Marginal Curves Research Articles

Caustic and marginal ray curves obtained from images generated by means of a star test using digital image processing

Caustic and marginal ray curves obtained from images generated by means of a star test using digital image processing

Gossen’s first law in the modeling for demand side management: a thorough heat pump case study with deep learning based partial time series data generation

Gossen’s First Law describes the law of diminishing marginal utility. This paper aims to further verify the proposed hypothesis that Gossen’s First Law also holds in the modeling for Demand Side Management (DSM) with a thorough heat pump case study. The proposed hypothesis states that in general the complexity-utility relationship in the field of DSM modeling could be represented by a diminishing marginal utility curve. On the other hand, in data based modeling, when utilizing a large dataset for validation, the data integrity is critical to the reliability of the results. However, the absence of partial time series data may occur during the measurement due to missing sensors or IT related issues. In this work, an extensive real-world open dataset of a ground source heat pump is utilized for the case study. In the raw data, one key variable namely the flow rate is missing. Thus, three different algorithms based on machine learning and deep learning architectures namely Random Forest (RF), Long Short-Term Memory (LSTM) and Transformer are applied to predict the flow rate by utilizing an open loop forecasting. The raw data are first pre-processed with a time interval of one hour and then used for training, validation and forecast. Furthermore, a modified persistence model as the baseline is also defined. The predicted flow rate using LSTM yields the lowest error of 7.47%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} nMAE and 10.56%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} nRMSE respectively. The forecast results are then utilized in the following step of modeling of a heat pump use case. With the introduced quantification method for complexity and a modified version for utility, we further verify the proposed hypothesis with a longer time horizon of 7 days.

Warming the MATRIX: Uncertainty and heterogeneity in climate change impacts and policy targets in the Euro Area

This paper explores the potential impacts of climate change and mitigation policies in the Euro Area, considering the uncertainty and heterogeneity in both climate and economic systems. Using the MATRIX model, a multi-sector and multi-agent macroeconomic model, we simulate various climate scenarios by employing different carbon cycle models, damage functions, and marginal abatement curves found in the literature. We find that heterogeneous climate damages amplify both the magnitude and the volatility of GDP losses associated with global warming. By the end of the century, we estimate that assuming homogeneous shocks may underestimate the effects of climate change on aggregate output by up to one-third. Moreover, we find that the speed and feasibility of a low-carbon transition crucially depend on (i) the ambition in emission reduction targets set by the policymaker, which determine the level of a carbon tax, and (ii) the rate of technological progress, which influences the shape of the abatement cost curve.

Follow-up results of BI-RADS 3 lesions on magnetic resonance imaging: a retrospective study

The categorization of Breast Imaging Reporting and Data System (BI-RADS) 3 lesions is not as clear in magnetic resonance imaging (MRI) as it is in mammography (MG). With the increasing number of MRI scans currently being conducted globally, incidentally detected lesions falling into the probably benign category are frequently being observed. In this study, our aim was to investigate the imaging characteristics and follow-up results of BI-RADS 3 lesions detected by MRI and to determine their malignancy rates. Breast MRI scans performed between January 2010 and January 2020 and classified as BI-RADS 3 lesions were retrospectively analyzed. The study included 216 lesions with known biopsy or surgical excision results or with at least one year of radiological follow-up. We assessed the patients' age, the presence of breast cancer, the follow-up interval, and the imaging findings at the beginning and during the follow-up. Lesions that remained stable, disappeared, or decreased in size and had a benign histopathological diagnosis were classified as benign. Lesions with the histopathological diagnosis of malignancy, identified by either biopsy or surgical excision, were classified as malignant. We determined the malignancy rate based on the histopathology and follow-up results. Considering the follow-up results of all cases, 8% of lesions were excised, 0.5% decreased in size, 1.4% became enlarged, 17.1% disappeared, and 73% remained stable. The malignancy rate was 2.8%. A significant relationship was found between lesion shape and malignancy, as progression to malignancy was more likely in round lesions than in other types. An irregular margin, heterogeneous enhancement, and kinetic curve (type 2) features were significant for lesion upgrade to malignancy. The malignancy rate in BI-RADS 3 lesions detected by MRI is low and falls within the accepted cancer rate for MG and sonography. Changes in size, morphology, and enhancement pattern should be considered in terms of malignancy development during follow-up. The follow-up intervals should be determined on a case-by-case basis.

