Pair Of Nodes Research Articles

Mask-Guided Target Node Feature Learning and Dynamic Detailed Feature Enhancement for lncRNA-Disease Association Prediction.

Identifying new relevant long noncoding RNAs (lncRNAs) for various human diseases can facilitate the exploration of the causes and progression of these diseases. Recently, several graph inference methods have been proposed to predict disease-related lncRNAs by exploiting the topological structure and node attributes within graphs. However, these methods did not prioritize the target lncRNA and disease nodes over auxiliary nodes like miRNA nodes, potentially limiting their ability to fully utilize the features of the target nodes. We propose a new method, mask-guided target node feature learning and dynamic detailed feature enhancement for lncRNA-disease association prediction (MDLD), to enhance node feature learning for improved lncRNA-disease association prediction. First, we designed a heterogeneous graph masked transformer autoencoder to guide feature learning, focusing more on the features of target lncRNA (disease) nodes. The target nodes were increasingly masked as training progressed, which helps develop a more robust prediction model. Second, we developed a graph convolutional network with dynamic residuals (GCNDR) to learn and integrate the heterogeneous topology and features of all lncRNA, disease, and miRNA nodes. GCNDR employs an interlayer residual strategy and a residual evolution strategy to mitigate oversmoothing caused by multilayer graph convolution. The interlayer residual strategy estimates the importance of node features learned in the previous GCN encoding layer for nodes in the current encoding layer. Additionally, since there are dependencies in the importance of features of individual lncRNA (disease, miRNA) nodes across multiple encoding layers, a gated recurrent unit-based strategy is proposed to encode these dependencies. Finally, we designed a perspective-level attention mechanism to obtain more informative features of lncRNA and disease node pairs from the perspectives of mask-enhanced and dynamic-enhanced node features. Cross-validation experimental results demonstrated that MDLD outperformed 10 other state-of-the-art prediction methods. Ablation experiments and case studies on candidate lncRNAs for three diseases further proved the technical contributions of MDLD and its capability to discover disease-related lncRNAs.

Energy-Aware 3D Path Planning by Autonomous Ground Vehicle in Wireless Sensor Networks

Wireless sensor networks are used to monitor the environment, to detect anomalies or any other problems and risks in the system. If used in the transportation network, they can monitor traffic and detect traffic risks. In wireless sensor networks, energy constraints must be handled to enable continuous environmental monitoring and surveillance data gathering and communication. Energy-aware path planning of autonomous ground vehicle charging for sensor nodes can solve energy and battery replacement problems. This paper uses the Nearest Neighbour algorithm for the energy-aware path planning problem with an autonomous ground vehicle. Path planning simulations show that the Nearest Neighbour algorithm converges faster and produces a better solution than the genetic algorithm. We offer robust and energy-efficient path planning algorithms to swiftly collect sensor data with less energy, allowing the monitoring system to respond faster to anomalies. Positioning communicating sensors closer minimizes their energy usage and improves the network lifetime. This study also considers the scenario in which it is recommended to avoid taking direct travelling pathways between particular node pairs for a variety of different reasons. To address this more challenging scenario, we provide an Obstacle-Avoided Nearest Neighbour-based approach that has been adapted from the Nearest Neighbour approach. Within the context of this technique, the direct paths that connect the nodes are restricted. Even in this case, the Obstacle-Avoided Nearest Neighbour-based approach achieves almost the same performance as the the Neighbour-based approach.

