Random Walk Algorithm Research Articles

Question Embedding on Weighted Heterogeneous Information Network for Knowledge Tracing

Knowledge Tracing (KT) aims to predict students’ future performance on answering questions based on their historical exercise sequences. To alleviate the problem of data sparsity in KT, recent works have introduced auxiliary information to mine question similarity, resulting in the enhancement of question embeddings. Nonetheless, there remains a gap in developing an approach that effectively incorporates various forms of auxiliary information, including relational information (e.g., question-student , question-skill relation), relationship attributes (e.g., correctness indicating a student's performance on a question), and node attributes (e.g., student ability ). To tackle this challenge, the Similarity-enhanced Question Embedding (SimQE) method for KT is proposed, with its central feature being the utilization of weighted and attributed meta-paths for extracting question similarity. To capture multi-dimensional question similarity semantics by integrating multiple relations, various meta-paths are constructed for learning question embeddings separately. These embeddings, each encoding different similarity semantics, are then fused to serve the task of KT. To capture finer-grained similarity by leveraging the relationship attributes and node attributes on the meta-paths, the biased random walk algorithm is designed. In addition, the auxiliary node generation method is proposed to capture high-order question similarity. Finally, extensive experiments conducted on 6 datasets demonstrate that SimQE performs the best among 10 representative question embedding methods. Furthermore, SimQE proves to be more effective in alleviating the problem of data sparsity.

Calculation and application of elastic modulus of mineral components in tight sandstone based on adaptive method

Abstract For the petrophysics modelling of tight sandstones, the elastic modulus of their sandstone and mudstone components are often substituted with those of quartz and clay, which affects model accuracy. To solve this problem, we innovate an adaptive approach for modelling the rock physics characteristics of tight sandstone. First, based on the relationship between P- and S-wave velocities from well logs and the elastic modulus of the rocks, the equivalent elastic modulus of tight sandstone under saturated conditions is calculated. Next, The Lee model and the Gassmann equation were jointly used to determine the equivalent elasticity modulus of tight sandstone matrix. The upper and lower limits of the equivalent elasticity modulus for mudstone and sandstone are established using the mudstone content curve, the least squares method and the Voigt–Reuss–Hill (V-R-H) model. We used the random-walk algorithm to accurately calculate the equivalent elastic modulus of the sandstone and mudstone components. Finally, using the accurately obtained elastic modulus of sandstone and mudstone, the equivalent elastic modulus of the matrix is calculated. The Kuster–Toksöz (K-T) model is subsequently applied to compute the dry frame bulk modulus and shear modulus of the rock. Following this, the Brie model is used to calculate the elastic modulus of the mixed fluid, thereby completing the construction of the rock physics model for the study area. The results demonstrate that our improved petrophysics model can predict the S-wave velocity curve with ≤ 15% errors relative to the true curve. When sweet spot prediction was performed using reservoir-sensitive parameter (Vp/Vs) derived from the petrophysics template, the agreement between the predictions and well-log data was 80%. Thus, our petrophysics modelling method can be used to predict tight gas reservoirs effectively and will aid efforts to improve petroleum exploration works in the study area.

Bayesian Inference for Estimating Heat Sources through Temperature Assimilation

Abstract This paper utilizes a Bayesian inference framework to address the two-dimensional steady-state heat conduction problem, focusing on the estimation of unknown distributed heat sources in a thermally-conducting medium with uniform conductivity. The goal is to infer the locations, strength, and shape of heaters by assimilating temperature data in Euclidean space, employing a Fourier series to represent each heater's shape. The Markov Chain Monte Carlo method, incorporating the random-walk Metropolis-Hasting algorithm and parallel tempering, is utilized for posterior distribution exploration in both unbounded and wall-bounded domains. It is found that multiple solutions arise in cases where the number of temperature sensors is less than the number of unknown states. Moreover, smaller heaters introduce greater uncertainty in estimated strength. To address the challenge of estimating the heater's strength and shape simultaneously due to their strong correlation, our method incorporates sharp priors on one to ensure accurate and feasible solutions of the other. The diffusive nature of heat conduction smooths out any deformations in the temperature contours, especially in the presence of multiple heaters positioned near each other, impacting convergence. In wall-bounded domains with Neumann boundary conditions, the inference of heater parameters tends to be more accurate than in unbounded domains.

