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Geochemical data are expressed in closed numerical systems due to their non-normality and the presence of outliers. The specificity of such data makes it challenging to analyze them using standard statistical techniques. The U-modeling of log-transformed data represents a novel approach to geochemical anomaly separation. This method models the geochemical open or log-transformed data by the U-spatial statistics algorithm and has been used for the first time in this paper. In this research, Additive and Centered Logarithmic Transformations (ALR and CLR) were applied to data from the Doostbiglou region in Ardabil province, Iran, known for its copper-gold and molybdenum mineralization. After transforming the data into an open numerical system, the correlation between elements was calculated for both systems to compare the results. The output data were modeled using the U-spatial statistics method, and anomaly maps were subsequently generated. Validation and comparison of the results, considering field data obtained from the local and regional exploration, revealed that both models produced similar results in separating anomalous areas and showed a high degree of agreement with field data. However, the U-modeling of the ALR data more closely aligns with field observations and provides a more precise representation of the mineralization trend. Therefore, these new models are recommended for evaluating the spatial distribution of elements and determining the threshold value.

This paper proposes a new integrable generalized (3+1)-dimensional nonlinear partial differential equation. We apply the standard Painlevé test to check the integrability, which shows the complete integrability of this equation. We employ symbolic computation directly to create the rogue waves using the center-controlled parameters β and γ . We create first-, second-, and third-order rogue wave solutions via direct computation for various values of center-controlled parameters and suitable choices of different constants in the said equation. We obtain the bilinear equation in the auxiliary function f of the transformed variables ξ and η by using the transformation for dependent variable u . Using Hirota’s direct method to create rogue waves up to the third order, we apply the generalized formula for rogue waves formulated by N -soliton. Using the symbolic system tool Mathematica , we illustrate the dynamics for the rogue wave solutions with various center-controlled parameters. We demonstrate how massive rogue waves, present in many nonlinear events, behave dominantly over tiny rogue waves. The equation investigates the development of long waves with small amplitudes traveling in plasma physics and wave motion in fluids and other weakly dispersive mediums. Scientific areas, including oceanography, fluid dynamics, dusty plasma, optical fibers, nonlinear dynamics, and numerous other nonlinear fields, show the occurrence of rogue waves in one way or another.

One of the major telecommunication and network service providers in Indonesia is PT Indosat Tbk. During the coronavirus (COVID-19) pandemic, the daily stock price of that company was influenced by government policies. This study addresses stock data movement from February 5, 2020 to February 5, 2021, resulted in 243 data, using the Geometric Brownian motion (GBM). The stochastic process realization of this stock price fluctuates and increases exponentially, especially in the 40 latest data. Because of this situation, the realization is transformed into log 10 and calculated its return. As a result, weak stationary in variance is obtained. Furthermore, only data from December 7, 2020 to February 5, 2021 fulfill the GBM assumption of stock price return, as R t 1 * , t 1 * = 1 , 2 , 3 , … , 40 . The main idea of this study is adding datum one by one as much as 10% – 15% of the total data R t 1 * , starting from December 4, 2020 backwards. Following this procedure, and based on the 3% < p -value < 10%, the study shows that its datum can be included in R t 1 * , so t 1 * = − 4. − 3 , − 2 , … , 40 and form five other data groups, R t 2 * , … , R t 6 * . Considering Mean Absolute Percentage Error (MAPE) and amount of data from each group, R t 6 * is selected for modelling. Thus, GBM succeeded in representing the stock price movement of the second most popular Indonesian telecommunication company during COVID-19 pandemic.

Machine vision-based navigation in the maize field is significant for intelligent agriculture. Therefore, precision detection of the tasseled crop rows for navigation of agricultural machinery with an accurate and fast method remains an open question. In this article, we propose a new crop rows detection method at the tasseling stage of maize fields for agrarian machinery navigation. The whole work is achieved mainly through image augment and feature point extraction by micro-region of interest (micro-ROI). In the proposed method, we first augment the distinction between the tassels and background by the logarithmic transformation in RGB color space, and then the image is transformed to hue-saturation-value (HSV) space to extract the tassels. Second, the ROI is approximately selected and updated using the bounding box until the multiple-region of interest (multi-ROI) is determined. We further propose a feature points extraction method based on micro-ROI and the feature points are used to calculate the crop rows detection lines. Finally, the bisector of the acute angle formed by the two detection lines is used as the field navigation line. The experimental results show that the algorithm proposed has good robustness and can accurately detect crop rows. Compared with other existing methods, our method's accuracy and real-time performance have improved by about 5 and 62.3%, respectively, which can meet the accuracy and real-time requirements of agricultural vehicles' navigation in maize fields.