Efficient entropy-stable discontinuous spectral-element methods using tensor-product summation-by-parts operators on triangles and tetrahedra

We present a new class of efficient and robust discontinuous spectral-element methods of arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular and tetrahedral unstructured grids. Such discretizations employ a recently introduced family of sparse tensor-product summation-by-parts (SBP) operators in collapsed coordinates within an entropy-conservative modal formulation, which is rendered entropy stable when a dissipative numerical flux is used at element interfaces. The proposed algorithms exploit the structure of such SBP operators alongside that of the Proriol–Koornwinder–Dubiner polynomial basis used to represent the numerical solution on the reference triangle or tetrahedron, and a weight-adjusted approximation is employed in order to efficiently invert the local mass matrix for curvilinear elements. Using such techniques, we obtain an improvement in time complexity from O(p2d) to O(pd+1) relative to existing entropy-stable formulations using multidimensional SBP operators not possessing such a tensor-product structure, where p is the polynomial degree of the approximation and d is the number of spatial dimensions. The number of required entropy-conservative two-point flux evaluations between pairs of quadrature nodes is accordingly reduced by a factor ranging from 1.56 at p=2 to 4.57 at p=10 for triangles, and from 1.88 at p=2 to 10.99 at p=10 for tetrahedra. Through numerical experiments involving smooth solutions to the compressible Euler equations on isoparametric triangular and tetrahedral grids, the proposed methods using tensor-product SBP operators are shown to exhibit similar levels of accuracy for a given mesh and polynomial degree to those using multidimensional operators based on symmetric quadrature rules, with both approaches achieving order p+1 convergence with respect to the element size in the presence of interface dissipation as well as exponential convergence with respect to the polynomial degree. Furthermore, both operator families are shown to give rise to entropy-stable schemes which exhibit excellent robustness for test problems characteristic of under-resolved turbulence simulations. Such results suggest that the algorithmic advantages resulting from the use of tensor-product operators are obtained without compromising accuracy or robustness, enabling the efficient extension of the benefits of entropy stability to higher polynomial degrees than previously considered for triangular and tetrahedral elements.

Intra-patient spatial comparison of non-metastatic and metastatic lymph nodes reveals the reduction of CD169+ macrophages by metastatic breast cancers

Breast cancer cells suppress the host immune system to efficiently invade the lymph nodes; however, the underlying mechanism remains incompletely understood. Here, we aimed to comprehensively characterise the effects of breast cancers on immune cells in the lymph nodes. We collected non-metastatic and metastatic lymph node samples from 6 patients with breast cancer with lymph node metastasis. We performed bulk transcriptomics, spatial transcriptomics, and imaging mass cytometry to analyse the obtained lymph nodes. Furthermore, we conducted histological analyses against a larger patient cohort (474 slices from 58 patients). The comparison between paired lymph nodes with and without metastasis from the same patients demonstrated that the number of CD169+ lymph node sinus macrophages, an initiator of anti-cancer immunity, was reduced in metastatic lymph nodes (36.7±21.1 vs 7.3±7.0cells/mm2, p=0.0087), whereas the numbers of other major immune cell types were unaltered. We also detected that the infiltration of CD169+ macrophages into metastasised cancer tissues differed by section location within tumours, suggesting that CD169+ macrophages were gradually decreased after anti-cancer reactions. Furthermore, CD169+ macrophage elimination was prevalent in major breast cancer subtypes and correlated with breast cancer staging (p=0.022). We concluded that lymph nodes with breast cancer metastases have fewer CD169+ macrophages, which may be detrimental to the activity of anti-cancer immunity. JSPS KAKENHI (16H06279, 20H03451, 20H04842, 22H04925, 19K16770, and 21K15530, 24K02236), JSPS Fellows (JP22KJ1822), AMED (JP21ck0106698), JST FOREST (JPMJFR2062), Caravel, Co., Ltd, Japan Foundation for Applied Enzymology, and Sumitomo Pharma Co., Ltd. under SKIPS.

