Interpolation Model Research Articles

A three-dimensional sampling design based on the coefficient of variation method for soil environmental damage investigation.

A traditional grid model for soil sampling may suffer from poor efficiency and low accuracy. With a nonferrous metal processing plant as the study area, a three-dimensional kriging interpolation model was built based on this plant's preliminary investigation data for arsenic (As), and a detailed survey sampling programme was proposed. The sampling density at the pollution interval of the surface soil was estimated by the coefficient of variation method, and the sampling depth was determined by the pollution interval of the vertical prediction results. The results showed that the encrypted soil sampling distribution optimisation method obtains greater pointing accuracy with fewer points. The sampling accuracy was 87.62% after optimising the depth of pointing. Moreover, this approach could save 66.13% of the sampling costs and 56.93% of the testing costs compared to a full deployment programme. This study provides a new and cost-effective method for predicting the extent of contamination exceedance at a site and provides valuable information to guide post-remediation strategies for contaminated sites.

Personalized mood prediction from patterns of behavior collected with smartphones

Over the last ten years, there has been considerable progress in using digital behavioral phenotypes, captured passively and continuously from smartphones and wearable devices, to infer depressive mood. However, most digital phenotype studies suffer from poor replicability, often fail to detect clinically relevant events, and use measures of depression that are not validated or suitable for collecting large and longitudinal data. Here, we report high-quality longitudinal validated assessments of depressive mood from computerized adaptive testing paired with continuous digital assessments of behavior from smartphone sensors for up to 40 weeks on 183 individuals experiencing mild to severe symptoms of depression. We apply a combination of cubic spline interpolation and idiographic models to generate individualized predictions of future mood from the digital behavioral phenotypes, achieving high prediction accuracy of depression severity up to three weeks in advance (R2 ≥ 80%) and a 65.7% reduction in the prediction error over a baseline model which predicts future mood based on past depression severity alone. Finally, our study verified the feasibility of obtaining high-quality longitudinal assessments of mood from a clinical population and predicting symptom severity weeks in advance using passively collected digital behavioral data. Our results indicate the possibility of expanding the repertoire of patient-specific behavioral measures to enable future psychiatric research.

Respiratory Analysis with Electrocardiogram Data: Evaluation of Pan-Tompkins Algorithm and Cubic Curve Interpolation Method

Advancements in bioinstrumentation have facilitated the easier monitoring of biometric signals such as electrocardiogram (ECG) and respiration. This development is particularly crucial for the diagnosis and management of various conditions like stress and sleep disorders. Two commonly used features in heart rate variability (HRV) analysis derived from ECG data are standard deviation and serial correlation coefficients of R-R intervals (the time durations between heartbeats). The former utilizes the fundamental components of QRS complexes, while the latter is designed to extract relationships between respiration and heart rate. In the proposed methodology, R-R wave detection is performed on processed ECG data using the Pan-Tompkins algorithm, and the respiration duration for each R-R interval from respiration data is selected. Additionally, missing respiration data for selected R-R intervals is interpolated based on the interpolation method. The results of this study are compared with the standard interpolation and cubic spline interpolation models to assess the effectiveness of the proposed method and its ability to capture temporal fluctuations. Since standard interpolation fails to accurately detect respiration data from R-R intervals and cannot precisely handle missing R-R intervals in short samples, cubic spline interpolation is recommended as a replacement and its results are presented. The obtained results provide insights into the effectiveness and application of the Pan-Tompkins algorithm, FFT (fast fourier transform) implementation, and cubic spline interpolation in the selection of respiration and R-wave features. According to the findings of the study, in the analysis conducted on 2-second samples with a 1000 Hz sampling frequency created from each participant's respiratory data set, missing respiratory data were successfully reconstructed from the R-R intervals of the EKG data using standard and cubic curve interpolation methods. Upon examination of RMSE (Root mean square error) values, it was observed that for 30% of the participants, as RMSE values increased, completion counts for standard interpolation increased, while completion counts for cubic curve interpolation decreased. Conversely, when RMSE values decreased, 60% of the participants showed a decrease in completion counts for standard interpolation and an increase in completion counts for cubic curve interpolation. A 10% participant group was identified where there was no apparent relationship between RMSE values and interpolation method. This indicates that in 90% of the participants, there is a linear relationship between the study's interpolation method, RMSE values, and completion counts for missing R-R intervals.

