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Water is an indispensable resource for human production and life. The evaluation of water quality by scientific methods provides sufficient support for the regeneration and recycling of water resources. In this study, entropy theory was used to evaluate water quality and overcomes the limitations of traditional water quality assessment, which does not consider the impact of different environmental factors on water quality. Considering the complexity of the traditional evaluation process, two typical machine learning (ML) methods – generalized regression neural network (GRNN) and support vector machine (SVM) – were used to predict the entropy water quality index (EWQI). Correlation analysis was applied to divide environmental factors into different combinations that subsequently acted as the input vector for the ML model. According to the results of the root mean squared error (RMSE), the SVM was selected as the better prediction model. Then, four different types of optimization algorithms were used to optimize the SVM to calculate nonlinear regression predictions and classifications of water quality. After analyzing the prediction results with different types of scientific evaluation indicators, the algorithm of differential evaluation and gray wolf optimization (DE-GWO) achieved markedly better performance than the other three algorithms, which has important advantages in avoiding the prediction model falling into a local optimal solution. The results of this study have significant guidance for water quality prediction and could make further contributions to the rational use and protection of water resources.

The edible flowers have in their constitution proteins, lipids, starch, vitamins, important minerals for a healthy diet, as well as bioactive compounds recognized for their potential effects on human health. Due to the high perishability of the flowers, their marketing represents a challenge, and drying is a method that contributes to the preservation of the product. Given the above, the present study aims verify which is the curve that best adjusts to the mass loss during the dehydration process through the proposition of Boltzmann nonlinear regression model in face of classical dehydration curve models, as well measure in frozen flowers centesimal composition of Viola × wittrockiana flowers. The flowers were dehydrated at 30°C in an air circulation oven up to constant weight. The centesimal composition of the dehydrated Viola × wittrockiana is 84.69% humidity, 8.76% carbohydrates, 2.51% proteins, 2.41% crude fiber, 1.23% ash, 0.40% lipids and 48.68 Kcal. With respect to phenolic compounds, the frozen and dehydrated flowers showed 423 and 301 mg gallic acid equivalents per gram and, about antioxidant activity, showed 90.67 to 94.93% inhibition of the DPPH radical (2,2-Diphenyl-1-picrylhydrazyl) and 44.00 and 49.00 mg of Trolox.100 g-1. The Boltzmann model showed best fit the mass loss of Viola × wittrockiana and through this model the maximum mass loss occurs with 0.16 g, the maximum rate of mass loss of Viola × wittrockiana occurs in 46.7 min, whose mass loss is 0.66 g. The dehydration proved to be an efficient method to preserve the flowers because the bioactive compounds did not present significant losses after the application of this process.

Using the Plethysmograph (PPG) signal to estimate blood pressure (BP) is attractive given the convenience and possibility of continuous measurement. However, due to the personal differences and the insufficiency of data, the dilemma between the accuracy for a small dataset and the robustness as a general method remains. To this end, we scrutinized the whole pipeline from the feature selection to regression model construction based on a one-month experiment with 11 subjects. By constructing the explanatory features consisting of five general PPG waveform features that do not require the identification of dicrotic notch and diastolic peak and the heart rate, three regression models, which are partial least square, local weighted partial least square, and Gaussian Process model, were built to reflect the underlying assumption about the nature of the fitting problem. By comparing the regression models, it can be confirmed that an individual Gaussian Process model attains the best results with 5.1 mmHg and 4.6 mmHg mean absolute error for SBP and DBP and 6.2 mmHg and 5.4 mmHg standard deviation for SBP and DBP. Moreover, the results of the individual models are significantly better than the generalized model built with the data of all subjects.

Forecasting is a common data science task that helps organizations with capacity planning, goal setting, and anomaly detection. Despite its importance, there are serious challenges associated with producing reliable and high-quality forecasts-especially when there are a variety of time series and analysts with expertise in time series modeling are relatively rare. To address these challenges, we describe a practical approach to forecasting \"at scale\" that combines configurable models with analyst-in-the-loop performance analysis. We propose a modular regression model with interpretable parameters that can be intuitively adjusted by analysts with domain knowledge about the time series. We describe performance analyses to compare and evaluate forecasting procedures, and automatically flag forecasts for manual review and adjustment. Tools that help analysts to use their expertise most effectively enable reliable, practical forecasting of business time series.

The diameter at breast height (DBH) is the most important independent variable in biomass allometry models based on metabolic scaling theory (MST) or geometric theory. However, the fixed position DBH can be misleading in its use of universal scaling laws and lead to some deviation for the biomass model. Therefore, it is still an urgent scientific problem to build a high-precision biomass model system. A dataset of 114 trees was destructively sampled to obtain dry biomass components, including stems, branches, and foliage, and taper measurements to explore the applicability of biomass components to allometric scaling laws and develop a new system of additive models with the diameter in relative height (DRH) for each component of a Larch ( Larix principis-rupprechtii Mayr) plantation in northern China. The variable exponential taper equations were modelled using nonlinear regression. In addition, applying nonlinear regression and nonlinear seemingly unrelated regression (NSUR) enabled the development of biomass allometric models and the system of additive models with DRH for each component. The results showed that the Kozak’s (II) 2004 variable exponential taper equation could accurately describe the stem shape and diameter in any height of stem. When the diameters in relative height were D 0.2 , D 0.5 , and D 0.5 for branches, stems, and foliage, respectively, the allometric exponent of the stems and branches was the closest to the scaling relations predicted by the MST, and the allometric exponent of foliage was the most closely related to the scaling relations predicted by geometry theory. Compared with the nonlinear regression, the parameters of biomass components estimated by NSUR were lower, and it was close to the theoretical value and the most precise at forecasting. In the study of biomass process modelling, utilizing the DRH by a variable exponential taper equation can confirm the general biological significance more than the DBH of a fixed position.

