Walk Algorithm Research Articles

Joint L2,p-norm and random walk graph constrained PCA for single-cell RNA-seq data

The development and widespread utilization of high-throughput sequencing technologies in biology has fueled the rapid growth of single-cell RNA sequencing (scRNA-seq) data over the past decade. The development of scRNA-seq technology has significantly expanded researchers’ understanding of cellular heterogeneity. Accurate cell type identification is the prerequisite for any research on heterogeneous cell populations. However, due to the high noise and high dimensionality of scRNA-seq data, improving the effectiveness of cell type identification remains a challenge. As an effective dimensionality reduction method, Principal Component Analysis (PCA) is an essential tool for visualizing high-dimensional scRNA-seq data and identifying cell subpopulations. However, traditional PCA has some defects when used in mining the nonlinear manifold structure of the data and usually suffers from over-density of principal components (PCs). Therefore, we present a novel method in this paper called joint -norm and random walk graph constrained PCA (RWPPCA). RWPPCA aims to retain the data’s local information in the process of mapping high-dimensional data to low-dimensional space, to more accurately obtain sparse principal components and to then identify cell types more precisely. Specifically, RWPPCA combines the random walk (RW) algorithm with graph regularization to more accurately determine the local geometric relationships between data points. Moreover, to mitigate the adverse effects of dense PCs, the -norm is introduced to make the PCs sparser, thus increasing their interpretability. Then, we evaluate the effectiveness of RWPPCA on simulated data and scRNA-seq data. The results show that RWPPCA performs well in cell type identification and outperforms other comparison methods.

Intelligent search strategy applied in heat exchanger network synthesis

Heat exchanger network (HEN) synthesis has been acknowledged as an effective design technique to achieve significant energy savings in a wide range of industrial and engineering applications. In this regard, heuristic methods have been demonstrated as a powerful means to solve the HEN synthesis problem. However, because the new structure is generated at random, the structures that can effectively make the objective cost descend are limited in comparison to the entire evolutionary process. In addition, such heuristic methods are usually time-consuming processes. In this work, an intelligent search strategy is proposed to increase the efficiency of heuristic methods. Based on the defined objective cost, this strategy could rapidly and effectively find a route that could satisfy cost minimization. It can also achieve further evolution aimed at highlighting potential structures. The proposed search strategy can increase the ability of searching and reduce time consumption. Considering the random walk algorithm with compulsive evolution as an example, the principle and impact of intelligent search were clearly demonstrated. Furthermore, applying the intelligent search strategy to the random walk algorithm with compulsive evolution to some cases in the existing literature was found to yield better solutions.

Enhanced Hamiltonian Monte Carlo simulations using Hamiltonian neural networks

AbstractMarkov Chain Monte Carlo simulations form an essential tool for exploring high‐dimensional target distributions. Metropolis developed a fundamental random walk algorithm which was improved by Hastings later. The result is known as the Metropolis‐Hastings algorithm, which enables the exploration of multi‐dimensional distributions. The main drawbacks of this algorithm are its high auto‐correlation and slow exploration of the target distribution space. In order to increase efficiency, researchers have proposed various modifications to this algorithm. In particular, the Hamiltonian Monte Carlo simulation enhances the efficient exploration of the target probability density. The algorithm uses mechanisms inspired by Hamiltonian dynamics to propose a new sample for the target distribution. For reliability analysis, the incorporation of subset simulation and Hamiltonian Monte Carlo methods has shown promising results. However, using the Hamiltonian Monte Carlo method to sample is computationally expensive, especially when dealing with high‐dimensional problems and performing several steps to propose a new state. In this contribution, we show the general applicability of Hamiltonian neural networks to speed up the proposal of new samples within the Hamiltonian Monte Carlo method.

