Random Walk Method Research Articles

LUSTC: A Novel Approach for Predicting Link States on Dynamic Attributed Networks

Predicting link states on dynamic attributed networks is one of the most fundamental problems for network analysis. To accurately predict the formations and disappearances of links, we need to utilize three types of information, that is, structural information, node content information, and temporal information, simultaneously. To this end, we propose a novel approach called LUSTC for predicting links and unlinks with structural information, temporal information, and node content information on dynamic attributed networks. For each snapshot, LUSTC first randomly chooses some sets of active nodes whose degree changes between adjacent snapshots and collects higher-order structural information using a random walk method based on the active nodes. Then, LUSTC generates two global matrices containing the temporal structural information and temporal node content information, respectively, as well as a sequence of auxiliary matrices for reconstructing the structural information and node content information of snapshots. These generated matrices are optimized using a nonnegative matrix factorization (NMF) method based on the structural information and node content information of snapshots. Finally, LUSTC estimates the similarity matrix for future snapshots to predict the links that are more likely to be formed or broken. The experimental results on various dynamic attributed networks demonstrate the effectiveness of LUSTC on the link prediction and unlink prediction tasks.

An anti-greedy random walk algorithm for heat exchanger network synthesis

Heat exchanger network (HEN) synthesis is a vibrant research field in process system engineering, with substantial contributions to energy conservation and emissions reduction initiatives. The optimal design of a heat exchanger network is not an easy task due to the abundance of local optima in the solution space caused by the non-linear, non-convex, and discontinuous nature of the problem. Generally, several heuristic algorithms employ a greedy evolutionary mechanism, optimize through greedily accepting the decrease in the objective function, and converge to obtain the optimal solution. The Random Walk algorithm has a simple evolutionary mechanism, is prone to mutation, and exhibits high flexibility. However, the algorithm's inherent persistent greediness in searching restrict the scope of the search. Thus, this paper proposes an anti-greedy concept based on the Random Walk method to serve as the basis of a new synthesis approach called the Anti-greedy Random Walk algorithm. Two strategies are proposed in the algorithm, which broaden the solution domain by slowing down rapid unit reduction and accepting imperfect solutions, respectively. One strategy is to thoroughly search for the integer and continuous variables of the HEN problem by covering a much larger search space. Another is to escape the local extrema and move forward to discover more possibilities. Quantitative data demonstrates the algorithm's ability to avoid the local extrema and enhance the search effectiveness. Three different scales of classical cases are used in this work and the obtained results are superior to the published ones.

Temporally-aware node embeddings for evolving networks topologies

Static node embedding algorithms applied to snapshots of real-world applications graphs are unable to capture their evolving process. As a result, the absence of information about the dynamics in these node representations can harm the accuracy and increase processing time of machine learning tasks related to these applications. Aiming at fill the gap regarding the inability of static methods to capture evolving processes on dynamic networks, we propose a biased random walk method named Evolving Node Embedding (EVNE). EVNE leverages the sequential relationship of graph snapshots by incorporating historic information when generating embeddings for the next snapshot. It learns node representations through a neural network, but differs from existing methods as it: (i) incorporates previously run walks at each step; (ii) starts the optimization of the current embedding from the parameters obtained in the previous iteration; and (iii) uses two time-varying parameters to regulate the behavior of the biased random walks over the process of graph exploration. Through a wide set of experiments we show that our approach generates better embeddings, outperforming baselines by up to 20% in a downstream node classification task. EVNE’s embeddings achieve better performance than others, based on experiments with four classifiers and five datasets. In addition, we present seven variations of our model to show the impact of each of EVNE’s mechanisms.

