For the symmetrical mixture model and mixture test area, the lattice point set is used to partition, and then the corresponding test statistics can be constructed. In this paper, we first propose the partition methods under the lattice point sets and obtain several sub-simplexes without common interior points. Furthermore, we present a method for constructing a uniform design on the simplex using the center points of these sub-simplexes. The designs satisfy the uniformity of maximum distance deviation and provide good results for the mean square error deviation. Finally, the uniformity test on the mixture region is considered and illustrated by examples.

This paper devotes to the almost sure quasi-synchronization of reaction-diffusion neural networks (RDNNs) with stochastic switching. Markov switching (MS) and independent and identically distributed switching (IIDS) are considered. By designing a boundary controller, some almost sure bounded decay results are presented to analyze the error system obtained from the leader and RDNNs. Almost sure quasi-synchronization of RDNNs with stochastic switching is realized under the ergodic theory of Markov chain and the law of large numbers for independent and identically distributed process (IIDP). Meanwhile, an example with simulations is provided to verify the conclusion.

This study has made significant findings in A-share market data processing and portfolio management. Firstly, by adopting the Lasso method and CPCA framework, we effectively addressed the problem of multicollinearity among feature indicators, with the Lasso method demonstrating superior performance in handling this issue, thus providing a new method for financial data processing. Secondly, Deep Feedforward Neural Networks (DFN) exhibited exceptional performance in portfolio management, significantly outperforming other evaluated machine learning methods, and achieving high levels of out-of-sample performance and Sharpe ratios. Additionally, we consistently identified price changes, earnings per share, net assets per share, and excess returns as key factors influencing predictive signals. Finally, this study combined the Lasso method with DFN, providing a new perspective and methodological support for asset pricing measurement in the financial field.

For the symmetrical mixture model and mixture test area, the lattice point set is used to partition, and then the corresponding test statistics can be constructed. In this paper, we first proposes the partition methods under the lattice point sets and obtains several sub-simplexes without common interior points. Furthermore, we present the method for constructing a uniform design on the simplex using the center points of these sub-simplexes. The designs satisfy the uniformity of maximum distance deviation and provide good results for the mean square error deviation. Finally, the uniformity test on the mixture region is considered and illustrated by examples.