Downscaling MERRA-2 Reanalysis PM2.5 Series over the Arabian Gulf by Inverse Distance Weighting, Bicubic Spline Smoothing, and Spatio-Temporal Kriging.

This study offers a detailed analysis of the fine particulate matter (PM2.5) series in the Arabian Gulf zone, employing three interpolation models, Inverse Distance Weighting (IDW), Bicubic Spline Smoothing (BSS) and Spatio-Temporal Kriging (STK). Unique advancements include the use of complete temporal records in IDW, the management of edge effects in S with synthetic buffer points, and the application of STK to detrended data residuals. The results indicated that the BBS, particularly adept at handling boundary conditions, significantly outperformed the other methods. Compared to IDW, the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE) decreased by 21%, 15%, and 21%, respectively, in BSS. Compared to STK, MAE, RMSE, and MAPE were lower with around 60%, 61%, and 58%, respectively in BSS. These findings underscore the efficacy of the BSS method in spatial interpolation for environmental monitoring, contributing to enhanced PM2.5 analysis and public health management in the region.

Building a reference indicator model using co-kriging interpolation to determine the geographical origin of the flighted spongy moth complex in China.

Using stable isotopes to detect and analyze the geographical origin of insects represents an important traceability technology, which requires a rich isotope database. In this study, we representatively sampled the Chinese provinces where flighted spongy moth complex (FSMC) has been reported and, for the first time, used co-kriging interpolation to predict the distribution patterns of FSMC δ13C values in the main distribution areas. From 2020 to 2022, we set up 60 traps in 12 provinces and cities in China and collected 795 FSMCs. Then, 6 main climatic factors were obtained by multi-collinearity screening from 21 types of meteorological data collected at the sample plots, and a correlation analysis was carried out by combining longitude, latitude, and altitude data with the δ13C values of FSMC. Next, we performed a co-kriging interpolation using the 2 climatic factors with the highest correlation (isothermality and altitude) and the δ13C values of FSMC. A cross-validation was performed to systematically test 11 candidate models and select the best semi-variogram model ("Exponential"), which was then used to build a co-kriging interpolation model. The geographical distribution patterns of the FSMC δ13C values obtained from the 2 interpolation models (i.e., interpolated with isothermality and altitude, respectively) were almost the same. Moreover, the δ13C values varied significantly at the regional scale, showing regular changes in spatial distribution. Overall, the reference indicator map of the δ13C values generated from stable isotopes can be used to greatly improve the efficiency of discrimination analyses on the geographical origin of FSMC.

Spatial Prediction of Soil Contaminants Using a Hybrid Random Forest–Ordinary Kriging Model

The accurate prediction of soil contamination in abandoned mining areas is necessary to address their environmental risks. This study employed a combined model of machine learning and geostatistics to predict the spatial distribution of soil contamination using heavy metal data collected in an abandoned metal mine. An exploratory data analysis was used to identify patterns in the collected data, the root mean squared error (RMSE) and coefficient of determination (R2) were used to verify the predicted values, and the model was validated using K-fold cross-validation. The prediction results were produced as a map by applying hyperparameter tuning to Random Forest (RF) and Ordinary Kriging (OK) through GridSearchCV using optimal parameter selections. Furthermore, the prediction residuals of the RF model were calculated, and the RF prediction map and OK interpolation results of the RF prediction residuals were summarized to construct an RF–OK prediction map. The RMSE and R2 values for the RF, OK, and RF–OK interpolation models were 66.214, 65.101, and 52.884 mg/kg and 0.867, 0.871, and 0.915, respectively. In addition, the optimization results with the minimum RMSE and maximum R2 were obtained through hyperparameter tuning. The proposed RF–OK hybrid model demonstrated superior prediction performance compared to the individual models.

Exposure to PM2.5 Metal Constituents and Liver Cancer Risk in REVEAL-HBV.

