Random Walk Algorithm Research Articles

Objective Bayesian analysis for the differential entropy of the Weibull distribution

This article addresses the estimation of differential entropy of the Weibull distribution based on different non-informative prior distributions. We first derive non-informative priors using formal rules, such as Jeffreys prior and maximal data information prior based on Fisher information and entropy, respectively. We also develop reference prior and probability matching prior for the differential entropy. Next, we investigate the effects of these priors in the Bayes estimates of the differential entropy of the Weibull distribution based on complete sample. The Bayes estimates are computed using random-walk Metropolis-Hastings algorithms. We use Monte Carlo simulation to evaluate the performance of the Bayes estimates of differential entropy in terms of bias and root mean-squared error, while highest posterior density credible intervals are assessed in terms of average width and coverage probabilities. Finally, a real data set has been analyzed for illustrative purposes.

The identification of six risk genes for ovarian cancer platinum response based on global network algorithm and verification analysis.

Ovarian cancer is the most lethal gynaecological cancer, and resistance of platinum‐based chemotherapy is the main reason for treatment failure. The aim of the present study was to identify candidate genes involved in ovarian cancer platinum response by analysing genes from homologous recombination and Fanconi anaemia pathways. Associations between these two functional genes were explored in the study, and we performed a random walk algorithm based on reconstructed gene‐gene network, including protein‐protein interaction and co‐expression relations. Following the random walk, all genes were ranked and GSEA analysis showed that the biological functions focused primarily on autophagy, histone modification and gluconeogenesis. Based on three types of seed nodes, the top two genes were utilized as examples. We selected a total of six candidate genes (FANCA, FANCG, POLD1, KDM1A, BLM and BRCA1) for subsequent verification. The validation results of the six candidate genes have significance in three independent ovarian cancer data sets with platinum‐resistant and platinum‐sensitive information. To explore the correlation between biomarkers and clinical prognostic factors, we performed differential analysis and multivariate clinical subgroup analysis for six candidate genes at both mRNA and protein levels. And each of the six candidate genes and their neighbouring genes with a mutation rate greater than 10% were also analysed by network construction and functional enrichment analysis. In the meanwhile, the survival analysis for platinum‐treated patients was performed in the current study. Finally, the RT‐qPCR assay was used to determine the performance of candidate genes in ovarian cancer platinum response. Taken together, this research demonstrated that comprehensive bioinformatics methods could help to understand the molecular mechanism of platinum response and provide new strategies for overcoming platinum resistance in ovarian cancer treatment.

Coupling network vertex representation learning based on network embedding method

Network representation learning is a basic problem in network data analysis. By learning network representation vectors, network vertices can be represented more accurately. With the development of deep learning, embedding methods have been widely used for network vertex representation learning. Providing that network data have changed in terms of their scale and modality, the research focus gradually shifted from single network mining to coupling network mining. This paper first analyzes the research status of embedding methods for single networks and then compares their advantages and disadvantages. Furthermore, the paper presents a model called CWCNE for coupling network embedding. The random walk and training algorithms of the proposed model are improved to adapt to coupling network features. The validity of the proposed model was verified using social, academic, film, poetry, and work coupling network data. Good results were obtained on community detection, entity recognition, and label classification tasks.

Fair and trustworthy: Lock-free enhanced tendermint blockchain algorithm

Blockchain Technology is exclusively used to make online transactions secure by maintaining a distributed and decentralized ledger of records across multiple computers. Tendermint is a general-purpose blockchain engine that is composed of two parts; Tendermint Core and the blockchain application interface. The application interface makes Tendermint suitable for a wide range of applications. In this paper, we analyze and improve Practical Byzantine Fault Tolerant (PBFT), a consensus-based Tendermint blockchain algorithm. In order to avoid negative issues of locks, we first propose a lock-free algorithm for blockchain in which the proposal and voting phases are concurrent whereas the commit phase is sequential. This consideration in the algorithm allows parallelism. Secondly, a new methodology is used to decide the size of the voter set which is a subset of blockchain nodes, further investigating the block sensitivity and trustworthiness of nodes. Thirdly, to fairly select the voter set nodes, we employ the random walk algorithm. Fourthly, we imply the wait-freedom property by using a timeout due to which all blocks are eventually committed or aborted. In addition, we have discussed voting conflicts and consensuses issues that are used as a correctness property, and provide some supportive techniques.

