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Pressure measurement is of great importance due to its wide range of applications in many fields. AT-cut quartz, with its exceptional precision and durability, stands out as an excellent pressure transducer due to its superior accuracy and stable performance over time. However, its intrinsic temperature dependence significantly hinders its potential application in varying temperature environments. Herein, three different learning algorithms (i.e., multivariate polynomial regression, multilayer perceptron networks, and support vector regression) are elaborated in detail and applied to establish the prediction models for compensating the temperature effect of the resonant pressure sensor, respectively. The AC-cut quartz, which is sensitive to temperature variations, is paired with the AT-cut quartz, providing the essential temperature information. The output frequencies derived from the AT-cut and AC-cut quartzes are selected as input data for these learning algorithms. Through experimental validation, all three methods are effective, and a remarkable improvement in accuracy can be achieved. Among the three methods, the MPR model has exceptionally high accuracy in predicting pressure. The calculated residual error over the temperature range of −10–40 °C is less than 0.008% of 40 MPa full scale (FS). An intelligent automatic compensation and real-time processing system for the resonant pressure sensor is developed as well, which may contribute to improving the efficiency in online calibration and large-scale industrialization. This paper paves a promising way for the temperature compensation of resonant pressure sensors. [ABSTRACT FROM AUTHOR]

Stone columns have been extensively advocated as a traditional approach to increase the undrained bearing capacity and reduce the settlement of footings sitting on cohesive ground. However, due to the complex interaction between the soil and the stone columns, there currently needs to be a commonly acknowledged approach that can be used to precisely predict the undrained bearing capacity of the system. For this reason, the bearing capacity of a sandy bed reinforced with geogrid and sitting above a collection of geogrid-encased stone columns floating in soft clay was studied in this research. Using a white-box machine learning (ML) technique called Multivariate Polynomial Regression (MPR), this work aims to develop a model for predicting the bearing capacity of the referred foundation system. For this purpose, two hundred and forty-five experimental results were collected from the literature. In addition, the model was compared to two other ML models, namely, a black-box model known as Random Forest (RF) and a white-box ML model called Linear Regression (LR). In terms of R2 (coefficient of determination) and RMSE (Root Mean Absolute Error) values, the newly proposed model outperforms the two other referred models and demonstrates robust estimation capabilities. In addition, a parametric analysis was carried out to determine the contribution of each input variable and its relative significance on the output. [ABSTRACT FROM AUTHOR]

We present the methods for constructing a multivariate polynomial given by a redundant representation based on the results of a limited active experiment. We solve the problem in two formulations. The first is the problem of constructing a multivariate polynomial regression given by a redundant representation based on the results of a limited active experiment. The solution method is based on the previous results of Professor A. A. Pavlov and his students showing the fundamental possibility of reducing this problem to the sequential construction of univariate polynomial regressions and solving the corresponding nondegenerate systems of linear equations. There are two modifications of this method. The second modification is based on proving for an arbitrary limited active experiment the possibility of using only one set of normalized orthogonal polynomials of Forsythe. The second formulation refers to the solution of this problem for a particular but sufficient from the practical point of view case when an unknown implementation of a random variable is not added to the initial measurement results during an active experiment. This method is a modification of the solution method for the multivariate polynomial regression problem. Also, we used the main results of the general theory (which reduces the multivariate polynomial regression problem solving to the sequential construction of univariate polynomial regressions and solution of corresponding nondegenerate systems of linear equations) to consider and strictly substantiate fairly wide from the practical point of view particular cases leading to estimating the coefficients at nonlinear terms of the multivariate polynomial regression as a solution of linear equations with a single variable.

The formulation of coffee blends is of paramount importance for the coffee industry, as it provides the product with an expressive ability to compete in the market and adds sensory attributes that complement the consumption experience. Through redundancy analysis and canonical correspondence analysis, it is possible to study the relationships between a set of sensory notes and a set of blends with different proportions of coffee variety through multivariate linear regression models. However, it is unrealistic to assume that such sensory responses are given linearly in relation to the formulation of the blends, since some coffee species have greater weight in the sensory evaluation (quadratic terms) and the effect of the mixtures (term of interaction). With this motivation, this work aims to propose the use of redundancy analysis and nonlinear correspondence analysis through multivariate polynomial regression to evaluate the acceptance of different varieties of coffee blends according to the scores given by the evaluators. Finally, it is concluded that there were gains in the percentage of total explained variance in the polynomial models in relation to the classic models.

