Random Walk Method Research Articles

Memory-aware framework for fast and scalable second-order random walk over billion-edge natural graphs

Second-order random walk is an important technique for graph analysis. Many applications including graph embedding, proximity measure and community detection use it to capture higher-order patterns in the graph, thus improving the model accuracy. However, the memory explosion problem of this technique hinders it from analyzing large graphs. When processing a billion-edge graph like Twitter, existing solutions (e.g., alias method) of the second-order random walk may take up 1796TB memory. Such high memory consumption comes from the memory-unaware strategies for the node sampling during the random walk. In this paper, to clearly compare the efficiency of various node sampling methods, we first design a cost model and propose two new node sampling methods: one follows the acceptance-rejection paradigm to achieve a better balance between memory and time cost, and the other is optimized for fast sampling the skewed probability distributions existed in natural graphs. Second, to achieve the high efficiency of the second-order random walk within arbitrary memory budgets, we propose a novel memory-aware framework on the basis of the cost model. The framework applies a cost-based optimizer to assign desirable node sampling method for each node or edge in the graph within a memory budget meanwhile minimizing the time cost of the random walk. Finally, the framework provides general programming interfaces for users to define new second-order random walk models easily. The empirical studies demonstrate that our memory-aware framework is robust with respect to memory and is able to achieve considerable efficiency by reducing 90% of the memory cost.

A Novel Approach for Potential Human LncRNA-Disease Association Prediction Based on Local Random Walk.

In recent years, lncRNAs (long non-coding RNAs) have been proved to be closely related to many diseases that are seriously harmful to human health. Although researches on clarifying the relationships between lncRNAs and diseases are developing rapidly, associations between the lncRNAs and diseases are still remaining largely unknown. In this manuscript, a novel Local Random Walk based prediction model called LRWHLDA is proposed for inferring potential associations between human lncRNAs and diseases. In LRWHLDA, a new heterogeneous network is established first, which allows that LRWHLDA can be implemented in the case of lacking known lncRNA-disease associations. And then, an improved local random walk method is designed for prediction of novel lncRNA-disease associations, which can help LRWHLDA achieve high prediction accuracy but with low time complexity. Finally, in order to evaluate the prediction performance of LRWHLDA, different frameworks such as LOOCV, 2-folds CV, and 5-folds CV have been implemented, simulation results indicate that LRWHLDA can achieve reliable AUCs of 0.8037, 0.8354, and 0.8556 under the frameworks of 2-fold CV, 5-fold CV, and LOOCV, respectively. Hence, it is easy to know that LRWHLDA contains the potential to be a representative of emerging methods in the field of research on potential lncRNA-disease associations prediction.

Review of the Science behind Oil Spill Fate Models: Are Updates Needed?

AbstractOil spill models play an important role in the oil spill response decision making and contingency planning processes. The current generation of spill models mostly use Lagrangian based particle tracking random walk methods for oil transport processes combined with individual algorithms for oil fate processes (Spaulding, 2017). The fate of near surface oil movement is modeled using algorithms describing oil spreading, evaporation, emulsification, entrainment, dissolution, and biodegradation. These fate processes are applied to oil in the Lagrangian particle tracking elements to alter the physical and chemical properties of the oil, and subsequently the oil behavior.In this paper, we review the major algorithms used in oil spill models and identify the science and physics underpinning them. For each, we evaluated how far the science has advanced since the algorithms were developed to identify those that could be upgraded based on current understanding. We also identified algorithms where future research is needed because the physical and chemical behaviors are not fully understood. These areas include the spreading behavior of surface slicks, surface-slick emulsification, and the physical transport of small oil droplets near the air-water interface.

Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media

In this article, we present new random walk methods to solve flow and transport problems in saturated/unsaturated porous media, including coupled flow and transport processes in soils, heterogeneous systems modeled through random hydraulic conductivity and recharge fields, processes at the field and regional scales. The numerical schemes are based on global random walk algorithms (GRW) which approximate the solution by moving large numbers of computational particles on regular lattices according to specific random walk rules. To cope with the nonlinearity and the degeneracy of the Richards equation and of the coupled system, we implemented the GRW algorithms by employing linearization techniques similar to the L-scheme developed in finite element/volume approaches. The resulting GRW L-schemes converge with the number of iterations and provide numerical solutions that are first-order accurate in time and second-order in space. A remarkable property of the flow and transport GRW solutions is that they are practically free of numerical diffusion. The GRW solvers are validated by comparisons with mixed finite element and finite volume solvers in one- and two-dimensional benchmark problems. They include Richards’ equation fully coupled with the advection-diffusion-reaction equation and capture the transition from unsaturated to saturated flow regimes.

