Allometric equations to estimate the leaf area of Psychotria colorata (Willd. Ex Schult.) Müll.Arg.

Estimating leaf area using non-destructive methods from regression equations has become a more efficient, quick, and accurate way. Thus, this study aimed to propose an equation that significantly estimates the leaf area of Psychotria colorata (Rubiaceae) through linear leaf dimensions. For this purpose, 200 leaves of different shapes were collected, and length (L), width (W), product of length by width (L.W), and real leaf area (LA) of each leaf blade were determined. Then, equations were adjusted for predicting leaf area using simple linear, linear (0.0), quadratic, cubic, power, and exponential regression models. The proposed equation was selected according to the coefficient of determination (R²), Willmott's agreement index (d), Akaike's information criterion (AIC), mean absolute error (MAE), mean squared error (RMSE) and BIAS index. It was noted that the equations adjusted using L.W met the best criteria for estimating leaf area, but the equation LA = 0.59 * L.W from linear regression without intercept was the most suitable. This equation predicts that 59% of leaf area is explained by L.W. Concluding, the leaf area of P. colorata can be estimated using an allometric equation that uses linear leaf blade dimensions.

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Estimation of leaf area of Erythroxylum citrifolium from linear leaf dimensions

Bioscience Journal ◽

10.14393/bj-v35n6a2019-41743 ◽

2019 ◽

Vol 35 (6) ◽

Author(s):

João Everthon da Silva Ribeiro ◽

Ester dos Santos Coêlho ◽

Francisco Romário Andrade Figueiredo ◽

Sérgio de Faria Lopes ◽

Manoel Bandeira de Albuquerque

Keyword(s):

Leaf Area ◽

Leaf Blade ◽

Information Criterion ◽

Coefficient Of Determination ◽

Concordance Index ◽

R And D ◽

Linear Dimensions ◽

Bias Index ◽

Linear Leaf ◽

Leaf Dimensions

Erythroxylum citrifolium is a neotropical plant species recorded in all regions of Brazil. Determining leaf area is of fundamental importance to studies related to plant propagation and growth. The objective was to obtain an equation to estimate the leaf area of E. citrifolium from linear dimensions of the leaf blade (length and width). A total of 200 leaf blades were collected in Parque Estadual Mata do Pau-Ferro in the municipality of Areia, state of Paraíba, Northeast Brazil. The models evaluated were: linear, linear without intercept, quadratic, cubic, power and exponential. The best model was determined by the criteria of: high coefficient of determination (R²), low root mean square error (RMSE), low Akaike information criterion (AIC), high Willmott concordance index (d) and a BIAS index close to zero. All of the models constructed satisfactorily estimated the leaf area of E. citrifolium, with coefficients of determination above 0.9050, but the power model using the product between length and width (L*W) ŷ = 0.5966 * LW1.0181 was the best, with the highest values of R² and d, low values of RMSE and AIC, and a BIAS index closest to zero.

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Estimative of Black Pepper leaf area with basis on the leaf blade linear dimension

Ciência Rural ◽

10.1590/s0103-84782007000500039 ◽

2007 ◽

Vol 37 (5) ◽

pp. 1458-1461 ◽

Cited By ~ 1

Author(s):

Fábio Luiz Partelli ◽

Henrique Duarte Vieira ◽

Alexandre Pio Viana

Keyword(s):

Leaf Area ◽

Leaf Blade ◽

Correlation Coefficients ◽

Black Pepper ◽

Regression Equation ◽

Piper Nigrum ◽

Regression Equations ◽

Linear Regression Equation ◽

Linear Leaf ◽

Predicted Values

This research was aimed at establishing regression equations to estimate black pepper (Piper nigrum) leaf area based on linear leaf measures. Different black pepper varieties where growth on the field, four different size leaves were collected per plant with a total of 52 leaves to establish the regression equation and 28 to validate the equation for each variety (Bragantina, Laçará, Guajarina e Cingapura). Leaf midrib length (LML), maximum leaf broad width (MLBW) and leaf area (LA) were measured. Pearson's linear correlation coefficients were determined between observed and predicted measures with the observed LA, besides estimating the linear regression equation for each variety. The equations best-fitted to estimate LA based on circumscript rectangle were: 1) LA = 2.2689 + 0.6900 x LML x MLBW; 2) LA = 1.6402 + 0.6816 x LML x MLBW; 3) LA = 1.4942 + 0.6215 x LML x MLBW and 4) LA = 0.7467 + 0.6735 x LML x MLBW, for Bragantina, Laçará, Guajarina and Cingapura varieties respectively. For all equations predicted values had high correlation coefficient with observed values thus showing that these equations must be variety specific and that they are appropriate for black pepper leaf area estimative.