The attitude closed-loop control of the parallel platform in the working space needs to determine the relationship between the pose of the top moving platform and the length of each mechanical arm, that is, the kinematics problem of the parallel platform. In this study, the kinematics model of the six-degree-of-freedom parallel platform was established. The kinematics forward solution algorithm based on Newton–Raphson iteration was studied. The kinematics forward solution method usually adopts a numerical solution, which often needs multiple iterations, and the algorithm has a poor real-time performance. In order to improve the real-time performance of the parallel platform control system, a multivariate polynomial regression kinematics forward solution algorithm is proposed in this paper. Moreover, by combining the multivariate polynomial regression with the Newton iterative method, we obtained an efficient solution algorithm with controllable solution accuracy. The effectiveness of the proposed method was verified by simulation tests and physical tests. [ABSTRACT FROM AUTHOR]

Pressure measurement is of great importance due to its wide range of applications in many fields. AT-cut quartz, with its exceptional precision and durability, stands out as an excellent pressure transducer due to its superior accuracy and stable performance over time. However, its intrinsic temperature dependence significantly hinders its potential application in varying temperature environments. Herein, three different learning algorithms (i.e., multivariate polynomial regression, multilayer perceptron networks, and support vector regression) are elaborated in detail and applied to establish the prediction models for compensating the temperature effect of the resonant pressure sensor, respectively. The AC-cut quartz, which is sensitive to temperature variations, is paired with the AT-cut quartz, providing the essential temperature information. The output frequencies derived from the AT-cut and AC-cut quartzes are selected as input data for these learning algorithms. Through experimental validation, all three methods are effective, and a remarkable improvement in accuracy can be achieved. Among the three methods, the MPR model has exceptionally high accuracy in predicting pressure. The calculated residual error over the temperature range of −10–40 °C is less than 0.008% of 40 MPa full scale (FS). An intelligent automatic compensation and real-time processing system for the resonant pressure sensor is developed as well, which may contribute to improving the efficiency in online calibration and large-scale industrialization. This paper paves a promising way for the temperature compensation of resonant pressure sensors.

We substantiate the structure of the efficient numerical axis segment an active experiment on which allows finding estimates of the coefficients for nonlinear terms of univariate polynomial regression with high accuracy using normalized orthogonal Forsyth polynomials with a sufficiently small number of experiments. For the case when an active experiment can be executed on a numerical axis segment that does not satisfy these conditions, we substantiate the possibility of conducting a virtual active experiment on an efficient interval of the numerical axis. According to the results of the experiment, we find estimates for nonlinear terms of the univariate polynomial regression under research as a solution of a linear equalities system with an upper non-degenerate triangular matrix of constraints. Thus, to solve the problem of estimating the coefficients for nonlinear terms of univariate polynomial regression, it is necessary to choose an efficient interval of the numerical axis, set the minimum required number of values of the scalar variable which belong to this segment and guarantee a given value of the variance of estimates for nonlinear terms of univariate polynomial regression using normalized orthogonal polynomials of Forsythe. Next, it is necessary to find with sufficient accuracy all the coefficients of the normalized orthogonal polynomials of Forsythe for the given values of the scalar variable. The resulting set of normalized orthogonal polynomials of Forsythe allows us to estimate with a given accuracy the coefficients of nonlinear terms of univariate polynomial regression in an arbitrary limited active experiment: the range of the scalar variable values can be an arbitrary segment of the numerical axis. We propose to find an estimate of the constant and of the coefficient at the linear term of univariate polynomial regression by solving the linear univariate regression problem using ordinary least squares method in active experiment conditions. Author and his students shown in previous publications that the estimation of the coefficients for nonlinear terms of multivariate polynomial regression is reduced to the sequential construction of univariate regressions and the solution of the corresponding systems of linear equalities. Thus, the results of the paper qualitatively increase the efficiency of finding estimates of the coefficients for nonlinear terms of multivariate polynomial regression given by a redundant representation.

