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In the theory of cosmology, de Sitter space is the symmetrical model of accelerated expansions of the universe. It is derived from the solution of the Einstein field equation, which has a positive cosmological constant. In this paper, we define the evolutes and focal surfaces of timelike Sabban curves in de Sitter space. We find that de Sitter focal surfaces can be regarded as caustics and de Sitter evolutes corresponding to the locus of the polar vectors of osculating de Sitter subspaces. By using singularity theory, we classify the singularities of the de Sitter focal surfaces and de Sitter evolutes and show that there is a close relationship between a new geometric invariant and the types of singularities. Moreover, the Legendrian dual relationships between the hyperbolic tangent indicatrix of timelike Sabban curves and the focal surfaces are given. Finally, we provide an example to illustrate our main results. [ABSTRACT FROM AUTHOR]

Essentially, the solution to an attribute reduction problem can be viewed as a reduct searching process. Currently, among various searching strategies, meta-heuristic searching has received extensive attention. As a new emerging meta-heuristic approach, the forest optimization algorithm (FOA) is introduced to the problem solving of attribute reduction in this study. To further improve the classification performance of selected attributes in reduct, an ensemble framework is also developed: firstly, multiple reducts are obtained by FOA and data perturbation, and the structure of those multiple reducts is symmetrical, which indicates that no order exists among those reducts; secondly, multiple reducts are used to execute voting classification over testing samples. Finally, comprehensive experiments on over 20 UCI datasets clearly validated the effectiveness of our framework: it is not only beneficial to output reducts with superior classification accuracies and classification stabilities but also suitable for data pre-processing with noise. This improvement work we have performed makes the FOA obtain better benefits in the data processing of life, health, medical and other fields. [ABSTRACT FROM AUTHOR]

Symmetry-based channel digital twin is a great technology which can reproduce the communication channel of real scenes for performance evaluation of the wireless sensor network (WSN) inside tower buildings, based on the ray tracing (RT) method and machine learning (ML) theories, a cluster-based channel model is proposed in this paper. Meanwhile, an improved k-means method, which considers the weight of different dimensions in the multipath component distance (MCD) is presented for clustering, which has better clustering performance over the sparsity-based algorithm and traditional k-means algorithm. Moreover, the channel parameters such as cluster delay and cluster power are also investigated. On this basis, the communication performance of WSN, i.e., bit error rate (BER) and channel capacity are derived and analyzed. The simulation and analysis results show that the cluster model based on the RT method can get approximately equivalent channel impulse response (CIR), and the BER of proposed model is consistent with the simulated one. These results can provide reference for the node layout and optimization of WSN inside tower buildings. [ABSTRACT FROM AUTHOR]