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Let f and g be two Anosov diffeomorphisms on \mathbb {T}^3 with three-subbundles partially hyperbolic splittings where the weak stable subbundles are considered as center subbundles. Assume that f is conjugate to g and the conjugacy preserves the strong stable foliation, then their center Lyapunov exponents of corresponding periodic points coincide. This is the converse of the main result of Gogolev and Guysinsky [Discrete Contin. Dyn. Syst. 22 (2008), pp. 183–200]. Moreover, we get the same result for partially hyperbolic diffeomorphisms derived from Anosov on \mathbb {T}^3. [ABSTRACT FROM AUTHOR]

With the rapid development of higher education, the evaluation of the academic growth potential of universities has received extensive attention from scholars and educational administrators. Although the number of papers on university academic evaluation is increasing, few scholars have conducted research on the changing trend of university academic performance. Because traditional statistical methods and deep learning techniques have proven to be incapable of handling short time series data well, this paper proposes to adopt topological data analysis (TDA) to extract specified features from short time series data and then construct the model for the prediction of trend of university academic performance. The performance of the proposed method is evaluated by experiments on a real-world university academic performance dataset. By comparing the prediction results given by the Markov chain as well as SVM on the original data and TDA statistics, respectively, we demonstrate that the data generated by TDA methods can help construct very discriminative models and have a great advantage over the traditional models. In addition, this paper gives the prediction results as a reference, which provides a new perspective for the development evaluation of the academic performance of colleges and universities. [ABSTRACT FROM AUTHOR]

With the globalization of higher education, academic evaluation is increasingly valued by the scientific and educational circles. Although the number of published papers of academic evaluation methods is increasing, previous research mainly focused on the method of assigning different weights for various indicators, which can be subjective and limited. This paper investigates the evaluation of academic performance by using the statistical K-means (SKM) algorithm to produce clusters. The core idea is mapping the evaluation data from Euclidean space to Riemannian space in which the geometric structure can be used to obtain accurate clustering results. The method can adapt to different indicators and make full use of big data. By using the K-means algorithm based on statistical manifolds, the academic evaluation results of universities can be obtained. Furthermore, through simulation experiments on the top 20 universities of China with the traditional K-means, GMM and SKM algorithms, respectively, we analyze the advantages and disadvantages of different methods. We also test the three algorithms on a UCI ML dataset. The simulation results show the advantages of the SKM algorithm. [ABSTRACT FROM AUTHOR]

Session-based recommendation models users' interests in sessions to make recommendations. Many previous studies have shown that users usually have similar interests to their friends, and are easily influenced by friends. However, these studies also tend to ignore the fact that users' interests may merely be similar to certain friends' interests in certain aspects. To address the above issues, we propose a novel H ierarchical Social Similarity-guided M odel with D ual-mode A ttention (HMDA) for Session-based Recommendation. Specifically, we first calculate the item-level similarity between users and their friends to select influential friends. We then compute the aspect-level similarity to explore the aspect difference between users' interests and friends' interests. Under the guidance of the item-level and aspect-level similarity, HMDA is capable of effectively and accurately aggregating the social influence exerted by friends on users, and further combining users' individual interests to enhance recommendation performance. In addition, we design a dual-mode attention mechanism to capture the internal dependence and mutual dependence between the long-term and short-term interests of users. The proposed model is extensively evaluated on three real-world datasets. Experimental results demonstrate that our model outperforms the state-of-the-art baseline methods. [ABSTRACT FROM AUTHOR]