Observation of void formation patterns in SnAg films undergoing electromigration and simulation using random walk methods

With the ever-reducing sizes of electronic devices, the problem of electromigration (EM) has become relevant and requires attention. However, only the EM behavior of Sn–Ag solders within the solder joint structure has been focused on thus far. Therefore, in this study, a thin metallic film composed of Sn–3.5Ag (wt.%) was subjected to a current density of 7.77 × 104 A/cm2 at a temperature of 15 °C to test the ability of existing EM models to predict the nucleation and evolution of voids generated by the resulting atomic migration. A computer simulation was then used to compute the coupled current distribution, thermal distribution, and atomic migration problems. It relied on an original random walk (RW) method, not previously applied to this problem, that is particularly well suited for modelling domains that undergo changes owing to the formation of voids. A comparison of the experimental results and computer simulations proves that the RW method can be applied successfully to this class of problems, but it also shows that imperfections in the film can lead to deviations from predicted patterns.

DFNSC: A particle tracking discrete fracture network simulator considering successive spatial correlation

Discrete fracture network (DFN) models are currently a suitable tool representing the anisotropic and discontinuity features of fractured media. Literatures has shown that it is challenging to obtain accurate DFN considering the quantitative spatial correlation in DFN modeling. This study proposes a particle tracking simulator for DFN modeling considering the successive spatial correlation of fracture distribution (DFNSC) by coupling fracture generating method, groundwater flow and solute transport theory, graph theory, and random walk method. By carrying out simulation calculations of seepage field and particle tracking on four DFNs with different distributions, more detailed conclusions have been obtained: The areas with dense fracture distribution have smaller hydraulic gradient than areas with sparse fracture distribution. The high flow velocity basically appears in the areas where the fractures are relatively sparse. Dense areas of fractures hinder the migration of particles. In essence, dense fractures create a low velocity zone, which makes the transport speed of solute particles slower. In the DFN with uniformly distribution and centralized distribution of fractures, the proportion of penetrating particles reaches 100%, whereas it is only 62% in the DFN with fractures gathered on one side. This study can provide reliable technology for the calculation of the seepage field of fractured media and the study of the pollutant migration process.

Hybrid Embedding via Cross-Layer Random Walks on Multiplex Networks

Node embedding aims to encode network nodes as a set of low-dimensional vectors while preserving certain structural properties of the network. In recent years, extensive studies have been conducted to preserve network communities, i.e., structural proximity of network nodes. However, few of them have focused on preserving the structural equivalence of network nodes, which describes the similarity of structural roles between network nodes. In this paper, we focus on a hybrid network embedding problem of how to flexibly and simultaneously preserve both structural proximity and equivalence. Here, we introduce the concept of graphlet degree vector (GDV) to describe structure roles of network nodes, and further measure structural equivalence based on their similarity. Specifically, we capture both structural proximity and equivalence by building a multiplex network, where both unsupervised and semi-supervised cross-layer random walk (CL-Walk) methods are implemented. By carrying out experiments on both synthetic and real-world datasets, we evaluate the performance of the proposed CL-Walk methods for the tasks of node clustering, node classification, and label prediction. The experimental results indicate that the CL-Walk method outperforms several state-of-the-art methods when both structural proximity and structural equivalence are relevant to specific network analytic task.

A Computational Information Criterion for Particle-Tracking with Sparse or Noisy Data

Traditional probabilistic methods for the simulation of advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, e.g., the number of particles, within associated numerical methods. Many times, the gain in accuracy of a highly discretized numerical model is outweighed by its associated computational costs or the noise within the data. We address the question of how many particles are needed in a simulation to best approximate and estimate parameters in one-dimensional advective-diffusive transport. To do so, we use the well-known Akaike Information Criterion (AIC) and a recently-developed correction called the Computational Information Criterion (COMIC) to guide the model selection process. Random-walk and mass-transfer particle tracking methods are employed to solve the model equations at various levels of discretization. Numerical results demonstrate that the COMIC provides an optimal number of particles that can describe a more efficient model in terms of parameter estimation and model prediction compared to the model selected by the AIC even when the data is sparse or noisy, the sampling volume is not uniform throughout the physical domain, or the error distribution of the data is non-IID Gaussian.

