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There have been very few studies done on measuring the influence of all prefecture‐level cities on a national scale due to the limited availability of public data, challenges in data collection, and insufficient data comprehensiveness. In this paper, we aim to fill this gap by investigating this problem in China. We first collected 692,859 news articles spanning one full year from the WeChat Official Accounts of 339 cities and Taiwan Province, which served as our study area and dataset. Then, we developed a city extractor module to reduce the ambiguity of place names and constructed a city interaction network. Then, we modeled the City Influence Index (CII) and the intensity of its influence. Finally, we proposed an analytical framework that examines the relationship between CII and Gross Domestic Product (GDP), compares it with the Global Cities Index, conducts influence analysis of cities at different levels, and more. The experimental results demonstrate that our analytical framework can effectively measure the influence of cities on a national scale and uncover the implicit relationships between cities. In doing so, our study offers a new perspective for measuring city influence. Code is available at: https://github.com/vczero/CII. [ABSTRACT FROM AUTHOR]

Over the past few decades, the study of leadership theory has expanded across various disciplines, delving into the intricacies of human behavior and defining the roles of individuals within organizations. Its primary objective is to identify leaders who play significant roles in the communication flow. In addition, behavioral theory posits that leaders can be distinguished based on their daily conduct, while social network analysis provides valuable insights into behavioral patterns. Our study investigates five and six types of social networks frequently observed in different organizations. This study is conducted using datasets we collected from an IT company and public datasets collected from a manufacturing company for the thorough evaluation of prediction performance. We leverage PageRank and effective word embedding techniques to obtain novel features. State-of-the-art performance is obtained using various statistical machine learning methods, graph convolutional networks (GCN), automated machine learning (AutoML), and explainable artificial intelligence (XAI). More specifically, our approach can achieve state-of-the-art performance with an accuracy close to 90 % for leaders identification with data from projects of different types. This investigation contributes to the establishment of sustainable leadership practices by aiding organizations in retaining their leadership talent. [ABSTRACT FROM AUTHOR]

PageRank can be viewed as a hyperlink-based method for estimating the importance of nodes in a network, and has attracted a lot of attention from researchers. In this paper, we first propose an extrapolation procedure for PageRank vector estimation based on the linear combination of the Ritz values computed from the Hessenberg process and eigenvectors from the classical power method. In order to improve the convergence rate of the PageRank computations, the extrapolation procedure is introduced into the Hessenberg-type algorithm by Gu et al. (Numer. Algorithms, 89(4): 1845–1863, 2022), then a new algorithm is derived and named Hessenberg-extrapolation algorithm whose convergence and construction are investigated in detail. In addition, we further analyze the convergence of the Hessenberg-type algorithm and discuss the relationship between the approximate vectors of the Hessenberg-type algorithm and the Arnoldi-type algorithm. Numerical experiments on several examples demonstrate that our presented algorithm has great potential in PageRank approximation. [ABSTRACT FROM AUTHOR]

Non-backtracking PageRank is a variation of Google's PageRank, which is based on non-backtracking random walk. However, if the number of dangling nodes of a graph is large, the non-backtracking PageRank algorithm proposed in [F. Arrigo, D. Higham, and V. Noferini, Non-backtracking PageRank, Journal of Scientific Computing, 80: 1419–1437, 2019] may suffer from huge memory requirements and heavy computational costs. Thus, the non-backtracking PageRank algorithm is only applicable to small-scale or medium-sized graphs with few dangling nodes. In this work, we first consider how to compute the non-backtracking PageRank vector efficiently by using the Jacobi iteration, and then propose two strategies to speed up the computation of non-backtracking PageRank, in which we add some edges to a graph in a randomized and a fixed way, respectively. The computational issues are discussed in detail. The advantages of the proposed algorithms are two-fold. First, the sizes of the matrix computation problems are much smaller than that of the original one. Second, there is no kronecker product in the involved non-backtracking edge matrices, and the structures of the non-backtracking PageRank problems are greatly simplified. Comprehensive numerical experiments are performed on some real-world network matrices, which show that the solutions obtained from the two proposed algorithms and that from the original non-backtracking PageRank algorithm are highly correlated, while the two proposed algorithms can be tens or even hundreds times faster than their original counterpart. [ABSTRACT FROM AUTHOR]

Precisely recommending relevant items to users is a challenging task because the user’s rating can be influenced by various features. Therefore, social recommender systems have recently been introduced to leverage both the user-item interaction graph and the user-user social relation graph for more accurate rating predictions. Moreover, as graph neural networks (GNN) have demonstrated superior performance in graph representation learning, several algorithms have been developed to incorporate GNN into social recommender systems. However, when the sizes of the social graph and user-item graph are very large, the computational demands of existing GNN-based social recommender systems for aggregating user and item nodes becomes the primary bottleneck. In this paper, we develop a novel lightweight GNN-based social recommender system (called LiteGSR) that effectively reduces the computational overhead associated with aggregation operations while maintaining accuracy. To achieve this, we propose a new approach for refining the social graph by utilizing PageRank-based centrality scores of users and adapting representative virtual users in the user-item graph. Experimental results demonstrate that our new social recommender systems outperform existing state-of-the-art recommender systems in both accuracy and training time. [ABSTRACT FROM AUTHOR]

In recent years, the PageRank algorithm has garnered significant attention due to its crucial role in search engine technologies and its applications across various scientific fields. It is well-known that the power method is a classical method for computing PageRank. However, there is a pressing demand for alternative approaches that can address its limitations and enhance its efficiency. Specifically, the power method converges very slowly when the damping factor is close to 1. To address this challenge, this paper introduces a modified multi-step splitting iteration approach for accelerating PageRank computations. Furthermore, we present two variants for computing PageRank, which are variants of the modified multi-step splitting iteration approach, specifically utilizing the thick restarted Arnoldi and adaptively accelerated Arnoldi methods. We provide detailed discussions on the construction and theoretical convergence results of these two approaches. Extensive experiments using large test matrices demonstrate the significant performance improvements achieved by our proposed algorithms. [ABSTRACT FROM AUTHOR]

