Homotopy-based training of NeuralODEs for accurate dynamics discovery

Conceptually, Neural Ordinary Differential Equations (NeuralODEs) pose an attractive way to extract dynamical laws from time series data, as they are natural extensions of the traditional differential equation-based modeling paradigm of the physical sciences. In practice, NeuralODEs display long training times and suboptimal results, especially for longer duration data where they may fail to fit the data altogether. While methods have been proposed to stabilize NeuralODE training, many of these involve placing a strong constraint on the functional form the trained NeuralODE can take that the actual underlying governing equation does not guarantee satisfaction. In this work, we present a novel NeuralODE training algorithm that leverages tools from the chaos and mathematical optimization communities - synchronization and homotopy optimization - for a breakthrough in tackling the NeuralODE training obstacle. We demonstrate architectural changes are unnecessary for effective NeuralODE training. Compared to the conventional training methods, our algorithm achieves drastically lower loss values without any changes to the model architectures. Experiments on both simulated and real systems with complex temporal behaviors demonstrate NeuralODEs trained with our algorithm are able to accurately capture true long term behaviors and correctly extrapolate into the future.Comment: 12 pages, 6 figures, submitted to ICLR202

Relationships of walking activity with depressed mood and suicidal ideation among the middle-aged Korean population: a nationwide cross-sectional study

IntroductionThe suicide rate of middle-aged adults has increased rapidly, which is a significant public health concern. A depressed mood and suicidal ideation are significant risk factors for suicide, and non-pharmacological interventions such as exercise therapy have been suggested as potential treatments. Walking is a feasible and accessible form of exercise therapy for middle-aged adults.MethodsWe conducted a study based on the Seventh Korea National Health and Nutrition Examination Survey (2016–2018) data of 6,886 general middle-aged adults in South Korea to investigate the relationships of walking exercise with depressed mood and suicidal ideation. Multiple logistic regression analysis was used to adjust for confounding variables. Sampling weights were applied to obtain estimates for the general Korean population.ResultsParticipants who walked ≥5 days per week had a significantly lower odds ratio (OR) for depressed mood [OR = 0.625, 95% confidence interval (CI): 0.424–0.921, p = 0.018] and suicidal ideation (OR = 0.252, 95% CI: 0.125–0.507, p < 0.001) compared to those who never walked, regardless of the duration of exercise. The same results were obtained for males after stratifying the data by sex and suicidal ideation was associated with walking in females.ConclusionRegular walking exercise was associated with diminished mental health problems in middle-aged adults. Light walks may serve as a useful starting point for patients with serious mental health issues, such as suicidal ideation

Interrelationship of Pyrogenic Polycyclic Aromatic Hydrocarbon (PAH) Contamination in Different Environmental Media

Interrelationships between pyrogenic polycyclic aromatic hydrocarbons (PAHs) were assessed in air, soil, water, sediment, and tree leaves by using multi-media monitoring data. Concurrent concentration measurements were taken bimonthly for a year for the multi-media at urban and suburban sites. PAH level correlations between air and other media were observed at the urban site but were less clear at the suburban site. Considering a closer PAHs distribution/fate characteristics to soil than suspended solids, contamination in sediment seemed to be governed primarily by that in soil. The partitioning of PAHs in waters could be better accounted for by sorption onto black carbon and dissolved organic carbon

Modified cardiovascular SOFA score in sepsis: development and internal and external validation

Background : The Sepsis-3 criteria introduced the system that uses the Sequential Organ-Failure Assessment (SOFA) score to define sepsis. The cardiovascular SOFA (CV SOFA) scoring system needs modification due to the change in guideline-recommended vasopressors. In this study, we aimed to develop and to validate the modified CV SOFA score. Methods : We developed, internally validated, and externally validated the modified CV SOFA score using the suspected infection cohort, sepsis cohort, and septic shock cohort. The primary outcome was 28-day mortality. The modified CV SOFA score system was constructed with consideration of the recently recommended use of the vasopressor norepinephrine with or without lactate level. The predictive validity of the modified SOFA score was evaluated by the discrimination for the primary outcome. Discrimination was assessed using the area under the receiver operating characteristics curve (AUC). Calibration was assessed using the calibration curve. We compared the prognostic performance of the original CV/total SOFA score and the modified CV/total SOFA score to detect mortality in patients with suspected infection, sepsis, or septic shock. Results : We identified 7,393 patients in the suspected cohort, 4038 patients in the sepsis cohort, and 3,107 patients in the septic shock cohort in seven Korean emergency departments (EDs). The 28-day mortality rates were 7.9%, 21.4%, and 20.5%, respectively, in the suspected infection, sepsis, and septic shock cohorts. The model performance is higher when vasopressor and lactate were used in combination than the vasopressor only used model. The modified CV/total SOFA score was well-developed and internally and externally validated in terms of discrimination and calibration. Predictive validity of the modified CV SOFA was significantly higher than that of the original CV SOFA in the development set (0.682 vs 0.624, p < 0.001), test set (0.716 vs 0.638), and all other cohorts (0.648 vs 0.557, 0.674 vs 0.589). Calibration was modest. In the suspected infection cohort, the modified model classified more patients to sepsis (66.0 vs 62.5%) and identified more patients at risk of septic mortality than the SOFA score (92.6 vs 89.5%). Conclusions : Among ED patients with suspected infection, sepsis, and septic shock, the newly-developed modified CV/total SOFA score had higher predictive validity and identified more patients at risk of septic mortality.National Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF2020R1A2C3004508) to Kyuseok Kim. National Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF2020R1F1A1052908) to Tae Gun Shin