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Mathematical Modeling to Estimation Leaf Area of Pimenta dioica from Linear Dimensions

International Journal of Plant & Soil Science ◽

10.9734/ijpss/2019/v28i230104 ◽

2019 ◽

pp. 1-8

Author(s):

Vinicius De Souza Oliveira ◽

Lucas Caetano Gonçalves ◽

Amanda Costa ◽

Karina Tiemi Hassuda dos Santos ◽

Jéssica Sayuri Hassuda Santos ◽

...

Keyword(s):

Leaf Area ◽

Linear Equations ◽

Selection Criterion ◽

Absolute Error ◽

Coefficient Of Determination ◽

Regression Equations ◽

Maximum Width ◽

Independent Variable ◽

Pimenta Dioica ◽

Non Destructive

The objective of this work was to obtain regression equations and to indicate the most appropriate from different mathematical models for the estimation of the leaf area of Allspice (Pimenta dioica) by non - destructive method. 500 leaves of plants located in the municipality of São Mateus, North of Espírito Santo State, Brazil, were collected, 400 of which were used to adjust the equations and 100 for validation. The length (L) along the main midrib, the maximum width (W), the product of the length with the width (LW) and the observed leaf area (OLA) were measured from all leaves. We fitted models of linear equations of first degree, quadratic and power, where OLA was the dependent variable in function of L, W and LW. From the 100 sheets intended for validation, and using the adjusted equations for each mathematical model, the estimated leaf area (ELA) was obtained. Subsequently, a simple linear regression was fitted for each model of the proposed equation in which ELA was the dependent variable and OLA the independent variable. The mean absolute error (MAE), the root mean square error (RMSE) and Willmott's index d also determined. The best fit had as selection criterion the non-significance of the comparative means of ELA and OLA, MAE and RMSE values closer to zero and value of the coefficient of determination coefficient (R2) close to one. Thus, the power model (ELA = 0.7605(LW)0.9926, R2 = 0.9764, MAE = 1.0066, RMSE = 1.7759 and d = 0.9950) based on the product of length and width (LW) is the most appropriate for estimating the leaf area of Pimenta dioica.

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A NON-DESTRUCTIVE METHOD FOR ESTIMATING LEAF AREA OF Ceiba glaziovii (Kuntze) K. Schum.

FLORESTA ◽

10.5380/rf.v50i1.61088 ◽

2019 ◽

Vol 50 (1) ◽

pp. 1063

Author(s):

João Everthon da Silva Ribeiro ◽

Francisco Romário Andrade Figueiredo ◽

Ester Dos Santos Coêlho ◽

Walter Esfrain Pereira ◽

Manoel Bandeira de Albuquerque

Keyword(s):

Leaf Area ◽

Regression Models ◽

Information Criterion ◽

Coefficient Of Determination ◽

Linear Measurements ◽

Maximum Width ◽

Bias Index ◽

Different Shapes ◽

Non Destructive

The determination of leaf area is of fundamental importance in studies involving ecological and ecophysiological aspects of forest species. The objective of this research was to adjust an equation to determine the leaf area of Ceiba glaziovii as a function of linear measurements of leaves. Six hundred healthy leaf limbs were collected in different matrices, with different shapes and sizes, in the Mata do Pau-Ferro State Park, Areia, Paraíba state, Northeast Brazil. The maximum length (L), maximum width (W), product between length and width (L.W), and leaf area of the leaf limbs were calculated. The regression models used to construct equations were: linear, linear without intercept, quadratic, cubic, power and exponential. The criteria for choosing the best equation were based on the coefficient of determination (R²), Akaike information criterion (AIC), root mean square error (RMSE), Willmott concordance index (d) and BIAS index. All the proposed equations satisfactorily estimate the leaf area of C. glaziovii, due to their high determination coefficients (R² ≥ 0.851). The linear model without intercept, using the product between length and width (L.W), presented the best criteria to estimate the leaf area of the species, using the equation 0.4549*LW.

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Alometric Model for Estimation of Leaf Area of Garcinia brasiliensis Mart. Through Non-destructive Method

Journal of Agricultural Science ◽

10.5539/jas.v11n10p154 ◽

2019 ◽

Vol 11 (10) ◽

pp. 154

Author(s):

Vinicius de Souza Oliveira ◽

Cássio Francisco Moreira de Carvalho ◽

Juliany Morosini França ◽

Flávia Barreto Pinto ◽

Karina Tiemi Hassuda dos Santos ◽

...