Google employs PageRank to rank web pages, determining the order in which search results are presented to users based on their queries. PageRank is primarily utilized for directed networks, although there are instances where it is also applied to undirected networks. In this paper, we have applied PageRank to undirected networks, showing that a vertex's PageRank relies on its initial value, often referred to as an intrinsic, non-network contribution. We have analytically proved that when the initial value of vertices is either proportional to their degrees or set to zero, the PageRank values of the vertices become directly proportional to their degrees. Simulated and empirical data are employed to bolster our research findings. Additionally, we have investigated the impact of initial values on PageRank localization. [ABSTRACT FROM AUTHOR]

Many ranking algorithms and metrics have been proposed to identify high-impact papers. Both the direct citation counts and the network-based PageRank-like algorithms are commonly used. Ideally, the more complete the data on the citation network, the more informative the ranking. However, obtaining more data on citation relations is often costly and challenging. In some cases, obtaining the citation counts can be relatively simple. In this paper, we look into using the additional citation counts but without additional citation relations to form more informative metrics for identifying high-impact papers. As an example, we propose enhancing the original PageRank algorithm by combining the local citation network with the additional citation counts from a more complete data source. We apply this enhanced method to American Physical Society (APS) papers to verify its effectiveness. The results indicate that the proposed ranking algorithm is robust against missing data and can improve the identification of high-quality papers. This shows that it is possible to enhance the effectiveness of a network-based metric calculated on a relatively small citation network by including only the additional data of the citation counts, without the additional citation relations. [ABSTRACT FROM AUTHOR]

With the ongoing biodiversity crisis, identifying which species are of particular importance to prevent the extinction of other species has become a pressing issue. However, most approaches to detect these important species are made at a local (i.e, community) level, without considering the potential effect of species dispersion in a landscape. As habitat fragmentation has important effects on biodiversity, we need methods to better assess how local and spatial processes interact to determine important species and therefore better inform conservation efforts.We present a modified PageRank algorithm to determine the importance of species in meta‐communities. Species importance is defined as the ability of species in the meta‐community to spread nutrients within two sets of networks: food webs that depict local trophic interactions and landscape networks representing the movement of species across different habitat patches.We show that dispersal and trophic links jointly determine the importance of the different species, both at the local scale (within habitat patches) and at larger scales (landscape). More precisely, we observed that (i) what is considered an important species changes between isolated communities and meta‐communities and (ii) the importance of a species in a meta‐community depends on the position of its habitat patch in the landscape network.The importance of a species is influenced by both intrinsic factors (dispersal capacity, trophic position) and extrinsic factors (position of the patch in the landscape network). Our results stress the need for a larger‐scale consideration of space in the identification of important species. [ABSTRACT FROM AUTHOR]

A network evolution with predicted tail and extremal indices of PageRank and the Max-Linear Model used as node influence indices in random graphs is considered. The tail index shows a heaviness of the distribution tail. The extremal index is a measure of clustering (or local dependence) of the stochastic process. The cluster implies a set of consecutive exceedances of the process over a sufficiently high threshold. Our recent results concerning sums and maxima of non-stationary random length sequences of regularly varying random variables are extended to random graphs. Starting with a set of connected stationary seed communities as a hot spot and ranking them with regard to their tail indices, the tail and extremal indices of new nodes that are appended to the network may be determined. This procedure allows us to predict a temporal network evolution in terms of tail and extremal indices. The extremal index determines limiting distributions of a maximum of the PageRank and the Max-Linear Model of newly attached nodes. The exposition is provided by algorithms and examples. To validate our theoretical results, our simulation and real data study concerning a linear preferential attachment as a tool for network growth are provided. [ABSTRACT FROM AUTHOR]

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The growth in academic and scientific publications has increased very rapidly. Researchers must choose a representative and significant literature for their research, which has become challenging worldwide. Usually, the paper citation number indicates this paper's potential influence and importance. However, this standard metric of citation numbers is not suitable to assess the popularity and significance of recently published papers. To address this challenge, this study presents an effective prediction method called FutureCite to predict the future citation level of research articles. FutureCite integrates machine learning with text and graph mining techniques, leveraging their abilities in classification, datasets in-depth analysis, and feature extraction. FutureCite aims to predict future citation levels of research articles applying a multilabel classification approach. FutureCite can extract significant semantic features and capture the interconnection relationships found in scientific articles during feature extraction using textual content, citation networks, and metadata as feature resources. This study's objective is to contribute to the advancement of effective approaches impacting the citation counts in scientific publications by enhancing the precision of future citations. We conducted several experiments using a comprehensive publication dataset to evaluate our method and determine the impact of using a variety of machine learning algorithms. FutureCite demonstrated its robustness and efficiency and showed promising results based on different evaluation metrics. Using the FutureCite model has significant implications for improving the researchers' ability to determine targeted literature for their research and better understand the potential impact of research publications. [ABSTRACT FROM AUTHOR]

The object of this study is the processes related to the assessment of the closeness of publication ties among scientists and taking into account their productivity related to scientific activity. This is necessary to increase the efficiency of management of research projects. To this end, the PR, TWPR, TWPR-CI methods for calculating scientific productivity estimates of scientists were described. In particular, the TWPR-CI method gives preference to those scientists whose works were more intensively published and cited during the last period of time, which is important for the formation of the composition of the executors of scientific research projects. The method for calculating the closeness of publication ties among scientists or average asymmetric tie strength was also described. The verification of dependence between the evaluation of the closeness of publication ties among scientists and their scientific productivity was carried out based on the analysis of the citation network of scientific publications and the network of scientific cooperation. The networks are built on the basis of the open access Citation Network Dataset (ver. 14). The dataset contains information on more than 5 million scientific publications and more than 36 million citations to them. The correlation analysis revealed the presence of a weak inverse relationship between these estimates. However, the weakness of the connection allows us to state that for this case there is no established correlation between the assessment of scientific productivity and the assessment of the closeness of publication ties. That is, the hypothesis that the weak connection between scientists makes it possible to increase the productivity and innovativeness of their publications was not confirmed. The results allow for a systematic approach to the process of evaluation and planning of the results of research projects, as well as the formation of the composition of their executors. [ABSTRACT FROM AUTHOR]