A critical analysis of physical activity's promising function in the management of Type 2 Diabetes Mellitus

Physical activity (PA) has been demonstrated to have negative correlations with type 2 diabetes mellitus. Considering provided the establishment of the dose‒response interactions still additionally undiscovered. For investigating the association involving extra cases of type 2-diabetes and PA, the study utilizes model nonlinearity. Implementing together study findings from multidemographic long-term studies. A metric that exclusively considers energy employed above resting metabolic rate was used to translate PA exposures through reduced metabolic equivalent of task (MET) and the physiological equivalent of task hours per the previous week. The association involving radiation and illness was modeled utilizing restricted quadratic splices. The results point to a general nonlinear association; utilizing the rectangular spline model, we discovered a probability decrease for type 2 diabetes of twenty-six percent among people who attained eleven twenty-five MET hours per month. A risk decrease of 36% was shown when this quantity of PA was doubled, and more significant reductions were seen at higher dosages. For moderate-intensity PA the power source marginal MET week dose‒response curve's findings revealed comparable. However, the advantages of higher-intensity PA were more significant, and those of lower-intensity activity substantially decreased. Among the overall population, higher levels of has been connected to a significantly decreased risk of type 2 diabetes. The relationships between type’s two diabetics with LTPA were curved. At quantities far higher than those recommended by the health department standards, however, further benefits may be possible. The most significant insufficient quantities of exercise result in relative improvements.

Reform and exploration of biopharmaceutics blended teaching in the context of "first-class undergraduate education"

In recent years, the biopharmaceutical industry has developed rapidly, creating urgent demand for high-quality, innovative, and application-oriented talents. In the context of "first-class undergraduate education", it is of great significance to reform and explore biopharmaceutics blended learning to foster professional talents who can adapt to the industrial development. The blended teaching of biopharmaceutics course in Hubei University was based on small private online course (SPOC) and ChaoXing platform, aiming to meet the first-class "AIC (advanced, innovation, challenge)". The course strengthened the three phases of teaching: before, during, and after class, and innovated teaching methods actively to achieve curriculum goals, and integrated typical cases organically. In addition, the course improved the discriminative power of assessment by strengthening the formative performance evaluation. Moreover, the course provided guidance for students to improve the learning efficiency through investigating the students' learning behavior and employing the marginal utility curve to analyze the characteristics of group activities. Furthermore, the course also offered students personalized learning guidance based on their career planning. The reform of biopharmaceutics blended teaching has achieved significant outcomes, such as improving students' satisfaction, students' innovation and entrepreneurship ability, and curriculum construction level, thus may serve as a reference for the teaching reform and research of the related courses.

An illness-death multistate model to implement delta adjustment and reference-based imputation with time-to-event endpoints.

With a treatment policy strategy, therapies are evaluated regardless of the disturbance caused by intercurrent events (ICEs). Implementing this estimand is challenging if subjects are not followed up after the ICE. This circumstance can be dealt with using delta adjustment (DA) or reference-based (RB) imputation. In the survival field, DA and RB imputation have been researched so far using multiple imputation (MI). Here, we present a fully analytical solution. We use the illness-death multistate model with the following transitions: (a) from the initial state to the event of interest, (b) from the initial state to the ICE, and (c) from the ICE to the event. We estimate the intensity function of transitions (a) and (b) using flexible parametric survival models. Transition (c) is assumed unobserved but identifiable using DA or RB imputation assumptions. Various rules have been considered: no ICE effect, DA under proportional hazards (PH) or additive hazards (AH), jump to reference (J2R), and (either PH or AH) copy increment from reference. We obtain the marginal survival curve of interest by calculating, via numerical integration, the probability of transitioning from the initial state to the event of interest regardless of having passed or not by the ICE state. We use the delta method to obtain standard errors (SEs). Finally, we quantify the performance of the proposed estimator through simulations and compare it against MI. Our analytical solution is more efficient than MI and avoids SE misestimation-a known phenomenon associated with Rubin's variance equation.