Integrating renewables has been recognised as the appropriate way for cleaner development in response to climate change and energy shortfall. The present study aims at developing sustainable hybrid energy system in Doomadgee, Far North Queensland, Australia, which is near areas with greater biodiversity such as great barrier reef. Six different configuration of hybrid renewable energy systems has been simulated by HOMER PRO software for average load demand of 49.07 MWh/day with a 4.83 MW peak in an off-grid condition. Every scenario has been analysed in terms of technical, financial, socio and ecological aspects. A multi-objective optimisation technique, TOPSIS has been implemented to determine final optimal scenario based on thirteen parameters. Solar Photovoltaic-wind-hydrogen system is found best combination with net present cost and cost of energy of respective 165 MAUD and 0.646 AUD/kWh. This system can preserve the region's ecology by reducing 12,330,597 kg/year of CO 2 emission. In addition, the system has positive effect on the society with creation of 90.647 jobs and human development index of 0.9063. Triple sensitivity study such as variation of solar and wind resources including demand and implementation of multivariate polynomial regression which is key contribution of present study, have provided a clear view that cost of energy is sensorial to change in resources and demand. Wind resources are the most influential parameter, whose exploitation helps to lessen cost of energy greatly. [ABSTRACT FROM AUTHOR]

Stone columns have been extensively advocated as a traditional approach to increase the undrained bearing capacity and reduce the settlement of footings sitting on cohesive ground. However, due to the complex interaction between the soil and the stone columns, there currently needs to be a commonly acknowledged approach that can be used to precisely predict the undrained bearing capacity of the system. For this reason, the bearing capacity of a sandy bed reinforced with geogrid and sitting above a collection of geogrid-encased stone columns floating in soft clay was studied in this research. Using a white-box machine learning (ML) technique called Multivariate Polynomial Regression (MPR), this work aims to develop a model for predicting the bearing capacity of the referred foundation system. For this purpose, two hundred and forty-five experimental results were collected from the literature. In addition, the model was compared to two other ML models, namely, a black-box model known as Random Forest (RF) and a white-box ML model called Linear Regression (LR). In terms of R2 (coefficient of determination) and RMSE (Root Mean Absolute Error) values, the newly proposed model outperforms the two other referred models and demonstrates robust estimation capabilities. In addition, a parametric analysis was carried out to determine the contribution of each input variable and its relative significance on the output.

Li-rich micas, such as zinnwaldite and lepidolite, constitute a dominant component of Li resources ([30]; [4]; [32]; [41]). In addition to the Weilasituo mining area, the Jiabusi area seems to have a good potential for Li resources in terms of dominant Li-rich micas in the granite and greisen samples (samples JBS-1-4), with the compositions ranging from Li-phengite and zinnwaldite to lepidolite (Fig. Keywords: Lithium; mica; multivariate polynomial regression; machine learning; Li resources EN Lithium mica multivariate polynomial regression machine learning Li resources 1034 1044 11 06/01/22 20220601 NES 220601 Introduction Micas are members of phyllosilicates in which the structural unit consists of one octahedral (O) sheet between two opposing tetrahedral (T) sheets to form a "TOT" layer. Lithium enters the mica crystal lattice via several competing substitution mechanisms, which include 3Li SP VI sp <-> Al SP VI sp + 2 SP VI sp , Si SP IV sp + 2Li SP VI sp <-> 2Al SP VI sp + SP VI sp , and 2Si SP IV sp + Li SP VI sp <-> 3Al SP Tot sp for Al-rich micas, and Si SP IV sp + Li SP VI sp <-> Al SP IV sp + R SP VI sp , Si SP IV sp + 2Li SP VI sp <-> 3 R SP VI sp , and Al SP VI sp + Li SP VI sp <-> 2 R SP VI sp , where R SP VI sp = Fe + Mg + Mn, for Fe-rich micas ([16]; [21]; [11]; [44]; [43]; [56]; [33]; [7]). [Extracted from the article]

The Lost Hills oilfield, located ∼70 km northwest of Bakersfield in the San Joaquin Valley, has a long history of oil/gas extraction, and it suffers from long-term ground deformation. Many SAR datasets include information about the Lost Hills oilfield over the past two decades. This study focused on calculating and analysing the long-term vertical ground deformation due to oil and gas extraction in the Lost Hills oilfield and proposed a new strategy inspired by the “Small Baseline Subset” idea for jointly processing multi-track SAR images to obtain long-term time-series deformations. The experimental results showed a maximum vertical deformation rate of 20 mm/year in the uplift region and –90 mm/year in the subsidence region of the Lost Hills field from August 1995 to September 2010, and the long-term vertical time-series deformations had a precision of 5 mm. In addition, a multivariate polynomial regression model was used to quantify the relationship between surface deformation volume changes and water, oil, and gas injection-production data. The results demonstrated that the relationship between the ground volume change and injection/production dataset in the subsidence region followed a multivariate linear model, whereas the uplift region satisfied a multivariate quadratic polynomial model. The modelling results provided a new perspective on interpreting ground deformation due to oil/gas extraction.

