Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics

We present an algorithm for C1 Hermite interpolation using Möbius transformations of planar polynomial Pythagoreanhodograph (PH) cubics. In general, with PH cubics, we cannot solve C1 Hermite interpolation problems, since their lack of parameters makes the problems overdetermined. In this paper, we show that, for each Möbius transformation, we can introduce an extra parameter determined by the transformation, with which we can reduce them to the problems determining PH cubics in the complex plane ℂ. Möbius transformations preserve the PH property of PH curves and are biholomorphic. Thus the interpolants obtained by this algorithm are also PH and preserve the topology of PH cubics. We present a condition to be met by a Hermite dataset, in order for the corresponding interpolant to be simple or to be a loop. We demonstrate the improved stability of these new interpolants compared with PH quintics

Investigating the Influence of Heavy Metals and Environmental Factors on Metabolic Syndrome Risk Based on Nutrient Intake: Machine Learning Analysis of Data from the Eighth Korea National Health and Nutrition Examination Survey (KNHANES)

This study delves into the complex interrelations among nutrient intake, environmental exposures (particularly to heavy metals), and metabolic syndrome. Utilizing data from the Korea National Health and Nutrition Examination Survey (KNHANES), machine learning techniques were applied to analyze associations in a cohort of 5719 participants, categorized into four distinct nutrient intake phenotypes. Our findings reveal that different nutrient intake patterns are associated with varying levels of heavy metal exposure and metabolic health outcomes. Key findings include significant variations in metal levels (Pb, Hg, Cd, Ni) across the clusters, with certain clusters showing heightened levels of specific metals. These variations were associated with distinct metabolic health profiles, including differences in obesity, diabetes prevalence, hypertension, and cholesterol levels. Notably, Cluster 3, characterized by high-energy and nutrient-rich diets, showed the highest levels of Pb and Hg exposure and had the most concerning metabolic health indicators. Moreover, the study highlights the significant impact of lifestyle habits, such as smoking and eating out, on nutrient intake phenotypes and associated health risks. Physical activity emerged as a critical factor, with its absence linked to imbalanced nutrient intake in certain clusters. In conclusion, our research underscores the intricate connections among diet, environmental factors, and metabolic health. The findings emphasize the need for tailored health interventions and policies that consider these complex interplays, potentially informing future strategies to combat metabolic syndrome and related health issues

Image_1_Association between household income levels and nutritional intake of allergic children under 6 years of age in Korea: 2019 Korea National Health and Nutrition Examination Survey and application of machine learning.png

IntroductionThis study investigated the prevalence of allergic diseases in Korean children aged 6 and below, focusing on the interplay between nutritional status, household income levels, and allergic disease occurrence.MethodsThis study used data from the 2019 Korea National Health and Nutrition Examination Survey, a nationwide comprehensive survey, and included a representative sample of 30,382 children under the age of 6 to investigate in detail the relationship between allergic diseases, nutritional intake, and socioeconomic factors. Logistic regression analysis was performed to identify factors associated with allergic diseases, including gender, BMI, eating habits, dietary supplement intake, and nutrient consumption. To predict childhood asthma, 14 machine learning models were compared using the ‘pycaret’ package in Python.ResultsWe discerned that 24.7% were diagnosed with allergic conditions like atopic dermatitis, asthma, and allergic rhinitis. Notably, household income exhibited a significant influence, with the lowest income quartile exhibiting higher prevalence rates of asthma, allergic rhinitis, and multiple allergic diseases. In contrast, the highest income quartile displayed lower rates of allergic rhinitis. Children diagnosed with allergic diseases demonstrated compromised intake of essential nutrients such as energy, dietary fiber, vitamin B1, sodium, potassium, and iron. Particularly noteworthy were the deficits in dietary fiber, vitamin A, niacin, and potassium intake among children aged 3–5 with allergies. Logistic regression analysis further elucidated that within low-income families, female children with higher BMIs, frequent dining out, dietary supplement usage, and altered consumption of vitamin B1 and iron faced an elevated risk of allergic disease diagnosis. Additionally, machine learning analysis pinpointed influential predictors for childhood asthma, encompassing BMI, household income, subjective health perception, height, and dietary habits.DiscussionOur findings underscore the pronounced impact of income levels on the intricate nexus between allergic diseases and nutritional status. Furthermore, our machine learning insights illuminate the multifaceted determinants of childhood asthma, where physiological traits, socioeconomic circumstances, environmental factors, and dietary choices intertwine to shape disease prevalence. This study emphasizes the urgency of tailored nutritional interventions, particularly in socioeconomically disadvantaged populations, while also underscoring the necessity for comprehensive longitudinal investigations to unravel the intricate relationship between allergic diseases, nutritional factors, and socioeconomic strata.</p

Machine learning enhances the performance of short and long-term mortality prediction model in non-ST-segment elevation myocardial infarction

Abstract Machine learning (ML) has been suggested to improve the performance of prediction models. Nevertheless, research on predicting the risk in patients with acute myocardial infarction (AMI) has been limited and showed inconsistency in the performance of ML models versus traditional models (TMs). This study developed ML-based models (logistic regression with regularization, random forest, support vector machine, and extreme gradient boosting) and compared their performance in predicting the short- and long-term mortality of patients with AMI with those of TMs with comparable predictors. The endpoints were the in-hospital mortality of 14,183 participants and the three- and 12-month mortality in patients who survived at discharge. The performance of the ML models in predicting the mortality of patients with an ST-segment elevation myocardial infarction (STEMI) was comparable to the TMs. In contrast, the areas under the curves (AUC) of the ML models for non-STEMI (NSTEMI) in predicting the in-hospital, 3-month, and 12-month mortality were 0.889, 0.849, and 0.860, respectively, which were superior to the TMs, which had corresponding AUCs of 0.873, 0.795, and 0.808. Overall, the performance of the predictive model could be improved, particularly for long-term mortality in NSTEMI, from the ML algorithm rather than using more clinical predictors