In this study, we explore how transformer models, which are known for their attention mechanisms, can improve pathogen prediction in pastured poultry farming. By combining farm management practices with microbiome data, our model outperforms traditional prediction methods in terms of the F1 score—an evaluation metric for model performance—thus fulfilling an essential need in predictive microbiology. Additionally, the emphasis is on making our model's predictions explainable. We introduce a novel approach for identifying feature importance using the model's attention matrix and the PageRank algorithm, offering insights that enhance our comprehension of established techniques such as DeepLIFT. Our results showcase the efficacy of transformer models in pathogen prediction for food safety and mark a noteworthy contribution to the progress of explainable AI within the biomedical sciences. This study sheds light on the impact of effective farm management practices and highlights the importance of technological advancements in ensuring food safety. [ABSTRACT FROM AUTHOR]

This research leverages Memgraph, an open-source graph database, to analyze graph-based network data and apply Graph Neural Networks (GNNs) for a detailed classification of cyberattack tactics categorized by the MITRE ATT&CK framework. As part of graph characterization, the page rank, degree centrality, betweenness centrality, and Katz centrality are presented. Node classification is utilized to categorize network entities based on their role in the traffic. Graph-theoretic features such as in-degree, out-degree, PageRank, and Katz centrality were used in node classification to ensure that the model captures the structure of the graph. The study utilizes the UWF-ZeekDataFall22 dataset, a newly created dataset which consists of labeled network logs from the University of West Florida's Cyber Range. The uniqueness of this study is that it uses the power of combining graph-based characterization or analysis with machine learning to enhance the understanding and visualization of cyber threats, thereby improving the network security measures. [ABSTRACT FROM AUTHOR]

Evaluating academic papers and groups is important in scholar evaluation and literature retrieval. However, current evaluation indices, which pay excessive attention to the citation number rather than the citation importance and unidirectionality, are relatively simple. This study proposes new evaluation indices for papers and groups. First, an improved PageRank (PR) algorithm introducing citation importance is proposed to obtain a new citation-based paper index (CPI) via a pre-ranking and fine-tuning strategy. Second, to evaluate the paper's influence inside and outside its research field, the focus citation-based paper index (FCPI) and diversity citation-based paper index (DCPI) are proposed based on topic similarity and diversity, respectively. Third, aside from the statistical indices for academic papers, we propose a foreign academic degree of dependence (FAD) to characterise the dependence between two academic groups. Finally, artificial intelligence (AI) papers from 2005 to 2019 are utilised for a case study. [ABSTRACT FROM AUTHOR]

Co-evolving network models, wherein dynamics such as random walks on the network influence the evolution of the network structure, which in turn influences the dynamics, are of interest in a range of domains. While much of the literature in this area is currently supported by numerics, providing evidence for fascinating conjectures and phase transitions, proving rigorous results has been quite challenging. We propose a general class of co-evolving tree network models driven by local exploration, started from a single vertex called the root. New vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the direction of the root, connecting to the terminal vertex. Specific choices of the exploration step distribution lead to the well-studied affine preferential attachment and uniform attachment models, as well as less well understood dynamic network models with global attachment functionals such as PageRank scores (Chebolu and Melsted, in: SODA, 2008). We obtain local weak limits for such networks and use them to derive asymptotics for the limiting empirical degree and PageRank distribution. We also quantify asymptotics for the degree and PageRank of fixed vertices, including the root, and the height of the network. Two distinct regimes are seen to emerge, based on the expected exploration distance of incoming vertices, which we call the 'fringe' and 'non-fringe' regimes. These regimes are shown to exhibit different qualitative and quantitative properties. In particular, networks in the non-fringe regime undergo 'condensation' where the root degree grows at the same rate as the network size. Networks in the fringe regime do not exhibit condensation. Further, non-trivial phase transition phenomena are shown to arise for: (a) height asymptotics in the non-fringe regime, driven by the subtle competition between the condensation at the root and network growth; (b) PageRank distribution in the fringe regime, connecting to the well known power-law hypothesis. In the process, we develop a general set of techniques involving local limits, infinite-dimensional urn models, related multitype branching processes and corresponding Perron–Frobenius theory, branching random walks, and in particular relating tail exponents of various functionals to the scaling exponents of quasi-stationary distributions of associated random walks. These techniques are expected to shed light on a variety of other co-evolving network models. [ABSTRACT FROM AUTHOR]

Copyright of Iraqi Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The PageRank model, which was first proposed by Google for its web search engine application, has since become a popular computational tool in a wide range of scientific fields, including chemistry, bioinformatics, neuroscience, bibliometrics, social networks, and others. PageRank calculations necessitate the use of fast computational techniques with low algorithmic and memory complexity. In recent years, much attention has been paid to Krylov subspace algorithms for solving difficult PageRank linear systems, such as those with large damping parameters close to one. In this article, we examine the full orthogonalization method (FOM). We present a convergence study of the method that extends and clarifies part of the conclusions reached in Zhang et al. (J Comput Appl Math. 2016; 296:397–409.). Furthermore, we demonstrate that FOM is breakdown free when solving singular PageRank linear systems with index one and we investigate the effect of using weighted inner‐products instead of conventional inner‐products in the orthonormalization procedure on FOM convergence. Finally, we develop a shifted polynomial preconditioner that takes advantage of the special structure of the PageRank linear system and has a good ability to cluster most of the eigenvalues, making it a good choice for an iterative method like FOM or GMRES. Numerical experiments are presented to support the theoretical findings and to evaluate the performance of the new weighted preconditioned FOM PageRank solver in comparison to other established solvers for this class of problem, including conventional stationary methods, hybrid combinations of stationary and Krylov subspace methods, and multi‐step splitting strategies. [ABSTRACT FROM AUTHOR]