Salient Object Detection Based on Weighted Hypergraph and Random Walk

Recently, salient object detection based on the graph model has attracted extensive research interest in computer vision because the graph model can represent the relationship between two regions better. However, it is difficult to capture the high-level relationship between multiple regions. In this algorithm, the input image is segmented into superpixels first. Then, a weighted hypergraph model is established using fuzzy C-means clustering algorithm and a new weighting strategy. Finally, the random walk algorithm is used to sort all superpixels on the weighted hypergraph model to obtain the salient object. The experimental results on three benchmark datasets demonstrate that the proposed method performs better than some other state-of-the-art methods.

Adversarial Attack: A New Threat to Smart Devices and How to Defend It

This article introduces adversarial attack, a recently-unveiled security threat to consumer electronics, especially those utilizing machine learning techniques. We start with the fundamental knowledge including what are adversarial examples, how to realize such attacks, and common defense methods. Adversarial training enhances models' resilience to adversarial attacks by taking both regular and adversarial examples for training. However, applying adversarial examples under a single adversarial strength provide defense in a very limited effective range. We propose a multiple-strength adversarial training method. A random walk algorithm is adopted to optimize the selection of adversarial strengths, which is closely related to the design cost and training time. We also analyze the hardware cost and quantization loss to guide future consumer electronics designs.

Accurate moving object segmentation in unconstraint videos based on robust seed pixels selection

Due to the clutter background motion, accurate moving object segmentation in unconstrained videos remains a significant open problem, especially for the slow-moving object. This article proposes an accurate moving object segmentation method based on robust seed selection. The seed pixels of the object and background are selected robustly by using the optical flow cues. Firstly, this article detects the moving object’s rough contour according to the local difference in the weighted orientation cues of the optical flow. Then, the detected rough contour is used to guide the object and the background seed pixel selection. The object seed pixels in the previous frame are propagated to the current frame according to the optical flow to improve the robustness of the seed selection. Finally, we adopt the random walker algorithm to segment the moving object accurately according to the selected seed pixels. Experiments on publicly available data sets indicate that the proposed method shows excellent performance in segmenting moving objects accurately in unconstraint videos.

A Nodes-Based Non-Structural Model Considering a Series Structure for Heat Exchanger Network Synthesis

The aim of heat exchanger network synthesis is to design a cost-effective network configuration with the maximum energy recovery. Therefore, a nodes-based non-structural model considering a series structure (NNM) is proposed. The proposed model utilizes a simple principle based on setting the nodes on streams such that to achieve optimization of a heat exchanger network synthesis (HENS) problem. The proposed model uses several nodes to quantify the possible positions of heat exchangers so that the matching between hot and cold streams is random and free. Besides the stream splits, heat exchangers with series structures are introduced in the proposed model. The heuristic algorithm used to solve NNM model is a random walk algorithm with compulsive evolution. The proposed model is used to solve four scale cases of a HENS problem, the results show that the costs obtained by NNM model can be respectively lower 3226 $/a(Case 1), 11,056 $/a(Case 2), 2463 $/a(Case 3), 527 $/a(Case 4) than the best costs listed in literature.

Stochastic simulation algorithms for solving a nonlinear system of drift–diffusion-Poisson equations of semiconductors

Stochastic simulation algorithms for solving transient nonlinear drift diffusion recombination transport equations are developed. The governing system of equations includes two drift–diffusion equations coupled with a Poisson equation for the potential whose gradient forms the drift velocity. A stochastic algorithm for solving nonlinear drift–diffusion equations is proposed here for the first time. In each time step, the method calculates the solution on a cloud of points using a new global Monte Carlo random walk and Cellular Automata algorithms. The Poisson equation is solved by a global version of the Random Walk on Spheres method which calculates both the solutions and the derivatives without using finite difference approximations. The method is also able to calculate fluxes to any desired part of the boundary, from arbitrary sources. For transient drift–diffusion equations we suggest a stochastic expansion from cell to cell algorithm for calculating the whole solution field. All new global random walk algorithms developed in this paper are validated by comparing the simulation results with exact solutions. Application of the developed method to solve a system of 2D transport equations for electrons and holes in a semiconductor is given.

