Complexity最新文献

In this paper, the fixed-time consensus problem for leader–follower multiagent systems with directed graphs is discussed. First, a new fixed-time state observer of the multiagent system is designed. In the new state observer, an auxiliary matrix is introduced which can be theoretically obtained by solving a linear matrix inequality. The important role of the auxiliary matrix is that it makes the upper bound of the fixed time for the state observation of multiagent system solvable and more accurate, which enable the observation error system converges faster. Based on the new fixed-time state observer, a sufficient condition is given with which the observation of the state of multiagent system can be reached in fixed time. Second, a new fixed-time control protocol is designed for the leader–follower multiagent system. In the new controller, another auxiliary matrix is introduced which can also be theoretically obtained with linear matrix inequality. With the new control protocol, the closed-loop leader–follower multiagent system is theoretically shown that the fixed-time consensus can be reached in fixed time by means of the concept of fixed-time stability, Lyapunov stability theory, and LaSalle’s invariance principle. The important role of the new control protocol is that it also makes the fixed time for the consensus multiagent system solvable and then the closed-loop multiagent system converges faster. Finally, some numerical simulations are presented to demonstrate convincingly the superiority of the method and results obtained in this paper. From the simulations, it can be seen that in comparison with some existing works, the estimate of fixed time for the consensus problem may be more accurate and faster.

This work examines a discrete prey–predator model using the fractional derivative. The conditions for the existence and stability of the fixed points in the model are identified. The analysis is centered on exploring various bifurcations at the positive fixed point to understand their ecological implications. Using bifurcation theory, bifurcations related to period doubling, Neimark–Sacker, and strong resonances are studied. Lastly, the analytical results are confirmed through numerical simulations using the MATLAB package MatContM, and a controller is applied to relieve the extreme instability within the system.

With the development of social media and online platforms, the speed of dissemination and influence of emergencies in cyberspace have increased significantly. The rapid change of public opinion, especially the reversal of public opinion, may have a significant impact on social stability and government credibility. The hypernetwork structure has complex multilevel and multidimensional characteristics, and it is of great significance to analyze the multiple participating subjects of public opinion evolution and their complex relationships based on the hypernetwork theory, and to further identify the public opinion reversal for the public opinion response and guidance of emergencies. According to the complex interaction between the participants of emergencies and internal and external factors, this paper constructs a hypernetwork model including four subnets of users, time series, opinions, and emotions, and analyzes the network structure in detail. On this basis, the method steps of emergency public opinion inversion recognition are proposed. Taking the public opinion event caused by Hongxing Erke donation during the rainstorm in Henan Province of China as an example, the empirical analysis is carried out. The research shows that the proposed emergency hypernetwork model provides effective support for the identification of public opinion inversion, and the identification method of public opinion inversion based on the hypernetwork is helpful to find the trend of public opinion evolution, so as to infer the tendency of public opinion inversion, which provides new ideas for the related research of public opinion monitoring and emergency response.

While modeling students’ learning behavior or preferences has been found to be a crucial indicator for their course achievement, very few studies have considered it in predicting the achievement of students in online courses. This study aims to model students’ online learning behavior and accordingly predict their course achievement. First, feature vectors are developed using their aggregated action logs during a course. Second, some of these feature vectors are quantified into three numeric values that are used to model students’ learning behavior, namely, accessing learning resources (content access), engaging with peers (engagement), and taking assessment tests (assessment). Both students’ feature vectors and behavior models constitute a comprehensive student’s learning behavioral pattern which is later used for the prediction of their course achievement. Lastly, using a multiple-criteria decision-making method (i.e., TOPSIS), the best classification methods were identified for courses with different sizes. Our findings revealed that the proposed generalizable approach could successfully predict students’ achievement in courses with different numbers of students and features, showing the stability of the approach. Decision tree and AdaBoost classification methods appeared to outperform other existing methods on different datasets. Moreover, our results provide evidence that it is feasible to predict students’ course achievement with high accuracy through modeling their learning behavior during online courses.