Recent spectral graph sparsification research aims to construct ultra-sparse subgraphs for preserving the original graph spectral (structural) properties, such as the first few Laplacian eigenvalues and eigenvectors, which has led to the development of a variety of nearly-linear time numerical and graph algorithms. However, there is very limited progress for spectral sparsification of directed graphs. In this work, we prove the existence of nearly-linear-sized spectral sparsifiers for directed graphs under certain conditions. Furthermore, we introduce a practically-efficient spectral algorithm (diGRASS) for sparsifying real-world, large-scale directed graphs leveraging spectral matrix perturbation analysis. The proposed method has been evaluated using a variety of directed graphs obtained from real-world applications, showing promising results for solving directed graph Laplacians, spectral partitioning of directed graphs, and approximately computing (personalized) PageRank vectors. [ABSTRACT FROM AUTHOR]

Motivated by the PageRank model for graph partitioning, we develop an extension of PageRank for partitioning uniform hypergraphs. Starting from adjacency tensors of uniform hypergraphs, we establish the multi-linear pseudo-PageRank (MLPPR) model, which is formulated as a multi-linear system with nonnegative constraints. The coefficient tensor of MLPPR is a kind of Laplacian tensors of uniform hypergraphs, which are almost as sparse as adjacency tensors since no dangling corrections are incorporated. Furthermore, all frontal slices of the coefficient tensor of MLPPR are M-matrices. Theoretically, MLPPR has a solution, which is unique under mild conditions. An error bound of the MLPPR solution is analyzed when the Laplacian tensor is slightly perturbed. Computationally, by exploiting the structural Laplacian tensor, we propose a tensor splitting algorithm, which converges linearly to a solution of MLPPR. Finally, numerical experiments illustrate that MLPPR is effective and efficient for hypergraph partitioning problems. [ABSTRACT FROM AUTHOR]

The article discusses a Bayesian measure of association, B-index, and compares it with the other existing measures of agreement, association, and similarity, both chance-corrected and non-corrected: Scott's π, Krippendorff's α, Cohen's κ, Bennett, Alpert & Goldstein's S, Cosine similarity, and the Jaccard similarity coefficient. PageRank adapted to particularities of annotation is also added to this list. Two versions of B-index are considered: with the informative and non-informative priors. An algorithm for calculating B-index written in pseudocode is provided. Particular attention is devoted to the uses of those measures in content analysis, communication studies, computational linguistics, psychology, computer science and network science. Real-world data gathered using an online platform for content analysis allowed comparing the behavior of all eight measures included in the scope of analysis. Three short texts (164 data points/sentences in total) were coded by 66 annotators. The behaviors of B-index with the non-informative prior and Bennett, Alpert & Goldstein's S have some common patterns. [ABSTRACT FROM AUTHOR]

Back in 1988, the partial game trees explored by computer chess programs were among the largest search structures in real-world computing. Because the game tree is too large to be fully evaluated, chess programs must make heuristic strategic decisions based on partial information, making it an illustrative subject for teaching AI search. In one of his lectures that year on AI search for games and puzzles, Professor Hans Berliner—a pioneer of computer chess programs1—stated: "Intelligent heuristics are the future of computing." As a student in the field of the theory of computation, I was naturally perplexed but fascinated by this perspective. I had been trained to believe that "Algorithms and computational complexity theory are the foundation of computer science." However, as it happens, my attempts to understand heuristics in computing have subsequently played a significant role in my career as a theoretical computer scientist. I have come to realize that Berliner's postulation is a far-reaching worldview, particularly in the age of big, rich, complex, and multifaceted data and models, when computing has ubiquitous interactions with science, engineering, humanity, and society. In this article,2I will share some of my experiences on the subject of heuristics in computing, presenting examples of theoretical attempts to understand the behavior of heuristics on real data, as well as efforts to design practical heuristics with desirable theoretical characterizations. My hope is that these theoretical insights from past heuristics—such as spectral partitioning, multilevel methods, evolutionary algorithms, and simplex methods—can shed light on and further inspire a deeper understanding of the current and future techniques in AI and data mining. [ABSTRACT FROM AUTHOR]

Creating policy measures is the final step in the process of e-learning roadmap development. Policy measures can be seen as long-term activities that need to be implemented and constantly upgraded to achieve strategic goals. For resource allocation, it is useful to prioritize policy measures. Prioritization can be implemented using multi-criteria decision-making methods. This paper analyzes policy measures in the Maldives National University's e-learning roadmap using the social network analysis process (SNAP), which includes the analytic hierarchy process (AHP), the decision-making trial and evaluation laboratory (DEMATEL), and the PageRank centrality. In policy measure evaluation, there were more than 20 participants: persons with managerial functions at the Maldives National University (MNU) (deans, heads of departments) and persons in lecturer and researcher positions. By using the AHP, participants prioritized policy measures with respect to their importance to them. By using the DEMATEL, participants identified and prioritized policy measures with respect to their effect on other measures. Finally, by using the SNAP, it was possible to determine the prioritization list for resource allocation since it aggregates the aspects of the policy measures, their importance, and their effect on other measures. [ABSTRACT FROM AUTHOR]

Image sentiment analysis technology can predict, measure and understand the emotional experience of human beings through images. Aiming at the problem of extracting emotional characteristics in art appreciation, this article puts forward an innovative method. Firstly, the PageRank algorithm is enhanced using tweet content similarity and time factors; secondly, the SE-ResNet network design is used to integrate Efficient Channel Attention (ECA) with the residual network structure, and ResNeXt50 is optimized to enhance the extraction of image sentiment features. Finally, the weight coefficients of overall emotions are dynamically adjusted to select a specific emotion incorporation strategy, resulting in effective bimodal fusion. The proposed model demonstrates exceptional performance in predicting sentiment labels, with maximum classification accuracy reaching 88.20%. The accuracy improvement of 21.34% compared to the traditional deep convolutional neural networks (DCNN) model attests to the effectiveness of this study. This research enriches images and texts' emotion feature extraction capabilities and improves the accuracy of emotion fusion classification. [ABSTRACT FROM AUTHOR]