Ambient particulate matter is classified as a human Class 1 carcinogen, and recent studies found a positive relationship between fine particulate matter (PM2.5) and liver cancer. Nevertheless, little is known about which specific metal constituent contributes to the development of liver cancer. To evaluate the association of long-term exposure to metal constituents in PM2.5 with the risk of liver cancer using a Taiwanese cohort study. A total of 13,511 Taiwanese participants were recruited from the REVEAL-HBV in 1991-1992. Participants' long-term exposure to eight metal constituents (Ba, Cu, Mn, Sb, Zn, Pb, Ni, and Cd) in PM2.5 was based on ambient measurement in 2002-2006 followed by a land-use regression model for spatial interpolation. We ascertained newly developed liver cancer (ie, hepatocellular carcinoma [HCC]) through data linkage with the Taiwan Cancer Registry and national health death certification in 1991-2014. A Cox proportional hazards model was utilized to assess the association between exposure to PM2.5 metal component and HCC. We identified 322 newly developed HCC with a median follow-up of 23.1 years. Long-term exposure to PM2.5 Cu was positively associated with a risk of liver cancer. The adjusted hazard ratio (HR) was 1.13 (95% confidence interval [CI], 1.02-1.25; P = 0.023) with one unit increment on Cu normalized by PM2.5 mass concentration in the logarithmic scale. The PM2.5 Cu-HCC association remained statistically significant with adjustment for co-exposures to other metal constituents in PM2.5. Our findings suggest PM2.5 containing Cu may attribute to the association of PM2.5 exposure with liver cancer.

High-resolution MRI synthesis using a data-driven framework with denoising diffusion probabilistic modeling

Objective. High-resolution magnetic resonance imaging (MRI) can enhance lesion diagnosis, prognosis, and delineation. However, gradient power and hardware limitations prohibit recording thin slices or sub-1 mm resolution. Furthermore, long scan time is not clinically acceptable. Conventional high-resolution images generated using statistical or analytical methods include the limitation of capturing complex, high-dimensional image data with intricate patterns and structures. This study aims to harness cutting-edge diffusion probabilistic deep learning techniques to create a framework for generating high-resolution MRI from low-resolution counterparts, improving the uncertainty of denoising diffusion probabilistic models (DDPM). Approach. DDPM includes two processes. The forward process employs a Markov chain to systematically introduce Gaussian noise to low-resolution MRI images. In the reverse process, a U-Net model is trained to denoise the forward process images and produce high-resolution images conditioned on the features of their low-resolution counterparts. The proposed framework was demonstrated using T2-weighted MRI images from institutional prostate patients and brain patients collected in the Brain Tumor Segmentation Challenge 2020 (BraTS2020). Main results. For the prostate dataset, the bicubic interpolation model (Bicubic), conditional generative-adversarial network (CGAN), and our proposed DDPM framework improved the noise quality measure from low-resolution images by 4.4%, 5.7%, and 12.8%, respectively. Our method enhanced the signal-to-noise ratios by 11.7%, surpassing Bicubic (9.8%) and CGAN (8.1%). In the BraTS2020 dataset, the proposed framework and Bicubic enhanced peak signal-to-noise ratio from resolution-degraded images by 9.1% and 5.8%. The multi-scale structural similarity indexes were 0.970 ± 0.019, 0.968 ± 0.022, and 0.967 ± 0.023 for the proposed method, CGAN, and Bicubic, respectively. Significance. This study explores a deep learning-based diffusion probabilistic framework for improving MR image resolution. Such a framework can be used to improve clinical workflow by obtaining high-resolution images without penalty of the long scan time. Future investigation will likely focus on prospectively testing the efficacy of this framework with different clinical indications.

EUPollMap: the European atlas of contemporary pollen distribution maps derived from an integrated Kriging interpolation approach