The attitude closed-loop control of the parallel platform in the working space needs to determine the relationship between the pose of the top moving platform and the length of each mechanical arm, that is, the kinematics problem of the parallel platform. In this study, the kinematics model of the six-degree-of-freedom parallel platform was established. The kinematics forward solution algorithm based on Newton–Raphson iteration was studied. The kinematics forward solution method usually adopts a numerical solution, which often needs multiple iterations, and the algorithm has a poor real-time performance. In order to improve the real-time performance of the parallel platform control system, a multivariate polynomial regression kinematics forward solution algorithm is proposed in this paper. Moreover, by combining the multivariate polynomial regression with the Newton iterative method, we obtained an efficient solution algorithm with controllable solution accuracy. The effectiveness of the proposed method was verified by simulation tests and physical tests.

The high fuel requirements for downdraft gasifiers prevent the technology's breakthrough. To identify the limitations for the woodchips fines content (FC), bark content (BC) and water content (WC), this work developed novel and easy-to-use functions to predict the gas composition based on these fuel properties. While previous prediction tools require the elemental fuel composition, the presented tool uses only typical commercial fuel properties. Multivariate polynomial regression is performed using 24 different operating points of an 85-kW open-top gasifier. The evaluations revealed three novel findings: (1) The polynomial functions of first order were the most suitable to describe the effects of the fuel properties on the gas composition. (2) According to the developed approach, the optimum fuel leading to the highest product gas lower heating value and a total hydrocarbon content below 8000 ppm contains 0 m% FC , 6.1 m% BC and 7.2 m% WC. (3) The achieved average deviation of the predicted gas composition compared to the measured one was in the same range as the typical variations between experiments. Therefore, a satisfying accuracy was achieved. The developed functions can be applied in academia and industry to identify suitable woodchips and to predict the gas quality when buying woodchips. [ABSTRACT FROM AUTHOR]

• Ethylene glycol steam reforming in a micro-reformer for hydrogen production. • High values of EG conversion and H 2 yield for the NPGA bimetallic catalyst. • High hydrogen productivity at 450°C and WHSV of 80.8 h−1. • Using of MPR and GP approaches to modeling of the EGSR process. • GP model as the optimal model with the highest prediction power. Three types of catalysts, i.e. Pt/γ-alumina (PGA), Ni/γ-alumina (NGA) and Ni–Pt/γ-alumina (NPGA), were prepared by incipient wetness impregnation (IWI) and deposited on a micro-reformer for hydrogen production by ethylene glycol steam reforming (EGSR). Multivariate polynomial regression (MPR) and genetic programming (GP) approaches were used to model the EGSR process based on experimental data. In these models, temperature and weight hourly space velocity (WHSV) as independent variables and ethylene glycol (EG) conversion, H 2 selectivity, H 2 yield and CO selectivity were considered as target functions. Based on the results, the GP model predicts objective functions with the highest prediction power and this model was selected as the optimal model. For example, for the NGA catalyst and the dependent variable of EG conversion, the values of correlation coefficient (R2) and root mean squared error (RMSE) were 0.9980 and 1.3191, respectively based on the GP model while for the best MPR (cubic) model; these parameters were 0.9735 and 4.2476, respectively. The results showed that the EG conversion values for the NPGA bimetallic catalyst were higher than for the PGA or NGA monometallic catalysts. The maximum values of EG conversion, H 2 selectivity and H 2 yield for all the catalysts were obtained at a temperature of 450°C and at a WHSV of 80.8 h−1. [ABSTRACT FROM AUTHOR]