Advancing cancer driver gene identification through an integrative network and pathway approach

ObjectiveCancer is a complex genetic disease characterized by the accumulation of various mutations, with driver genes playing a crucial role in cancer initiation and progression. Distinguishing driver genes from passenger mutations is essential for understanding cancer biology and discovering therapeutic targets. However, the majority of existing methods ignore the mutational heterogeneity and commonalities among patients, which hinders the identification of driver genes more effectively. MethodsThis study introduces MCSdriver, a novel computational model that integrates network and pathway information to prioritize the identification of cancer driver genes. MCSdriver employs a bidirectional random walk algorithm to quantify the mutual exclusivity and functional relationships between mutated genes within patient cohorts. It calculates similarity scores based on a mutual exclusivity-weighted network and pathway coverage patterns, accounting for patient-specific heterogeneity and molecular profile similarity. ResultsThis approach enhances the accuracy and quality of driver gene identification. MCSdriver demonstrates superior performance in identifying cancer driver genes across four cancer types from The Cancer Genome Atlas, showing a higher F-score, Recall and Precision compared to existing ranking list-based and module-based models. ConclusionThe MCSdriver model not only outperforms other models in identifying known cancer driver genes but also effectively identifies novel driver genes involved in cancer-related biological processes. The model’s consideration of patient-specific heterogeneity and similarity in molecular profiles significantly enhances the accuracy and quality of driver gene identification. Validation through Gene Ontology enrichment analysis and literature mining further underscores its potential application value in personalized cancer therapy, offering a promising tool for advancing our understanding and treatment of cancer.

Entity Linking Model Based on Cascading Attention and Dynamic Graph

The purpose of entity linking is to connect entity mentions in text to real entities in the knowledge base. Existing methods focus on using the text topic, entity type, linking order, and association between entities to obtain the target entities. Although these methods have achieved good results, they ignore the exploration of candidate entities, leading to insufficient semantic information among entities. In addition, the implicit relationship and discrimination within the candidate entities also affect the accuracy of entity linking. To address these problems, we introduce information about candidate entities from Wikipedia and construct a graph model to capture implicit dependencies between different entity decisions. Specifically, we propose a cascade attention mechanism and develop a novel local entity linkage model termed CAM-LEL. This model leverages the interaction between entity mentions and candidate entities to enhance the semantic representation of entities. Furthermore, a global entity linkage model termed DG-GEL based on a dynamic graph is established to construct an entity association graph, and a random walking algorithm and entity entropy are used to extract the implicit relationships within entities to increase the differentiation between entities. Experimental results and in-depth analyses of multiple datasets show that our model outperforms other state-of-the-art models.

A combined Markov Chain Monte Carlo and Levenberg–Marquardt inversion method for heterogeneous subsurface reservoir modeling

In this study, we systematically investigate an inverse method for heterogeneous porous media to obtain porosity and permeability fields considering only production well data. The forward modeling of the input data, namely pressure and saturation fields, is based on the motion equations of a coupled Darcy flow system involving two phases of isothermal fluid flow. We discretize these equations using a multiscale finite volume simulation technique in the spatial domain, and the backward Euler method in time domain. In the inversion procedure, we combine a global optimization method, the Markov Chain Monte Carlo (MCMC) method, with a local optimization method, the Levenberg–Marquardt (LM) method. The MCMC was implemented as the Random Walk algorithm, and to generate the samples of the porosity and permeability fields, we employed Karhunen–Loève (KL) expansion of second-order stationary fields with Gaussian covariance. The coefficients of the KL expansion are estimated by minimizing the norm of the residual dependent on these fields. At the end of the MCMC iterations, we refine the KL coefficients associated with the porosity and permeability fields using the LM method. We verify in the numerical experiments that the accuracy of the porosity and permeability fields is improved by the LM refinement step.