Ranking algorithms play a crucial role in information technologies and numerical analysis due to their efficiency in high dimensions and wide range of possible applications, including internet ranking, scientometrics, and systemic risk in finance (SinkRank and DebtRank). The traditional approach to internet ranking goes back to the seminal work of Sergey Brin and Larry Page, who developed the initial method PageRank (PR) in order to rank websites for search engine results based on linear algebra rules. But how robust is this method in times of rapid internet growth? Recent works have studied robust reformulations of the PageRank model for the case when links in the network structure may vary; that is, some links may appear or disappear, influencing the transportation matrix defined by the network structure. In this article, the authors make a further step forward, allowing the network to vary not only in links but also in the number of nodes. The authors focus on growing network structures and develop methods for ranking of networks uncertain both in size and in structure. Internet ranking algorithms play a crucial role in information technologies and numerical analysis due to their efficiency in high dimensions and wide range of possible applications, including scientometrics and systemic risk in finance (SinkRank, DebtRank, etc.). The traditional approach to internet ranking goes back to the seminal work of Sergey Brin and Larry Page, who developed the initial method PageRank (PR) in order to rank websites in search engine results. Recent works have studied robust reformulations of the PageRank model for the case when links in the network structure may vary; that is, some links may appear or disappear influencing the transportation matrix defined by the network structure. We make a further step forward, allowing the network to vary not only in links, but also in the number of nodes. We focus on growing network structures and propose a new robust formulation of the PageRank problem for uncertain networks with fixed growth rate. Defining the robust PageRank in terms of a nonconvex optimization problem, we bound our formulation from above by a convex but nonsmooth optimization problem. Driven by the approximation quality, we analyze the resulting optimality gap theoretically and demonstrate cases for its reduction. In the numerical part of the article, we propose some techniques which allow us to obtain the solution efficiently for middle-size networks avoiding all nonsmooth points. Furthermore, we propose a coordinate-wise descent method with near-optimal step size and address high-dimensional cases using multinomial transition probabilities. We analyze the impact of the network growth on ranking and numerically assess the approximation quality using real-world data sets on movie repositories and on journals on computational complexity. Funding: This work was supported by the Austrian Science Fund [Grant J3674-N26]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/opre.2022.2298. [ABSTRACT FROM AUTHOR]

We consider several families of network centrality measures induced by graph kernels, which include some well-known measures and many new ones. The Self-consistency and Bridge axioms, which appeared earlier in the literature, are closely related to certain kernels and one of the families. We obtain a necessary and sufficient condition for Self-consistency, a sufficient condition for the Bridge axiom, indicate specific measures that satisfy these axioms and show that under some additional conditions they are incompatible. PageRank centrality applied to undirected networks violates most conditions under study and has a property that according to some authors is 'hard to imagine' for a centrality measure. We explain this phenomenon. Adopting the Self-consistency or Bridge axiom leads to a drastic reduction in survey time in the culling method designed to select the most appropriate centrality measures. [ABSTRACT FROM AUTHOR]

In the field of deep matching, a large amount of noisy data in Chinese long texts affects the matching effect. Most long-form text matching models use all text data indiscriminately, which results in a large amount of noisy data, and thus the PageRank algorithm is combined with Transformer to filter noise. For sentence-level noise detection, after calculating the overlap rate of words to evaluate the similarity, a sentence-level relationship graph is constructed and filtered by using the PageRank algorithm; for word-level noise detection, based on the attention score in Transformer, a word graph is established, then the PageRank algorithm is executed on graph, combined with self-attention weights, to select keywords to highlight topic relevance, the noisy words are filtered sequentially at different layers in the module, layer by layer. In addition, during the model training, PolyLoss is applied to replace the traditional binary Cross-Entropy loss function, thus reducing the difficulty of hyperparameter tuning. Finally, a better filtering strategy is proposed and experiments are conducted to verify it on two Chinese long-form text matching datasets. The result shows that the matching model based on the noise filtering strategy of this paper can better filter the noise and capture the matching signal more accurately. [ABSTRACT FROM AUTHOR]

Climate risk is one of the key factors affecting the energy industry, and then affects the global energy trade. By adopting a network approach to the global energy trade and based on the data of global energy trade during 1996–2018, the evolution characteristics of the global energy trade network are hereby investigated, and the impact of climate risk on the global energy trade is explored. The results demonstrate that the global energy trade network has scale-free characteristics and significant regional characteristics and that its heterogeneity is weakening on the whole. Climate risk is negatively correlated with the energy trade relationship between countries. The simulation results show that climate risk has a greater impact on the import status of all countries than their export status and that only a few countries have large climate risk spillover effects. In addition, the climate risk spillover effects of countries are closely related to their import statuses. Overall, the present study provides policy suggestions for identifying important energy trading countries under climate risk shock and preventing the negative impact of climate risks on global energy trade. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Northeastern University (Natural Science) is the property of Dongbei Daxue Xuebao and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

PageRank is a popular measure of centrality that is often applied to rank nodes in real-world networks. However, in many cases, the notion of teleportation is counterintuitive because it implies that whatever is moving around the network will jump or 'teleport' directly from one node to any other, without considering how far apart the nodes are. To overcome this issue, we propose here a general measure of PageRank centrality whereby the teleportation probabilities depend, in some way, on the distance separating the nodes. We accomplish this by drawing upon recent advances in non-local random walks, which allow the proposed measure to be tailored for various real-world networks and applications. To illustrate the flexibility of the proposed measure and to demonstrate how it differs from PageRank centrality, we present and discuss experimental results for a selection of real-world spatial and social networks, including an air transportation network, a collaboration network and an urban street network. [ABSTRACT FROM AUTHOR]