Bidirectional encoder representation from transformer (BERT) models are increasingly being employed in the development of natural language processing (NLP) systems, predominantly for English and other European languages. However, because of the complexity of the language’s morphology and the scarcity of models and resources, the BERT model is not widely employed for Amharic text processing and other NLP applications. This paper describes the fine-tuning of a pretrained BERT model to classify Amharic news documents into different news labels. We modified and retrained the model using a custom news document dataset separated into seven key categories. We utilized 2181 distinct Amharic news articles, each comprising a title, a summary lead, and a comprehensive main body. An experiment was carried out to assess the performance of the fine-tuned BERT model, which achieved 88% accuracy, 88% precision, 87.61% recall, and 87.59% F1-score, respectively. In addition, we evaluated our fine-tuned model against baseline models such as bag-of-words with MLP, Word2Vec with MLP, and fastText classifier utilizing the identical dataset and preprocessing module. Our model outperformed these baselines by 6.3%, 14%, and 8% in terms of accuracy, respectively. In conclusion, our refined BERT model has demonstrated encouraging outcomes in the categorization of Amharic news documents, surpassing conventional methods. Future research could explore further fine-tuning techniques and larger datasets to enhance performance.

This article presents a method of constructing counter-examples and a complete counter-example to the linear programming model alleged to be the solution to the traveling salesman problem. The counter-example is checked against the model proposed by Diaby et al. However, it applies to all similar formulations of the TSP problem.

Although the model in question was published in 2006, and there were several discussions regarding its correctness, the counter-example was never presented.

The presented counter-example is a regular graph, and the aim was not to have an example with the least possible size; therefore, the focus was on clarity. The counter-example has, therefore, 366 nodes in two main clusters, each node (in the main part) having exactly four connections to other nodes in the cluster.

In our statistical analysis, we have discovered that the distance distribution (referring to Euclidean distance) of many real networks follows certain patterns, especially the distances between connected nodes obey a scale-free distribution. However, the classic BA model does not exhibit this characteristic. Furthermore, existing network models are mostly evolved based on degree-preference mechanisms, without considering the potential influence of factors such as edge weights like spatial geographical factors on node-edge connections in real networks. Taking distance-weighted preferences as an example, this study proposes a network evolution model based on distance preference connections as the fundamental mechanism. By applying probability theory and mean-field theory, the model’s degree distribution is calculated to be exponential, with a clustering coefficient greater than that of the BA model and consistent with data from some real networks. Our model reveals that this distance preference mechanism may be the fundamental mechanism underlying the emergence of high clustering in real networks. Additionally, by incorporating degree-preference connection mechanisms, the model is further analyzed and improved to better match actual network evolution behaviors. The research results provide a possible explanation for resolving the controversy surrounding the scale-free nature of networks.

Many organisms, ranging from modern humans to extinct species, exhibit movement patterns that can be described by Lévy walk dynamics. It has been demonstrated that such behavior enables optimal foraging when resource distribution is sparse. Here, we analyze a dataset of football player trajectories, recorded during the matches of the Japanese football league, to elucidate the presence of statistical signatures of Lévy walks, such as the heavy-tailed distribution of distances traveled between significant turns and the characteristic superdiffusive behavior. We conjecture that the competitive environment of a football game leads to bursty movement dynamics reminiscent of that observed in hunter-gathering populations and more broadly in any biological organisms foraging for resources, whose exact distribution is unknown to them. Apart from analyzing individual players’ movements, we investigate the dynamics of the whole team by studying the movements of its center of mass (team’s centroid). Remarkably, the trajectory of the centroid also exhibits Lévy walk properties, marking the first instance of such type of motion observed at the group level. Our work concludes with a comparative analysis of different teams and some discussion on the relevance of our findings to sports science and science more generally.

Due to the significant tension–compression asymmetry of rocks, the disparity between the results of Brazilian splitting tests and those derived from the linear elastic constitutive theory has been a topic of extensive discussion. In order to delve into the stress–strain field evolution and crack propagation process of Brazilian splitting tests under tension–compression varying modulus constitutive models, finite element software was employed. By means of self-developed subroutines, a method was employed to control the rock’s tension and compression with different modulus. Comparative analysis was conducted to scrutinize the distinctions between linear elastic constitutive models and variational modulus constitutive models. The results elucidate that under the variational modulus constitutive model: (1) Stress concentration in the x-direction does not occur at the center of the rock but is offset toward the two sides of the rock loading end, with stress peaks similar to linear elasticity; (2) under the variable modulus constitutive model, shear effects are pronounced at both ends of the rock loading axis, and initial cracks in the rock originate near the two sides of the loading end, forming initial cracks of tensile-shear mixed mode; and (3) due to the influence of shear stresses at both ends of the rock loading, the ultimate load of the rock is lower than that of a linear elastic structure, and the calculated tensile strength is lower than the true strength of the rock.