by MSGNN with a link prediction framework based on complex-valued gene embeddings. The potential regulatory relationships were predicted with direction and sign. We apply our pipeline in colorectal cancer, liver cancer, and colorectal liver metastasis including$11,000,19,000$, and 1,300 literature, respectively. The pipeline achieve$84.5 \%, 80.7 \%, 93.3 \%$accuracy in predicting unknown gene regulatory relationship. External cell line data also provide evidence for the predicted gene regulation in these cancers.

mRNA expression is vital for understanding the mechanisms of breast cancer initiation and metastasis, with mRNA-based biomarkers closely linked to tumor grade, metastasis, and prognosis. However, gene expression analyses often suffer from batch effects, high inter-sample variability, and poor cross-cohort generalizability, which can obscure true biological signals. To overcome these limitations, we developed the Support Vector Gene Pair (SVP) algorithm, which emphasizes within-sample relative gene pair relationships rather than absolute expression levels. This design effectively mitigates inter-sample interference and enhances robustness across heterogeneous datasets. By in-corporating intra- and inter-sample variability, SVP accurately identifies informative gene pair features. Applied to 16 GEO datasets (852 samples) and one TCGA dataset, SVP discovered 23 breast cancer-related gene pairs and outperformed traditional Differentially Expressed Gene (DEG) and unadjusted statistical approaches. Comparative analyses showed consistent performance gains, with average improvements of 8% in AUC and 6% in PRC. SVP offers a robust and interpretable framework for breast cancer biomarker discovery, holding strong promise for translational applications in precision medicine.

Recent neural heuristics for the Vehicle Routing Problem (VRP) primarily rely on node coordinates as input, which may be less effective in practical scenarios where real cost metrics—such as edge-based distances—are more relevant. To address this limitation, we introduce EFormer, an Edge-based Transformer model that uses edge as the sole input for VRPs. Our approach employs a precoder module with a mixed-score attention mechanism to convert edge information into temporary node embeddings. We also present a parallel encoding strategy characterized by a graph encoder and a node encoder, each responsible for processing graph and node embeddings in distinct feature spaces, respectively. This design yields a more comprehensive representation of the global relationships among edges. In the decoding phase, parallel context embedding and multi-query integration are used to compute separate attention mechanisms over the two encoded embeddings, facilitating efficient path construction. We train EFormer using reinforcement learning in an autoregressive manner. Extensive experiments on the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) reveal that EFormer outperforms established baselines on synthetic datasets, including large-scale and diverse distributions. Moreover, EFormer demonstrates strong generalization on real-world instances from TSPLib and CVRPLib. These findings confirm the effectiveness of EFormer’s core design in solving VRPs.

Neural solvers for the Vehicle Routing Problem (VRP) have typically relied on either node or edge inputs, limiting their flexibility and generalization in real-world scenarios. We propose UniteFormer, a unified neural solver that supports node-only, edge-only, and hybrid input types through a single model trained via joint edge-node modalities. UniteFormer introduces: (1) a mixed encoder that integrates graph convolutional networks and attention mechanisms to collaboratively process node and edge features, capturing cross-modal interactions between them; and (2) a parallel decoder enhanced with query mapping and a feed-forward layer for improved representation. The model is trained with REINFORCE by randomly sampling input types across batches. Experiments on the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) demonstrate that UniteFormer achieves state-of-the-art performance and generalizes effectively to TSPLib and CVRPLib instances. These results underscore UniteFormer’s ability to handle diverse input modalities and its strong potential to improve performance across various VRP tasks.

RNA-protein interactions (RPIs) are essential for many biological functions and are associated with various diseases. Traditional methods for detecting RPIs are labor-intensive and costly, necessitating efficient computational methods. In this study, we proposed a novel sequence-based RPI prediction framework based on graph neural networks (GNNs) that addressed key limitations of existing methods, such as inadequate feature integration and negative sample construction. Our method represented RNAs and proteins as nodes in a unified interaction graph, enhancing the representation of RPI pairs through multi-feature fusion and employing self-supervised learning strategies for model training. The model's performance was validated through five-fold cross-validation, achieving accuracy of 0.880, 0.811, 0.950, 0.979, 0.910, and 0.924 on the RPI488, RPI369, RPI2241, RPI1807, RPI1446, and RPImerged datasets, respectively. Additionally, in cross-species generalization tests, our method outperformed existing methods, achieving an overall accuracy of 0.989 across 10 093 RPI pairs. Compared with other state-of-the-art RPI prediction methods, our approach demonstrates greater robustness and stability in RPI prediction, highlighting its potential for broad biological applications and large-scale RPI analysis.