High-precision ultra-fast minimum cut approximation through aggregated hash of cut collection

Due to the wide application of s-t minimum cut (min-cut) in various scenarios, many acceleration algorithms have been proposed to solve it. However, the query times of the acceleration algorithms currently available are still high in large-scale graphs, rendering them useless in frequently solving scenarios. We re-examine the min-cut problem from a novel perspective of cut collection hash. By extracting aggregated hashes of mapped cut collections in one-dimensional space, a Monte Carlo-like method is used to quickly compare them and estimate the minimum cut between any two nodes with low computational effort and high accuracy. After the graph is preprocessed using a few hundred depth-first traversals, the time complexity of the min-cut solution can be logarithmic in terms of the average degree and capacity of the graph. Experiments on large-scale graphs show that compared to the fastest exact algorithm, the proposed algorithm can increase the speed of the min-cut solution by up to seven orders of magnitude, when only a few mathematical comparisons per pair are needed to obtain exact min-cut values of no less than 99.9% node pairs.

Path-based reasoning for biomedical knowledge graphs with BioPathNet.

Understanding complex interactions in biomedical networks is crucial for advancements in biomedicine, but traditional link prediction (LP) methods are limited in capturing this complexity. Representation-based learning techniques improve prediction accuracy by mapping nodes to low-dimensional embeddings, yet they often struggle with interpretability and scalability. We present BioPathNet, a novel graph neural network framework based on the Neural Bellman-Ford Network (NBFNet), addressing these limitations through path-based reasoning for LP in biomedical knowledge graphs. Unlike node-embedding frameworks, BioPathNet learns representations between node pairs by considering all relations along paths, enhancing prediction accuracy and interpretability. This allows visualization of influential paths and facilitates biological validation. BioPathNet leverages a background regulatory graph (BRG) for enhanced message passing and uses stringent negative sampling to improve precision. In evaluations across various LP tasks, such as gene function annotation, drug-disease indication, synthetic lethality, and lncRNA-mRNA interaction prediction, BioPathNet consistently outperformed shallow node embedding methods, relational graph neural networks and task-specific state-of-the-art methods, demonstrating robust performance and versatility. Our study predicts novel drug indications for diseases like acute lymphoblastic leukemia (ALL) and Alzheimer's, validated by medical experts and clinical trials. We also identified new synthetic lethality gene pairs and regulatory interactions involving lncRNAs and target genes, confirmed through literature reviews. BioPathNet's interpretability will enable researchers to trace prediction paths and gain molecular insights, making it a valuable tool for drug discovery, personalized medicine and biology in general.

Braess's Paradox Analog in Physical Networks of Optimal Exploration.

In stochastic exploration of geometrically embedded graphs, intuition suggests that providing a shortcut between a pair of nodes reduces the mean first passage time of the entire graph. Counterintuitively, we find a Braess's paradox analog. For regular diffusion, shortcuts can worsen the overall search efficiency of the network, although they bridge topologically distant nodes. We propose an optimization scheme under which each edge adapts its conductivity to minimize the graph's search time. The optimization reveals a relationship between the structure and diffusion exponent and a crossover from dense to sparse graphs as the exponent increases.

The ultrametric backbone is the union of all minimum spanning forests

Minimum spanning trees and forests are powerful sparsification techniques that remove cycles from weighted graphs to minimize total edge weight while preserving node reachability, with applications in computer science, network science, and graph theory. Despite their utility and ubiquity, they have several limitations, including that they are only defined for undirected networks, they significantly alter dynamics on networks, and they do not generally preserve important network features such as shortest distances, shortest path distribution, and community structure. In contrast, distance backbones, which are subgraphs formed by all edges that obey a generalized triangle inequality, are well defined in directed and undirected graphs and preserve those and other important network features. The backbone of a graph is defined with respect to a specified path-length operator that aggregates weights along a path to define its length, thereby associating a cost to indirect connections. The backbone is the union of all shortest paths between each pair of nodes according to the specified operator. One such operator, the max function, computes the length of a path as the largest weight of the edges that compose it (a weakest link criterion). It is the only operator that yields an algebraic structure for computing shortest paths that is consistent with De Morgan's laws. Applying this operator yields the ultrametric backbone of a graph in that (semi-triangular) edges whose weights are larger than the length of an indirect path connecting the same nodes (i.e. those that break the generalized triangle inequality based on max as a path-length operator) are removed. We show that the ultrametric backbone is the union of minimum spanning forests in undirected graphs and provides a new generalization of minimum spanning trees to directed graphs that, unlike minimum equivalent graphs and minimum spanning arborescences, preserves all shortest paths and De Morgan's law consistency.