A multilayer network diffusion-based model for reviewer recommendation

With the rapid growth of manuscript submissions, finding eligible reviewers for every submission has become a heavy task. Recommender systems are powerful tools developed in computer science and information science to deal with this problem. However, most existing approaches resort to text mining techniques to match manuscripts with potential reviewers, which require high-quality textual information to perform well. In this paper, we propose a reviewer recommendation algorithm based on a network diffusion process on a scholar–paper multilayer network, with no requirement for textual information. The network incorporates the relationship of scholar–paper pairs, the collaboration among scholars, and the bibliographic coupling among papers. Experimental results show that our proposed algorithm outperforms other state-of-the-art recommendation methods that use graph random walk and matrix factorization and methods that use machine learning and natural language processing, with improvements of over 7.62% in recall, 5.66% in hit rate, and 47.53% in ranking score. Our work sheds light on the effectiveness of multilayer network diffusion-based methods in the reviewer recommendation problem, which will help to facilitate the peer-review process and promote information retrieval research in other practical scenes.

Hybrid optimization of laser-driven fusion targets and laser profiles

Quasi-isentropic compression is an effective method to achieve high-density and high-temperature implosion in laser-driven inertial confinement fusion (ICF). However, it requires precise matching between the laser profile and the target structure. Designing the optimal laser profile and the corresponding target for ICF is a challenge due to the large number of parameters involved. In this paper, we present a novel method that combines random walk and Bayesian optimization. The basic sampling data for Bayesian optimization are a series of laser pulse profiles and target structures that can produce relatively high areal densities obtained by the random walk method. This approach reduces the number of samples required for Bayesian optimization and mitigates low efficiency in the latter stages of the random walk method. The method also reduces the randomness in the optimization process and enhances the optimization efficiency. It should have important applications in ICF research.

P2 random walk: self-supervised anomaly detection with pixel-point random walk

In the domain of intelligent manufacturing, automatic anomaly detection plays a pivotal role and holds great significance for improving production efficiency and product quality. However, the scarcity and uncertainty of anomalous data pose significant challenges in this field. Data augmentation methods, such as Cutout, which are widely adopted in existing methodologies, tend to generate patterned data, leading to biased data and compromised detection performance. To deal with this issue, we propose an approach termed self-supervised anomaly detection with pixel-point random walk (P2 Random Walk), which combines data augmentation and Siamese neural networks. We develop a pixel-level data augmentation technique to enhance the randomness of generated data and establish a two-stage anomaly classification framework. The effectiveness of the P2 Random Walk method has been demonstrated on the MVTec dataset, achieving an AUROC of 96.2% and 96.3% for classification and segmentation, respectively, by using only data augmentation-based techniques. Specifically, our method outperforms other state-of-the-art methods in several categories, improving the AUROC for classification and segmentation by 0.5% and 0.3%, respectively, which demonstrates the high performance and strong academic value of our method in anomaly detection tasks.

Research on a Link Prediction Algorithm Based on Hypergraph Representation Learning

Link prediction is a crucial area of study within complex networks research. Mapping nodes to low-dimensional vectors through network embeddings is a vital technique for link prediction. Most of the existing methods employ “node–edge”-structured networks to model the data and learn node embeddings. In this paper, we initially introduce the Clique structure to enhance the existing model and investigate the impact of introducing two Clique structures (LECON: Learning Embedding based on Clique Of the Network) and nine motifs (LEMON: Learning Embedding based on Motif Of the Network), respectively, on experimental performance. Subsequently, we introduce a hypergraph to model the network and reconfigure the network by mapping hypermotifs to two structures: open hypermotif and closed hypermotif, respectively. Then, we introduce hypermotifs as supernodes to capture the structural similarity between nodes in the network (HMRLH: HyperMotif Representation Learning on Hypergraph). After that, taking into account the connectivity and structural similarity of the involved nodes, we propose the Depth and Breadth Motif Random Walk method to acquire node sequences. We then apply this method to the LEMON (LEMON-DB: LEMON-Depth and Breadth Motif Random Walk) and HMRLH (HMRLH-DB: HMRLH-Depth and Breadth Motif Random Walk) algorithms. The experimental results on four different datasets indicate that, compared with the LEMON method, the LECON method improves experimental performance while reducing time complexity. The HMRLH method, utilizing hypernetwork modeling, proves more effective in extracting node features. The LEMON-DB and HMRLH-DB methods, incorporating new random walk approaches, outperform the original methods in the field of link prediction. Compared with state-of-the-art baselines, the proposed approach in this paper effectively enhances link prediction accuracy, demonstrating a certain level of superiority.