Serum lncRNAs in early pregnancy as potential biomarkers for the prediction of pregnancy-induced hypertension, including preeclampsia

Long noncoding RNAs (lncRNAs) are key mediators of biological regulation with diagnostic value as disease biomarkers. We explored serum lncRNA levels in early pregnancy as potential biomarkers of pregnancy-induced hypertension (PIH), including gestational hypertension (GH) and preeclampsia (PE). We performed a two-phase nested case-control study in pregnant women before 20 weeks’ gestation (before clinical diagnosis). The screening phase assessed lncRNA expression profiles with a human lncRNA microarray in 5 pairs of serum samples (5 PE patients and 5 matched controls). The second phase validated levels of 8 candidate lncRNAs selected via the random walk method by quantitative real-time polymerase chain reaction (qRT-PCR). Serum levels of the 8 lncRNAs were markedly increased in women with PIH compared with matched normotensive pregnant (NP) women (p < 0.001), consistent with the microarray results. In addition, 7 candidate lncRNAs were correlated with PIH severity. Logistic regression analysis revealed that serum levels of ENST00000527727 (odds ratio [OR], 1.113; 95% confidence interval [CI], 1.024–1.209; p = 0.0113) and ENST00000415029 (OR, 1.126; 95% CI, 1.000–1.267; p = 0.0496) were associated with adverse pregnancy outcomes, such as fetal growth restriction (FGR) and placenta accreta of PIH. Nine pathways associated with the candidate lncRNAs had confirmed associations with PIH.

Outlier detection based on weighted neighbourhood information network for mixed-valued datasets

Outlier detection is of great importance in industry as unexpected errors or faults, abnormal behaviours or phenomena, etc. can occur due to a variety of human, system, and environmental reasons. To identify and analyse these rare items, events or observations can find either anomalies or novelties and, as a result, can help avoid potential unexpected consequences or improve industrial system performance. The operating data collected from industrial systems in the Industry 4.0 era are characterized as multi-attribute (e.g., both numerical and categorical) compared to previous studies. Therefore, a new outlier detection method for mixed-valued datasets based on the weighted network model is proposed in this paper. Concretely, a weighted neighbourhood information network (WNIN) is constructed by considering the neighbourhood relations and similarities among objects to represent a dataset with mixed-valued attributes (DMA). A tailored Markov random walk method is employed to detect outlier on the predefined network model. After reaching the equilibrium, the inlier score is defined according to the out-degree of nodes in the WNIN to represent the inlier degree of objects. Experiments on two real datasets and a case study illustrate the effectiveness and adaptability of the proposed method.

Analysis of the Results of Applying the Bee Colony Method in the Problem of Coloring General Graphs

Purpose of research. We have discovered a wide range of problems that are important in practice and which can be reduced in polynomial time to discrete combinatorial optimization problems, many of which can be solved using graph theory. One of these tasks is finding the chromatic number of a graph and its corresponding coloring. Taking into account the fact that the combinatorial problem of finding the chromatic number of a graph belongs to the complexity class and does not allow obtaining an optimal solution in a rational time for problems of practically important dimension, the search for a suitable heuristic method that allows obtaining high-quality solutions with low costs required for computation is demanded and relevant. The aim of the study is to analyze the results of using the bee colony method in the task at hand. The tasks of this research are: description of algorithmic techniques in a formalized form, which make it possible to apply the bee colony method in the problem to be solved, making modifications to the bee colony method that increase the efficiency of the method, namely the quality of the resulting final colorings, as well as the determination of factors affecting the quality and the time spent in finding solutions. Methods. To conduct research in the selected area, computational experiments were organized based on the use of heuristic methods in the problem under consideration. Meta-optimization of the tuning parameters of the methods and determination of their convergence rate was carried out, as well as a comparison of the quality and time of obtaining solutions. Results. As a result of the study, the convergence rate of the method was found to be higher than that of the random walk method; the dependence of the quality of the resulting final colorings on the graph size N and density d was found. It was found that the chosen method is faster than the method of weighted random enumeration with the variation of vertices according to the minimum of admissible colors on »67% , which currently generates solutions with the lowest chromatic number, while losing quality to it on »7% . A higher rate of convergence was noticed when compared with the method of random walks, the principle of which is the same as that of foraging bees. Conclusion. It was found that the bee colony method finds colorings with the same average chromatic number in fewer iterations than the random walk method, i.e. it has a higher convergence rate, while remaining significantly fast relative to the method of random search with a variation of vertices to reduce the allowed colors.