Central-Smoothing Hypergraph Neural Networks for Predicting Drug-Drug Interactions.

Predicting drug-drug interactions (DDIs) is the problem of predicting side effects (unwanted outcomes) of a pair of drugs using drug information and known side effects of many pairs. This problem can be formulated as predicting labels (i.e., side effects) for each pair of nodes in a DDI graph, of which nodes are drugs and edges are interacting drugs with known labels. State-of-the-art methods for this problem are graph neural networks (GNNs), which leverage neighborhood information in the graph to learn node representations. For DDI, however, there are many labels with complicated relationships due to the nature of side effects. Usual GNNs often fix labels as one-hot vectors that do not reflect label relationships and potentially do not obtain the highest performance in the difficult cases of infrequent labels. In this brief, we formulate DDI as a hypergraph where each hyperedge is a triple: two nodes for drugs and one node for a label. We then present CentSmoothie, a hypergraph neural network (HGNN) that learns representations of nodes and labels altogether with a novel " central-smoothing " formulation. We empirically demonstrate the performance advantages of CentSmoothie in simulations as well as real datasets.

Shortest-Path Percolation on Random Networks.

We propose a bond-percolation model intended to describe the consumption, and eventual exhaustion, of resources in transport networks. Edges forming minimum-length paths connecting demanded origin-destination nodes are removed if below a certain budget. As pairs of nodes are demanded and edges are removed, the macroscopic connected component of the graph disappears, i.e., the graph undergoes a percolation transition. Here, we study such a shortest-path-percolation transition in homogeneous random graphs where pairs of demanded origin-destination nodes are randomly generated, and fully characterize it by means of finite-size scaling analysis. If budget is finite, the transition is identical to the one of ordinary percolation, where a single giant cluster shrinks as edges are removed from the graph; for infinite budget, the transition becomes more abrupt than the one of ordinary percolation, being characterized by the sudden fragmentation of the giant connected component into a multitude of clusters of similar size.

Identifying circRNA-disease association based on relational graph attention network and hypergraph attention network

In recent years, with the in-depth study of circRNA, scholars have begun to discover a synergistic relationship between circRNA and microorganisms. Traditional wet lab experiments in biology require expensive financial, material, and human resources to investigate the relationship between circRNA and diseases. Therefore, we propose a new predictive model for inferring the association between circRNA and diseases, called HAGACDA. Specifically, we first aggregate the unique features of circRNA and diseases themselves through singular value decomposition, Pearson similarity, and the biological information characteristics of circRNA and diseases. Utilizing the competitive relationships between miRNA and other microorganisms, we construct a circRNA-miRNA-disease multi-source heterogeneous network. Subsequently, we use a relational graph attention network to aggregate features based on the structural connections between different nodes. To address the inherent limitations in capturing high-order patterns in edge sets, we integrate a hypergraph attention network to extract features of circRNA and diseases. Finally, association prediction scores for node pairs are obtained through a multilayer perceptron. We conducted a comprehensive analysis of the model, including comparative experiments and case studies. Experimental results demonstrate that our model accurately predicts the association between circRNA and diseases.

Streamflow Prediction Using Complex Networks.