Quantification analysis of potential risk in railway accidents: A new random walk based approach

Safety and efficiency are the fundamental goals to improve the transportation capacity and service level of railway system. Moreover, the accurate description and in-depth exploration of potential risks are essential in reducing the railway accidents. However, there have been limited publications that focus on quantitatively analyzing the potential risk of railway accidents by using the random walk method. In this paper, a new random walk method named Comprehensive-Biased Random Walk with Different Restart (CBDRWR) is proposed in analyzing the potential risk of railway accident generation process. Combined with the established accident causation network, we give each node a different restart probability and comprehensively improve the biased transition probabilities. According to the solution algorithm of CBDRWR equation, we propose four evaluation indexes for quantifying and analyzing the potential risk of accident occurrence. In the case study, the proposed method is used to analyze the Federal Railroad Administration (FRA) dataset. The experimental results verify that the proposed method can effectively quantify the potential risk and quickly locate the key risk sources. Resultantly, this research can provide an accurate, scientific and reasonable basis for railway accident prevention and rescue.

Universal to nonuniversal transition of the statistics of rare events during the spread of random walks.

Through numerous experiments that analyzed rare event statistics in heterogeneous media, it was discovered that in many cases the probability density function for particle position, P(X,t), exhibits a slower decay rate than the Gaussian function. Typically, the decay behavior is exponential, referred to as Laplace tails. However, many systems exhibit an even slower decay rate, such as power-law, log-normal, or stretched exponential. In this study, we utilize the continuous-time random walk method to investigate the rare events in particle hopping dynamics and find that the properties of the hop size distribution induce a critical transition between the Laplace universality of rare events and a more specific, slower decay of P(X,t). Specifically, when the hop size distribution decays slower than exponential, such as e^{-|x|^{β}} (β>1), the Laplace universality no longer applies, and the decay is specific, influenced by a few large events, rather than by the accumulation of many smaller events that give rise to Laplace tails.

Controlling the spread of infectious diseases by using random walk method to remove many important links

Understanding the network structure is critical for controlling and mitigating the spread of infectious diseases. Removing many important links to control the spread of infectious diseases is often more convenient and cost-saving than isolating individuals. Therefore, we develop an algorithm (RW) for identifying important links based on random walks in complex networks. With the guarantee of network connectivity, removing many important links from the network can better reduce the largest eigenvalue of the adjacency matrix, thus increasing the epidemic threshold and reducing the fraction of infected individuals, and further effectively controlling the spread of infectious diseases. In order to verify the effectiveness and scalability of our algorithm, we conducted many experiments on top of a large number of real-world networks and synthesis networks to compare with some classical algorithms. The results show that our algorithm can effectively identify important links to control the spread of infectious diseases in social networks.

Random walks and moving boundaries: Estimating the penetration of diffusants into dense rubbers

For certain materials science scenarios arising in rubber technology, one-dimensional moving boundary problems with kinetic boundary conditions are capable of unveiling the large-time behavior of the diffusants penetration front, giving a direct estimate on the service life of the material. Driven by our interest in estimating how a finite number of diffusant molecules penetrate through a dense rubber, we propose a random walk algorithm to approximate numerically both the concentration profile and the location of the sharp penetration front. The proposed scheme decouples the target evolution system in two steps: (i) the ordinary differential equation corresponding to the evaluation of the speed of the moving boundary is solved via an explicit Euler method, and (ii) the associated diffusion problem is solved by a random walk method. To verify the correctness of our random walk algorithm we compare the resulting approximations to computational results based on a suitable finite element approach with a controlled convergence rate. Our numerical results recover well penetration depth measurements of a controlled experiment designed specifically for this setting.