The Procoagulant Phospholipid Dependent Clotting Time and the Initiation Phase of Thrombin Generation Test Are Mandatory for the Evaluation of the Risk for Severe Early Onset Preeclampsia

Bakground: Preeclampsia occurs in up to 7% of pregnancies in Western Countries and is a leading cause of maternal and fetal morbidity and mortality. Classification of preeclampsia is based on the timing of symptoms' onset and the severity of the clinical status. Accordingly, early and late preeclampsia are characterized by symptom onset before or after 32-34 weeks of gestation respectively. Pathogenesis of preeclampsia is characterized by abnormal placental vascular development with impaired invasion of the uterine spiral arteries by trophoblasts, resulting in fetal complications and maternal endothelial dysfunction. Intact antithrombotic properties of the endothelial cells and efficient regulation of thrombin generation and platelet activation at the microenvironment of the uterus are necessary conditions for successful trophoblast invasion and development of feto-maternal circulation during normal pregnancy. , Prompt identification of pregnant women at risk of preeclampsia worsening could help to anticipated therapeutic intervention and improvement of the clinical outcome. Aim: The ROADMAP-Early Onset Preeclampsia study (ROADMAP-EOP) aiming to respond to this unmet need assessed the clinical relevance of biomarkers of hypercoagulability and endothelial activation for prompt identification of pregnant women at high risk of preeclampsia. Materials and Methods: An observational single center retrospective case-control study was conducted in pregnant women diagnosed with preeclampsia from July 2020 to July 2021. Pregnant women were retrospectively enrolled upon EOP diagnosis and stratified in mild EOP group (n=34) and severe EOP group (n=15 according to the criteria of the International Society for the Study of Hypertension in Pregnancy ). Eligible women were included in the study before initiation of any treatment for preeclampsia. The control group (n=35) consisted of women with uncomplicated pregnancy. All women were assessed with thromboelastometry, Calibrated Automated Thrombo-gram®, tissue factor activity (TFa), Procoagulant phospholipid dependent clotting time (Procoag-PPL), Proteins S, TFPI, D-dimer, antithrombin, thrombomodulin, fibrinogen prothrombin time and activated partial thromboplastin time. Primary and secondary end points were severe EOP and EOP respectively. Principal component analysis (PCA) was performed to check for associations among the biomarkers and the clinical out-come. Results: There were no significant differences regarding age, gravidity, gestational age and the body mass index (BMI) between EOP groups and normal pregnancy as well as within the EOP groups. Platelet counts were similar in healthy pregnant women, and mild EOP group, and significantly lower in severe EOP (p<0.05). No other statistically significant differences were found between-groups. The PCA showed that the repartition of data allowed to discriminate the patients with EOP from healthy pregnant women as well as patients with mild EPO from those with severe EOP. When biomarkers of hypercoagulability were considered according to the severity of EOP in PCA analysis the lag-time and PPL clotting time were independently associated with the risk of severe EOP (Table 1and Figure 1)). The increase of the lag-time by 1 min was associated with a 20.2-fold increase of the risk of severe EOP. The marginal effects curve shows that for a lag-time longer than 2.6 min, the probability of severe EOP was higher than 50% .Longer Procoag-PPL clotting time was associated with lower risk of severe EOP. The marginal effects curve, showed that for Procoag-PPL clotting time longer than 58.75 sec the probability of severe EOP decreased by 50%. These data suggest that a biological score composed of the Procoag-PPL® clotting time and thrombin generation (Throbmogram-Thrombinoscope® PPP-reagent 1 pM-TF as-say) could be a useful tool to identify pregnant women with high probability of EOP Conclusion: the Procoag-PPL® clotting time and thrombin generation assay reflect cellular derived hypercoagulability and allow accurate screening of pregnant women for the prompt identification of those at risk of EOP and the evaluation of its severity. This concept has to be validated in a large prospective cohort trial. . An external validation of the proposed methodology needs to be performed in a large prospective observational study.

Outside good utility and substitution patterns in direct utility models

This paper investigates the role of the outside good utility function on admissible substitution patterns in multiple discrete/continuous demand models. We first present a set of novel results that characterize the functional form of quantity price effects within this class of models. The results highlight the relative inflexibility of many standard outside good utility functions. We then propose a new outside good utility function that admits more flexible marginal utility curves. Our empirical analysis uses household scanner panel data from the potato chip category, where we find empirical support for non-standard rates of satiation for the outside good. We then show how the restrictive substitution patterns induced by standard utility specifications may distort price elasticities and the evaluation of loyalty coupon targeting programs.