Abstract Air-to-air energy recovery ventilators (AERVs) are widely applied in building heating, ventilation, and air conditioning (HVAC) systems to reduce energy consumption by reducing heating and cooling loads caused by ventilation. Its energy exchange efficiency data are typically acquired experimentally and are time consuming to be applied to engineering fields when the number of working scenarios to be tested is large. Instead of manual labor and time, detailed numerical calculation methods require the characteristic information of the membrane material, which is difficult for manufacturers to provide. Hence, an energy exchange efficiency prediction approach based on a multivariate polynomial regression model is proposed herein to predict the energy exchange efficiency of the membrane-based AERV (MERV) core. In the proposed approach, a simplified numerical efficiency calculation model of a cross-flow air-to-air enthalpy exchanger is trained with a small sample of experimentally measured efficiency data. Subsequently, the trained model is adopted to predict the energy exchange efficiency of the MERV core made of the same membrane, under other flowrates and structures. As verified by the experimental data, the proposed approach can predict the energy exchange efficiency with absolute deviation limits within ±8.0%. Compared to detailed numerical calculation methods, the proposed approach requires less membrane characteristic information and calculations; thus, the proposed approach is practical for engineering applications to simulate the equipment performance over different conditions and help sizing the equipment with less requirements. Highlights • A combination of theoretical ε-NTU method and data-mining methods. • No requisition of known thermal properties of the membrane. • Rapid prediction based on a small sample of experimental test data. [ABSTRACT FROM AUTHOR]

Pressure measurement is of great importance due to its wide range of applications in many fields. AT-cut quartz, with its exceptional precision and durability, stands out as an excellent pressure transducer due to its superior accuracy and stable performance over time. However, its intrinsic temperature dependence significantly hinders its potential application in varying temperature environments. Herein, three different learning algorithms (i.e., multivariate polynomial regression, multilayer perceptron networks, and support vector regression) are elaborated in detail and applied to establish the prediction models for compensating the temperature effect of the resonant pressure sensor, respectively. The AC-cut quartz, which is sensitive to temperature variations, is paired with the AT-cut quartz, providing the essential temperature information. The output frequencies derived from the AT-cut and AC-cut quartzes are selected as input data for these learning algorithms. Through experimental validation, all three methods are effective, and a remarkable improvement in accuracy can be achieved. Among the three methods, the MPR model has exceptionally high accuracy in predicting pressure. The calculated residual error over the temperature range of -10-40 °C is less than 0.008% of 40 MPa full scale (FS). An intelligent automatic compensation and real-time processing system for the resonant pressure sensor is developed as well, which may contribute to improving the efficiency in online calibration and large-scale industrialization. This paper paves a promising way for the temperature compensation of resonant pressure sensors.

Ever-increasing launch of small satellites demands an effective and efficient computer-aided analysis approach to shorten the ground test cycle and save the economic cost. However, the multiple influencing factors hamper the efficiency and accuracy of separation reliability assessment. In this study, a novel evaluation approach based on active subspace identification and response surface construction is established and verified. The formulation of small satellite separation is firstly derived, including equations of motion, separation and gravity forces, and quantity of interest. The active subspace reduces the dimension of uncertain inputs with minimum precision loss and a 4th degree multivariate polynomial regression (MPR) using cross validation is hand-coded for the propagation and error analysis. A common spring separation of small satellites is employed to demonstrate the accuracy and efficiency of the approach, which exhibits its potential use in widely existing needs of satellite separation analysis. [ABSTRACT FROM AUTHOR]

Biosensors are small analytical devices incorporating a biological recognition element and a physico-chemical transducer to convert a biological signal into an electrical reading. Nowadays, their technological appeal resides in their fast performance, high sensitivity and continuous measuring capabilities; however, a full understanding is still under research. This paper aims to contribute to this growing field of biotechnology, with a focus on Glucose-Oxidase Biosensor (GOB) modeling through statistical learning methods from a regression perspective. We model the amperometric response of a GOB with dependent variables under different conditions, such as temperature, benzoquinone, pH and glucose concentrations, by means of several machine learning algorithms. Since the sensitivity of a GOB response is strongly related to these dependent variables, their interactions should be optimized to maximize the output signal, for which a genetic algorithm and simulated annealing are used. We report a model that shows a good generalization error and is consistent with the optimization. [ABSTRACT FROM AUTHOR]