Multimodal omics provide deeper insight into the biological processes and cellular functions, especially transcriptomics and proteomics. Computational methods have been proposed for the integration of single-cell multimodal omics of transcriptomics and proteomics. However, existing methods primarily concentrate on the alignment of different omics, overlooking the unique information inherent in each omics type. Moreover, as the majority of single-cell cohorts only encompass one omics, it becomes critical to transfer the knowledge learnt from multimodal omics to enhance unimodal omics analysis. Therefore, we proposed a novel framework that leverages masked autoencoder with cross-attention mechanism, called scMMAE (single-cell multimodal masked autoencoder), to fuse multimodal omics and enhance unimodal omics analysis. scMMAE simultaneously captures both the shared features and the distinctive information of two single-cell omics modalities and transfers the knowledge to enhance single-cell transcriptome data. Comparative evaluations against benchmarking methods across various cohorts revealed a notable improvement, with an increase of up to 21% in the adjusted Rand index and up to 12% in normalized mutual information in the context of multimodal fusion. In the realm of unimodal omics, scMMAE demonstrated an overall enhancement of approximately 20% in the adjusted Rand index and nearly 10% in normalized mutual information. Other nine metrics, including the Fowlkes-Mallows index and silhouette coefficient, further underscored the high performance of scMMAE. Significantly, scMMAE exhibits an elevated level of proficiency in distinguishing between different cell types, particularly on CD4 and CD8 T cells. Availability and implementation: scMMAE source code at https://github.com/DM0815/scMMAE/.

Sepsis is a life-threatening condition characterized by an exaggerated immune response to pathogens, leading to organ damage and high mortality rates in the intensive care unit. Although deep learning has achieved impressive performance on prediction and classification tasks in medicine, it requires large amounts of data and lacks explainability, which hinder its application to sepsis diagnosis. We introduce a deep learning framework, called scCaT, which blends the capsulating architecture with Transformer to develop a sepsis diagnostic model using single-cell RNA sequencing data and transfers it to bulk RNA data. The capsulating architecture effectively groups genes into capsules based on biological functions, which provides explainability in encoding gene expressions. The Transformer serves as a decoder to classify sepsis patients and controls. Our model achieves high accuracy with an AUROC of 0.93 on the single-cell test set and an average AUROC of 0.98 on seven bulk RNA cohorts. Additionally, the capsules can recognize different cell types and distinguish sepsis from control samples based on their biological pathways. This study presents a novel approach for learning gene modules and transferring the model to other data types, offering potential benefits in diagnosing rare diseases with limited subjects.

In future smart cities supported by cyber-physical social intelligence, autonomous behavioral decision for vehicular agents is going to become a general demand. Despite much progress achieved in autonomous behavioral decision of vehicular agents, the existing works can just be used in scenarios of short-distance behavioral decision. Naturally, they are not well suitable for long-distance behavioral decision tasks, posing much challenge in realistic cyber-physical environment. To bridge the existing gaps, this article proposes an autonomous behavioral decision framework for vehicular agents using cyber-physical social intelligence. First, it is expected to establish a dynamic planning model with multiple objectives and constraints. This can be embedded into the control unit of a vehicular agent to endow it with proper social intelligence. On this basis, an iterative search algorithm is specifically designed for it to find the optimal solutions from the whole solution space. Finally, two typical situation cases are implemented with use of simulation modeling to display the working architecture of the proposed method. In addition, a universal optimization search algorithm is selected as the baseline to be compared with the proposed method. The comparison results reveal both planning utility and running efficiency of the proposed method.