그래프 트랜스포머 기반 농가 사과 품질 이미지의 그래프 표현 학습 연구

Recently, a convolutional neural network (CNN) based system is being developed to overcome the limitations of human resources in the apple quality classification of farmhouse. However, since convolutional neural networks receive only images of the same size, preprocessing such as sampling may be required, and in the case of oversampling, information loss of the original image such as image quality degradation and blurring occurs. In this paper, in order to minimize the above problem, to generate a image patch based graph of an original image and propose a random walk-based positional encoding method to apply the graph transformer model. The above method continuously learns the position embedding information of patches which don`t have a positional information based on the random walk algorithm, and finds the optimal graph structure by aggregating useful node information through the self-attention technique of graph transformer model. Therefore, it is robust and shows good performance even in a new graph structure of random node order and an arbitrary graph structure according to the location of an object in an image. As a result, when experimented with 5 apple quality datasets, the learning accuracy was higher than other GNN models by a minimum of 1.3% to a maximum of 4.7%, and the number of parameters was 3.59M, which was about 15% less than the 23.52M of the ResNet18 model. Therefore, it shows fast reasoning speed according to the reduction of the amount of computation and proves the effect.

Classification of Individual Tree Species Using UAV LiDAR Based on Transformer

Tree species surveys are crucial in forest resource management and can provide references for forest protection policymakers. Traditional tree species surveys in the field are labor-intensive and time-consuming. In contrast, airborne LiDAR technology is highly capable of penetrating forest vegetation; it can be used to quickly obtain three-dimensional information regarding vegetation over large areas with a high level of precision, and it is widely used in the field of forestry. At this stage, most studies related to individual tree species classification focus on traditional machine learning, which often requires the combination of external information such as hyperspectral cameras and has difficulty in selecting features manually. In our research, we directly processed the point cloud from a UAV LiDAR system without the need to voxelize or grid the point cloud. Considering that relationships between disorder points can be effectively extracted using Transformer, we explored the potential of a 3D deep learning algorithm based on Transformer in the field of individual tree species classification. We used the UAV LiDAR data obtained in the experimental forest farm of Northeast Forestry University as the research object, and first, the data were preprocessed by being denoised and ground filtered. We used an improved random walk algorithm for individual tree segmentation and made our own data sets. Six different 3D deep learning neural networks and random forest algorithms were trained and tested to classify the point clouds of three tree species. The results show that the overall classification accuracy of PCT based on Transformer reached up to 88.3%, the kappa coefficient reached up to 0.82, and the optimal point density was 4096, which was slightly higher than that of the other deep learning algorithms we analyzed. In contrast, the overall accuracy of the random forest algorithm was only 63.3%. These results show that compared with the commonly used machine learning algorithms and a few algorithms based on multi-layer perceptron, Transformer-based networks provide higher accuracy, which means they can provide a theoretical basis and technical support for future research in the field of forest resource supervision based on UAV remote sensing.

A heuristic approach to design a cost-effective and low-CO2 emission synthesis in a heat exchanger network with crude oil distillation units

This paper presents a tradeoff grassroots design of cost-effective and low-CO2 emissions heat exchanger networks for crude oil distillation units (CDUs) to address high energy consumption in CDUs. To reduce the impact of the objective's magnitude on the optimization searching direction, a normalization process handling the objectives to the dimensionless indexes to assess the performance of CDU is presented. An originally designed random walk algorithm with compulsive evolution (RWCE) and a special superstructure nodes-based non-structural model (NNM) is adopted for the multi-objective optimization problem. The comparison analysis shows that the proposed model and the heuristic algorithm are robust in solving the global optimization problem. In addition, aiming to investigate the evolution mode of utilities in RWCE, an active evolution strategy of utilities (RWCE-AU) is proposed to promote structural evolution by altering the heat loads of utilities by a certain probability. Finally, several industrial CDU cases are optimized by RWCE and RWCE-AU in this work. The continuous improvement solutions have highlighted that the RWCE could yield a better optimal total annual cost (TAC) compared to the reported initial case. Moreover, the RWCE-AU enhances the searching ability of RWCE and provides a better tradeoff between the economic benefits and the environmental impacts.

Coupling Quantum Random Walks with Long- and Short-Term Memory for High Pixel Image Encryption Schemes.

This paper proposes an encryption scheme for high pixel density images. Based on the application of the quantum random walk algorithm, the long short-term memory (LSTM) can effectively solve the problem of low efficiency of the quantum random walk algorithm in generating large-scale pseudorandom matrices, and further improve the statistical properties of the pseudorandom matrices required for encryption. The LSTM is then divided into columns and fed into the LSTM in order for training. Due to the randomness of the input matrix, the LSTM cannot be trained effectively, so the output matrix is predicted to be highly random. The LSTM prediction matrix of the same size as the key matrix is generated based on the pixel density of the image to be encrypted, which can effectively complete the encryption of the image. In the statistical performance test, the proposed encryption scheme achieves an average information entropy of 7.9992, an average number of pixels changed rate (NPCR) of 99.6231%, an average uniform average change intensity (UACI) of 33.6029%, and an average correlation of 0.0032. Finally, various noise simulation tests are also conducted to verify its robustness in real-world applications where common noise and attack interference are encountered.