Biosensors are small analytical devices incorporating a biological recognition element and a physico-chemical transducer to convert a biological signal into an electrical reading. Nowadays, their technological appeal resides in their fast performance, high sensitivity and continuous measuring capabilities; however, a full understanding is still under research. This paper aims to contribute to this growing field of biotechnology, with a focus on Glucose-Oxidase Biosensor (GOB) modeling through statistical learning methods from a regression perspective. We model the amperometric response of a GOB with dependent variables under different conditions, such as temperature, benzoquinone, pH and glucose concentrations, by means of several machine learning algorithms. Since the sensitivity of a GOB response is strongly related to these dependent variables, their interactions should be optimized to maximize the output signal, for which a genetic algorithm and simulated annealing are used. We report a model that shows a good generalization error and is consistent with the optimization.

Abstract: In this study, linear and nonlinear modeling was performed to predict the urban air quality of the Lucknow city (India). Partial least squares regression (PLSR), multivariate polynomial regression (MPR), and artificial neural network (ANN) approach-based models were constructed to predict the respirable suspended particulate matter (RSPM), SO2, and NO2 in the air using the meteorological (air temperature, relative humidity, wind speed) and air quality monitoring data (SPM, NO2, SO2) of five years (2005–2009). Three different ANN models, viz. multilayer perceptron network (MLPN), radial-basis function network (RBFN), and generalized regression neural network (GRNN) were developed. All the five different models were compared for their generalization and prediction abilities using statistical criteria parameters, viz. correlation coefficient (R), standard error of prediction (SEP), mean absolute error (MAE), root mean squared error (RMSE), bias, accuracy factor (Af), and Nash–Sutcliffe coefficient of efficiency (Ef). Nonlinear models (MPR, ANNs) performed relatively better than the linear PLSR models, whereas, performance of the ANN models was better than the low-order nonlinear MPR models. Although, performance of all the three ANN models were comparable, the GRNN over performed the other two variants. The optimal GRNN models for RSPM, NO2, and SO2 yielded high correlation (between measured and model predicted values) of 0.933, 0.893, and 0.885; 0.833, 0.602, and 0.596; and 0.932, 0.768 and 0.729, respectively for the training, validation and test sets. The sensitivity analysis performed to evaluate the importance of the input variables in optimal GRNN revealed that SO2 was the most influencing parameter in RSPM model, whereas, SPM was the most important input variable in other two models. The ANN models may be useful tools in the air quality predictions. [Copyright &y& Elsevier]

Abstract: The paper describes linear and nonlinear modeling of the wastewater data for the performance evaluation of an up-flow anaerobic sludge blanket (UASB) reactor based wastewater treatment plant (WWTP). Partial least squares regression (PLSR), multivariate polynomial regression (MPR) and artificial neural networks (ANNs) modeling methods were applied to predict the levels of biochemical oxygen demand (BOD) and chemical oxygen demand (COD) in the UASB reactor effluents using four input variables measured weekly in the influent wastewater during the peak (morning and evening) and non-peak (noon) hours over a period of 48 weeks. The performance of the models was assessed through the root mean squared error (RMSE), relative error of prediction in percentage (REP), the bias, the standard error of prediction (SEP), the coefficient of determination (R 2), the Nash–Sutcliffe coefficient of efficiency (E f), and the accuracy factor (A f), computed from the measured and model predicted values of the dependent variables (BOD, COD) in the WWTP effluents. Goodness of the model fit to the data was also evaluated through the relationship between the residuals and the model predicted values of BOD and COD. Although, the model predicted values of BOD and COD by all the three modeling approaches (PLSR, MPR, ANN) were in good agreement with their respective measured values in the WWTP effluents, the nonlinear models (MPR, ANNs) performed relatively better than the linear ones. These models can be used as a tool for the performance evaluation of the WWTPs. [Copyright &y& Elsevier]

The study of the structural order of charcoals embedded in pyroclastic density currents provides information on their emplacement temperature during volcanic eruptions. In the present work, a set of charcoals from three distinct pyroclastic density currents deposits whose temperatures have been previously estimated by charcoal reflectance analyses to lie between 250 °C and 550 °C, was studied by means of Raman spectroscopy. The analyses reveal a very disordered structural ordering of the charcoals, similar to kerogen matured under diagenetic conditions. Changes in Raman spectra at increasing temperatures reflect depolymerization and an increase of aromaticity and can be expressed by parameters derived from a simplified fitting method. Based on this approach, a second order polynomial regression with a high degree of correlation and a minimum error was derived to predict paleotemperatures of pyroclastic deposits. Our results show that Raman spectroscopy can provide a reliable and powerful tool for volcanological studies and volcanic hazard assessment given its advantage of minimum samples preparation, rapid acquisition processes and high precision. [ABSTRACT FROM AUTHOR]