Keyword(s):

Leaf Area ◽

Linear Equations ◽

Absolute Error ◽

Coefficient Of Determination ◽

Maximum Width ◽

Linear Dimensions ◽

Length Width ◽

Independent Variable ◽

The Mean ◽

Non Destructive

The objective of the present study was to test and establish mathematical models to estimate the leaf area of Garcinia brasiliensis Mart. through linear dimensions of the length, width and product of both measurements. In this way, 500 leaves of trees with age between 4 and 6 years were collected from all the cardinal points of the plant in the municipality of São Mateus, North of the State of Espírito Santo, Brazil. The length (L) along the main midrib, the maximum width (W), the product of the length with the width (LW) and the observed leaf area (OLA) were obtained for all leaves. From these measurements were adjusted linear equations of first degree, quadratic and power, in which OLA was used as dependent variable as function of L, W and LW as independent variable. For the validation, the values of L, W and LW of 100 random leaves were substituted in the equations generated in the modeling, thus obtaining the estimated leaf area (ELA). The values of the means of ELA and OLA were tested by Student’s t test 5% of probability. The mean absolute error (MAE), root mean square error (RMSE) and Willmott’s index d for all proposed models were also determined. The choice of the best model was based on the non significant values in the comparison of the means of ELA and OLA, values of MAE and RMSE closer to zero and value of the index d and coefficient of determination (R2) close to unity. The equation that best estimates leaf area of Garcinia brasiliensis Mart. in a way non-destructive is the power model represented by por ELA = 0.7470(LW)0.9842 and R2 = 0.9949.

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Machine learning and Grad-Cam based vascular aging assessment using photoplethysmogram (Preprint)

10.2196/preprints.31709 ◽

2021 ◽

Author(s):

Hangsik Shin

Keyword(s):

Machine Learning ◽

Correlation Coefficient ◽

Age Estimation ◽

Mean Squared Error ◽

Mean Absolute Error ◽

Absolute Error ◽

Coefficient Of Determination ◽

Vascular Aging ◽

Squared Error ◽

Vascular Age

BACKGROUND Arterial stiffness due to vascular aging is a major indicator for evaluating cardiovascular risk. OBJECTIVE In this study, we propose a method of estimating age by applying machine learning to photoplethysmogram for non-invasive vascular age assessment. METHODS The machine learning-based age estimation model that consists of three convolutional layers and two-layer fully connected layers, was developed using segmented photoplethysmogram by pulse from a total of 752 adults aged 19–87 years. The performance of the developed model was quantitatively evaluated using mean absolute error, root-mean-squared-error, Pearson’s correlation coefficient, coefficient of determination. The Grad-Cam was used to explain the contribution of photoplethysmogram waveform characteristic in vascular age estimation. RESULTS Mean absolute error of 8.03, root mean squared error of 9.96, 0.62 of correlation coefficient, and 0.38 of coefficient of determination were shown through 10-fold cross validation. Grad-Cam, used to determine the weight that the input signal contributes to the result, confirmed that the contribution to the age estimation of the photoplethysmogram segment was high around the systolic peak. CONCLUSIONS The machine learning-based vascular aging analysis method using the PPG waveform showed comparable or superior performance compared to previous studies without complex feature detection in evaluating vascular aging. CLINICALTRIAL 2015-0104

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Estimation of Carbon Fluxes from Eddy Covariance Data and Satellite-Derived Vegetation Indices in a Karst Grassland (Podgorski Kras, Slovenia)

Remote Sensing ◽

10.3390/rs11060649 ◽

2019 ◽

Vol 11 (6) ◽

pp. 649 ◽

Cited By ~ 3

Author(s):

Koffi Noumonvi ◽

Mitja Ferlan ◽

Klemen Eler ◽

Giorgio Alberti ◽

Alessandro Peressotti ◽

...

Keyword(s):