Diffusion effect on passive solute transport inside an infinite two-dimensional array of vortices

The transport process of solute in a two-dimensional liquid flow is studied. The infinite plane is “covered” by square cells with periodic conditions at its boundaries. The flow is provided by a periodic external force. If the amplitude of the external force reaches a certain critical value, then the flow in each cell contains a pair of vortices. The analysis of the transport of a passive solute in such a flow is investigated in terms of a special flow. In the framework of this approach the transport process is described by mapping functions that determine the coordinates of the particle at the end of the unit cell and the time of passage of the cell as a function of the coordinates at the entrance to the cell. These functions are obtained numerically by the random walk method taking diffusion into account. Using the special flow approach the distribution of an initially uniform distributed ensemble of passive particles with time is calculated for the passage of a long array of the unit cells. It is shown that for tiny values of diffusivity the transport slowing down some particles regarding the ensemble is observed. The speed-up of some particles regarding the ensemble is observed for moderate values of diffusivity and for high diffusivity we obtain the standard diffusion.

Random Walk와 Simplex 방법을 이용한 V-shape 매입형 영구자석 동기전동기의 코깅토크 저감 최적 설계

This paper presents random walk and simplex optimization algorithm on an optimal design of V-shape interior permanent synchronous motor (V-shape IPMSM). The IPMSM can easily generates a cogging torque because of change in magnetic circuit by interaction between permanent magnets and stator slots. Therefore minimization of the cogging torque, which generates vibration and noise, is an important factor in design of IPMSM. This paper proposes the optimal shape design of V-shape IPMSM using random walk and simplex method for minimizing cogging torque.

An improved antlion optimizer with dynamic random walk and dynamic opposite learning

Antlion optimization algorithm (ALO) has been one of the most popular meta-heuristic algorithms to solve engineering optimization problems with a fast convergence speed and steady performance. However, the long runtime and the weak capability of local optima avoidance prevent ALO from being applied in real-time and complex engineering problems. This paper proposes a dynamic random walk and dynamic opposite learning improved ALO (DALO), where a new random walk method named dynamic random walk (DRW) is presented, and a dynamic opposite learning strategy (DOL) is embedded in ALO. The DOL-inspired DRW method has a better exploration capability for converging to the best optimum due to the dynamic changing search space and is more efficient in computation due to the low complexity. The DOL strategy contributes to two steps of the ALO algorithm, i.e. DOL population initialization and DOL generation jumping, for further enhancing the algorithm to avoid premature convergence. The improvements of DRW and DOL were verified by testing benchmark problems from ALO paper, CEC 2014 and CEC 2017, and an optimal weight factor of DRW was selected by conducting a sensitivity analysis. The results, confirmed by Wilcoxon rank-sum test and Friedman test, show that DRW helps ALO greatly reduce the runtime with an excellent performance in finding the best optimum, and the DALO algorithm with the further enhancement enable by DOL is significantly superior to ALO. In addition, the results of the test on three representative engineering problems show that the ability of DALO to solve real-world problems is enhanced.

Effect of random walk methods on searching efficiency in swarm robots for area exploration

The objective of area exploration is to traverse the area effectively and random walk methods are the most commonly used searching strategy for swarm robots. Existing research mainly compares the effectiveness of various random walk methods through experimental verification, which has relatively large limitations. In order to make the application of the random walk methods more convenient, this paper quantitatively analyzes the searching efficiency (SE) of random walk methods. Firstly, the formula of the mean square displacement (MSD) of the robot position is given, and it is shown that the mean and the variance of the random step length are the factors that affect the SE. In addition, in order to produce the suitable step length, a truncated random walk method is constructed to make the generated step lengths follow a given distribution and the step lengths are within a specified range, thereby improving the SE. Thirdly, the correlations between the step length threshold (SLT), the area of the region, and the number of robots are provided based on MSD and truncated random walk method. When the area of region and the number of robots are fixed, there exists a SLT. When the expectation of the step length is greater than SLT, the swarm robots can achieve the highest SE. The area exploration task of swarm robots are carried out in simulation experiments and the coverage ratio is used to evaluate the SE of each random walk method. The experimental results show that when the area and the number of robots are given, there exist an optimal step length, which can enable the robots to achieve the optimal search.