In this paper, a new multi-parameter iterative algorithm is proposed to address the PageRank problem based on the multi-splitting iteration method. The proposed method solves two linear subsystems at each iteration by splitting the coefficient matrix, considering therefore inner and outer iteration to find the approximate solutions of these linear subsystems. It can be shown that the iterative sequence generated by the multi-parameter iterative algorithm finally converges to the PageRank vector when the parameters satisfy certain conditions. Numerical experiments show that the proposed algorithm has better convergence and numerical stability than the existing algorithms. [ABSTRACT FROM AUTHOR]

Computational drug repositioning approaches are important, as they cost less compared to the traditional drug development processes. This study proposes a novel network-based drug repositioning approach, which computes similarities between disease-causing genes and drug-affected genes in a network topology to suggest candidate drugs with highest similarity scores. This new method aims to identify better treatment options by integrating systems biology approaches. It uses a protein-protein interaction network that is the main topology to compute a similarity score between candidate drugs and disease-causing genes. The disease-causing genes were mapped on this network structure. Transcriptome profiles of drug candidates were taken from the LINCS project and mapped individually on the network structure. The similarity of these two networks was calculated by different network neighborhood metrics, including Adamic-Adar, PageRank and neighborhood scoring. The proposed approach identifies the best candidates by choosing the drugs with significant similarity scores. The method was experimented on melanoma, colorectal, and prostate cancers. Several candidate drugs were predicted by applying AUC values of 0.6 or higher. Some of the predictions were approved by clinical phase trials or other in-vivo studies found in literature. The proposed drug repositioning approach would suggest better treatment options with integration of functional information between genes and transcriptome level effects of drug perturbations and diseases. [ABSTRACT FROM AUTHOR]

Search engine optimization (SEO), the practice of improving website visibility on search engines, faces the considerable challenges posed by the opacity of Google’s relevance ranking algorithm. Attempts at understanding how this algorithm operates have generated a sizeable number of studies in the worlds of both business and academia. Indeed, this research tradition has managed to present strong evidence regarding the participation of certain factors and their relative importance. For instance, there is a widespread consensus that domain authority is one of the key factors in optimizing positioning. This study seeks to determine the reliability of the domain authority scores provided by three leading platforms for SEO professionals: Moz’s Domain Authority, Semrush’s Authority Score, and Ahrefs’ Domain Rating, values obtained using different indices and applying different procedures. We hypothesize that the degree of coincidence is high, allowing us to deduce that the three tools are, therefore, highly reliable. The method of data triangulation is used to compare the values from these three sources. The degree of coincidence is determined using a statistical analysis based on Spearman’s correlation coefficient (rho). The sample of domains analyzed was selected from 61 neutral queries, which provided 16,937 results and a total of 3,151 domains. When examining the tools in pairs, the correlation coefficients obtained were above 0.9 in all cases. The rho coefficient of the global analysis was also 0.9. This confirms our hypothesis and demonstrates that the three platforms can be considered as providing reliable data. These results are clearly relevant given that SEO professionals depend heavily on domain authority values in their work, and the degree of reliability detected ensures that decision-making based on this indicator can be undertaken with confidence. [ABSTRACT FROM AUTHOR]

We study the complexity of local graph-centrality estimation, with the goal of approximating the centrality score of a given target node while exploring only a sublinear number of nodes/arcs of the graph and performing a sublinear number of elementary operations. We develop a technique, which we apply to PageRank and Heat Kernel, for constructing a low-variance score estimator through a local exploration of the graph. We obtain an algorithm that, given any node in any graph of n nodes and m arcs, with probability (1 - \delta ) computes a multiplicative (1\pm \epsilon )-approximation of its score by examining only O\~(min(n 1/2\Delta 1/2 , n 1/2m1/4 )) nodes/arcs, where \Delta is the maximum outdegree of the graph and poly(\epsilon - 1 ) and polylog(\delta - 1 ) factors are omitted for readability. A similar bound holds for computational cost. We also prove a lower bound of \Omega (min(n 1/2\Delta 1/2, n1/3m1/3 )) for both query complexity and computational complexity. Moreover, in the jump-and-crawl graphaccess model, our technique yields a O\~(min(n 1/2\Delta 1/2 , n2/3 ))-queries algorithm; we show that this algorithm is optimal up to a logarithmic factor-in fact, sublogarithmic in the case of PageRank. These are the first algorithms with sublinear worst-case bounds for general directed graphs and any choice of the target node. [ABSTRACT FROM AUTHOR]

Consider chemical elements as a system, we create an undirected chemical network with 99 elements and 1916 edges from Chemspider, a website that provide search engines to collect compounds. Using this network and the network that we used in our previous work with 97 elements and 2198 edges, we found that RootedPageRank, a link prediction tool in complex network, can be used to predict potential binary compounds, because the changing trend of PageRank probability of each element in these networks all follow the periodic law, despite of the difference of scale of these networks. The accuracy test indicates that at least 7 among top 10 predicted compoundss in one network can be verified using the compoundss in the other network or in other chemical database, proving that this method can be used to provide guidance in finding potential binary compounds, suggesting that we can study chemical properties from the view of complex network. [ABSTRACT FROM AUTHOR]