Key message We developed two additive systems of biomass equations based on diameter and tree height for nine hardwood species by SUR, and used a likelihood analysis to evaluate the model error structures. In this study, a total of 472 trees were harvested and measured for stem, root, branch, and foliage biomass from nine hardwood species in Northeast China. Two additive systems of biomass equations were developed, one based on tree diameter ( D ) only and one based on both tree diameter ( D ) and height ( H ). For each system, three constraints were set up to account for the cross-equation error correlations between four tree component biomass, two sub-total biomass, and total biomass. The model coefficients were simultaneously estimated using seemly unrelated regression (SUR). Likelihood analysis was used to verify the error structures of power functions in order to determine if logarithmic transformation should be applied on both sides of biomass equations. Jackknifing model residuals were used to validate the prediction performance of biomass equations. The results indicated that (1) stem biomass accounted for the largest proportion (62 %) of the total tree biomass; (2) the two additive systems of biomass equations obtained good model fitting and prediction, of which the model R a 2 was >0.89, and the mean absolute percent bias (MAB %) was <35 %; (3) the system of biomass equations based on both D and H significantly improved model fitting and performance, especially for total, aboveground, and stem biomass; and (4) the anti-log correction was not necessary in this study. The established additive systems of biomass equations can provide reliable and accurate estimation for individual tree biomass of the nine hardwood species in Chinese National Forest Inventory.

Quantitative and accurate urban land information on regional and global scales is urgently required for studying socioeconomic and eco-environmental problems. The spatial distribution of urban land is a significant part of urban development planning, which is vital for optimizing land use patterns and promoting sustainable urban development. Composite nighttime light (NTL) data from the Defense Meteorological Program Operational Line-Scan System (DMSP-OLS) have been proven to be effective for extracting urban land. However, the saturation and blooming within the DMSP-OLS NTL hinder its capacity to provide accurate urban information. This paper proposes an optimized approach that combines NTL with multiple index data to overcome the limitations of extracting urban land based only on NTL data. We combined three sources of data, the DMSP-OLS, the normalized difference vegetation index (NDVI), and the normalized difference water index (NDWI), to establish a novel approach called the vegetation–water-adjusted NTL urban index (VWANUI), which is used to rapidly extract urban land areas on regional and global scales. The results show that the proposed approach reduces the saturation of DMSP-OLS and essentially eliminates blooming effects. Next, we developed regression models based on the normalized DMSP-OLS, the human settlement index (HSI), the vegetation-adjusted NTL urban index (VANUI), and the VWANUI to analyze and estimate urban land areas. The results show that the VWANUI regression model provides the highest performance of all the models tested. To summarize, the VWANUI reduces saturation and blooming, and improves the accuracy with which urban areas are extracted, thereby providing valuable support and decision-making references for designing sustainable urban development.

The outcome of proficiency tests (PTs) is influenced, among others, by the evaluation procedure chosen by the PT provider. In particular for PTs on GMO testing a log-data transformation is often applied to fit skewed data distributions into a normal distribution. The study presented here has challenged this commonly applied approach. The 56 data populations from proficiency testing rounds organised since 2010 by the European Union Reference Laboratory for Genetically Modified Food and Feed (EURL GMFF) were used to investigate the assumption of a normal distribution of reported results within a PT. Statistical evaluation of the data distributions, composed of 3178 reported results, revealed that 41 of the 56 datasets showed indeed a normal distribution. For 10 datasets, the deviation from normality was not statistically significant at the raw or log scale, indicating that the normality assumption cannot be rejected. The normality of the five remaining datasets was statistically significant after log-data transformation. These datasets, however, appeared to be multimodal as a result of technical/experimental issues with the applied methods. On the basis of the real datasets analysed herein, it is concluded that the log transformation of reported data in proficiency testing rounds is often not necessary and should be cautiously applied. It is further shown that the log-data transformation, when applied to PT results, favours the positive performance scoring for overestimated results and strongly penalises underestimated results. The evaluation of the participants’ performance without prior transformation of their results may highlight rather than hide relevant underlying analytical problems and is recommended as an outcome of this study.