A link criticality approach for pedestrian network design to promote walking

Measures of walkability generally do not provide a detailed quantitative assessment of pedestrian infrastructure development prioritization. In this study, a link-based composite measure of walkability and walking is introduced to overcome this limitation. This measure, called ‘pednet score’, is based on a weighted pedestrian network (‘pednet’) made of sidewalks and crosswalks whose edge weights are descriptive of their popularity. Edge popularity is derived from home-based walk trip assignments derived from simulated pedestrian demand. Properties of the pednet score are studied using three hypothetical variants of the pednet in three North American cities, each involving the addition of candidate sidewalk and/or crosswalk segments. It is shown that a strategic selection of these segments based on pednet score can substantially increase walking trips, in some cases up to 236%, and reduce current mean pedestrian trip distances by up to 340 m. A mixed development approach involving both sidewalks and crosswalks also shows considerably higher improvement than those segments considered alone. Results from marginal benefit curves strongly indicate the utility of the pednet score as a measure of link criticality for segment prioritization in pedestrian network design.

Rayleigh–Bénard Convection of Water-Copper and Water-Alumina Nanofluids Based on Minimal- and Higher-Mode Lorenz Models

Linear and nonlinear stability analyses of Rayleigh–Bénard convection in water-copper and water-alumina nanofluids are studied in the paper by considering a minimal as well as an extended truncated Fourier representation. These representations respectively result in a third-order classical Lorenz model and a five-dimensional extended Lorenz model. The marginal stability plots reveal that the influence of added dilute concentration of nanoparticles in water is to destabilize the system. The rate of destabilization depends on the nanoparticles’ thermophysical properties and their volume fraction. Influence of adding an additional mode in the horizontal direction is to modify the cell size. This can be observed through the marginal curves as well as the stream line plots. Further, from the Nusselt number plots it is evident that the presence of dilute concentration of nanoparticles in water is to enhance heat transport in the system significantly. The dynamical behavior of the minimal and the extended Lorenz models is investigated using the bifurcation diagram. From the study an important finding that emerges is that the Fourier truncated solution is predicted to have different effects in lower-order and higher-order models. The extended penta-modal Lorenz system predicts advanced onset of chaos compared to that predicted by the classical third-order Lorenz model. The individual influence of both nanoparticles in water is to advance the onset of convection as well as to advance the onset of chaos.

Management of Digital Dermatitis in Dairy Herds: Optimization and Time Allocation

The objective of this study is to determine the most effective time allocation for digital dermatitis management and to quantify the marginal economic gain from extra time devoted to digital dermatitis management. The model simulating foot disease occurrence and the associated management was Dairy Health Simulator©. Then, an econometric model was applied to identify the relationship between the dairy workshop’s gross margin and time for lameness management as well as the hourly marginal gain curve associated with lameness management. The gross margin was optimized under two constraints, i.e., the overall time spent for lameness management and the mean lameness duration (mimicking cow welfare). The results show that allocating less time to lameness detection and more to footbath application can contribute as follows: (i) reduces time spent for lameness management, (ii) maintains the best welfare level, and (iii) obtains the highest gross margin. The optimal time to devote to footbath application ranged from 17.8 to 22.3 h/month. A hiring strategy was investigated, and the break-even point ranged from 16.1 to 19.8 h/month. The recommended time to spend on footbath application is relatively important; therefore, stakeholders should consider the importance of lameness to the dairy industry and should devote enough time for footbath applications.

Individual and Combined Effects of 3D Buildings and Green Spaces on the Urban Thermal Environment: A Case Study in Jinan, China

This study aimed to accurately grasp the impact mechanism and change rule of buildings and green spaces on land surface temperature (LST), which is of great significance for alleviating urban heat islands (UHIs) and formulating adaptation measures. Taking Jinan, China, as the study area, combined multisource remote sensing data were used in this study to construct an index system of the influencing factors. We used a spatial regression model to explore the relative contribution of the influencing indicators on LST. We also drew a marginal utility curve to quantify the heating/cooling effect of the leading indicators. The results showed that, firstly, among the 3D building indicators, the leading indicators affecting LST were the degree of spatial convergence (SCD) and the building surface area (BSA). Among the green space indicators, the largest patch index (LPI), green coverage rate (GCR), and edge density (ED) were significantly negatively correlated with LST. Secondly, when we considered the 15 indicators comprehensively, SCD was the most influential indicator, with a contribution of 24.7%, and the contribution of the green space indicators to LST was significantly reduced. Thirdly, among the leading indicators, SCD was positively correlated with LST. When SCD was less than 60%, LST increased by about 0.38 °C for every 10% increase. When GCR > 44%, LST was significantly reduced, and when GCR > 62%, a cooling effect of 1.1 °C was observed. Beyond this threshold, the cooling effect will not improve significantly. This study shows that when 3D buildings are densely distributed and crowded, the cooling effect of green space will be limited to some extent by 3D buildings. The key to mitigating UHIs is to rationally configure and optimize the spatial structure of 3D buildings.