Abstract. Modern and fossil pollen data are widely used in paleoenvironmental research to characterize past environmental changes in a given location. However, their discrete and discontinuous nature can limit the inferences that can be made from them. Deriving continuous spatial maps of the pollen presence from point-based datasets would enable more robust regional characterization of such past changes. To address this problem, we propose a comprehensive collection of European pollen presence maps including 194 pollen taxa derived from the interpolation of pollen data from the Eurasian Modern Pollen Database (EMPD v2) restricted to the Euro-Mediterranean Basin. To do so, we developed an automatic Kriging-based interpolation workflow to select an optimal geostatistical model describing the spatial variability for each taxon. The output of the interpolation model consists of a series of multivariate predictive maps of Europe at 25 km scale, showing the occurrence probability of pollen taxa, the predicted presence based on diverse probability thresholds, and the interpolation uncertainty for each taxon. Combined visual inspections of the maps and systematic cross-validation tests demonstrated that the ensemble of predictions is reliable even in data-scarce regions, with a relatively low uncertainty, and robust to complex and non-stationary pollen distributions. The maps, freely distributed as GeoTIFF files (https://doi.org/10.5281/zenodo.10015695, Oriani et al., 2023), are proposed as a ready-to-use tool for spatial paleoenvironmental characterization. Since the interpolation model only uses the coordinates of the observation to spatialize the data, the model can also be employed with fossil pollen records (or other presence/absence indicators), thus enabling the spatial characterization of past changes, and possibly their subsequent use for quantitative paleoclimate reconstructions.

Spatially transferable machine learning wind power prediction models: [formula omitted]logit random forests

Wind power prediction models provide essential information to wind farm developers and power system operators on the power available at an undeveloped location. Traditionally, statistical models require recalibration of the model’s parameters in order to fit the model to a specific location’s dynamics. To mitigate this computational expense, this research develops a data-driven wind power prediction model that is spatially transferable, without the need for recalibration of the model’s parameters at a new location. This study also develops a wind direction prediction and interpolation model, as well as a transferability metric that demonstrates the model’s predictive accuracy at a new location. The transferability metric is evaluated in an exhaustive experimental setting. Results show that a v-logit random forest with minimum information requirements is the most transferable random forest variant for wind power prediction, with an error rate as low as 9% and never more than 20% when a transferred model is applied to a new location. The case study illustrates that the transferred model outperforms a site-specific, in-situ model for several existing wind farms. Clustering based on similarity, validated by cophenetic correlation and mapping, reveal that both the latitude of the farms, and the similarity of their turbine layouts, increase model transferability.

Integrated multi-material and multi-scale optimization of compliant structure with embedded movable piezoelectric actuators

Piezoelectric actuators embedded in compliant structures have many potential applications, which call for effective design approaches. Existing optimization driven design methods focus on the piezoelectric actuator location or the macro topology of the host compliant structure while ignoring the possibility to exploit the use of multiple materials and hierarchical material design. In this study, an integrated, density-based multi-material and multi-scale optimization method for compliant structures with embedded movable piezoelectric actuators is proposed. The design variables in the optimization represent the location of the piezoelectric actuators and the layout of the macro/micro host structures. To mitigate the risk of suboptimal designs, the three sets of design variables are simultaneously optimized using gradient-based optimization where the gradients are computed using the adjoint method. A material interpolation model that describes the piezoelectric actuators, multiple lattice materials of the host structure as well as their coating layer is proposed. To illustrate the formulation, several compliant structures embedded with movable piezoelectric actuators are designed such that the displacement at an output port is maximized. Macro and micro volume fractions, and overlapping of piezoelectric actuators are constrained in the optimization.

Topology optimisation for vibration bandgaps of periodic composite plates using the modified couple stress continuum

We propose a topology optimisation approach that can effectively account for the size effect of periodic composite plates to determine the optimal material distribution for achieving the largest bandgap width. The approach is based on the modified couple stress continuum and uses the relative bandgap width as the objective function, with volume constraints defined as the constraint function. The material properties are represented by the solid isotropic material with penalisation (SIMP) interpolation model, and the optimality criteria (OC) algorithm is employed to update the design variables. To address the significant size effect of the microplate structure, we use the modified couple stress continuum to model the dynamic behaviour of the unit cell. The Melosh–Zienkiewicz–Cheung (MZC) finite element is employed to ensure nodal C 1 continuity and achieve high-order elasticity with respect to inter-element continuity. Our results demonstrate that the proposed topology optimisation methodology is capable of effectively designing optimal unit cell configurations that account for size effect and significantly improve the bandgap width. We also investigate the impact of thickness and volume limitations on the optimised unit cell configuration. The obtained results suggest that the proposed topology optimisation framework is a promising approach for designing unit cell geometries with the account for size effect.

