We demonstrate the formation of hierarchical structures in two-dimensional systems with multiple length scales in the inter-particle interaction. These include states such as clusters of clusters, concentric rings, clusters inside a ring, and stripes in a cluster. We propose to realize such systems in vortex matter (where a vortex is mapped onto a particle with multi-scale interactions) in layered superconducting systems with varying inter-layer thicknesses and different layer materials.
Topological superconductors possess a nodeless superconducting gap in the bulk and gapless zero energy modes, known as "Majorana zero modes", at the boundary of a finite system. In this work, we introduce a new class of topological superconductors, which are protected by nonsymmorphic crystalline symmetry and thus dubbed "topological nonsymmorphic crystalline superconductors". We construct an explicit Bogoliubov-de Gennes type of model for this superconducting phase in the D class and show how Majorana zero modes in this model are protected by glide plane symmetry. Furthermore, we generalize the classification of topological nonsymmorphic crystalline superconductors to the classes with time reversal symmetry, including the DIII and BDI classes, in two dimensions. Our theory provides a guidance to search for new topological superconducting materials with nonsymmorphic crystal structures.
As the internationalisation of education around the world continues to advance, cross-border cooperation between institutions is rapid, especially in the domain of higher education. As a Significant part of China's educational undertaking, Chinese-foreign cooperative education, while developing an abundance of practical international talent, has also promoted the reform and prosperity of higher education, covering various fields of economic and social construction. In this paper, a SWOT analysis of S (Strengths) W (Weaknesses) O (Opportunities) T (Threats) is conducted on the Sino-foreign higher education cooperation model. The results show that the development of Sino-foreign cooperative universities has great advantages and prospects, but the opportunities also bring the fact of fierce competition from universities of the same nature. In response to the unsatisfactory enrolment situation in 2020, strategies related to sustainable development are proposed. The enrolment aspect needs to be reasonably advertised to highlight the university's strengths; the university needs to clarify its positioning, improve the quality of teaching and increase its research output in order to improve their social status in the country.
Tag recommendation, as a branch of recommendation engine, has drawn more and more attention, which is also extensively exploited in e-commerce and SNS (Social Networking Services). The results generated by the current algorithms could describe the items with a high relevance. However, they are often of poor diversity in the recommended results. That indicates there is a redundancy in the results in term of semantics. Such a case reduces the novelty and diversity of the recommended results, seriously affecting the user's experience. In this paper, we define the tag correlation metric based on the local and global tag co-occurrence matrices, which improves the recommendation accuracy by incorporating both the user's interests and the popularity of tags. Moreover, we propose the concept of semantic coverage, by which the redundancy of semantics can be removed efficiently. To our best knowledge, it is first proposed in the context of tag recommendation. Finally, a diversified coverage based tag recommendation algorithm, namely EDC, is developed. By converting the problem of diversified coverage tag recommendation to the MIDS (Minimum Independent Dominating Set) problem, EDC first handles the cliques and the bipartites in the graph. Then, it recursively searches the MIDSs in the remaining graph. Further, a greedy algorithm GDC is proposed. The experiments conducted on the real datasets of MovieLens and Last.fm show that the proposed EDC and GDC improve the diversity significantly.
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