Tensorial graph learning for link prediction in generalized heterogeneous networks

Tensorial graph learning frameworks are proposed for link predictions in heterogeneous, homogeneous and generalized heterogeneous networks. In these frameworks, tensorial graphs are used to represent different networks by incorporating node and edge tensors into the graphs. A tensorial graph kernel method is developed for link predictions in these networks using four types of, i.e., structural, behavioral, content and node/edge characteristics, data. In this method, a n-strand iterated algorithm and a tensorial graph based random walk algorithm are proposed to measure node similarities in different networks within the generalized heterogeneous networks, and a tensorial graph multi-kernel learning method is developed to integrate the results. Experimental results on two real-world social media databases show that the tensorial graph kernel method has better performance using all types of data than using one type of data alone or combinations of some types of data. The tensorial graph kernel method also performs considerably better than existing competitive methods.

Quantum fast hitting on glued trees mapped on a photonic chip

Quantum walks on graphs play an important role in the field of quantum algorithms. Fast hitting is one of the properties that quantum walk algorithms can utilize to outperform classical random walk algorithms. Fast hitting refers to a particle starting from the entrance node on a graph and trying to hit the exit node quickly. Especially, continuous-time quantum walks on random glued binary trees have been investigated in theories extensively for their exponentially faster hitting speed over classical random walks. Here, using heralded single photons to represent quantum walkers and laser-written waveguide arrays to simulate the theoretical graph, we are able to demonstrate the hitting efficiency of quantum walks with tree depth as high as 16 layers for the first time. Furthermore, we expand the graph’s branching rate from 2 to 5, revealing that quantum walks can exhibit more superiority over classical random walks as the branching rate increases. Our results may shed light on the physical implementation of quantum walk algorithms as well as quantum computation and quantum simulation.

Attentional multi-level representation encoding based on convolutional and variance autoencoders for lncRNA-disease association prediction.

As the abnormalities of long non-coding RNAs (lncRNAs) are closely related to various human diseases, identifying disease-related lncRNAs is important for understanding the pathogenesis of complex diseases. Most of current data-driven methods for disease-related lncRNA candidate prediction are based on diseases and lncRNAs. Those methods, however, fail to consider the deeply embedded node attributes of lncRNA-disease pairs, which contain multiple relations and representations across lncRNAs, diseases and miRNAs. Moreover, the low-dimensional feature distribution at the pairwise level has not been taken into account. We propose a prediction model, VADLP, to extract, encode and adaptively integrate multi-level representations. Firstly, a triple-layer heterogeneous graph is constructed with weighted inter-layer and intra-layer edges to integrate the similarities and correlations among lncRNAs, diseases and miRNAs. We then define three representations including node attributes, pairwise topology and feature distribution. Node attributes are derived from the graph by an embedding strategy to represent the lncRNA-disease associations, which are inferred via their common lncRNAs, diseases and miRNAs. Pairwise topology is formulated by random walk algorithm and encoded by a convolutional autoencoder to represent the hidden topological structural relations between a pair of lncRNA and disease. The new feature distribution is modeled by a variance autoencoder to reveal the underlying lncRNA-disease relationship. Finally, an attentional representation-level integration module is constructed to adaptively fuse the three representations for lncRNA-disease association prediction. The proposed model is tested over a public dataset with a comprehensive list of evaluations. Our model outperforms six state-of-the-art lncRNA-disease prediction models with statistical significance. The ablation study showed the important contributions of three representations. In particular, the improved recall rates under different top $k$ values demonstrate that our model is powerful in discovering true disease-related lncRNAs in the top-ranked candidates. Case studies of three cancers further proved the capacity of our model to discover potential disease-related lncRNAs.

Identification of prognostic biomarkers and drug target prediction for colon cancer according to a competitive endogenous RNA network.