A conditional random field recommendation method based on tripartite graph

Recommender System (RS) has generated widespread attention with the aim of expanding different items. Among graph-based recommendation methods, the tripartite graph can better manage data sparsity and cold start, while improving the metrics of various recommendations such as recall, precision, and diversity. Existing tripartite graph-based methods encounter numerous challenges, including mitigating data sparsity, improving diversity, and capturing potential user preferences via social relations. To address these challenges, a Conditional Random Field based on Tripartite Graph (CRF-TG) is proposed. The tripartite graph consists of the user, item, and trust level. The method can mine potentially similar users, create probabilistic models based on TG, and uncover potential user preferences. Moreover, to mine the users with similar preferences outside the social relationship, the random walk method is used to test CRF-TG. Experiments are designed to verify the validity of CRF-TG. Compared to the others considered methods, CRF-TG gives a 15% increase on average in performance indicators such as diversity, recall, and F1.

Nuclear Structure Effects in Fission

Three examples of nuclear structure effects in fission dynamics are discussed: (i) The appearance of a super-short symmetric mode in the fission of nuclei around 264Fm leading to two double-magic 132Sn, (ii) Fission of some super-heavy elements where the heavy cluster is focused around double-magic 208Pb, and (iii) A saw-tooth distribution in angular momenta versus the fission fragment mass in the fission of 239U. The Metropolis random walk method is used to simulate the strongly damped fission dynamics on a 5D deformation grid. The dynamics is driven by pairing-, shape- and energy-dependent level densities. When available, a good agreement with experimental data is obtained.

Improved Random Walk Method Verified in a Large-Scale Urban Network for the Sampling of Alternatives in Route Choice Modeling

The first stage in route choice modeling is the generation of the route choice sets, which directly affects the accuracy of model estimation. The random walk method proposed by Frejinger et al. for this purpose has the advantage of directly calculating the probabilities of paths chosen. However, its application has seldom been seen in a large-scale network of a real large city in the literature. To fill this gap, the performance of the random walk algorithm is examined on a real network in Shanghai, China. It is found that it cannot avoid loops and frequently produces overlong alternative paths. By locating the root cause, an improved random walk algorithm is proposed in this paper. The idea of the new algorithm is to change the value of the shape parameters. Instead of a fixed value in Frejinger et al.’s method, the shape parameter in this approach is dynamically changing, controlled by the allowable probability difference and generalized minimum cost. The algorithm is validated in a large-scale network using real travel survey data. The results of the empirical analysis suggest that the proposed random walk algorithm has a significant improvement with respect to the number and length of generated alternative paths compared to those from the original algorithm. This study's primary contribution is to significantly improve the adaptability of the random walk method in large-scale road networks, which is crucial for improving the accuracy of route choice models and understanding of route choice behaviors.

LUNCRW: Prediction of potential lncRNA-disease associations based on unbalanced neighborhood constraint random walk

Accumulating evidence suggests that long non-coding RNAs (lncRNAs) are associated with various complex human diseases. They can serve as disease biomarkers and hold considerable promise for the prevention and treatment of various diseases. The traditional random walk algorithms generally exclude the effect of non-neighboring nodes on random walking. In order to overcome the issue, the neighborhood constraint (NC) approach is proposed in this study for regulating the direction of the random walk by computing the effects of both neighboring nodes and non-neighboring nodes. Then the association matrix is updated by matrix multiplication for minimizing the effect of the false negative data. The heterogeneous lncRNA-disease network is finally analyzed using an unbalanced random walk method for predicting the potential lncRNA-disease associations. The LUNCRW model is therefore developed for predicting potential lncRNA-disease associations. The area under the curve (AUC) values of the LUNCRW model in leave-one-out cross-validation and five-fold cross-validation were 0.951 and 0.9486 ± 0.0011, respectively. Data from published case studies on three diseases, including squamous cell carcinoma, hepatocellular carcinoma, and renal cell carcinoma, confirmed the predictive potential of the LUNCRW model. Altogether, the findings indicated that the performance of the LUNCRW method is superior to that of existing methods in predicting potential lncRNA-disease associations.