In this paper, a stochastic HIV/AIDS model with a bilinear incidence rate is established by perturbing the incidence coefficient. Solving this model is crucial for quantitatively studying HIV/AIDS transmission. However, owing to the complexity and nonlinearity of the random terms, an analytical solution is unattainable, making it necessary to find a suitable numerical method. In practical applications, ensuring the positivity of the numerical solution is key. To achieve this, we perform a logarithmic transformation on the model to obtain a new system. It is note that the drift and diffusion coefficients of the new system grow exponentially, failing to meet monotonicity conditions. We then use the truncated Euler–Maruyama (TEM) method to obtain the numerical solution of the transformed system and derive the positivity-preserving log-truncated EM (PPLTEM) scheme for the original system through an inverse transformation. Importantly, the logarithmic transformation alters the coupling intensity among the variables, which has a nontrivial influence on the convergence rate and stability of the numerical solution. Therefore, we begin by showing the existence and uniqueness of the analytical solution, and then carry out a deep and comprehensive analysis of the boundedness and exponential integrability of both the numerical and analytical solutions with the Burkholder–Davis–Gundy inequality, Bihari’s inequality, etc. Through this process, we derive detailed and comprehensive analytical conclusions pertaining to the convergence, convergence rate, and stability of the numerical solution. Finally, the effectiveness of the theoretical results of the numerical method is illustrated via numerical experiments.

Key messageSeemingly unrelated mixed-effects models were used to model biomass models forLarix olgensis, Pinus koraiensis, andPinus sylvestris, and the developed models considered multiple variables to enhance the practicality of the models.Korean larch (Larix olgensis), Korean pine (Pinus koraiensis), and Mongolian pine (Pinus sylvestris) are important coniferous species in the northeastern area of the P.R. China; hence, accurate biomass estimates of these species are meaningful for evaluating forest health and calculating carbon storage. Based on the tree variables of diameter at breast height (DBH), tree height (H), age, live crown length and crown width, three log-transformed species-specific biomass functions were developed using linear seemingly unrelated regression (SUR) since the error structures of the component biomass model (stem, branches, foliage and roots) were proven to be multiplicative. Furthermore, the plot-level random effect was introduced into the SUR model, namely the SURM model, to achieve more accurate biomass estimates. The results showed that the SURM model has a better fitting performance than the SUR models for three species and model types. The determination coefficient, R2, was always larger for the SURM models than for the corresponding SUR models, while the root mean square error, RMSE, was always smaller for the SURM models. By leave-one-out validation, the SURM models were proven to provide more accurate predictions because the mean prediction percent error (MPE) was close to 0 and the mean absolute percentage error (MAPE) was smaller than that of the corresponding SUR models across species and model types. In addition, the size and design of the sample used to calibrate for random effects were assessed using the MAPE statistical index, MAPE. The calibration of the SURM showed a decreasing pattern of bias as the sample size increased, indicating that more available sampled trees improved the prediction accuracy of SURM models, while only slight differences existed across sampling designs. Overall, the newly developed biomass models have advantages in various data structures, and will be meaningful and useful in terms of accurately predicting the biomass of three important species in Northeast China.

Critical values and p-values of statistical hypothesis tests are often derived using asymptotic approximations of sampling distributions. However, this sometimes results in tests that are conservative (i.e., understate the frequency of an incorrectly rejected null hypothesis by employing too stringent of a threshold for rejection). Although computationally rigorous options (e.g., the bootstrap) are available for such situations, we illustrate that simple transformations can be used to improve both the size and power of such tests. Using a logarithmic transformation, we show that the transformed statistic is asymptotically equivalent to its untransformed analogue under the null hypothesis and is divergent from the untransformed version under the alternative (yielding a potentially substantial increase in power). The transformation is applied to several easily-accessible statistical hypothesis tests, a few of which are taught in introductory statistics courses. With theoretical arguments and simulations, we illustrate that the log transformation is preferable to other forms of correction (such as statistics that use a multiplier). Finally, we illustrate application of the method to a well-known dataset. Supplementary materials for this article are available online.