Transitioning from diesel backup generators to PV-plus-storage microgrids in California public buildings

Climate-related wildfires have caused significant power outages in California, including planned outages called Public Safety Power Shutoffs (PSPS). Consequently, concerns about grid reliability have increased public and private demands for backup generators, including diesel-fueled ones. However, diesel generators bear high environmental costs, emitting greenhouse gases and air pollutants that negatively impact public health. This research quantifies the economic value and environmental benefit of replacing diesel backup generators with PV-plus-storage microgrids for public buildings in California, which has a net zero carbon emissions target in the electricity sector by 2045. Using an energy integration and optimization model, REopt, and empirical data, this study demonstrates that replacing diesel backup generators in just one building would save almost $3M of public expenditures and reduce over 10,000 tons of CO2 emissions over a 20-year period. The resulting implication is that public buildings and critical facilities in the state's 22 air districts could save $31-385M annually by the same application. Also, this research develops a marginal resilience curve for the cost and environmental impact of extended outages, which demonstrates that increasing energy storage capacity greatly outweighs increasing PV or generator capacity to enhance resilience, while reducing costs and emissions.

A Water Allocation Model for Multiple Uses Based on a Proposed Hydro-Economic Method

Water scarcity drives society to conflict over the allocation of water. Economical externalities based on the development of water production improve the decision-making process for planning water allocation and the operation of the water infrastructure. We present a proposed water allocation model using a priority-based and hydro-economic optimization kernel as a framework for improving the quality of information for the different user sectors, stakeholders, and institutions for the water allocation decision-making process. In addition, we propose a method for using hydro-economic optimization models without the marginal benefit curve of water demand. The proposed model, called AcquaNetGIS, was applied to the São Francisco Transboundary System, and the hydro-economic optimization was improved, allocating 7.0% more water for all users considered, including water supply, irrigation, and hydropower. Moreover, the minimum flow downstream from the Xingó hydropower station reached 98.5% (priority-based optimization) and 99.0% (hydro-economic optimization) during the optimization period. Depending on the rules and legislation, the sustainability of water allocation based on hydro-economic externalities may be a better solution for the planning and operation of complex water infrastructure systems. Multicriteria decision-making methods should consider the results of the proposed model in order to understand the stochastics of the hydrological regimes and economic production based on the availability of water.

The influence of social capital on network effects

Introduction. The current social and eco­nomic changes caused by networking relations in the economic system are a significant element of contemporary scientific research aimed to identify the essential characteristics of such new concepts as "network economy" and "social ca-pital". This situation has resulted from the deve­lopment of Internet technologies, the increasing role of intangible assets in value creation, and the need to study the state involvement in these processes, which identifies the level of their development.Problem. The impact of social capital on the economic system has been observed in various patterns of economic system relationships, and it is amid the network economy that this impact is clearly revealed through the changes in the mani­festation of network effects. It is necessary to spe­cify such changes for the effective organization of economic relations under the conditions of the network economy as well as for the determina­tion of the role of social capital in them.The aim of the article is to identify the relationship between social capital and the net­work economy and determine in which interact­tion patterns of the economic system social capital changes (or levels) the manifestation of network effects.Methods. In the course of the research, the following methods were used: analysis, genera­lization, comparison, analogy, scenario constru­ction, graphic, and microeconomic analysis (marginal utility curve).Results. In the course of the research, there has been revealed the relationship between the levels of social capital and network readiness, as well as theoretical and practical aspects of the outlined issues. The findings obtained while analyzing the nature of the formation of various relationship patterns of the economic system and the role of social capital in those patterns show that social capital determines the manifestation character of network effects (posi­tive and nega­tive) in such patterns.Conclusions. The components of social capi­tal are identical to the elements of network via­bility. Thus, social capital becomes a key mana­gement object in the network economy. The obtai­ned results of the research will form the basis for further scientific research on the social capital management system of an enterprise in the network economy.