The reliable prediction of streamflow is crucial for various water resources, environmental, and ecosystem applications. The current study employs a complex networks-based approach for the prediction of streamflow. The approach consists of three major steps: (1) the formation of a network using streamflow time series; (2) the calculation of the clustering coefficient (CC) as a network measure; and (3) the use of a clustering coefficient-based nearest neighbor search procedure for streamflow prediction. For network construction, each timestep is considered as a node and the existence of link between any node pair is identified based on the difference (distance) between the streamflow values of the nodes. Different distance threshold values are used to identify the critical distance threshold to form the network. The complex networks-based approach is implemented for the prediction of daily streamflow at 142 stations in the contiguous United States. The prediction accuracy is quantified using three statistical measures: correlation coefficient (R), normalized root mean square error (NRMSE), and Nash-Sutcliffe efficiency (NSE). The influence of the number of neighbors on the prediction accuracy is also investigated. The results, obtained with the critical distance threshold, reveal that the clustering coefficients for the 142 stations range from 0.799 to 0.999. Overall, the prediction approach yields reasonably good results for all 142 stations, with R values ranging from 0.05 to 0.99, NRMSE values ranging from 0.1 to 12.3, and the NSE values ranging from -0.89 to 0.99. An attempt is also made to examine the relationship between prediction accuracy and the catchment characteristics/streamflow statistical properties (drainage area, mean flow, coefficient of variation of flow). The results suggest that the prediction accuracy does not have much of a relationship with the drainage area and the mean streamflow values, but with the coefficient of variation of flow. The outcomes from this study are certainly promising regarding the application of complex networks-based concepts for the prediction of streamflow (and other hydrologic) time series.

MTdyg: Multi-scale transformers with continuous time dynamic graph model for link prediction

Link prediction through continuous dynamic graph neural networks is a challenging endeavour. Previous studies have considered historic interaction sequences among pairs of nodes. However, this approach does not sufficiently model the links between them. Thus, the frequency of historical common neighbours was proposed to obtain more information about node pairs. Nonetheless, this measure fails to consider the timing of interactions because the relative importance of different interactions shifts over time.Multi-scale transformers with a continuous time dynamic graph model (MTdyg) are our response to this challenge to enhance link prediction. The novel MTdyg model employs a multi-scale patching strategy that dynamically adjusts based on the interaction frequency, feeding segmented interaction sequences into the transformer. This methodology significantly improves the model’s ability to assimilate historical data. Furthermore, we developed a temporal attention-based historical common neighbour encoding technique to effectively identify linkages between source and target nodes in interaction sequences. Extensive testing on eight public datasets confirmed that MTdyg delivers superior performance on most datasets, demonstrating its effectiveness in capturing the nuances of node interactions over time.

Search for an antiferromagnetic Weyl semimetal in (MnTe) m (Sb2Te3) n and (MnTe) m (Bi2Te3) n superlattices

The interaction between topology and magnetism can lead to novel topological materials including Chern insulators, axion insulators, and Dirac and Weyl semimetals. In this work, a family of van der Waals layered materials using MnTe and Sb2Te3 or Bi2Te3 superlattices as building blocks are systematically examined in a search for antiferromagnetic Weyl semimetals, preferably with a simple node structure. The approach is based on controlling the strength of the exchange interaction as a function of layer composition to induce the phase transition between the topological and the normal insulators. Our calculations, utilizing a combination of first-principles density functional theory and tight-binding analyses based on maximally localized Wannier functions, clearly indicate a promising candidate for a type-I magnetic Weyl semimetal. This centrosymmetric material, Mn10Sb8Te22 (or (MnTe) m (Sb2Te3) n with m = 10 and n = 4), shows ferromagnetic intralayer and antiferromagnetic interlayer interactions in the antiferromagnetic ground state. The obtained electronic bandstructure also exhibits a single pair of Weyl points in the spin-split bands consistent with a Weyl semimetal. The presence of Weyl nodes is further verified with Berry curvature, Wannier charge center, and surface state (i.e. Fermi arc) calculations. Other combinations of the MnSbTe-family materials are found to be antiferromagnetic topological or normal insulators on either side of the Mn:Sb ratio, respectively, illustrating the topological phase transition as anticipated. A similar investigation in the homologous (MnTe) m (Bi2Te3) n system produces mostly nontrivial antiferromagnetic insulators due to the strong spin–orbit coupling. When realized, the antiferromagnetic Weyl semimetals in the simplest form (i.e. a single pair of Weyl nodes) are expected to provide a promising candidate for low-power spintronic applications.