Colorectal cancer is one of the commoner digestive tract malignant tumor types, and its incidence and mortality rate are high. Accumulating evidence indicates that long-chain non-coding RNAs (lncRNAs) and protein-coding RNAs interact with each other by competing with the same micro(mi)RNA response element (MREs) and serve an important role in the regulation of gene expression in a variety of tumor types. However, the regulatory mechanism and prognostic role of lncRNA-mediated competing endogenous (ce)RNA networks in colon cancer have yet to be elucidated. The expression profiles of mRNAs, lncRNAs and miRNAs from 471 colon cancer and 41 paracancerous tissue samples were downloaded from The Cancer Genome Atlas database. A lncRNA-miRNA-mRNA ceRNA network in colon cancer was constructed and comprised 17 hub lncRNAs, 87 hub miRNA and 144 hub mRNAs. The topological properties of the network were analyzed, and the random walk algorithm was used to identify the nodes significantly associated with colon cancer. Survival analysis using the UALCAN database indicated that 2/17 lncRNAs identified [metastasis-associated lung adenocarcinoma transcript (MALAT1) and maternally expressed gene 3 (MEG3)] and 5/144 mRNAs [FES upstream region (FURIN), nuclear factor of activated T-cells 5 (NFAT5), RNA Binding Motif Protein 12B (RBM12B), Ras related GTP binding A (RRAGA) and WD repeat domain phosphoinositide-interacting protein 2 (WIPI2)] were significantly associated with the overall survival of patients with colon cancer, and may therefore be used as potential prognostic biomarkers of colon cancer. According to extracted lncRNA-miRNA-mRNA interaction pairs, the GSE26334 dataset was used to confirm that the lncRNA MALAT1/miR-129-5p/NFAT5 axis may represent a novel regulatory mechanism concerning the progression of colon cancer. The clusterProfiler package was used to analyze Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways in colon cancer. Finally, drugs that significantly interact with the core genes identified in colon cancer were predicted using a hypergeometric test. Of these, fostamatinib was identified to be a targeted drug for colon cancer therapy. The present findings provide a novel perspective for improved understanding of the lncRNA-associated ceRNA network and may facilitate the development of novel targeted therapeutics in colon cancer.

Optimal scaling of random-walk metropolis algorithms on general target distributions

One main limitation of the existing optimal scaling results for Metropolis–Hastings algorithms is that the assumptions on the target distribution are unrealistic. In this paper, we consider optimal scaling of random-walk Metropolis algorithms on general target distributions in high dimensions arising from practical MCMC models from Bayesian statistics. For optimal scaling by maximizing expected squared jumping distance (ESJD), we show the asymptotically optimal acceptance rate 0.234 can be obtained under general realistic sufficient conditions on the target distribution. The new sufficient conditions are easy to be verified and may hold for some general classes of MCMC models arising from Bayesian statistics applications, which substantially generalize the product i.i.d. condition required in most existing literature of optimal scaling. Furthermore, we show one-dimensional diffusion limits can be obtained under slightly stronger conditions, which still allow dependent coordinates of the target distribution. We also connect the new diffusion limit results to complexity bounds of Metropolis algorithms in high dimensions.

Prediction of Specific Subtypes and Common Markers of Non-Small Cell Lung Cancer Based on Competing Endogenous RNA Network.

BackgroundThere are various pathological types of lung cancer, including squamous cell carcinoma and adenocarcinoma. Although both of them are lung cancers, there are significant differences in diagnosis, pathogenesis, location, imaging, metastasis, and treatment. According to the competing endogenous RNA (ceRNA) theory, long non-coding RNAs (lncRNAs) compete with encoding protein genes (mRNAs) to connect with miRNAs, thus affecting the level of mRNA.Material/MethodsFirst, using the t test, we identified mRNAs and lncRNAs that have different expressions (fold change >2, P<0.01) in normal samples and in tumor samples. We calculated the significance of the shared miRNAs for mRNAs and lncRNAs by hypergeometric test (P<0.01). Further, mRNA and lncRNA pairs with co-expression relationships in cancer samples were used to establish ceRNA networks. Then, the random walk algorithm was used to optimize the specific ceRNA networks and identify potential prognostic markers of survival. Finally, we built a common ceRNA network to find markers of non-small-cell lung cancer.ResultsWe identified some potential key markers, such as PVT1, LINC00472, CDKN2A, and FAM83B, in LUSC and HOXA11-AS, HNF1A-AS1, LINC00511, and HOTAIR in LUAD by analyzing the ceRNA networks. Moreover, a number of common ceRNA pairs, such as CDC25C/CDK1/RRM2-LINC00355, have been found, and they are also significant markers for tumor survival and prognosis.ConclusionsIn summary, the present study provides a comparative analysis in 2 kinds of lung cancer ceRNA networks. Some specific and common markers we predicted that may be of great importance for clinical diagnosis and treatment.