Research on optimization of approach procedures for airports in an alpine environment

Obstacles in alpine environments pose significant challenges to aircraft safety during terminal operations. Key challenges include constraints from obstacles within the terminal clearance area and the labor-intensive manual calculations of flight procedures. The focal point of concern lies in the design of approach procedures, particularly due to the heightened risk of collisions with obstacles during the descent segment in such terrain. To address these challenges, initially, this paper proposes processing the terrain data and visualizing and extracting the topographic data of the alpine airport by adopting a bi-cubic b-spline interpolation and cellular automatic machine model. Then, the paper proposes improving the A* path algorithm to make sure it can obey the standards of flight procedure design, utilizing the improved A* path algorithm to design approach procedures. As fuel consumption is directly connected with the economy of aviation companies, this research finally suggests employing the fuel consumption evaluation model to select the most efficient approach flight procedures. This research takes a case study of a Yunnan airport and simulates and designs the optimized approach procedures by A* path algorithm and evaluation based on fuel consumption. Results indicate that the parameters of optimized approach procedures align with the regulation of flight procedure design and meet the requirements of real flight operation. Therefore, the core tenant of this research can provide a feasible idea for flight procedures with alpine airports and has the potential to reduce workload and enhance operational efficiency.

Black carbon particles in human breast milk: assessing infant's exposure.

Human breast milk is the recommended source of nutrition for infants due to its complex composition and numerous benefits, including a decline in infection rates in childhood and a lower risk of obesity. Hence, it is crucial that environmental pollutants in human breast milk are minimized. Exposure to black carbon (BC) particles has adverse effects on health; therefore, this pilot study investigates the presence of these particles in human breast milk. BC particles from ambient exposure were measured in eight human breast milk samples using a white light generation under femtosecond illumination. The carbonaceous nature of the particles was confirmed with BC fingerprinting. Ambient air pollution exposures (PM2.5, PM10, and NO2) were estimated using a spatial interpolation model based on the maternal residential address. Spearman rank correlation coefficients were obtained to assess the association between human breast milk's BC load and ambient air pollution exposure. BC particles were found in all human breast milk samples. BC loads in human breast milk were strongly and positively correlated with recent (i.e., 1 week) maternal residential NO2 (r = 0.79; p = 0.02) exposure and medium-term (i.e., 1 month) PM2.5 (r = 0.83; p = 0.02) and PM10 (r = 0.93; p = 0.002) exposure. For the first time, we showed the presence of BC particles in human breast milk and found a robust association with ambient air pollution concentrations. Our findings present a pioneering insight into a novel pathway through which combustion-derived air pollution particles can permeate the delicate system of infants.

Dynamic reliability calculation of random structures by conditional probability method

For the composite random reliability problem, based on the Markov hypothesis of the dynamic response spanning action, two procedures of conditional probability explanation are accomplished: to derive the 2nd-order approximate expression for the calculation of the dynamic reliability of the random structure based on Taylor expansion method; secondly is to determine a mathematical sampling technique based on the Kriging model derive from the statistical analysis. Between them, the sampling procedure by the Kriging interpolation model meets the nonlinear correlation among dynamic reliability and structural random boundaries. Consequently, the finite element results can be used instantly to anatomize the significance of random structural parameters on dynamic reliability, avoiding the tedious and cumbersome theoretical derivation. The numerical example outcomes demonstrate that the numerical sampling method established upon the Kriging model is inconsiderate to the ratio to represent the dispersion and has additional benefits in computational verisimilitude and calculation productivity

Identifying spatiotemporal trends of SARS-CoV-2 RNA in wastewater: from the perspective of upstream and downstream wastewater-based epidemiology (WBE).

Recently, many efforts have been made to address the rapid spread of newly identified COVID-19 virus variants. Wastewater-based epidemiology (WBE) is considered a potential early warning tool for identifying the rapid spread of this virus. This study investigated the occurrence of SARS-CoV-2 in eight wastewater treatment plants (WWTPs) and their sewerage systems which serve most of the population in Taoyuan City, Taiwan. Across the entire study period, the wastewater viral concentrations were correlated with the number of COVID-19 cases in each WWTP (Spearman's r = 0.23-0.76). In addition, it is confirmed that several treatment technologies could effectively eliminate the virus RNA from WWTP influent (> 90%). On the other hand, further results revealed that an inverse distance weighted (IDW) interpolation and hotspot model combined with the geographic information system (GIS) method could be applied to analyze the spatiotemporal variations of SARS-CoV-2 in wastewater from the sewer system. In addition, socio-economic factors, namely, population density, land use, and income tax were successfully identified as the potential drivers which substantially affected the onset of the COVID-19 outbreak in Taiwan. Finally, the data obtained from this study can provide a powerful tool in public health decision-making not only in response to the current epidemic situation but also to other epidemic issues in the future.