Subpixel water area mapping based on spatial information processing at superpixel scale for multispectral imagery

ABSTRACT Subpixel water area mapping based on spatial information processing at superpixel scale (SISS) for multispectral imagery is proposed in this paper. In SISS, the superpixels with irregular shape are first obtained by segmenting the first principal component of the improved imagery which is improved from the the original coarse multispectral imagery by using bicubic interpolation; The random walk algorithm is then introduced to calculate these superpixels to obtain the spatial information. Finally, according to this spatial information, the label of the water area or the non-water area is assigned to each subpixel by the class allocation method, producing the final mapping result. The experimental results on two datasets show that the proposed method can achieve the best performance in both visual effects and quantitative indicators.

A Hybrid Method Combining Voronoi Diagrams and the Random Walk Algorithm for Generating the Mesostructure of Concrete.

The modeling of the concrete matrix serves as a foundation for mesoscale analysis of concrete, which provides a crucial avenue for investigating the crack propagation and strength characteristics of concrete. However, the primary prerequisite for conducting such analyses is the generation of aggregate models. By combining the advantages of Voronoi diagrams and the random walk algorithm (RWA), a Voronoi-random walk algorithm is proposed in this paper. The algorithm overcomes the limitations of traditional methods, including constraints on aggregate volume fraction, low computational efficiency, and insufficient randomness in aggregate distribution. The meso-structure of a concrete block was modeled by the proposed method, and then its failure behavior under uniaxial compression was simulated using the finite element method. The numerical results agreed well with the experimental observations, indicating the effectiveness and accuracy of the proposed approach.

Identification of Drought Stress-Responsive Genes in Rice by Random Walk with Multi-Restart Probability on MultiPlex Biological Networks.

Exploring drought stress-responsive genes in rice is essential for breeding drought-resistant varieties. Rice drought resistance is controlled by multiple genes, and mining drought stress-responsive genes solely based on single omics data lacks stability and accuracy. Multi-omics correlation analysis and biological molecular network analysis provide robust solutions. This study proposed a random walk with a multi-restart probability (RWMRP) algorithm, based on the Restarted Random Walk (RWR) algorithm, to operate on rice MultiPlex biological networks. It explores the interactions between biological molecules across various levels and ranks potential genes. RWMRP uses eigenvector centrality to evaluate node importance in the network and adjusts the restart probabilities accordingly, diverging from the uniform restart probability employed in RWR. In the random walk process, it can be better to consider the global relationships in the network. Firstly, we constructed a MultiPlex biological network by integrating the rice protein-protein interaction, gene pathway, and gene co-expression network. Then, we employed RWMRP to predict the potential genes associated with rice tolerance to drought stress. Enrichment and correlation analyses resulted in the identification of 12 drought-related genes. We further conducted quantitative real-time polymerase chain reaction (qRT-PCR) analysis on these 12 genes, ultimately identifying 10 genes responsive to drought stress.

F-Deepwalk: A Community Detection Model for Transport Networks.

The design of transportation networks is generally performed on the basis of the division of a metropolitan region into communities. With the combination of the scale, population density, and travel characteristics of each community, the transportation routes and stations can be more precisely determined to meet the travel demand of residents within each of the communities as well as the transportation links among communities. To accurately divide urban communities, the original word vector sampling method is improved on the classic Deepwalk model, proposing a Random Walk (RW) algorithm in which the sampling is modified with the generalized travel cost and improved logit model. Urban spatial community detection is realized with the K-means algorithm, building the F-Deepwalk model. Using the basic road network as an example, the experimental results show that the Deepwalk model, which considers the generalized travel cost of residents, has a higher profile coefficient, and the performance of the model improves with the reduction of random walk length. At the same time, taking the Shijiazhuang urban rail transit network as an example, the accuracy of the model is further verified.

