This paper mainly tends to investigate finite-time stability and stabilization of impulsive stochastic delayed neural networks with randomly occurring uncertainties (ROUs) and randomly occurring nonlinearities (RONs). Firstly, by constructing the proper Lyapunov-Krasovskii functional and employing the average impulsive interval method, several novel criteria for ensuring the finite-time stability of impulsive stochastic delayed neural networks are obtained by means of linear matrix inequalities (LMIs). Then, some conditions about the state feedback controller are derived to ensure the finite-time stabilization of impulsive stochastic delayed neural networks with ROUs and RONs. Finally, numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed results.

Multimodal multiobjective optimization problems, characterized by multiple solutions mapping to identical objective vectors, are ubiquitous in real-world applications. Despite their prevalence, most existing multimodal multiobjective evolutionary algorithms (MMOEAs) predominantly focus on identifying global Pareto sets, often overlooking the equally significant local Pareto sets. While some algorithms attempt to address local Pareto sets, their performance in the objective space remains suboptimal. The inherent challenge lies in the fact that a single strategy cannot effectively tackle problems with and without local Pareto fronts. This study proposes a novel approach that first detects the presence of local Pareto fronts using a neural network, thereby enabling adaptive adjustments to the algorithm’s selection strategy and search scope. Based on this detection mechanism, we design a microscale searching multimodal multiobjective evolutionary algorithm (MMOEA_MS). Through extensive experiments on twenty-two benchmark problems, MMOEA_MS demonstrates superior performance in identifying local Pareto fronts and outperforms existing algorithms in the objective space. This study highlights the effectiveness of MMOEA_MS in solving multimodal multiobjective optimization problems with diverse Pareto front characteristics, thereby addressing key limitations of current methodologies.

Exploring and detecting the causal relations among variables have shown huge practical values in recent years, with numerous opportunities for scientific discovery, and have been commonly seen as the core of data science. Among all possible causal discovery methods, causal discovery based on a constraint approach could recover the causal structures from passive observational data in general cases, and had shown extensive prospects in numerous real world applications. However, when the graph was sufficiently large, it did not work well. To alleviate this problem, an improved causal structure learning algorithm named brain storm optimization (BSO), is presented in this paper, combining K2 with brain storm optimization (K2-BSO). Here BSO is used to search optimal topological order of nodes instead of graph space. This paper assumes that dataset is generated by conforming to a causal diagram in which each variable is generated from its parent based on a causal mechanism. We designed an elaborate distance function for clustering step in BSO according to the mechanism of K2. The graph space therefore was reduced to a smaller topological order space and the order space can be further reduced by an efficient clustering method. The experimental results on various real-world datasets showed our methods outperformed the traditional search and score methods and the state-of-the-art genetic algorithm-based methods.

Traditional fuzzy clustering algorithms construct sample partition criteria solely based on similarity measures but lack an effective representation of prior membership information, which limits further improvements in clustering accuracy. To address this issue, this paper proposes a semi-supervised fuzzy clustering algorithm based on prior membership (SFCM-PM). The proposed algorithm introduces prior information entropy as a metric to quantify the divergence between partition membership and prior membership and incorporates this as an auxiliary partition criterion into the objective function. By jointly optimizing data similarity and consistency with prior knowledge during the clustering process, the algorithm achieves more accurate and reliable clustering results. The experimental results demonstrate that the SFCM-PM algorithm achieves significant performance improvements by incorporating a small number of prior membership samples across several standard and real-world datasets. It also performs outstandingly on datasets with unbalanced sample distributions.

In the problem of causal discovery, conditional independence (CI) tests are generally used to detect the causal relationships among observed data. Due to the curse of dimensionality and the limitation of causal direction learning based on V -structure learning, it is difficult for constraint-based methods to distinguish the actual graph from a set of Markov equivalence classes. To alleviate this problem, in this work, a novel regression-based method to test CIs over linear Non-Gaussian data is proposed. The main purpose of this proposal is to relax the CI test of x±yǀZ to two unconditional independence tests x – f (Z)±y – g (Z) + ∑H (Z) and x – f (Z) + ∑H (Z)±y – g (Z), where f and g can be estimated by linear regression independently. In addition, we further show that x – f (Z)±y – g (Z) + ∑H (Z) ( or x – f (Z) + ∑H (Z)±y – g (Z) ) can lead to x← Z ( or y ← Z ). According to this regression-based method, we design a causal structure learning algorithm to learn the actual graph instead of a set of Markov equivalence classes over the observed data. Experiments indicate that our method can detect much more causal relationships than other existing methods, especially in large-scale cases.