Tropospheric Delay Parameter Estimation Strategy in BDS Precise Point Positioning

Tropospheric delay (TD) parameter estimation is a critical issue underlying high-precision data processing for global navigation satellite systems (GNSSs). The most widely used TD parameter estimation methods are the random walk (RW) and piece-wise constant (PWC). The RW method can effectively track rapid variations of tropospheric delay, but it may introduce excessive noise. In contrast, the PWC method introduces less noise, but it is less adaptable to cases of large variations of tropospheric delay. To address the problem of how to choose the optimal TD parameter estimation method, this paper investigates the variation patterns of international GNSS service zenith tropospheric delay (IGS ZTD) products and proposes a combined strategy model for TD parameter estimation. Firstly, this paper avoids the day-boundary jumps problem of IGS ZTD products by grouping based on single-day data. Secondly, this paper introduces discrete point areas (DPAs) to measure the magnitude of the ZTD values and uses comprehensive indicators to reflect the variation of ZTD. Next, based on the Köppen-Geiger climate classification, this study selected five different climate classifications with a total of 20 IGS stations as experimental data. The data assessed span from day of year (DOY) 001 to DOY 365 in 2022. This paper then applied 26 different parameter estimation strategies for static precise point positioning (PPP) data processing, and the parameter estimation strategies that were used include the RW and PWC (with the piece-wise constant ranging from twenty minutes to five hundred minutes at twenty-minute intervals). Finally, ZTD and positioning results were obtained using various parameter estimation methods, and a combined strategy model was established. We selected five different climate classifications of IGS stations as validation data and designed three sets of comparative experiments: RW, PWC120, and the combined strategy model, to verify the effectiveness of the combined strategy model. The experimental results revealed that: RW and the combined strategy model have a comparable ZTD accuracy and both are superior to PWC120. The combined strategy model improves the positioning accuracy in the U direction compared to RW and PWC120. In arid (B) and polar (E) regions with a small variation of TD, the PWC120 strategy displayed a better positioning accuracy than the RW strategy; in equatorial (A) and warm-temperate (C) regions, where there are large variations of TD, the RW strategy exhibited a better positioning accuracy than the PWC120 strategy. The combined strategy model can flexibly select the optimal parameter estimation method according to the comprehensive indicator while ensuring ZTD estimation accuracy; it enhances positioning accuracy.

Deep-Learning-Driven Random Walk Method for Capacitance Extraction

Random-walk based methods for solving Partial Differential Equations (PDEs) exhibit significant advantages and applicability to numerous domains. One of these is parasitic capacitance extraction in modern silicon technologies, where they are essentially called upon to solve a boundary-value problem. In this regime, fast and accurate calculation of the Green’s function within the transition domains of the random walk is critical for competitive performance. Silicon processes in advanced nodes introduce complex or special dielectric structures that challenge currently established methods for characterizing the Green’s function. In this paper, a novel approximation method for the Green’s function and the Green’s function gradient is presented, which leverages Group-Equivariant Convolutional Neural Networks (G-CNNs). This can accompany existing multi-tier Green’s function data pre-computation schemes. Additionally, it enables performing the crucial step of sampling according to the Green’s function without explicit calculation of the Green’s function itself. A novel end-to-end random-walk architecture is discussed which incorporates such deep neural-networks, and its utility is demonstrated though numerical experiments. The proposed scheme enjoys massive gains in terms of speed for advanced CMOS nm node setups with non-planar dielectric media, compared to a straight Finite Differences Method (FDM) solution, while maintaining good accuracy levels.

