In this paper we propose a novel clustering method for functional data based on the principal curve clustering approach. By this method functional data are approximated using functional principal component analysis (FPCA) and the principal curve clustering is then performed on the principal scores. The proposed method makes use of the nonparametric principal curves to summarize the features of the principal scores extracted from the original functional data, and a probabilistic model combined with Bayesian Information Criterion is employed to automatically and simultaneously find the appropriate number of features, the optimal degree of smoothing and the corresponding cluster members. The simulation studies show that the proposed method outperforms the existing functional clustering approaches considered. The capability of this method is also demonstrated by the applications in the human mortality and fertility data.

We conducted a large-scale epidemiological investigation to detect the prevalence of Toxoplasma gondii in four marine bivalve shellfish species collected from six representative coastal regions of Weihai, eastern China. Between January 2018 and December 2018, 14,535 marine bivalve shellfish pooled into 2907 samples were randomly collected and examined for T. gondii DNA by a nested PCR assay targeting B1 gene. The results showed that 2.8% (82) of the 2907 pooled samples were tested positive for T. gondii DNA. Two T. gondii genotype (ToxoDB Genotype #9 and ToxoDB Genotype #1) were identified PCR-restriction fragment length polymorphism analysis. Factors that were found significantly associated with the presence of T. gondii DNA in marine bivalve shellfish included the source of samples (being wild) (odds ratio [OR], 3.34; 95% confidence interval [CI], 2.00-5.84; p < 0.01), surface runoff near the sampling site (OR, 2.64; 95% CI, 1.47-4.72; p < 0.01), and presence of cats near the sampling site (OR, 1.77; 95% CI, 1.02-3.07; p = 0.04). Moreover, the prevalence of T. gondii DNA in marine bivalve shellfish correlated with temperature (Pearson's correlation: R = 0.75, p = 0.0049) and precipitation (R = 0.87, p = 0.00021). These findings provide new insights into the presence of T. gondii DNA in marine bivalve shellfish and highlight the impact of human activity on marine pollution by such an important terrestrial pathogen pollutant.

Optimization, particularly constrained optimization problems (COPs), is fundamental in engineering, influencing various sectors with its critical role in enhancing design efficiency, reducing experimental costs, and shortening testing cycles. This study explores the challenges inherent in COPs, with a focus on developing efficient solution methodologies under stringent constraints. Surrogate models, especially Gaussian Process Regression (GPR), are pivotal in our approach, enabling the approximation of complex systems with reduced computational demand. We evaluate the efficacy of the Efficient Global Optimization (EGO) algorithm, which synergizes GPR with the Expected Improvement (EI) function, and further extend this framework to Constrained Expected Improvement (CEI) and our novel methodology Constrained Expected Prediction Error (CEPE). We demonstrate the effectiveness of these methodologies by numerical benchmark simulations and the real-world application of optimizing a Three-Bar Truss Design. In essence, the innovative CEPE approach promises a potent balance between solution accuracy and computational prowess, offering significant potential in the broader engineering field.