Multivariate polynomial regression was used to generate polynomial iterators for time series exhibiting autocorrelations. A stepwise technique was used to add and remove polynomial terms to ensure the model contained only those terms that produce a statistically significant contribution to the fit. An approach is described in which datasets are divided into three subsets for identification, estimation, and validation. This produces a parsimonious global model that is can greatly reduce the tendency towards undesirable behaviours such as overfitting or instability. The technique was found to be able to identify the nonlinear dynamic behaviour of simulated time series, as reflected in the geometry of the attractor and calculation of multiple Lyapunov exponents, even in noisy systems. The technique was applied to times series data obtained from simulations of the Lorenz and Mackey - Glass equations with and without measurement noise. The model was also used to determine the embedding dimension of the Mackey - Glass equation. [ABSTRACT FROM AUTHOR]

Abstract: Nitrate nitrogen losses through subsurface drainage and crop yield are determined by multiple climatic and management variables. The combined and interactive effects of these variables, however, are poorly understood. Our objective is to predict crop yield, nitrate concentration, drainage volume, and nitrate loss in subsurface drainage from a corn (Zea mays L.) and soybean (Glycine max (L.) Merr.) rotation as a function of rainfall amount, soybean yield for the year before the corn–soybean sequence being evaluated, N source, N rate, and timing of N application in northeastern Iowa, U.S.A. Ten years of data (1994–2003) from a long-term study near Nashua, Iowa were used to develop multivariate polynomial regression equations describing these variables. The regression equations described over 87, 85, 94, 76, and 95% of variation in soybean yield, corn yield, subsurface drainage, nitrate concentration, and nitrate loss in subsurface drainage, respectively. A two-year rotation under average soil, average climatic conditions, and 125 kg N/ha application was predicted to loose 29, 37, 36, and 30 kg N/ha in subsurface drainage for early-spring swine manure, fall-applied swine manure, early-spring UAN fertilizer, and late-spring split UAN fertilizer (urea ammonium nitrate), respectively. Predicted corn yields were 10.0 and 9.7 Mg/ha for the swine manure and UAN sources applied at 125 kg N/ha. Timing of application (i.e., fall or spring) did not significantly affect corn yield. These results confirm other research suggesting that manure application can result in less nitrate leaching than UAN (e.g., 29 vs. 36 kg N/ha), and that spring application reduces nitrate leaching compared to fall application (e.g., 29 vs. 37 kg N/ha). The regression equations improve our understanding of nitrate leaching; offer a simple method to quantify potential N losses from Midwestern corn–soybean rotations under the climate, soil, and management conditions of the Nashua field experiment; and are a step toward development of easy to use N management tools. [Copyright &y& Elsevier]

The relation between stand density and structure of spring rape (Brassica napus L.) was described with the aid of comprehensive measurements of structure. The structural components measured were plant height, stem diameter at root collar, site of the lowest pod on the main raceme, number of pods on the main raceme, site of the lowest branch on the main stem, number of primary branches and number of pods on the branches. The experiment was conducted at two nitrogen levels, 110 and 180 kg ha-1, and was replicated in 3 years, 1988, 1989 and 1990. Stand density was varied by using five different seeding rates and the number of plants m-2 evaluated immediately prior to harvest was used to express the stand density. In the years considered, the densities varied between 16 and 520 plants m-2. The relationship between plant density and rape plant structure was adequately described each year by a multivariate second degree polynomial model. Varying the nitrogen application rate seemed to have no influence on this relationship. Denser plant stands produced thinner and shorter plants, the shortening occurring in the pod-producing section of the main raceme. Further, with increasing stand density, the number of branches decreased as did the number of pods on the branches and on the main raceme. These changes in plant structure retarded at densities over 150-200 plants m-2. This seems to be the minimum density that should be achieved in rape stands. [ABSTRACT FROM AUTHOR]