Single Index Research Articles

Functional partially linear single index models with measurement error in both functional and real covariates

In this paper, we investigate the functional partially linear single index models with contaminated functional and real covariates when the functional sample grid is dense. To eliminate the influence of measurement error on the estimations of the proposed models, a two-stage estimation procedure is introduced. In the first stage, we utilize a kernel presmoothing regression to denoise the corrupted functional curves. In the second stage, the fitted functional curves are applied to replace the original ones to obtain the predictor of unknown parameter in parametric component with the attenuation correction method and then we derive the predictor of unknown link function in nonparametric part with kernel method. Meanwhile, in order to improve computational efficiency, functional slice inverse regression method is employed to estimate the functional single index parameter. The asymptotic properties are also stated in this process at the situation of independent and identical distribution sample under some mild conditions. A simulation study and real data analysis are further explored to illustrate the good performance of our methodology.

Optimization and characterization of boric acid powder mixed electrical discharge machining of Ti-6Al-4V ELI

The powder mixed electrical discharge machining (PMEDM) process is used for enhancing machining efficiency and improving the surface characteristics of the workpiece compared to normal EDM. The present study evaluates the effect of boric acid powder mixed in deionized water in PMEDM of Ti-6Al-4V ELI (extra low interstitial). The PMEDM process is assessed by evaluating material removal rate (MRR) and surface roughness (SR) at varying powder concentration (PC), current and pulse duration ( Ton). Boric acid PMEDM exhibits advantageous for both MRR and SR, where MRR increases and SR decreases with an increase in PC. To simultaneously achieve higher MRR and lower SR, the grey-fuzzy logic method is employed. Initially, the raw input data is normalized into grey numbers and a single index is obtained through grey relational analysis. Subsequently, triangular membership functions are assigned to the inputs and output. Fuzzy logic rules are then formulated, and grey fuzzy relational grade (GFRG) is calculated for each condition. The optimum condition (GFRG = 0.787) is attained at 15 g/l PC, 9 A current and 106 µs Ton, resulting in a 63% improvement compared to the initial condition. At the optimum condition, MRR increased by 145% and SR decreased by 29% compared to the initial condition. The effect of boric acid in PMEDM can be visualized through the formation of smooth surfaces, exhibiting reduced SR, smaller and shallower craters, and fewer debris and globules. Additionally, the boric acid PMEDM experiments resulted in the formation of a hard TiB phase on Ti-6Al-4V, thus improving its wear resistance.

Carbon-mechanic dual-control design decision model of prefabricated structural components

Prefabricated enclosure structures (PES) have become the key technology for low-carbon construction in the engineering field due to their low labor demand, fast construction speed, and low environmental pollution. In the context of low-carbon development, efficiently designing PES that not only possess high-strength but also demonstrate significant greenhouse gas (GHG) reduction benefits has become a critical challenge. The objective of this study is to address the challenges of automated design and scientific decision-making methods for PES components. First, the Carbon-mechanic dual-control assessment model (CDAM) is proposed, providing a novel evaluation dimension for the design of prefabricated components. Subsequently, based on the CDAM, an automated design decision-making process, and model for components are established using an improved genetic algorithm and parameterized method. Finally, under the constraints of actual engineering conditions, adaptive solutions were automatically generated for specific cases. These solutions were comprehensively evaluated and optimized using CDAM, resulting in design guidelines and optimal solutions for PES that balance environmental performance and load-bearing capacity. The case analysis results show that the optimal scheme based on the carbon-mechanic dual-control (CM) index is: the sectional dimension is 830 mm, the reinforcement ratio is 0.9 % and the cavity ratio is 45 %, which shows the ideal characteristics of low-carbon and high-strength. Compared with the single index decision scheme, this scheme achieve a maximum of 42 % GHG emissions reduction. The high comprehensive performance scheme is characterized by small sectional dimension, high reinforcement ratio, and high cavity ratio. Cavity ratio is a key parameter to achieve high performance design. The research findings provide an important theoretical basis and technical support for the low-carbon transformation in the engineering field.