On the convergence of the mild random walk algorithm to generate random one-factorizations of complete graphs

The complete graph K n , for n even, has a one-factorization (proper edge coloring) with n – 1 colors. In the recent contribution [Dotan M., Linial N. (2017). ArXiv:1707.00477v2], the authors raised a conjecture on the convergence of the mild random walk on the Markov chain whose nodes are the colorings of K n . The mild random walk consists in moving from a coloring C to a recoloring C′ if and only if ϕ(C′) ≤ ϕ(C), where ϕ is the potential function that takes its minimum at one-factorizations. We show the validity of such algorithm with several numerical experiments that demonstrate convergence in all cases (not just asymptotically) with polynomial cost. We prove several results on the mild random walk, we study deeply the properties of local minimum colorings, we give a detailed proof of the convergence of the algorithm for K 4 and K 6, and we raise new conjectures. We also present an alternative to the potential measure ϕ by consider the Shannon entropy, which has a strong parallelism with ϕ from the numerical standpoint.

Identification of Novel Cancer-Related Genes with a Prognostic Role Using Gene Expression and Protein-Protein Interaction Network Data

Early cancer diagnosis and prognosis prediction are necessary for cancer patients. Effective identification of cancer-related genes and biomarkers and survival prediction for cancer patients would facilitate personalized treatment of cancer patients. This study aimed to investigate a method for integrating data regarding gene expression and protein-protein interaction networks to identify cancer-related prognostic genes via random walk with restart algorithm and survival analysis. Known cancer-related genes in protein-protein interaction networks were considered seed genes, and the random walk algorithm was used to identify candidate cancer-related genes. Thereafter, using the univariant Cox regression model, gene expression data were screened to identify survival-related genes. Furthermore, candidate genes and survival-related genes were screened to identify cancer-related prognostic genes. Finally, the effectiveness of the method was verified through gene function analysis and survival prediction. The results indicate that the cancer-related genes can be considered prognostic cancer biomarkers and provide a basis for cancer diagnosis.

A new Global Random Walk algorithm for calculation of the solution and its derivatives of elliptic equations with constant coefficients in an arbitrary set of points

A new random walk based stochastic algorithm for calculation of the solution and its derivatives of high-dimensional second order elliptic equations with constant coefficients in any desired set of points is suggested. In contrast to the conventional random walk methods the new Global Random Walk (GRW) algorithm is able to find the solution in many points using only one ensemble of random walks. The method is meshless, highly efficient, the cost is of the order of |log(ε)|∕ε2 independent of the complexity of the boundary shape, where ε is the desired accuracy. The method can be used to solve nonlinear equations by applying the GRW algorithm iteratively. We demonstrate this by solving a nonlinear system of semiconductor equations. The system includes drift–diffusion equations for electrons and holes, and the Poisson equation for a potential term whose gradient enters the drift–diffusion equations as a drift velocity. The nonlinear drift–diffusion–Poisson system is solved by the iteration procedure including alternating simulation of the drift–diffusion processes and solving the Poisson equation by the GRW algorithm.

Hamiltonian Cycles and Subsets of Discounted Occupational Measures

We study a certain polytope arising from embedding the Hamiltonian cycle problem in a discounted Markov decision process. The Hamiltonian cycle problem can be reduced to finding particular extreme points of a certain polytope associated with the input graph. This polytope is a subset of the space of discounted occupational measures. We characterize the feasible bases of the polytope for a general input graph G and determine the expected numbers of different types of feasible bases when the underlying graph is random. We utilize these results to demonstrate that augmenting certain additional constraints to reduce the polyhedral domain can eliminate a large number of feasible bases that do not correspond to Hamiltonian cycles. Finally, we develop a random walk algorithm on the feasible bases of the reduced polytope and present some numerical results. We conclude with a conjecture on the feasible bases of the reduced polytope.