A scheduling algorithm for heterogeneous computing systems by edge cover queue

In heterogeneous computing systems, excellent task scheduling algorithms can shorten the task completion time and improve system parallelism. With the large-scale deployment of edge computing, the task scheduling algorithm in heterogeneous edge computing servers has become a critical factor in improving the overall system performance. This paper proposes a new task scheduling algorithm called the edge cover scheduling algorithm (ECSA), which schedules tasks based on the edge cover queue of the directed acyclic graph (DAG) for heterogeneous computing systems. Based on the estimation of distribution algorithm (EDA) and the graph random walk algorithm, the ECSA generates an edge cover queue from DAG. Then, the ECSA uses the heuristics greedy method with low time and computational complexity to allocate the edge cover queue to processors. Theoretical analysis and simulation results on random DAGs and real-world DAGs show that the ECSA can achieve better scheduling results in terms of makespan, the schedule length ratio (SLR), efficiency, and frequency of best results with low time and computational complexity.

Solute transport in fractured porous media: Implementation of the time domain random walk algorithm for different injection boundaries

In this work, three variant Time Domain Random Walk (TDRW) algorithms were developed for the problem of solute transport in a single fracture-matrix system, where an arbitrary inlet boundary condition can be applied. One approach performs an additional evaluation of integral in terms of injection boundary and the solution to a Dirac delta case. One method makes use of two functions, dependent on specific boundary conditions, to estimate the particle arrival time. The other additionally introduces the concept of solute injection time, resulting from the injection boundary, into the calculation of particle arrival time. To validate the developed variant algorithms, two benchmark cases are considered with respect to a general Dirichlet injection mode and a Robin injection boundary, respectively. The results from three approaches all make a good agreement with those of inverse Laplace transform method. However, the Monte Carlo nature of the TDRW algorithm implies that the accuracy of the computational result is highly dependent on the number of particles applied in the simulation.

Lateral diffusion in the presence of obstacles, reexamined.

In transient anomalous subdiffusion, diffusion is anomalous at short times, crossing over to normal at long times. This behavior is well-known for obstructed diffusion with obstacle concentrations below the percolation threshold, and is characterized by the anomalous exponent alpha, the limiting diffusion coefficient D(inf), and the crossover time t(cross), all functions of the obstacle concentration. In my work [Biophys J 66 (1994) 394], the anomalous and normal regions are chosen by eye in a log-log plot of D(t) = RSQ/t versus time t. Straight lines are found for each region by a least-squares fit, and t(cross) is defined as the intersection of these lines. Ellery et al. [J Chem Phys 144 (2016) 171104] criticized this approach and presented a method based on eigenvalues of the transition matrix. Their crossover times were significantly different from mine, and Ellery et al. claimed that their method provides a simpler and more objective evaluation of t(cross). I examine an alternative interpretation, that their method is an elegant measurement of a different characteristic time of the random walk. To test this, I compare results of the eigenvalue method with results of standard Monte Carlo calculations for various characteristic times, including distinct sites visited as a function of time, the number of visits per site (yielding the cover time and the blanket time), and the first passage time from the center of the lattice to the boundary of the region without periodic boundary conditions. The calculations are done for random walks on a square lattice with random obstacles and periodic boundary conditions. Importantly, I examine the dependence of the results on system size, and include percolation analysis so that higher obstacle concentrations can be included in some calculations. The so-called lazy random walk algorithm is also examined.