Minimum profile Hellinger distance estimation for single-index models

Single-index models are the most commonly used covariate models and are widely used in statistical applications. Such models include linear models and generalised linear models as special cases. This article investigates efficient and robust estimates for single-index models. For this purpose, we employ the minimum distance approach which in general is automatically robust with respect to the stability of the quantity being estimated. In particular, the minimum Hellinger distance approach introduced by Beran [(1977), ‘Minimum Hellinger Distance Estimators for Parametric Models’, Annals of Statistics, 5, 445–463] produces estimators that are asymptotically efficient at the model density and simultaneously possess excellent robustness properties. In this paper, we construct a minimum profile Hellinger distance estimator (MPHDE) for single-index models. We prove the consistency of the proposed MPHDE and examine its finite-sample performance and robustness properties via Monte Carlo simulation studies and real data analysis.

ADHM wilson line defect indices

The Coulomb and Higgs indices of the 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 U(N) ADHM theories can be decorated by line defect operators as the line defect correlators. We obtain exact closed-form expressions and various non-trivial algebraic relations for the correlators of the Wilson lines in the fundamental and (anti)symmetric representations by means of the Hall-Littlewood expansion, the Fermi-gas method and the residue calculation. From the large N limit of the correlators we obtain the single particle gravity indices which are expected to encode the spectra of fluctuation modes on the gravity duals of line operators in M2-brane SCFTs.

Multidimensional Seismic Fragility Study of Intake Towers Based on Incremental Dynamic Analysis

Assessing the fragility of intake towers using a single damage index does not allow for accurate evaluation of the potential for structural damage under seismic conditions. In this study, based on the probabilistic seismic demand analysis method, the effects of ground motion intensity on maximum displacement, local damage index, and global damage index are considered, and the seismic fragility of an intake tower structure is analyzed. First, 10 natural ground motion records were selected from the ground motion database (PEER) and 2 artificial seismic waves were synthesized. These seismic waves were amplitude-modulated for incremental dynamic analysis (IDA). The trends of the IDA curves were analyzed to divide the performance levels of the intake tower structure. Furthermore, a two-dimensional fragility curve for the intake tower structure was plotted in this study. The maximum displacement in the direction of parallel flow and the damage index were taken into account in the two-dimensional fragility curve. The results show that, under the designed seismic acceleration, the two-dimensional fragility curve for the intake tower structure was lower than the one-dimensional curve. This indicates that the seismic design based on the one-dimensional performance index was unstable. This provides a theoretical reference for seismic optimization design and the strengthening of intake towers. Therefore, it is recommended to use multidimensional fragility analysis to study the seismic performance of intake tower structures in seismic design.

Drought Quantification in Africa Using Remote Sensing, Gaussian Kernel, and Machine Learning

Effective drought management requires precise measurement, but this is challenging due to the variety of drought indices and indicators, each with unique methods and specific uses, and limited ground data availability. This study utilizes remote sensing data from 2001 to 2020 to compute drought indices categorized as meteorological, agricultural, and hydrological. A Gaussian kernel convolves these indices into a denoised, multi-band composite image. Further refinement with a Gaussian kernel enhances a single drought index from each category: Reconnaissance Drought Index (RDI), Soil Moisture Agricultural Drought Index (SMADI), and Streamflow Drought Index (SDI). The enhanced index, encompassing all bands, serves as a predictor for classification and regression tree (CART), support vector machine (SVM), and random forest (RF) machine learning models, further improving the three indices. CART demonstrated the highest accuracy and error minimization across all drought categories, with root mean square error (RMSE) and mean absolute error (MAE) values between 0 and 0.4. RF ranked second, while SVM, though less reliable, achieved values below 0.7. The results show persistent drought in the Sahel, North Africa, and southwestern Africa, with meteorological drought affecting 30% of Africa, agricultural drought affecting 22%, and hydrological drought affecting 21%.

Study on the evaluation of shale reservoir brittleness based on mineral disorder

Brittleness serves as a critical indicator for assessing whether reservoirs can form complex fracture networks. While methods based on brittle mineral content or rock mechanical parameters are widely used, their lack of integration between mineralogy and mechanics introduces limitations. A single evaluation parameter cannot accurately assess shale brittleness. There is a need for a universally applicable method that comprehensively considers mineral composition, mechanical properties, and brittleness variations in shale evaluation. This study uses Longmaxi shale in the Sichuan Basin as an example, establishing a mineral disorder index based on shale mineral composition and mechanical characteristics, incorporating the influence of confining pressure to establish a shale brittleness index. Results indicate varying weights of brittleness contributions from different minerals, ranked in descending order: pyrite, quartz, calcite, dolomite, feldspar, and clay. Greater complexity in mineral combinations correlates with lower shale brittleness indices. Typically, single mineral disorder indices show a positive correlation with internal mineral disorder indices. Confining pressure exhibits an inversely proportional relationship with shale brittleness indices, with brittleness at 30, 50, and 70 MPa confining pressures being 0.737, 0.586, and 0.451 times those without confining pressure, respectively. This method guides current brittleness research and reservoir production enhancement.