Our objective is to survey recent results concerning the evolution of random networks and related extreme value statistics, which are a subject of interest due to numerous applications. Our survey concerns the statistical methodology but not the structure of random networks. We focus on the problems arising in evolving networks mainly due to the heavy-tailed nature of node indices. Tail and extremal indices of the node influence characteristics like in-degrees, out-degrees, PageRanks, and Max-linear models arising in the evolving random networks are discussed. Related topics like preferential and clustering attachments, community detection, stationarity and dependence of graphs, information spreading, finding the most influential leading nodes and communities, and related methods are surveyed. This survey tries to propose possible solutions to unsolved problems, like testing the stationarity and dependence of random graphs using known results obtained for random sequences. We provide a discussion of unsolved or insufficiently developed problems like the distribution of triangle and circle counts in evolving networks, or the clustering attachment and the local dependence of the modularity, the impact of node or edge deletion at each step of evolution on extreme value statistics, among many others. Considering existing techniques of community detection, we pay attention to such related topics as coloring graphs and anomaly detection by machine learning algorithms based on extreme value theory. In order to understand how one can compute tail and extremal indices on random graphs, we provide a structured and comprehensive review of their estimators obtained for random sequences. Methods to calculate the PageRank and PageRank vector are shortly presented. This survey aims to provide a better understanding of the directions in which the study of random networks has been done and how extreme value analysis developed for random sequences can be applied to random networks. [ABSTRACT FROM AUTHOR]

Graph coloring is widely used to parallelize scientific applications by identifying subsets of independent tasks that can be executed simultaneously. Graph coloring assigns colors the vertices of a graph, such that no adjacent vertices have the same color. The number of colors used corresponds to the number of parallel steps in a real-world end-application. Therefore, the total runtime of the graph coloring kernel adds to the overall parallel overhead of the real-world end-application, whereas the number of the vertices of each color class determines the number of the independent concurrent tasks of each parallel step, thus affecting the amount of parallelism and hardware resource utilization in the execution of the real-world end-application. In this work, we propose a high-performance graph coloring algorithm, named ColorTM, that leverages Hardware Transactional Memory (HTM) to detect coloring inconsistencies between adjacent vertices. ColorTM detects and resolves coloring inconsistencies between adjacent vertices with an eager approach to minimize data access costs, and implements a speculative synchronization scheme to minimize synchronization costs and increase parallelism. We extend our proposed algorithmic design to propose a balanced graph coloring algorithm, named BalColorTM, with which all color classes include almost the same number of vertices to achieve high parallelism and resource utilization in the execution of the real-world end-applications. We evaluate ColorTM and BalColorTM using a wide variety of large real-world graphs with diverse characteristics. ColorTM and BalColorTM improve performance by 12.98 × and 1.78 × on average using 56 parallel threads compared to prior state-of-the-art approaches. Moreover, we study the impact of our proposed graph coloring algorithmic designs on a popular end-application, i.e., Community Detection, and demonstrate the ColorTM and BalColorTM can provide high-performance improvements in real-world end-applications across various input data given. [ABSTRACT FROM AUTHOR]

Centrality is a relevant topic in the field of network research, due to its various theoretical and practical implications. In general, all centrality metrics aim at measuring the importance of nodes (according to some definition of importance), and such importance scores are used to rank the nodes in the network, therefore the rank improvement is a strictly related topic. In a given network, the rank improvement is achieved by establishing new links, therefore the question shifts to which and how many links should be collected to get a desired rank. This problem, also known as link-building has been shown to be NP-hard, and most heuristics developed failed in obtaining good performance with acceptable computational complexity. In this article, we present LB--GDM, a novel approach that leverages Geometric Deep Learning to tackle the link-building problem. To validate our proposal, 31 real-world networks were considered; tests show that LB--GDM performs significantly better than the state-of-the-art heuristics, while having a comparable or even lower computational complexity, which allows it to scale well even to large networks. [ABSTRACT FROM AUTHOR]

With the development of avionics industry, it is difficult for traditional combat equipment node evaluation method to meet our requirements under complex combat system. This paper presents a method of node importance evaluation which is suitable for modern avionics field and can be used for reference in other combat fields. In order to make better use of the different features of the node itself and the different connections between nodes, we use TOPSIS algorithm to model the characteristics of the node itself, and PageRank to measure the interdependence of all nodes. Therefore, a novel node contribution evaluation algorithm based on TOPSIS and PageRank is proposed in this paper. In addition, after the evaluation of node contribution, we found that there was also a functional relationship between the operational information entropy in the whole graph and the contribution of these nodes. On this basis, information entropy evaluation algorithm of the overall combat map is further proposed. After a lot of experiments, the reliability of our algorithm is evaluated on the indexes of the node's destruction-resistant performance and information transfer efficiency. Compared with the traditional universal algorithm, our proposed algorithm shows more interpretable and robust results in the field of avionics. [ABSTRACT FROM AUTHOR]

Network topology is the basic for the development of traffic management and control. In a road network, bayonets with installation of surveillance facilities are key components to recognize traffic congestion from time to time. Therefore, identifying the essential bayonets in a road network becomes one of the most efficient ways to alleviate traffic congestion for traffic engineers and transport department. To do so, this paper aims to propose a novel sorting algorithm based on similarity measurements and traffic flow information to efficiently identify key bayonets in road networks. Our research results show that by analyzing the bayonet data in a fixed period of time in a medium-sized city of China, we have successfully identified the location of key bayonet points. Most of these key bayonet points are closed to residential areas and important traffic stations. The rank of these bayonet points can help the city managers better understand the topological characteristics of the road network as well as the propagation of congestion so as to make the traffic policies or control strategies for traffic congestion alleviation. [ABSTRACT FROM AUTHOR]

In this paper we propose several new quantum computation algorithms as an original contribution to the domain of PageRank algorithm theory, Spectral Graph Theory and Quantum Signal Processing. We first propose an application to PageRank of the HHL quantum algorithm for linear equation systems. We then introduce one of the first Quantum-Based Algorithms to perform a directed Graph Fourier Transform with a low gate complexity. After proposing a generalized PageRank formulation, based on ideas stemming from Spectral Graph Theory, we show how our quantum directed graph Fourier Transform can be applied to compute our generalized version of the PageRank. [ABSTRACT FROM AUTHOR]