Development of a New Robust Stable Walking Algorithm for a Humanoid Robot Using Deep Reinforcement Learning with Multi-Sensor Data Fusion

The difficult task of creating reliable mobility for humanoid robots has been studied for decades. Even though several different walking strategies have been put forth and walking performance has substantially increased, stability still needs to catch up to expectations. Applications for Reinforcement Learning (RL) techniques are constrained by low convergence and ineffective training. This paper develops a new robust and efficient framework based on the Robotis-OP2 humanoid robot combined with a typical trajectory-generating controller and Deep Reinforcement Learning (DRL) to overcome these limitations. This framework consists of optimizing the walking trajectory parameters and posture balancing system. Multi-sensors of the robot are used for parameter optimization. Walking parameters are optimized using the Dueling Double Deep Q Network (D3QN), one of the DRL algorithms, in the Webots simulator. The hip strategy is adopted for the posture balancing system. Experimental studies are carried out in both simulation and real environments with the proposed framework and Robotis-OP2’s walking algorithm. Experimental results show that the robot performs more stable walking with the proposed framework than Robotis-OP2’s walking algorithm. It is thought that the proposed framework will be beneficial for researchers studying in the field of humanoid robot locomotion.

Toward Full-Immersive Multiuser Virtual Reality With Redirected Walking

We are witnessing a surge in the popularity and mass-availability of Virtual Reality (VR) technology. Toward enhancing its maturity, current research is focusing on achieving continuous full immersiveness of the VR users during their experiences in Virtual Environments (VEs), as well as on enabling multiuser experiences. In many cases, achieving the full immersiveness requires enabling the users’ perception of walking naturally in unbound VEs. Redirected Walking (RDW) algorithms provide a solution to this problem by exploiting the limitations of the human spatial perception. In other words, the RDW algorithms are envisioned to unnoticeably steer the VR users for constraining them within a certain tracking space. Regardless of notable research efforts targeting RDW, there are still not many experimental evaluations of the performance of RDW algorithms, especially in multiuser settings and utilizing contemporary Head-Mounted Devices (HMDs). Toward addressing this issue, we have developed a modular framework that enables straightforward experimentation with single and multiuser RDW in different tracking spaces and for varying VEs. The capabilities of the developed framework were demonstrated by carrying out an extensive experimentation study to capture the performance and noticeability of a contemporary RDW algorithm for a varying number of users in different tracking spaces and VEs. The lessons learned during the study have been conceptualized in a form of a set of RDW design enhancements that can be generically applied to existing RDW algorithms. We show that the proposed enhancements significantly increase the overall performance of RDW and decrease the noticeability of RDW-supported experiences in VEs.

Optimization of tips selection on the IOTA tangle for securing blockchain-based IoT transactions

Data integrity and security protection are needed in the Internet of Things. IOTA technology with a Directed Acyclic Graph (DAG) structure is a solution to realize secure and scalable data transactions. Recent research IOTA is still faced with the issue of being vulnerable to splitting attacks and left-behind transactions. The splitting attack causes the network to confirm conflict transactions. Then, left-behind transactions cause the network to generate transactions that will not be confirmed. The selection tip weighted random walk (WRW) algorithm uses the Markov Chain Monte Carlo (MCMC) to overcome these two issues by applying the appropriate bias parameter (α). However, when the α is too large, it will produce a lot of left-behind transactions. Determining the optimal value of α is still an important research topic today. An E-IOTA study that gives several α values statically with random selection but can still produce more left-behind transactions than pure WRW. This paper proposes an optimization of the tip selection algorithm (DA-IOTA) to determine the optimal alpha (α) using an approach to dynamically determine each WRW step. The experimental results show that DA-IOTA produces fewer left-behind transactions than MCMC (WRW) and E-IOTA which use α parameters statically.

Risk Identification of Critical Infrastructures Considering Dual Interdependency: A Complex Network Approach

Critical Infrastructures (CIs) are exposed to various risks, which hinder their successful operation and induce great losses. Due to the interdependency between risks and that between CIs, the identification of the most prominent risks becomes complex and challenging. However, existing studies rarely considered the dual interdependency of risks and CIs. This study proposes a double-layer network for multiple interdependent risks and CIs. The Design Structure Matrix (DSM) and Restart Random Walk (RRW) algorithm are combined to determine the impact of risks on CIs by incorporating the strength of dual interdependency. The LeaderRank algorithm is then used to rank these risk factors and an illustrative example is given to validate the model. The proposed model and algorithms can systematically quantify complex interdependencies embedded in the operation of CIs susceptible to multiple risks, and provide decision-makers with evidence to prioritize risks.