Clinical significance of peripheral blood UL16 and DR-70 for the early diagnosis and prognostic evaluation of colorectal cancer.

Early diagnosis of colorectal cancer (CRC) is of great significance to improve the survival rate and quality of life of patients, but early diagnosis of CRC requires more sensitive techniques. Peripheral blood UL16-binding protein 2 (ULBP2) and human fibrinogen degradation products (DR-70) are the main indicators for the diagnosis of malignant tumors. To assess ULBP2 and DR-70 potential for the early diagnosis and prognostic evaluation of CRC to provide a reference. This study involved 60 patients with early-stage CRC (CRC group), 50 patients with benign colorectal tumors (benign group), and 50 healthy patients (control group) enrolled at the Affiliated Hospital of Jiangnan University and Jiangsu Province Official Hospital between January, 2020 and January, 2022. ULBP2 and DR-70 levels in the blood were determined and differences among the three groups and early diagnostic values for CRC were determined. Patients with CRC were divided into the good prognosis and poor prognosis groups, and ULBP2 and DR-70 levels in the blood and diagnostic values were compared. ULBP2 and DR-70 serum levels were significantly higher in the CRC group than in the control and benign groups (P < 0.05); however, no significant differences were observed between the benign and control groups (P > 0.05). Among the 60 patients with CRC followed up for two years, two died (3.33%) and 15 exhibited tumor metastasis, progression, or recurrence (25.00%). ULBP2 and DR-70 serum levels were significantly higher in the poor prognosis group than in the good prognosis group (P < 0.05). A receiver operating characteristic curve was plotted. Area under the curve, sensitivity, and specificity of serum ULBP2 with DR-70 for the early diagnosis of CRC were higher than those of the single serum indices (P < 0.05) in both the good and poor prognosis groups. ULBP2 and DR-70 serum levels were significantly high in patients with early-stage CRC. They improved the diagnostic rate of early-stage CRC and predicted patient prognosis, thereby showing clinical application potential.

Supervised learning-based artificial senses for non-destructive fish quality classification

Human sensory techniques are inadequate for automating fish quality monitoring and maintaining controlled storage conditions throughout the supply chain. The dynamic monitoring of a single quality index cannot anticipate explicit freshness losses, which remarkably drops consumer acceptability. For the first time, a complete artificial sensory system is designed for the early detection of fish quality prediction. At non-isothermal storages, the rainbow trout quality is monitored by the gas sensors, texturometer, pH meter, camera, and TVB-N analysis. After data preprocessing, correlation analysis identifies the key parameters such as trimethylamine, ammonia, carbon dioxide, hardness, and adhesiveness to input into a back-propagation neural network. Using gas and textural key parameters, around 99 % prediction accuracy is achieved, precisely classifying fresh and spoiled classes. The regression analysis identifies a few gaps due to fewer datasets for model training, which can be reduced using few-shot learning techniques in the future. However, the multiparametric fusion of texture with gases enables early freshness loss detection and shows the capacity to automate the food supply chain completely.

A microfluidic patch for wireless wearable electrochemical detection of sweat metabolites

Wearable sweat sensors provide an innovative detection method for analyzing human physiological and biochemical parameters and play an important role in detecting the potential risks of chronic diseases. Existing commercial wearable sensors (Apple iWatch, HUAWEI smart band) have problems such as single detection index (heart rate or blood pressure), and mainly focus on the physical information. This work studied an integrated microfluidic patch to simultaneously detect several biomarkers (pH, sodium ions, and uric acid) in sweat. We achieved the detection of pH level, sodium, and uric acid in linear ranges of 4–8, 0–160 mM, and 5–160 μM, respectively, covering well the clinically relevant ranges in the healthy human sweat. Laser engraving was chosen to prepare a microfluidic layer, and the sweat collection function was realized by combining hydrophilic and hydrophobic microfluidic synergy. It could efficiently collect the required sweat sample volume (80 μL) within 30 s while avoiding the contamination caused by directly contact with the skin. In addition, a wireless signal acquisition and transmission system was designed with the signal reading, processing, and wireless transmission functions, which can display the testing results in real time on Android phone-specific application software. We combined the wireless system with a microfluidic patch for on-body testing to verify the good wearability of the sweat sensor. This research realized the wireless data processing and transmission while improving sweat collection efficiency. In addition, it could detect various sweat physiological components in real-time, and provides a multiparameter, real-time, and portable sensing platform.