Identifying cooperating cancer driver genes in individual patients through hypergraph random walk

ObjectiveIdentifying cancer driver genes, especially rare or patient-specific cancer driver genes, is a primary goal in cancer therapy. Although researchers have proposed some methods to tackle this problem, these methods mostly identify cancer driver genes at single gene level, overlooking the cooperative relationship among cancer driver genes. Identifying cooperating cancer driver genes in individual patients is pivotal for understanding cancer etiology and advancing the development of personalized therapies. MethodsHere, we propose a novel Personalized Cooperating cancer Driver Genes (PCoDG) method by using hypergraph random walk to identify the cancer driver genes that cooperatively drive individual patient cancer progression. By leveraging the powerful ability of hypergraph in representing multi-way relationships, PCoDG first employs the personalized hypergraph to depict the complex interactions among mutated genes and differentially expressed genes of an individual patient. Then, a hypergraph random walk algorithm based on hyperedge similarity is utilized to calculate the importance scores of mutated genes, integrating these scores with signaling pathway data to identify the cooperating cancer driver genes in individual patients. ResultsThe experimental results on three TCGA cancer datasets (i.e., BRCA, LUAD, and COADREAD) demonstrate the effectiveness of PCoDG in identifying personalized cooperating cancer driver genes. These genes identified by PCoDG not only offer valuable insights into patient stratification correlating with clinical outcomes, but also provide an useful reference resource for tailoring personalized treatments. ConclusionWe propose a novel method that can effectively identify cooperating cancer driver genes for individual patients, thereby deepening our understanding of the cooperative relationship among personalized cancer driver genes and advancing the development of precision oncology.

DC-RST: a parallel algorithm for random spanning trees in network analytics

The Mantel Test, discovered in the 1960s, determines whether two distance metrics on a network are related. More recently, DimeCost, an equivalent test with improved computational complexity, was proposed. It was based on computing a random spanning tree of a complete graph on n vertices—the spanning tree was computed using Wilson’s random walk algorithm. In this paper, we describe DC-RST, a parallel, divide-and-conquer random walk algorithm to further speed up this computation. Relative to Wilson’s sequential random-walk algorithm, on a system with 48 cores, DC-RST was up to 4X faster when first creating random partitions and up to 20X faster without this sub-step. DC-RST is shown to be a suitable replacement for the Mantel and DimeCost tests through a combination of theoretical and statistical results.

Random walk algorithms for solving nonlinear chemotaxis problems

Abstract Random walk based stochastic simulation methods for solving a nonlinear system of coupled transient diffusion and drift-diffusion equations governing a two-component chemotaxis process are developed. The nonlinear system is solved by linearization, the system is evolved in time, by small time steps, where on each step a linear system of equations is solved by using the solution from the previous time step. Three different stochastic algorithms are suggested, (1) the global random walk on grid (GRWG), (2) a randomized vector algorithm (RVA) based on a special transformation of the original matrix to a stochastic matrix, and (3) a stochastic projection algorithm (SPA). To get high precision results, these methods are combined with an iterative refinement method.

Tracer transport in fractured porous media: Distribution of tracer concentration within the rock matrix and the implementation of time domain random walk algorithm

In this work, a new Time Domain Random Walk (TDRW) algorithm is proposed to estimate the tracer distribution profile within the rock matrix. The development of the new algorithm stems from the statistical properties of the analytical solution to a single fracture-matrix system, in which the particle position at a certain time is calculated and recorded. With the position of each particle determined, the resulting distribution will then provide an estimate of the tracer distribution profile directly. In addition, the newly developed algorithm can readily be extended to a case of more complicated fracture-matrix system, in which an arbitrary injection boundary condition may also be used. To verify the accuracy and applicability of the new algorithm, three benchmark simulations are made, in which the results of different approaches are found to be identical. Nevertheless, the new algorithm has a higher computational efficiency, due to its lower calculation demand.