Construction of Marginal Effect Model for Reliability Improvement of Urban Distribution Network

With the development of the social economy in China, China’s power grid is facing severe challenges. In addition to effective supply, the more important thing is to provide the reliability of the power supply for the existing distribution network. The power supply reliability of the distribution network directly affects the safety and reliability of power users, and also relates to the development of power supply enterprises. To realize the safer and more stable operation and development of urban distribution networks, this paper researches the construction of a reliability enhancement marginal effect model of urban distribution networks. By determining the factors that affect the reliability of distribution network operation, the marginal benefit model is selected to construct the index. The specific value of the index and the boundary conditions of the model are set. The reliability improvement marginal benefit curve is analyzed in depth; and finally, the specific value of the reliability index marginal benefit is calculated. The new model is applied to the distribution network in the old urban area of a city, and the relationship between each index and reliability and marginal benefit is clarified. According to the analysis results, the future construction and development direction of the distribution network in the old urban area of the city is fully clarified, and the path scheme of reliability improvement is given according to the degree of urgency. Through the use of the marginal effect model, it can provide a more effective reference for the improvement of national distribution network reliability and the decision-making of distribution network construction planning projects.

Copula-based standardized precipitation evapotranspiration index and its evaluation in China

The standardized precipitation evapotranspiration index (SPEI) lacks the assessment mechanism for the coupling relationship between the magnitudes of the precipitation (P), potential evapotranspiration (ETP), and water deficit, making it hard to predict the drought precisely. This paper selected the marginal and joint cumulative distribution functions (CDF) of P and −ETP to present their magnitudes and water deficit, respectively. We formatted the Frank copula-based SPEI (SPEIC) to combine the marginal CDFs at 3, 6, 9, and 12-month scales. It indicated that the two-parameter Gamma distribution was the best-fitted marginal CDFs of the P (CDFP) and −ETP (CDF–ETP). The CDFP exerted a slightly more significant marginal effect on the joint CDF than the CDF–ETP at 6 to 12-month scales, indicated by the steeper slope of the CDFP’s marginal curves vs joint CDF. The verified more significant marginal effect denied the implied assumption of the same marginal effects of the P and −ETP using SPEI. The new-constructed SPEIC temporally fluctuated highly consistent with the SPEI in the whole, energy- and water-limited regions of China, indicated by the higher 3 to 12-month-averaged Nash-Sutcliffe efficiency coefficient ≥ 0.63 and determination coefficient ≥ 0.75. The SPEIC had a more sensitive detectivity of the drought frequency, indicated by more events detected. Besides, it had a minor sensitive detectivity of the drought severity, indicated by the larger SPEIC under the same specified frequencies of the P and −ETP.

Nonlinear relationships of runoff and sediment yield with natural and anthropogenic factors at event scale

AbstractUnderstanding how natural and anthropogenic factors affects the watershed runoff and sediment yield at event scale can provide useful insights into watershed hydrological processes to guide watershed management. This article investigates the nonlinear relationships between natural and anthropogenic factors and event runoff and sediment yield with a boosted regression tree (BRT) model for 38 watersheds within the Loess Plateau in China during 2006 to 2016. The BRT model captures the relative importance of each natural and anthropogenic factors to the variability in runoff and sediment yield. The results show that these relationships are complex and highly nonlinear. The event runoff was most related to NDVI in the grass land (NDVI_g), with a 21.3% contribution, followed by 3‐day antecedent precipitation index (AP3), 10‐day antecedent precipitation index (AP10), precipitation (P), and 7‐day antecedent precipitation index (AP7). For event sediment yield, the strongest factor is AP3, with contribution of 33.3%, followed by P, NDVI in the forest land (NDVI_f), AP7, and NDVI in the crop land (NDVI_c). The marginal effect curves produced by the BRT are often characterized by thresholds. For instance, NDVI_f has the greatest effect on event sediment yield reduction when NDVI_f = 0.42, suggesting that a very intense green coverage is not necessary to achieve maximal soil erosion control. Vegetation coverage and meteorological factors can explain 54.7% of event runoff variation and 55.6% of event sediment yield variation. Our study identify the nonlinear relationships between runoff and sediment yield with vegetation cover and meteorological factors and provide scientific support for the planning of subsequent reforestation projects in the Loess Plateau.

Rayleigh-Bénard-Marangoni Instability in a Self-rewetting Fluid Layer Overlying a Porous Medium

Rayleigh-Bénard-Marangoni instability in a bilayer system of self-rewetting fluid overlying a porous medium is investigated. The upper surface of the fluid layer is assumed non-deformable and a constant temperature gradient is imposed. Unlike in previous works, self-rewetting fluid is considered in this paper, whose surface tension is a quadratic function of temperature. As a result, it would reinforce or suppress the instability caused by buoyancy in different scenarios. Thorough study is carried out and the influence of depth ratio h, Rayleigh number Ra and Biot number Bi on instability of the system is discussed. It was found that the marginal curve is bimodal in certain combination of parameters and mode transition of convection is also found.