Group Recommendation Based on Heterogeneous Graph Algorithm for EBSNs

Emerging event-based social networks (EBSNs), such as Meetup, have grown rapidly and become popular in recent years. EBSNs differ from conventional social networks such as Facebook in that they not only involve online social interactions but also include offline, in-person interactions. Thus, EBSNs are naturally heterogeneous and possess more valuable social information. Group recommendations in EBSNs are typically only based on the interest information filled in by users, or friends’ group information. Both these methods may not well reflect users’ real intentions. In this study, we propose a recommender system to predict groups that may interest EBSN users, based on a novel heterogeneous augmented graph method and a random walk with restart algorithm. In this approach, online and offline social interactions are combined into a single heterogeneous augmented graph capturing all useful relationships, including user-to-group relationships, user-to-event relationships, user-to-attribute relationships, and group-to-attribute relationships, and among others. To our knowledge, this work is the first attempt to apply a random walk algorithm into group recommendation in EBSNs. Extensive experiments on Meetup datasets demonstrate that our proposed recommender system achieves better results in terms of recall, precision, F-Measure and MRR metrics in comparison with the other four commonly used algorithms, including random recommendation, interest-based recommendation, interest- and neighborhood-based recommendation, and Katz Centrality. The significant recommendation performance of our approach may further enhance user satisfaction of EBSNs. Moreover, our approach to group recommendation may also be extended to other recommendation-related applications such as event or friend recommendation.

Offline EEG hyper-scanning using anonymous walk embeddings in tacit coordination games.

In this paper we present a method to examine the synchrony between brains without the need to carry out simultaneous recordings of EEG signals from two people which is the essence of hyper-scanning studies. We used anonymous random walks to spatially encode the entire graph structure without relying on data at the level of individual nodes. Anonymous random walks enabled us to encapsulate the structure of a graph regardless of the specific node labels. That is, random walks that visited different nodes in the same sequence resulted in the same anonymous walk encoding. We have analyzed the EEG data offline and matched each possible pair of players from the entire pool of players that performed a series of tacit coordination games. Specifically, we compared between two network patterns associated with each possible pair of players. By using classification performed on the spatial distance between each pair of individual brain patterns, analyzed by the random walk algorithm, we tried to predict whether each possible pair of players has managed to converge on the same solution in each tacit coordination game. Specifically, the distance between a pair of vector embeddings, each associated with one of the players, was used as input for a classification model for the purpose of predicting whether the two corresponding players have managed to achieve successful coordination. Our model reached a classification accuracy of ~85%.

Evolutionary characteristics of microstructural hydration and chloride diffusion in UHPC

This paper presents the evolutionary characteristics of microstructural hydration and chloride migration in ultra-high performance concrete (UHPC). The physicochemical interactions of constituents are simulated in conjunction with a random walk algorithm. When the hydration of cementitious pastes proceeds, accompanied by the evolution of hardening, the quantity of silicates becomes larger alongside irregularly dispersed byproducts (calcium silica hydrate, C-S-H, and calcium hydroxide, CH). Owing to the formation of pozzolanic C-S-H consuming CH, the silicate reactions of UHPC are less than the reactions of the ordinary concrete. The implications of tricalcium silicate (C3S) are notable for the early-age strength gain of UHPC in comparison with its dicalcium silicate (C2S) counterpart. The matured pozzolanic reactions and invariable packing density of UHPC are responsible for preserving the proportion of silica fume in the mixtures. Relative to UHPC, the ordinary concrete releases more heat caused by exothermic reactions that are a function of saturated pores and silica fume with the contribution of C3S. Regarding corrosion durability, the chloride contents of a bridge deck cast with the ordinary concrete exceed the content of a deck with UHPC. As part of technology transfer, the notion of performance-based design applies and practice guidelines are suggested.