PANNER: POS-Aware Nested Named Entity Recognition Through Heterogeneous Graph Neural Network

Nested named entity recognition (Nested NER) in knowledge graph (KG) aims at obtaining all meaningful entities, including nested entities for sentences in longer text region. Those obtained entities are to facilitate downstream applications, such as relation extraction, entity resolution, and coreference resolution. This task, however, is challenging not only because of the demand to detect the boundary of the entity but also due to the complexity of those hierarchically nested entities. Since a substantial amount of work has been made to Flat NER (or Nested NER), a few of them can explicitly acquire the position of the entity and utilize the grammatical construction of text. In this work, we propose PANNER, a POS-aware Nested NER model, to solve all the above issues. Specifically, we first construct a heterogeneous graph by introducing the part-of-speech (POS) information of the word. Second, we design a dilated random walk (DRW) algorithm based on a grammatical path to sample a fixed size of neighbors for each node. Third, we aggregate the message from different types of neighbors through an attention mechanism. Finally, we use a bidirectional decoding module to recognize and categorize all the flat and nested entities based on the node embedding in a layer-wise manner. Our extensive experiments show the effectiveness of PANNER in both flat and nested NER.

New Random Walk Algorithm Based on Different Seed Nodes for Community Detection

A complex network is an abstract modeling of complex systems in the real world, which plays an important role in analyzing the function of complex systems. Community detection is an important tool for analyzing network structure. In this paper, we propose a new community detection algorithm (RWBS) based on different seed nodes which aims to understand the community structure of the network, which provides a new idea for the allocation of resources in the network. RWBS provides a new centrality metric (MC) to calculate node importance, which calculates the ranking of nodes as seed nodes. Furthermore, two algorithms are proposed for determining seed nodes on networks with and without ground truth, respectively. We set the number of steps for the random walk to six according to the six degrees of separation theory to reduce the running time of the algorithm. Since some traditional community detection algorithms may detect smaller communities, e.g., two nodes become one community, this may make the resource allocation unreasonable. Therefore, modularity (Q) is chosen as the optimization function to combine communities, which can improve the quality of detected communities. Final experimental results on real-world and synthetic networks show that the RWBS algorithm can effectively detect communities.

A Novel Method for Mining Regulatory sRNAs Related to Rice Resistance Against Blast Fungus from Multi-Omics Data

Background: Due to infection by the rice blast fungus, rice, a major global staple, faces yield challenges. While chemical control methods are common, their environmental and economic costs are growing concerns. Traditional biological experiments are also inefficient for exploring resistance genes. Therefore, understanding the interaction between rice and the rice blast fungus is urgent and important. Objective: This study aims to use multi-omics data to uncover key elements in rice's defense against rice blast fungus Magnaporthe oryzae. We built a detailed, multi-layered heterogeneous interaction network, employing an innovative graph embedding feature with a cross-layer random walk algorithm to identify crucial crucial resistance factors.This could inform strategies for enhancing disease resistance in rice. objective: This study aims to use multi-omics data to uncover key elements in rice's defense against rice blast fungus Magnaporthe oryzae. We built a detailed, multi-layered heterogeneous interaction network, employing an innovative graph embedding feature with a cross-layer random walk algorithm, to identify crucial crucial resistance factors. This could inform strategies for enhancing disease resistance in rice. Methods: We integrated genomics, transcriptomics, and proteomics data on Magnaporthe oryzae infecting rice. This multi-omics data was used to construct a multi-layer heterogeneous network.An advanced graph embedding algorithm (BINE) provided rich vector representations of network nodes. A multi-layer network walking algorithm was then used to analyze the network and identify key regulatory small RNA (sRNAs) in rice. Results: Node similarity rankings allowed us to identify significant regulatory sRNAs in rice that are integral to disease resistance. Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) analyses further revealed their roles in biological processes and key metabolic pathways.Our integrative method precisely and efficiently identified these crucial elements, offering a valuable systems biology tool. Conclusion: By integrating multi-omics data with computational analysis, this study reveals key regulatory sRNAs in rice's disease resistance mechanism. These findings enhance our understanding of rice disease resistance and provide genetic resources for breeding disease-resistant rice. Despite limitations in sRNA functional interpretation, this research demonstrates the power of applying multi- omics data to address complex biological problems.