A continuous time random walk method to predict dissolution in porous media based on validation of experimental NMR data

We develop a reactive transport model for dissolution of porous materials using a Continuous Time Random Walk (CTRW) formulation with first-order kinetics. Our model is validated with a dataset for a Ketton carbonate rock sample undergoing dissolution on injection of an acid, monitored using Nuclear Magnetic Resonance (NMR). The experimental data includes the 3D porosity distribution at the beginning and end of the experiment, 1D porosity profiles along the direction of flow during dissolution, as well as the molecular fluid displacement probability distributions (propagators). With the calibration of only a single parameter, we successfully predict the porosity changes and the propagators as a signature of flow heterogeneity evolution in the dissolution experiment.We also demonstrate that heterogeneity in the flow field leads to an effective reaction rate, limited by transport of reactants, that is almost three orders of magnitude lower than measured under batch reaction conditions. The effective reaction rate predicted by the model is in good agreement with the experimentally measured rate. Furthermore, as dissolution proceeds, the formation of channels in the rock focused the flow in a few fast-flowing regions. The predicted dissolution patterns are similar to those observed experimentally. This study establishes a workflow to calibrate and validate the CTRW reactive transport model with NMR experiments.

Multilevel thresholding using an improved cuckoo search algorithm for image segmentation

Multilevel thresholding image segmentation is an important technique, which has attracted much attention in recent years. The conventional exhaustive search method for image segmentation is efficient for bilevel thresholding. However, they are time expensive when dealing with multilevel thresholding image segmentation. To better tackle this problem, an improved cuckoo search algorithm (ICS) is proposed to search for the optimal multilevel thresholding in this paper, and Otsu is considered as its objective function. In the ICS, two modifications are used to improve the standard cuckoo search algorithm. First, a parameter adaptation strategy is utilized to improve exploration performance. Second, a dynamic weighted random-walk method is adopted to enhance the local search efficiency. A total of six benchmark test images are used to perform the experiments, and seven state-of-the-art metaheuristic algorithms are introduced to compare with the ICS. A series of measure indexes such as objective function value and standard deviation, PSNR, FSIM, and SSIM as well as the Wilcoxon rank sum and convergence performance are performed in the experiments; the experimental results show that the proposed algorithm is superior to other seven well-known heuristic algorithms.

Gas Steady-state Diffusion in Fractal Porous Media

Gas diffusion in fractal pores does not follow the classic Fick’s and Knudsen’s laws, so more research on gas diffusion in fractal porous media is needed. Fractal pore models are generated using the random walk method. The gas diffusion governing equations for the fractal pores are derived from the classic kineti theory of gases. The gas diffusion model is used to study the gas diffusion in fractal porous meida and to determine steady-state diffusion coefficient formulas. The results show that the diffusion coefficient is proportional to the mean proe diameter, porosity, and the exponetial function of the fractal dimension in the Knudsen diffusion regime. The diffusion coefficient is not only related to the three pore parameters but is also related to the molecular mean free path in the configurational diffusion regime.

Multilayer Network Representation Learning Method Based on Random Walk of Multiple Information

Network representation learning aims to map nodes in the network into low-dimensional dense vectors, which can be widely used to solve the network analysis tasks. Existing methods mainly focus on single-layer homogeneous networks. However, many real-world networks consist of multiple types of nodes and edges, which are called multilayer networks. The problem of how to capture node information and use multi-type relational information is a major challenge of multilayer network representation learning. To address this problem, we propose a method of random walk of multiple information, called IFMNE, to efficiently preserve and learn node information and multi-type relational information into a unified space. This method combines node structure information with network topology information to obtain the node random walk sequence, and trains the node walk sequence on the neural network model. Experimental results are performed on five real multilayer networks, and the embedding vectors were evaluated by link prediction task. The accuracy was significantly improved on the basis of low time complexity compared with the baseline methods.

Analytical Comparison of Resource Search Algorithms in Non-DHT Mobile Peer-to-Peer Networks

One of the key challenges in ad-hoc networks is the resource discovery problem. How efficiently & quickly the queried resource/object can be resolved in such a highly dynamic self-evolving network is the underlying question? Broadcasting is a basic technique in the Mobile Ad-hoc Networks (MANETs), and it refers to sending a packet from one node to every other node within the transmission range. Flooding is a type of broadcast where the received packet is retransmitted once by every node. The naive flooding technique floods the network with query messages, while the random walk scheme operates by contacting subsets of each node’s neighbors at every step, thereby restricting the search space. Many earlier works have mainly focused on the simulation-based analysis of flooding technique, and its variants, in a wired network scenario. Although, there have been some empirical studies in peer-to-peer (P2P) networks, the analytical results are still lacking, especially in the context of mobile P2P networks. In this article, we mathematically model different widely used existing search techniques, and compare with the proposed improved random walk method, a simple lightweight approach suitable for the non-DHT architecture. We provide analytical expressions to measure the performance of the different flooding-based search techniques, and our proposed technique. We analytically derive 3 relevant key performance measures, i.e., the avg. number of steps needed to find a resource, the probability of locating a resource, and the avg. number of messages generated during the entire search process.