Toward an Understanding of Long-tailed Runtimes of SLS Algorithms

The satisfiability problem (SAT) is one of the most famous problems in computer science. Traditionally, its NP-completeness has been used to argue that SAT is intractable. However, there have been tremendous practical advances in recent years that allow modern SAT solvers to solve instances with millions of variables and clauses. A particularly successful paradigm in this context is stochastic local search (SLS). In most cases, there are different ways of formulating the underlying SAT problem. While it is known that the precise formulation of the problem has a significant impact on the runtime of solvers, finding a helpful formulation is generally non-trivial. The recently introduced GapSAT solver [Lorenz and Wörz 2020] demonstrated a successful way to improve the performance of an SLS solver on average by learning additional information, which logically entails from the original problem. Still, there were also cases in which the performance slightly deteriorated. This justifies in-depth investigations into how learning logical implications affects runtimes for SLS algorithms. In this work, we propose a method for generating logically equivalent problem formulations, generalizing the ideas of GapSAT . This method allows a rigorous mathematical study of the effect on the runtime of SLS SAT solvers. Initially, we conduct empirical investigations. If the modification process is treated as random, then Johnson SB distributions provide a perfect characterization of the hardness. Since the observed Johnson SB distributions approach lognormal distributions, our analysis also suggests that the hardness is long-tailed. As a second contribution, we theoretically prove that restarts are useful for long-tailed distributions. This implies that incorporating additional restarts can further refine all algorithms employing above mentioned modification technique. Since the empirical studies compellingly suggest that the runtime distributions follow Johnson SB distributions, we also investigate this property on a theoretical basis. We succeed in proving that the runtimes for the special case of Schöning’s random walk algorithm [Schöning 2002] are approximately Johnson SB distributed.

On applying the lackadaisical quantum walk algorithm to search for multiple solutions on grids

Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than their classical counterparts. A quantum-walk-based algorithm standing out in the literature is the lackadaisical quantum walk. The lackadaisical quantum walk is an algorithm developed to search graph structures whose vertices have a self-loop of weight l. This paper addresses several issues related to applying the lackadaisical quantum walk to search for multiple solutions on grids successfully. Firstly, we show that only one of the two stopping conditions found in the literature is suitable for simulations. In the most discrepant case shown here, a stopping condition is prematurely satisfied at the step T=288 with a success probability Pr=0.593276, while the suitable condition captures the actual amplification that occurred until T=409 with Pr=0.878178. We also demonstrate that the final success probability depends on both the space density of solutions and the relative distance between solutions. For instance, we show here that decreases in the density of solutions can even take a success probability of 0.849178 to 0.961896. In contrast, increases in the relative distances can even take a success probability of 0.871665 to 0.940301. Furthermore, this work generalizes the lackadaisical quantum walk to search for multiple solutions on grids of arbitrary dimensions. In addition, we propose an optimal adjustment of the self-loop weight l for such d-dimensional grids. It turns out other fits of l found in the literature are particular cases. Our experiments demonstrate that successful searches for multiple solutions with higher than two dimensions are possible by achieving success probabilities such as 0.999979, with the value of l proposed here, where it would be 0.637346, with the value of l proposed in previous works. Finally, we observe a two-to-one relation between the steps of the lackadaisical quantum walk and Grover’s algorithm, which requires modifications in the stopping condition. That modified stopping condition can escape intermediary fluctuations that would produce premature stops at T=6 with Pr=0.000878 where the system can evolve until T=354 with Pr=0.99999, as an example that we show here. In conclusion, this work deals with practical issues one should consider when applying the lackadaisical quantum walk, besides expanding the technique to a broader range of search problems.

A quantitative evaluation of lung nodule spiculation based on image enhancement

Lung cancer manifests itself as lung nodules at an early stage. Segmentation of lung nodules and quantitative evaluation of spiculation can assist physicians in distinguishing benign and malignant lung nodules. The identification of malignant nodules for early diagnosis and treatment can improve the survival rate of patients. In this paper, a quantitative evaluation method of lung nodule spiculation is proposed based on image enhancement. The proposed method combines super-resolution reconstruction-based image enhancement techniques with lung nodule segmentation algorithms to improve the accuracy of segmentation and to quantify the degree of distinctness of the spiculation of lung nodule, which can provide a reliable basis for computer-aided diagnosis and treatment of lung nodules. First, the method uses Laplacian pyramid image restoration technique and Gaussian differential scale-invariant feature to enhance the details and edge information of lung CT images. Then the improved Random Walk algorithm is used to segment the enhanced lung images and extract lung nodules. Finally, the spiculation index, which measures the spiculation of breast nodules, is used to quantify the spiculation of nodules. The experimental results show that the method can effectively segment lung nodules and quantitatively evaluate the spiculation of lung nodules.