One-index vector quantization based adversarial attack on image classification

To improve storage and transmission, images are generally compressed. Vector quantization (VQ) is a popular compression method as it has a high compression ratio that suppresses other compression techniques. Despite this, existing adversarial attack methods on image classification are mostly performed in the pixel domain with few exceptions in the compressed domain, making them less applicable in real-world scenarios. In this paper, we propose a novel one-index attack method in the VQ domain to generate adversarial images by a differential evolution algorithm, successfully resulting in image misclassification in victim models. The one-index attack method modifies a single index in the compressed data stream so that the decompressed image is misclassified. It only needs to modify a single VQ index to realize an attack, which limits the number of perturbed indexes. The proposed method belongs to a semi-black-box attack, which is more in line with the actual attack scenario. We apply our method to attack three popular image classification models, i.e., Resnet, NIN, and VGG16. On average, 55.9 % and 77.4 % of the images in CIFAR-10 and Fashion MNIST, respectively, are successfully attacked, with a high level of misclassification confidence and a low level of image perturbation.

Innovation and Path to Inclusiveness in Developing Countries

This study examines the effect of innovation on inclusive growth in 63 developing countries and employs System Generalized Method of Moments (GMM) estimation techniques. The study used the global innovation index to measure innovation. In addition, we construct an index of inclusive growth. Further, due to the complex nature of inclusive growth, using a single index may not provide the full picture. So, for substantial empirical support, the study uses a set of dimensions of inclusive growth separately. The empirical results show a positive relationship between the measures of innovation with inclusive growth. Further, the study also constructs indifference curves for selected developing economies to measure the inclusiveness in growth. Finally, it is suggested that developing economies should put in policies to promote innovation activities that include poor segments of society to improve the impact of innovation on inclusive growth.

Analisis Markowitz dan Model Indeks Tunggal dalam Pembentukan Portofolio Optimal Saham Jakarta Islamic Index Periode 2019-2023

This research is motivated by the increasing number of sharia investors each year and the uncertainty of stock prices incorporated in the Jakarta Islamic Index in 2019-2023 so there is a needed to plan optimal portfolio to reduce the risk. Sampling in this study using purposive sampling method that meets the sample criteria as many as 15 stocks. The analysis technique used is descriptive analysis and hypothesis testing is done using the Independent Sample T-Test. The results showed that there were 3 stocks incorporated into the optimal portfolio of the Markowitz model, namely ADRO, ANTM, and BRPT, with an expected portfolio return of 0.0238 and a portfolio risk of 0.1066. And there are 4 stocks that are incorporated into the optimal portfolio of the Single Index Model, namely ADRO, BRPT, ANTM, and INCO, with an expected return of 0.0215 and a portfolio risk of 0.1035. Therefore, Markowitz portfolio is better to use than the Single Index Model portfolio because it has a greater expected return than the Single Index Model. However, statistical testing using t-test shows that the expected return and risk of the optimal portfolio of the Markowitz Model and the Single Index Model are not significantly different.

A Harmony-Based Approach for the Evaluation and Regulation of Water Security in the Yellow River Water-Receiving Area of Henan Province