An algorithm based on B-differentiable equations method for solving problems involving frictional contact coupled with concrete plastic damage

In this paper, an algorithm is proposed to solve the frictional contact problems while considering elasto-plastic material properties. The static and dynamic solution procedures are derived in incremental form, respectively. The proposed method employs a two-layer iteration strategy. In the outer iteration layer, the equilibrium equations are solved, with the stress and stiffness matrix updated at each iteration. Within the inner iteration layer, the contact force is calculated, where the contact equations, expressed as B-differentiable equations, incorporate only contact conditions in normal and tangential directions, and the contact flexibility matrix, obtained by applying unit force pair to all contact node pairs in turn, is introduced. Consequently, the solution for nonlinear equilibrium equations and contact equations is decoupled, requiring only one decomposition of the stiffness matrix for each calculation of the contact flexibility matrix, as it remains constant within the contact iteration layer. In addition, the constitutive model of concrete developed by Lee and Fenves is utilized. This model adopts two independent variables to describe tensile and compressive damage, together considering the strength recovery of the concrete. Numerical examples demonstrate the accuracy of the proposed method by comparing the results from Abaqus. Furthermore, the present algorithm is applied to static and dynamic analyses of a concrete arch dam with several transverse joints, where the effects of gravity, water level, the number of contact surfaces, and seismic load are considered, and some conclusions are obtained.

Multi-objective optimization of asymmetric bit rate partitioning for multipath protection in elastic optical networks

In survivable elastic optical networks, multi-path protection combined with traffic squeezing has gained attention. Link-disjoint multipath routing (LD-MPR) and bandwidth squeezing protection (BSP) when applied to the routing, modulation level and spectrum assignment problem are efficient strategies to address the excessive bandwidth demanded by protected services, spectral fragmentation and link-load balancing. LD-MPR enables the division of service transmission bit rate into independent flows, whereas BSP tolerates traffic reduction under link failure. An open issue in the literature is how to efficiently divide demanded traffic among the link-disjoint routes under dynamic-traffic and BSP, while complying the service level agreement (SLA). We propose in this paper a multi-objective-optimization genetic algorithm that defines how service transmission bit rate should be partitioned among the candidate link-disjoint routes. A customized partitioning definition is made for each source–destination node pair in the network, aiming the simultaneous minimization of network blocking probability and average squeezing transmission bit rate experienced by the services during single-link failure. We also propose, a fixed-alternate routing using groups of disjoint paths (FARgdp). Complex dynamic-traffic network scenarios that simultaneously consider BSP, LD-MPR and FARgdp are addressed.

Network embedding based on DepDist contraction

Networks provide an understandable and, in the case of small size, visualizable representation of data, which allows us to obtain essential information about the relationships between pairs of nodes, e.g., their distances. In visualization, networks have an alternative two-dimensional vector representation to which various machine-learning methods can be applied. More generally, networks can be transformed into a low-dimensional space using so-called embedding methods, which bridge the gap between network analysis and traditional machine learning by creating numerical representations that capture the essence of the network structure. In this article, we present a new embedding method that uses non-symmetric dependency to find the distance between nodes and applies an iterative procedure to find a satisfactory distribution of nodes in space. For dimension 2 and the visualization of the result, we demonstrate the method’s effectiveness on small networks. For higher dimensions and several larger networks, we present the results of two experiments comparing our results with two well-established methods in the research community, namely node2vec and DeepWalk. The first experiment focuses on a qualitative comparison of the methods, while the second focuses on applying and comparing the classification results to embeddings in a higher dimension. Although the presented method does not outperform the two chosen methods, its results are still comparable. Therefore, we also explain the limitations of our method and a possible way to overcome them.