Influence of Stress Distribution on the Ionic Conductivity of a Sulfide All-Solid-State Lithium-Ion Battery

Introduction, Objective, MethodsIt is widely known that the ionic conductivity of a sulfide based solid electrolyte (SE) is enhanced with pressurization[1]. In order to take advantage of this property, sulfide all-solid-state lithium-ion battery (SASSLiB) is expected to be pressurized. The electrodes of SASSLiB are composite material constituted by different substances such as SE and active material (AM). Hence, when pressurized, a non-uniform stress distribution forms within the electrodes due to the unique Young’s moduli of the constituting substances[2]. Considering the pressure dependence of ionic conductivity observed in SE, a non-uniform stress distribution is likely to affect the net ionic conductivity of the electrodes.Objective of this study is to elucidate the effect of stress distribution on the ion transportation characteristics of an electrode layer in SASSLiB by combining experiment and numerical calculation. The experiment includes internal visualization by x-ray CT and electrochemical measurement of a simplified electrode consisting SE (Li10GeP2S12)[3] and electrochemically stable zirconia. To separate the effect of stress distribution from morphological factors such as volumetric fraction and tortuosity, structural data collected from x-ray CT was used to quantify the volume of non-SE regions and used to quantify tortuosity by numerical calculation employing random-walk algorithm. Additionally, voxel-finite-element-stress calculation and electric field calculation was combined to perform ion transportation simulation. To elaborate, stress distribution was expressed in two different calculation models: isotropic and anisotropic. The isotropic model assumes that the ionic conductivity at a particular voxel is dependent on the minimum principal stress value in all x, y, z directions. The anisotropic model assumes that the ionic conduction occurs anisotropically with different ionic conductivity corresponding to the voxel’s perpendicular stresses in x, y, z direction. Furthermore, the ion transportation simulation was conducted for cases with SE’s Young’s modulus set to 0.3 GPa and 21.7 GPa. The former value is experimentally measured under low pressure condition, and the latter is the value obtained by first principle calculation[4]. We have assumed that the true value of unknown and pressure dependent Young’s modulus of SE lies in between these two values.Result and DiscussionThe ionic conductivity of a composite made by SE and zirconia was significantly lower than that of SE-only sample. Comparing the ionic conductivities obtained experimentally and numerically, the discrepancy was large when only void ratio and tortuosity were considered. When stress distribution was additionally considered, discrepancy drastically decreased. Fig.1 and Fig.2 show the magnitude of discrepancy between experimental and numerical results when composite was under 100 MPa of pressure, and are results obtained by isotropic model and anisotropic model respectively. The points plotted are relative conductivity with respect to a mixture with 0% zirconia, and the points represented are results from the composite with zirconia fraction varying from 19% to 67% from left to right. The dotted line represents a complete alignment of experimental and numerical results, and closer a value is to this line, smaller the discrepancy. It is apparent from the two figures that in both models that there is a significant offset between the line of complete alignment and the case stress distribution was not considered. On the other hand, the line of complete alignment lies in between the results from numerical models obtained with respective Young’s modulus. This validates our assumption that the true Young’s modulus lies in between the values mentioned earlier. Additionally, this implies that by accounting for the non-linearity of stress-strain relationship of SE, the discrepancy between the line of complete alignment and the numerical results can further be decreased.The discrepancy between the line of complete alignment and the results excluding stress distribution increases as the volumetric fraction of zirconia increases. Additionally, the discrepancy between the numerical results of two different Young’s moduli increases as zirconia fraction increases. These increasing discrepancies with the increased zirconia fraction can be attributed to the decreasing stress in SE, instigating decrease of ionic conductivity, and in turn, widening the discrepancy.ConclusionPresence of a material with different Young’s modulus than that of SE alters the ion transportation characteristics of an electrode layer by forming a non-uniform stress distribution. And the impact of such stress distribution is much greater as the volumetric ratio of materials with high Young’s modulus increase. Therefore, stress distribution is an important factor to consider to accurately evaluate the ion transportation characteristics in the electrode layers of SASSLiB, especially as volume of non-SE materials, such as AM, increases. Figure 1