Water security, as a crucial component of national security, plays a significant role in maintaining regional stability and ensuring the healthy and rapid development of the economy and society. The Yellow River water-receiving area of Henan Province (YRWAR-HN) is selected as the research area in this study. Firstly, a comprehensive evaluation index system is constructed based on the actual water security problems of the research area, and the single index quantification–multiple indices syntheses–poly-criteria integration method (SMI-P) is introduced to quantify the water security degree of 14 cities in the YRWAR-HN from 2010 to 2021. Then, the obstacle degree model is used to identify the key obstacle indexes that restrict the improvement of water security. Finally, the harmonious behavior set optimization method is adopted to carry out the regulation of water security, and the improvement path of water security in the YRWAR-HN is formulated. The results indicate the following: (1) the water security degree of the YRWAR-HN shows a fluctuating upward trend, increasing from 0.4348 (2010) to 0.6766 (2021), a significant rise of 55.61%. The water security level improves from the relatively unsafe level to the relatively safe level. Hebi City exhibits the fastest rate of water security improvement, while Xinxiang City shows the slowest rate. (2) The density of the river network (X1) and the proportion of investment in water conservancy and environmental protection in the total investment (X15) are the two indexes with the highest obstacle degree, with the average obstacle degrees being 15.09% and 10.79%, respectively. (3) The combination of the composite regulation scenario and improvement Path 2 is the optimal regulation strategy for water security in the YRWAR-HN. From the implementation process, Luoyang, Sanmenxia, Jiyuan, Xuchang, and Shangqiu may prioritize improving their flood and drought disaster defense capabilities and emergency response capabilities, continuously enhancing the flood prevention and disaster reduction system. Zhengzhou, Kaifeng, Xinxiang, Jiaozuo, Anyang, Hebi, Pingdingshan, and Zhoukou may prioritize resolving the regional water supply and demand conflicts, balancing development and conservation, actively seeking transboundary and external water transfers, and strengthening the capacity for water conservation and intensive utilization. Puyang City may prioritize enhancing its comprehensive water environment management capabilities, increasing investment in water conservancy and the environment, improving production processes, reducing pollutant emissions, and mitigating agricultural non-point source pollution.

Comparison of Markowitz Model and Single Index Model with ESG Factors Involved

ESG considerations have become increasingly prominent within the realms of investor and corporate decision-making, underscoring the importance of employing robust methodologies for incorporating ESG factors into portfolio construction. This study aims to leverage the Markowitz Model and Single Index Model to construct portfolios utilizing a selection of 10 stocks, evaluating their applicability across various conditions, particularly investors' risk tolerance levels. Utilizing the solver function within Microsoft Excel, graphical representations will be generated under four distinct constraints, facilitating comparisons based on both graphical depictions and accompanying data analysis. The findings reveal that, under specified conditions, the two models exhibit negligible differences, while highlighting the significant role of ESG constraints in portfolio construction. Nonetheless, given the distinct assumptions and conditions underlying each model's calculations, investors retain the flexibility to choose either approach for portfolio analysis. This research underscores the impact of ESG factors on asset allocation outcomes within both models, offering valuable insights into ESG investing practices and the comparative performances of the Markowitz Model and the Single Index Model.

412. COMPARISON BETWEEN PREOPERATIVE MALNUTRITION, AND SARCOPENIA AND POSTOPERATIVE COMPLICATIONS IN ESOPHAGEAL CANCER PATIENTS

Abstract Background Typical indicators of malnutrition in cancer patients include BMI, CONUT, PNI, and prealbumin, while SMI and PMI are often used as indicators of skeletal muscle mass loss (sarcopenia). Although these indicators have been reported to be associated with surgical outcomes, their combination may be useful in determining the effectiveness of perioperative management because these are closely related during the perioperative period. Methods A total of 132 esophageal cancer patients who underwent esophagectomy between January 2021 and May 2023 were included in this study. Preoperative BMI, CONUT, PNI, prealbumin, SMI (measured by BIA), and PMI (measured by CT imaging) were extracted from clinical record. We also selected BMI and SMI as a new indicator for combined malnutrition and loss of skeletal muscle. Then, we investigated the association between these indicator and postoperative complications (pneumonia, suture failure, total CD Grade ≥II, total CD ≥IIIa), and length of hospital stay. Results The mean age of patients was 67.3 years, 107 were male and 25 were female. Preoperative chemotherapy was administered to 58 patients. Although associations with each single index were found for postoperative pneumonia and low BMI, low SMI, and low PMI, there was no significant association with anastomotic leakage or overall complications. On the other hand, low BMI+SMI was strongly correlated with postoperative pneumonia, overall Grade≥II, and Grade≥IIIa complications. In postoperative hospital stay, low BMI, low PNI, and low SMI as single indicators showed a significant increase in hospital stay, while low BMI+SMI showed further statistically significant increase. Conclusion In patients who underwent esophagectomy, single index for malnutrition and low skeletal muscle mass may be predictors of postoperative complications respectively. However, because perioperative management is inseparable from nutritional therapy and exercise therapy, composite index of BMI and SMI may be better predictor of therapeutic efficacy of perioperative nutrition and exercise therapy.