STTraj2Vec: A spatio-temporal trajectory representation learning approach

Computing trajectory similarity plays a critical role in various spatio-temporal applications that involve trajectory analysis. In recent years, trajectory representation learning has been extensively studied and applied for trajectory similarity calculation. However the majority of existing algorithms for trajectory representation generally have two problems. The first problem is the emphasis of spatial similarity over temporal similarity, and even to discard the temporal dimension of spatio-temporal trajectories. As a result, the outputs of these approaches cannot fully represent the similarity of spatio-temporal trajectories. The second problem is the introduction of additional information, such as the topology of the road network, which increases the uncertainty of capturing the spatio-temporal correlation of trajectories and prevents their application in scenarios where it is difficult to obtain such information. This poses a significant challenge when dealing with complex and time-varying traffic networks. This paper proposes a novel method, named STTraj2Vec (Spatio-temporal Trajectory 2 Vector), which relies only on spatio-temporal trajectories to capture their similarity without spatio-temporal separation. This takes into account the whole spatio-temporal trajectory information. In this method, an extended clustering algorithm is introduced, which maps the trajectory into a point-region quadtree, and constructs a time-varying virtual network structure based on the point-region quadtree. In this method, an extended clustering algorithm is introduced, which maps each trajectory into a point-region quadtree, and then completes density clustering through the adjacency relation of leaf nodes to construct a time-varying virtual network structure. This virtual network structure not only considers the spatial proximity, but also the time, so as to reflect the spatio-temporal characteristics of the trajectory more accurately. Then, a novel spatially and temporally integrated random walk algorithm is designed, which carries out spatiotemporal random walk on the virtual network structure, to capture the spatiotemporal characteristics of the trajectory, and thus obtains the representation of all nodes in the virtual network. Furthermore, each trajectory is converted into a sequence of vectors on the virtual road network according to the latitude, longitude, and time of the trajectory points. Finally, based on these node representations and trajectories, a transformer model with ranking loss is employed to capture the distinct contributions of the various locations and times to the similarity computation and encode each sequence of vectors into target vectors. Experiments on two public datasets show that STTraj2Vec is superior to the state-of-the-art methods in terms of effectiveness for top-k trajectory similarity search and trajectory clustering, while exhibiting low parameter sensitivity and high model robustness.

Controlling numerical diffusion in solving advection-dominated transport problems

Numerical schemes for advection-dominated transport problems are are evaluated in a comparative study. Explicit and implicit finite difference methods are analyzed together with a global random walk algorithm in the frame of a splitting procedure. The efficiency of the methods with respect to the control of the numerical diffusion is investigated numerically on one-dimensional problems with constant coefficients and two-dimensional problems with variable coefficients consisting of realizations of space-random functions.

Berkeley‐RWAWC: A New CYGNSS‐Based Watermask Unveils Unique Observations of Seasonal Dynamics in the Tropics

AbstractThe UC Berkeley Random Walk Algorithm WaterMask from CYGNSS (Berkeley‐RWAWC) is a new data product designed to address the challenges of monitoring inundation in regions hindered by dense vegetation and cloud cover as is the case in most of the Tropics. The Cyclone Global Navigation Satellite System (CYGNSS) constellation provides data with a higher temporal repeat frequency compared to single‐satellite systems, offering the potential for generating moderate spatial resolution inundation maps with improved temporal resolution while having the capability to penetrate clouds and vegetation. This paper details the development of a computer vision algorithm for inundation mapping over the entire CYGNSS domain (37.4°N–37.4°S). The sole reliance on CYGNSS data sets our method apart in the field, highlighting CYGNSS's indication of water existence. Berkeley‐RWAWC provides monthly, low‐latency inundation maps starting in August 2018 and across the CYGNSS latitude range, with a spatial resolution of 0.01° × 0.01°. Here we present our workflow and parameterization strategy, alongside a comparative analysis with established surface water data sets (SWAMPS, WAD2M) in four regions: the Amazon Basin, the Pantanal, the Sudd, and the Indo‐Gangetic Plain. The comparisons reveal Berkeley‐RWAWC's enhanced capability to detect seasonal variations, demonstrating its usefulness in studying tropical wetland hydrology. We also discuss potential sources of uncertainty and reasons for variations in inundation retrievals. Berkeley‐RWAWC represents a valuable addition to environmental science, offering new insights into tropical wetland dynamics.