The Nesterov accelerated gradient algorithm for Auto-Regressive Exogenous models with random lost measurements: Interpolation method and auxiliary model method

For ARX models with random lost measurements, this article proposes an interpolation and auxiliary model based Nesterov accelerated gradient algorithm. This algorithm utilizes the interpolation and auxiliary model methods to fill in lost measurements. The parameters are estimated with better accuracy based on the interpolated input and predicted output data. Two simulation examples are presented to verify the effective of the proposed algorithm.

Physics-Informed DeepMRI: k-Space Interpolation Meets Heat Diffusion.

Recently, diffusion models have shown considerable promise for MRI reconstruction. However, extensive experimentation has revealed that these models are prone to generating artifacts due to the inherent randomness involved in generating images from pure noise. To achieve more controlled image reconstruction, we reexamine the concept of interpolatable physical priors in k-space data, focusing specifically on the interpolation of high-frequency (HF) k-space data from low-frequency (LF) k-space data. Broadly, this insight drives a shift in the generation paradigm from random noise to a more deterministic approach grounded in the existing LF k-space data. Building on this, we first establish a relationship between the interpolation of HF k-space data from LF k-space data and the reverse heat diffusion process, providing a fundamental framework for designing diffusion models that generate missing HF data. To further improve reconstruction accuracy, we integrate a traditional physics-informed k-space interpolation model into our diffusion framework as a data fidelity term. Experimental validation using publicly available datasets demonstrates that our approach significantly surpasses traditional k-space interpolation methods, deep learning-based k-space interpolation techniques, and conventional diffusion models, particularly in HF regions. Finally, we assess the generalization performance of our model across various out-of-distribution datasets. Our code are available at https://github.com/ZhuoxuCui/Heat-Diffusion.

A Family of Generalized Cardinal Polishing Splines.

Spline functions have received widespread attention in the fields of image sampling and reconstruction. To enhance the performance of splines in reconstruction and reduce the computational burden of solving large linear equations, we propose a family of generalized cardinal polishing splines (GCP-splines) and provide a system of linear equations to obtain the expressions of GCP-splines. First, we propose a cardinal polishing spline basis function with high-precision. Then, we propose a class of GCP-splines and give a general theory of GCP-splines. To calculate the expressions of GCP-splines, we adopt a system of linear equations to obtain the time shifts operator and the convolutional coefficients based on the search spacing and number of terms. Finally, we propose continuous and discrete interpolation models based on GCP-splines, and demonstrate several valuable properties, such as order of approximation and the Riesz basis. To evaluate the performance of GCP-splines, we conduct several experiments on test images from different modalities. The experimental results demonstrate that the GCP-splines for image interpolation and image denoising have better performance and outperform other methods.

Construction of risk warning model of agitated behavior of the elderly in Zhejiang pension institutions

Abstract Alzheimer’s disease is considered the epidemic of the twentieth century, particularly the radical behavior produced by the patients, which can easily lead to an increase in mortality. This paper focuses on optimizing the search path algorithm to forecast the likelihood of aggressive behavior, enabling the implementation of targeted preventive measures. Additionally, it performs preprocessing procedures like data cleansing on the health data of the elderly. We propose a feature extraction optimization model to calculate the feature contribution of elderly radical behavior data, filter the feature data associated with radical behavior based on this contribution, and establish an interpolation model for association rule learning. Using Logistic Regression, Simple Bayes, and Support Vector Machine classification models, the risk warning model for aggravated behavior is constructed. After one month’s intervention with the risk warning model, the aggressive behavior of the elderly decreased by 58.83%, 43.06%, and 67.94%, respectively, compared to the pre-intervention period, and the intervention effect of the model was good.