Soil moisture inversion based on multiple drought indices and RBFNN: A case study of northern Hebei Province

Drought has a significant impact on crop growth and productivity, highlighting the critical need for precise and timely soil moisture estimation to mitigate agricultural losses. This study focuses on soil moisture retrieval in northern Hebei Province during July 2012, utilizing eight widely employed remote sensing drought indices derived from MODIS satellite data. These indices were cross-referenced with measured soil moisture levels for analysis. Based on their correlation coefficients, a composite remote sensing drought index set comprising six indices was identified. Furthermore, a radial basis function neural network (RBFNN) was employed to estimate soil relative humidity. The accuracy evaluation of the soil moisture estimation model, which integrates multiple remote sensing drought indices and the RBFNN, demonstrated clear superiority over models relying on single drought indices. The model achieved an average estimation accuracy of 87.54 % for soil relative humidity at a depth of 10 cm (SM10) and 87.36 % for a 20 cm depth (SM20). The root mean square errors (RMSE) for the test sets were 0.093 and 0.092, respectively. Validation results for July 2013 indicated that the inversion accurately reflected the actual soil moisture conditions, effectively capturing dynamic moisture changes. These results fully verify the reliability and practicability of the model. These findings introduce a novel approach to local agricultural soil moisture estimation, with significant implications for enhancing agricultural water resource management and decision-making processes.

Recommendation for the practice of total intravenous anesthesia.

This Recommendation was developed by the Japanese Society of Intravenous Anesthesia Recommendation Making Working Group (JSIVA-WG) to promote the safe and effective practice of total intravenous anesthesia (TIVA), tailored to the current situation in Japan. It presents a policy validated by the members of JSIVA-WG and a review committee for practical anesthesia management. Anesthesiologists should acquire and maintain the necessary knowledge and skills to be able to administer TIVA properly. A secure venous access is critically important for TIVA. To visualize and understand the pharmacokinetics of intravenous anesthetics, use of real-time pharmacokinetic simulations is strongly recommended. Syringe pumps are essential for the infusion of intravenous anesthetics, which should be prepared according to the rules of each individual anesthesia department, particularly with regard to dilution. Syringes should be clearly labeled with content and drug concentration. Whenmanaging TIVA, particularly with the use of muscle relaxants, monitoring processed electroencephalogram (EEG) is advisable. However, the depth of sedation/anesthesia must be assessed comprehensively using various parameters, rather than simply relying on a single EEG index. TIVA should be swiftly changed to an alternative method that includes inhalation anesthesia if necessary. Use of antagonists at emergence may be associated with re-sedation risk. Casual administration of antagonists and sending patients back to surgical wards without careful observation are not acceptable.

Ecological risk assessment of heavy metals from application of sewage sludge on agricultural soils in Europe

AbstractThe present European Union (EU) Sewage Sludge Directive (86/278/EEC) is undergoing modifications aimed at enhancing its applicability in the agricultural sector. The Directive's existing limit values for heavy metal concentrations in soils are in the process of being revised. However, to comprehensively understand their effects on EU agricultural lands, additional evaluations are necessary. This is particularly important given that ecological risk assessments are often performed on a site‐specific basis, potentially overlooking broader regional implications. The main objective of the current work is to introduce a methodological approach to quantify the impact of sewage sludge (SS) application on agricultural soils in the EU and the United Kingdom. Concentrations of heavy metals (HMs) (Cd, Cu, Hg, Ni, Pb and Zn) in agricultural land from Land Use/Land Cover Area Frame Survey (LUCAS) 2009 topsoil database were used as a baseline. Maximum quantities of SS that can be safely applied to agricultural lands were obtained by a modeling procedure was used to determine the maximum safe quantities of SS that can be applied to agricultural lands for each country within the European Member States and the United Kingdom. Accumulation of HMs in soils was modelled by using a representative SS composition, distributed over 10 successive years at 5 Mg ha−1 year−1 rate. Ecological risk impact was assessed by using both the single ecological risk index (Er) and the integrated potential ecological risk index (RI). Maximum quantities of SS applied on agricultural soils in EU + UK were estimated to be 45 Mg ha−1 at the country level. We found that 19% of agricultural land (around 28,471,900 ha) in the EU + UK shows a higher RI than moderate risk after long time application of the representative SS. We show that the combination of the HM concentrations from the LUCAS topsoil survey and assumptions on the SS composition and soil HM partitioning can be used to define the actual and potential soil pollution rate in EU + UK. We demonstrate that the proposed methodology can be used by policymakers, farmers, regional authorities and other stakeholders, with possible adaptions based on local in‐depth soil and SS knowledge.