Uncertainty has always been a threat to system performance in both manufacturing and service industries. Although cost-budgeting may limit available resources, a more flexible structure can still improve the system's ability to deal with uncertainty. In this study, we develop a new measure to help find a more flexible structure without extensive simulation. We create a PageRank-analogous score whereby we can calculate the Flexibility Gap (FG) index to predict the better of two alternative structures with topological information only. We theoretically analyze how the FG index recognizes flexible sparse structures such as expander graphs with high expansion ratios. Numerical experiments show that the FG index is effective in ranking the flexibility performance of different structures in terms of average waiting time and expected lost sales. Moreover, we extend the FG index with minimal modification to accommodate the case of imperfect flexibility (i.e., flexible suppliers with shrinking capacities) and demonstrate that the generalized FG index is still a good predictor of expected lost sales. Our approach provides a novel view to explain flexibility. That is, sparse structures with higher graph expansion ratios disperse the demand fluctuation more "rapidly" among resources to cushion the shock of uncertainty. [ABSTRACT FROM AUTHOR]

The multi-step matrix splitting iteration (MPIO) for computing PageRank is an efficient iterative method by combining the multi-step power method with the inner-outer iterative method. In this paper, with the aim of accelerating the computation of PageRank problems, a new method is proposed by preconditioning the MPIO method with an adaptive generalized Arnoldi (GArnoldi) method. The new method is called as an adaptive GArnoldi-MPIO method, whose construction and convergence analysis are discussed in detail. Numerical experiments on several PageRank problems are reported to illustrate the effectiveness of our proposed method. [ABSTRACT FROM AUTHOR]

Today financial institutions have been investing billions of US dollars to detect money laundering. When financial institutions are found to have their customers conduct money laundering through them, they are subjected to large penalties. Moreover, their reputation suffers greatly through public exposure. In response, financial institutions have been exploring opportunities to use graph machine learning algorithms. This paper describes one of those algorithms called Anti-TrustRank and demonstrates how it can be used to identify money launderers. In contrast to many other algorithms, Anti-TrustRank calls for selecting a very small set of customers to be confirmed by human experts (e.g., compliance officers or analysts) as money launderers. Once this set has been identified, Anti-TrustRank seeks out customers linked (either directly or indirectly) to those money launderers. [ABSTRACT FROM AUTHOR]

As an important part of distributed graph computing, graph partitioning has been widely studied. However, the majority of the existing approaches to distributed graph partitioning barely take into consideration the relationship between the partition strategy and the graph algorithm's characteristics. The current graph partitioning strategies are on the basis of the graph structure, and the performance is diverse as running different graph algorithms. In this paper, considering the characteristics of a graph algorithm, we propose a distributed graph partitioning framework that can decide which partitioning strategy is better based on the program analysis. We also design a triangle-based partitioning strategy which benefits several graph algorithms such as the triangle counting. In addition, to reduce the number of shuffling operations in PageRank algorithm, we redesign the PageRank algorithm which considers the corresponding hash partitioning. The experimental results show that our adaptive graph partitioning framework implemented on Graphx surpasses the original one, especially for the triangle counting and PageRank, no matter on real-world graphs or synthetic graphs. [ABSTRACT FROM AUTHOR]

Neural network-based encoder–decoder (ED) models are widely used for abstractive text summarization. While the encoder first reads the source document and embeds salient information, the decoder starts from such encoding to generate the summary word-by-word. However, the drawback of the ED model is that it treats words and sentences equally, without discerning the most relevant ones from the others. Many researchers have investigated this problem and provided different solutions. In this paper, we define a sentence-level attention mechanism based on the well-known PageRank algorithm to find the relevant sentences, then propagate the resulting scores into a second word-level attention layer. We tested the proposed model on the well-known CNN/Dailymail dataset, and found that it was able to generate summaries with a much higher abstractive power than state-of-the-art models, in spite of an unavoidable (but slight) decrease in terms of the Rouge scores. [ABSTRACT FROM AUTHOR]

With the exponential growth of the volume of scientific literatures, academic evaluation is becoming one of the important problems of scientometrics. Considering the influence of disruption of papers, in this paper, we propose a disruption based PageRank (DPRank) model to rank the scientific significance of scientific papers. The disruption value of a paper is calculated by the local network structure of the paper in the citation network. DPRank model treats each citation differently based on paper's temporal information and disruption value. In DPRank model, the scores delivered from a paper's upstream nodes decay exponentially with the time gap between the publication time and reference time, and the decay rate is proportional to the paper's disruption value. We use the APS data set and some highly valued papers as benchmarks to evaluate the performance of the proposed DPRank model. The experimental results show that the DPRank model has a relatively better performance for both old and newly published papers, and can outperform other methods in identifying the benchmark papers. [ABSTRACT FROM AUTHOR]

On the e-learning system, student assignments are collected, but problems arise that based on observations from two classes of database courses, 73% of students make plagiarism so lecturers need to give motivation to students. Self motivate is needed by with a group of students. For this reason, using a bolzano method or bisection method will provide an overview of the development of the plagiarism trend between groups of students based on scores on similarity score that compute by PageRank algorithm used by Google. Research method is carried out by conducting preliminary observations of plagiarism scores and creating markov matrix. PageRank compute this ranking and Bolzano method find the intersection of two eigenvalues. Bolzano results the maximum and minimum values on range of intervals where each group consists of 5 students. Experiments were conducted in 3 classes of database courses. Trend analysis found that the plagiarism score averaged 54% with a gradient of 3°, this is relatively small but when spread in different groups it becomes larger and student group have a higher plagiarism score. Results implies a way of looking student motivation based on the plagiarism score by a small groupto motivate each other. [ABSTRACT FROM AUTHOR]

Recently, computing Google's PageRank iteratively has been receiving a lot of attention. Many numerical techniques are proposed to remedy the slow convergence of the traditional power method. Among them, lumped methods proceed with a much smaller matrix if the number of dangling nodes is large. In this paper, to further improve the extrapolation process based on matrix trace and the lumped methods, we first propose a new extrapolation approach for computing PageRank and then develop a lumped version to accelerate PageRank computation. Some numerical results of the new approach validate the theoretical analysis. [ABSTRACT FROM AUTHOR]