A Fast Adaptive Method for the Evaluation of Heat Potentials in One Dimension

We present a fast adaptive method for the evaluation of heat potentials, which plays a key role in the integral equation approach for the solution of the heat equation, especially in a non-stationary domain. The algorithm utilizes a sum-of-exponential based fast Gauss transform that evaluates the convolution of a Gaussian with either discrete or continuous volume distributions. The latest implementation of the algorithm allows for both periodic and free space boundary conditions. The history dependence is overcome by splitting the heat potentials into a smooth history part and a singular local part. We discuss the resolution of the history part on an adaptive volume grid in detail, providing sharp estimates that allow for the construction of an optimal grid, justifying the efficiency of the bootstrapping scheme. While the discussion in this paper is restricted to one spatial dimension, the generalization to two and three dimensions is straightforward. The performance of the algorithm is illustrated via several numerical examples.Comment: 14 pages, 3 table

Ammonia Nitrogen Pollution Characteristics of Natural Rainfall in Urban Business District in Southern China: A Case Study of Chengdu City

Chengdu city was chosen as the representative of southern cities in China in this work, characteristics of ammonia nitrogen (NH3-N) pollution in natural rainfall were analyzed by measuring the concentration in 15 natural rainfalls from April to September in 2017. The influence of ammonia emission from toilet vent of building on NH3-N pollution in rainfall was investigated, and the variation of total NH3-N pollutants and its influencing factors were expounded. The results showed that the average concentration of NH3-N in first rainfall was the highest, reaching 18.2mg/L, the average concentration of NH3-N in the subsequent 14 rainfalls was between 2.0 and 5.0mg/L, which is higher than Grade V (?2mg/L) of Environmental Quality Standards of Surface Water (GB 3838-2002), and was an important source of NH3-N pollution in water. The concentration of NH3-N in natural rainfalls decreased with the increase of the distance between the sampling point and the toilet vent, indicating that the ammonia discharged from toilet exhaust is a major source of NH3-N pollution in urban atmosphere. The main factors affecting total NH3-N pollutants in natural precipitation include rainfall intensity, rainfall duration and drought days. The total amount of NH3-N pollutants in surface runoff is less than that in natural rainfall

Heavy Metal Emission Characteristics of Urban Road Runoff

Pavement runoff sampling points were set up on the main roads of Chengdu city. Six rainfall-runoff events from July to September in 2017 were sampled by synchronous observation of rainfall, runoff and pollution. The concentration changes of copper, lead, zinc, chromium and cadmium in the runoff process were monitored, and the pollution emission regularity and initial scouring effect were studied. The results show that the emission regularity of pavement runoff pollution is closely related to rainfall characteristics and pollutant occurrence, and the concentration of dissolved heavy metals reaches its peak at the initial stage of runoff. The peak time of particulate heavy metal concentration lagged slightly behind that of rainfall intensity. There is a big difference between the strength of initial scouring degree and dissolved heavy metals the stronger the initial scouring degree of total heavy metals, the weaker the dissolved heavy metals. Reducing pavement runoff in the early stage of rainfall is an effective means to control heavy metal pollution

π\pi-Tuning: Transferring Multimodal Foundation Models with Optimal Multi-task Interpolation

Foundation models have achieved great advances in multi-task learning with a unified interface of unimodal and multimodal tasks. However, the potential of such multi-task learners has not been exploited during transfer learning. In this work, we present a universal parameter-efficient transfer learning method, termed Predict-Interpolate Tuning ($\pi$-Tuning), for vision, language, and vision-language tasks. It aggregates the parameters of lightweight task-specific experts learned from similar tasks to aid the target downstream task. The task similarities are predicted in a unified modality-independent space, yielding a scalable graph to demonstrate task relationships. $\pi$-Tuning has several appealing benefits. First, it flexibly explores both intra- and inter-modal transferability between similar tasks to improve the accuracy and robustness of transfer learning, especially in data-scarce scenarios. Second, it offers a systematical solution for transfer learning with multi-task prediction-and-then-interpolation, compatible with diverse types of parameter-efficient experts, such as prompt and adapter. Third, an extensive study of task-level mutual benefits on 14 unimodal and 6 multimodal datasets shows that $\pi$-Tuning surpasses fine-tuning and other parameter-efficient transfer learning methods both in full-shot and low-shot regimes. The task graph also enables an in-depth interpretable analysis of task transferability across modalities.Comment: To appear in ICML 202

Household Catastrophic Medical Expenses in Eastern China: Determinants and Policy Implications

Background: Much of research on household catastrophic medical expenses in China has focused on less developed areas and little is known about this problem in more developed areas. This study aimed to analyse the incidence and determinants of catastrophic medical expenses in eastern China. Methods: Data were obtained from a health care utilization and expense survey of 11,577 households conducted in eastern China in 2008. The incidence of household catastrophic medical expenses was calculated using the method introduced by the World Health Organization. A multi-level logistic regression model was used to identify the determinants. Results: The incidence of household catastrophic medical expenses in eastern China ranged from 9.24% to 24.79%. Incidence of household catastrophic medical expenses was lower if the head of household had a higher level of education, labor insurance coverage, while the incidence was higher if they lived in rural areas, had a family member with chronic diseases, had a child younger than 5 years old, had a person at home who was at least 65 years old, and had a household member who was hospitalized. Moreover, the impact of the economic level on catastrophic medical expenses was non-linear. The poorest group had a lower incidence than that of the second lowest income group and the group with the highest income had a higher incidence than that of the second highest income group. In addition, region was a significant determinant. Conclusions: Reducing the incidence of household catastrophic medical expenses should be one of the priorities of health policy. It can be achieved by improving residents’ health status to reduce avoidable health services such as hospitalization. It is also important to design more targeted health insurance in order to increase financial support for such vulnerable groups as the poor, chronically ill, children, and senior populations