Deep learning plays a key role in the recent developments of machine learning. This paper develops a deep residual neural network (ResNet) for the regression of nonlinear functions. Convolutional layers and pooling layers are replaced by fully connected layers in the residual block. To evaluate the new regression model, we train and test neural networks with different depths and widths on simulated data, and we find the optimal parameters. We perform multiple numerical tests of the optimal regression model on multiple simulated data, and the results show that the new regression model behaves well on simulated data. Comparisons are also made between the optimal residual regression and other linear as well as nonlinear approximation techniques, such as lasso regression, decision tree, and support vector machine. The optimal residual regression model has better approximation capacity compared to the other models. Finally, the residual regression is applied into the prediction of a relative humidity series in the real world. Our study indicates that the residual regression model is stable and applicable in practice.

An important task in the study of fast radio bursts (FRBs) remains the automatic classification of repeating and nonrepeating sources based on their morphological properties. We propose a statistical model that considers a modified logistic regression to classify FRB sources. The classical logistic regression model is modified to accommodate the small proportion of repeaters in the data, a feature that is likely due to the sampling procedure and duration and is not a characteristic of the population of FRB sources. The weighted logistic regression hinges on the choice of a tuning parameter that represents the true proportion τ of repeating FRB sources in the entire population. The proposed method has a sound statistical foundation, direct interpretability, and operates with only five parameters, enabling quicker retraining with added data. Using the CHIME/FRB Collaboration sample of repeating and nonrepeating FRBs and numerical experiments, we achieve a classification accuracy for repeaters of nearly 75% or higher when τ is set in the range of 50%–60%. This implies a tentative high proportion of repeaters, which is surprising, but is also in agreement with recent estimates of τ that are obtained using other methods.

Relying simply on bitwise operators, the recently introduced Tsetlin machine (TM) has provided competitive pattern classification accuracy in several benchmarks, including text understanding. In this paper, we introduce the regression Tsetlin machine (RTM), a new class of TMs designed for continuous input and output, targeting nonlinear regression problems. In all brevity, we convert continuous input into a binary representation based on thresholding, and transform the propositional formula formed by the TM into an aggregated continuous output. Our empirical comparison of the RTM with state-of-the-art regression techniques reveals either superior or on par performance on five datasets. This article is part of the theme issue ‘Harmonizing energy-autonomous computing and intelligence’.

Sorption of synthetic dyes on low-cost solid sorbents is a simple technique for their removal from wastewater. Recent initiatives in the sorption process have sought the use of activated carbon derived from agricultural wastes as it provides an attractive and cheaper alternative to commercial activated carbon, which is usually expensive. This research investigates the sorption kinetics and equilibrium of two synthetic cationic dyes, crystal violet and methylene blue from aqueous media using activated carbon prepared from an agro-waste, Millettia thonningii seed pods. Sorption experiments were carried out using the batch process. The kinetic data were analyzed using the pseudo-first-order, pseudo-second-order, and intraparticle diffusion models while the equilibrium data were analyzed using the Langmuir, Freundlich, and Redlich–Peterson isotherm models. Nonlinear regression method was used to fit the data to the isotherm models in order to determine model parameters and the best-fit isotherms. Thus, three error functions; coefficient of determination, Chi-square statistic test, and the sum of error squares were applied to evaluate the sorption data. The pseudo-second-order model best described the sorption kinetics of both dyes while the Redlich–Peterson model described the equilibrium data the most, followed closely by the Freundlich isotherm model indicating a heterogeneous sorbent surface. The experimental results indicate that the agro-waste derived activated carbon is a viable adsorbent for the remediation of dye-contaminated water.

Photosynthetic light response curves serve as powerful mathematical tools for quantitatively describing the rate of photosynthesis of plants in response to changes in irradiance. However, in practical applications, the daunting task of selecting an appropriate nonlinear model to accurately fit these curves persists as a significant challenge. Thus, there arises a need for a method to systematically evaluate the efficacy of such models. In the present study, four distinct nonlinear models, namely Exponential Model (EM), Rectangular Hyperbola Model (RHM), Nonrectangular Hyperbola Model (NHM), and Modified Rectangular Hyperbola Model (MRHM), were used to fit the relationship between light intensity and the rate of photosynthesis across 42 empirical datasets. The goodness of fit for each model was assessed using the root-mean-square error, and relative curvature measures of nonlinearity were employed to assess the nonlinear behavior of the models. In terms of goodness of fit, pairwise difference tests of the root-mean-square error revealed that there was little to choose among the four models, although RHM gave a marginally poorer fit. However, in terms of nonlinear behavior, EM not only provided the most favorable linear approximation performance at the global level, but also exhibited the best close-to-linear behavior at the individual parameter level among the four models across the 42 datasets. Consequently, the results strongly advocate for EM as the most suitable mathematical framework for fitting photosynthetic light response curves. These findings provide insights into the model assessment for nonlinear regression in describing the relationship between the photosynthetic rate and light intensity.