Household income and food security during the COVID-19 pandemic in the urban slums of Punjab, Pakistan

ABSTRACT The COVID-19 crisis has not only increased socio-economic inequalities globally but it also severely affected people's everyday lives. This study explores the impacts of COVID-19 on household income, food security, and food consumption patterns in the urban slums of Punjab, Pakistan. Using a multistage random sampling method, cross-sectional data was collected from 257 households through face-to-face interviews. Respondents were chosen randomly applying the random walk method. The data were analysed using Probit regression models. The household food security situation was estimated using the food insecurity experience scale (HFIES) developed by the Food and Agriculture Organization (FAO). Results show that household income and food security situations during the COVID-19 pandemic were significantly affected by education level, household size, daily-wage earnings, salaried employment, and household income slot-I. Household participation in social safety programs appears to help mitigate income shocks and decrease food insecurity. Due to the COVID-19 crisis, 73.92% and 54.86% of the surveyed households faced income shocks and worsened food security, respectively. The consumption of meat, poultry products, and seafood decreased by 21.01%, 17.50%, and 14.39%, respectively, during the pandemic, in comparison to the pre-pandemic period. The study recommends that authorities should consider continuously focusing on supporting existing national social safety programs and designing new ones by providing responsive packages during such adversities. Further, structuring robust financial institutions to aid business recovery and to ensure the availability of food to marginalised communities, particularly in urban slums, could sustain the masses.

Experimental and numerical analysis of a catalyst layer in the membrane electrode assembly of polymer electrolyte membrane fuel cells

Fuel cells constitute an important strategy for carbon-neutral Carbon Dioxide recycling because they utilize the green hydrogen produced from renewable electrical energy. To achieve low-cost and high-performance polymer electrolyte fuel cells, reducing active metals by optimizing the cathode catalyst layer structure is crucial. In this study, we combined image analysis, numerical analysis, and electrochemical approaches to clarify the diffusion characteristics of the cathode catalyst layer in a polymer electrolyte membrane fuel cell. The structure of a catalyst-supported carbon substrate and stacked catalyst-supported carbon substrate was determined using transmission electron microscopy and focused ion-beam scanning electron microscopy. Porosity was analyzed by image analysis and torsion by numerical analysis using the random walk method. Diffusivity near the catalyst and pores was evaluated using a recently developed method by analyzing the active metal surface resistance based on the dependence of the catalyst layer resistance on carbon monoxide coverage. These analytical methods were applied to catalyst-supported carbon materials with different structures. Diffusion through the catalyst surface, carbon support, and carbon support aggregates was also analyzed; furthermore, we obtained following guidelines for improving the specifications. Larger pores and smaller flexures in the cathode catalyst layer may improve the performance of Polymer Electrolyte Membrane Fuel Cells.

Simulation of the drift and diffusion of marine oil spill under the effect of wind, current and tides

Oil spill accidents occur in marine traffic accidents. Once the accidents happen, oil spill will drift and diffuse on the ocean as impacted by wind and tidal current, which has considerably impacted the work on wharfs and their surrounding environment. This study aimed to investigate the effect of wind, ocean current and tides on oil spill movement for the building of the drift and weathering models of oil particles to predict and assess the risks of oil spill on the ocean. In these models, the oil film drift algorithm considers the joint action of wind, ocean current, wave and density flow on oil spill. In this study, the fluid dynamic model was adopted to determine the drift motion generated by the tidal field, and the diffusion process was calculated with the random walk method. In addition, the random movement model of oil particles was employed for simulating the transport and weathering of the oil spill, as an attempt to simulate marine oil spill. Furthermore, the Ningbo port was taken as an example to obtain the numerical sum of the flow field obtained by the simulation, which can guide the prediction of oil spill risks near ports.