GCL-Leak: Link Membership Inference Attacks against Graph Contrastive Learning

Graph contrastive learning (GCL) has emerged as a successful method for self-supervised graph learning. It involves generating augmented views of a graph by augmenting its edges and aims to learn node embeddings that are invariant to graph augmentation. Despite its effectiveness, the potential privacy risks associated with GCL models have not been thoroughly explored. In this paper, we delve into the privacy vulnerability of GCL models through the lens of link membership inference attacks (LMIA). Specifically, we focus on the federated setting where the adversary has white-box access to the node embeddings of all the augmented views generated by the target GCL model. Designing such white-box LMIAs against GCL models presents a significant and unique challenge due to potential variations in link memberships among node pairs in the target graph and its augmented views. This variability renders members indistinguishable from non-members when relying solely on the similarity of their node embeddings in the augmented views. To address this challenge, our in-depth analysis reveals that the key distinguishing factor lies in the similarity of node embeddings within augmented views where the node pairs share identical link memberships as those in the training graph. However, this poses a second challenge, as information about whether a node pair has identical link membership in both the training graph and augmented views is only available during the attack training phase. This demands the attack classifier to handle the additional “identical-membership" information which is available only for training and not for testing. To overcome this challenge, we propose GCL-LEAK, the first link membership inference attack against GCL models. The key component of GCL-LEAK is a new attack classifier model designed under the “Learning Using Privileged Information (LUPI)” paradigm, where the privileged information of “same-membership” is encoded as part of the attack classifier's structure. Our extensive set of experiments on four representative GCL models showcases the effectiveness of GCL-LEAK. Additionally, we develop two defense mechanisms that introduce perturbation to the node embeddings. Our empirical evaluation demonstrates that both defense mechanisms significantly reduce attack accuracy while preserving the accuracy of GCL models.

Pangenome graph layout by Path-Guided Stochastic Gradient Descent.

The increasing availability of complete genomes demands for models to study genomic variability within entire populations. Pangenome graphs capture the full genomic similarity and diversity between multiple genomes. In order to understand them, we need to see them. For visualization, we need a human-readable graph layout: a graph embedding in low (e.g. two) dimensional depictions. Due to a pangenome graph's potential excessive size, this is a significant challenge. In response, we introduce a novel graph layout algorithm: the Path-Guided Stochastic Gradient Descent (PG-SGD). PG-SGD uses the genomes, represented in the pangenome graph as paths, as an embedded positional system to sample genomic distances between pairs of nodes. This avoids the quadratic cost seen in previous versions of graph drawing by SGD. We show that our implementation efficiently computes the low-dimensional layouts of gigabase-scale pangenome graphs, unveiling their biological features. We integrated PG-SGD in ODGI which is released as free software under the MIT open source license. Source code is available at https://github.com/pangenome/odgi.

Subgraph-Aware Graph Kernel Neural Network for Link Prediction in Biological Networks.

Identifying links within biological networks is important in various biomedical applications. Recent studies have revealed that each node in a network may play a unique role in different links, but most link prediction methods overlook distinctive node roles, hindering the acquisition of effective link representations. Subgraph-based methods have been introduced as solutions but often ignore shared information among subgraphs. To address these limitations, we propose a Subgraph-aware Graph Kernel Neural Network (SubKNet) for link prediction in biological networks. Specifically, SubKNet extracts a subgraph for each node pair and feeds it into a graph kernel neural network, which decomposes each subgraph into a combination of trainable graph filters with diversity regularization for subgraph-aware representation learning. Additionally, node embeddings of the network are extracted as auxiliary information, aiding in distinguishing node pairs that share the same subgraph. Extensive experiments on five biological networks demonstrate that SubKNet outperforms baselines, including methods especially designed for biological networks and methods adapted to various networks. Further investigations confirm that employing graph filters to subgraphs helps to distinguish node roles in different subgraphs, and the inclusion of diversity regularization further enhances its capacity from diverse perspectives, generating effective link representations that contribute to more accurate link prediction.