Linear Relationship ◽

Eddy Covariance ◽

Vegetation Index ◽

Gross Primary Production ◽

Vegetation Indices ◽

Information Criterion ◽

Growing Season ◽

Coefficient Of Determination ◽

Regression Equations ◽

Eddy Covariance Method

The Eddy Covariance method (EC) is widely used for measuring carbon (C) and energy fluxes at high frequency between the atmosphere and the ecosystem, but has some methodological limitations and a spatial restriction to an area, called a footprint. Remotely sensed information is usually used in combination with eddy covariance data in order to estimate C fluxes over larger areas. In fact, spectral vegetation indices derived from available satellite data can be combined with EC measurements to estimate C fluxes outside of the tower footprint. Following this approach, the present study aimed to model C fluxes for a karst grassland in Slovenia. Three types of model were considered: (1) a linear relationship between Net Ecosystem Exchange (NEE) or Gross Primary Production (GPP) and each vegetation index; (2) a linear relationship between GPP and the product of a vegetation index with PAR (Photosynthetically Active Radiation); and (3) a simplified LUE (Light Use-Efficiency) model assuming a constant LUE. We compared the performance of several vegetation indices derived from two remote platforms (Landsat and Proba-V) as predictors of NEE and GPP, based on three accuracy metrics, the coefficient of determination (R2), the Root Mean Square Error (RMSE) and the Akaike Information Criterion (AIC). Two types of aggregation of flux data were explored: midday average and daily average fluxes. The vapor pressure deficit (VPD) was used to separate the growing season into two phases, a wet and a dry phase, which were considered separately in the modelling process, in addition to the growing season as a whole. The results showed that NDVI is the best predictor of GPP and NEE during the wet phase, whereas water-related vegetation indices, namely LSWI and MNDWI, were the best predictors during the dry phase, both for midday and daily aggregates. Model 1 (linear relationship) was found to be the best in many cases. The best regression equations obtained were used to map GPP and NEE for the whole study area. Digital maps obtained can practically contribute, in a cost-effective way to the management of karst grasslands.

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Investigation and Optimization of the C-ANN Structure in Predicting the Compressive Strength of Foamed Concrete

Materials ◽

10.3390/ma13051072 ◽

2020 ◽

Vol 13 (5) ◽

pp. 1072 ◽

Cited By ~ 19

Author(s):

Dong Van Dao ◽

Hai-Bang Ly ◽

Huong-Lan Thi Vu ◽

Tien-Thinh Le ◽

Binh Thai Pham

Keyword(s):

Compressive Strength ◽

Civil Engineering ◽

Mean Squared Error ◽

Model Performance ◽

Absolute Error ◽

Machine Learning Algorithms ◽

Coefficient Of Determination ◽

Dry Density ◽

Statistical Measures ◽

Foamed Concrete

Development of Foamed Concrete (FC) and incessant increases in fabrication technology have paved the way for many promising civil engineering applications. Nevertheless, the design of FC requires a large number of experiments to determine the appropriate Compressive Strength (CS). Employment of machine learning algorithms to take advantage of the existing experiments database has been attempted, but model performance can still be improved. In this study, the performance of an Artificial Neural Network (ANN) was fully analyzed to predict the 28 days CS of FC. Monte Carlo simulations (MCS) were used to statistically analyze the convergence of the modeled results under the effect of random sampling strategies and the network structures selected. Various statistical measures such as Coefficient of Determination (R2), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE) were used for validation of model performance. The results show that ANN is a highly efficient predictor of the CS of FC, achieving a maximum R2 value of 0.976 on the training part and an R2 of 0.972 on the testing part, using the optimized C-ANN-[3–4–5–1] structure, which compares with previous published studies. In addition, a sensitivity analysis using Partial Dependence Plots (PDP) over 1000 MCS was also performed to interpret the relationship between the input parameters and 28 days CS of FC. Dry density was found as the variable with the highest impact to predict the CS of FC. The results presented could facilitate and enhance the use of C-ANN in other civil engineering-related problems.

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Mathematical models to describe the growth curves of white-egg layers

Semina Ciências Agrárias ◽

10.5433/1679-0359.2018v39n3p1327 ◽

2018 ◽

Vol 39 (3) ◽

pp. 1327

Author(s):

Cleber Franklin Santos de Oliveira ◽

João Marcos Novais Tavares ◽

Gerusa Da Silva Salles Corrêa ◽

Bruno Serpa Vieira ◽

Silvana Alves Pedrozo Vitalino Barbosa ◽

...

Keyword(s):

Mathematical Models ◽

Mean Squared Error ◽

Computer Software ◽

Logistic Models ◽

Growth Curves ◽

Gompertz Model ◽

Information Criterion ◽

Coefficient Of Determination ◽

Population Densities

The aim of this study was to compare mathematical models describing growth curves of white-egg layers at different population densities. To fit the models, 4,000 growing white-egg layers were utilized. The experimental design was completely randomized, with population densities of 71, 68, 65, 62, and 59 birds per cage in the starter phase and 19, 17, 15, 13, and 11 birds per cage in the grower phase, with 10 replicates each. Birds were weighed weekly to determine the average body weight and the weight gain. Gompertz and Logistic models were utilized to estimate their growth. The data analysis was carried out using the PROC NLMIXED procedure of the SAS® statistical computer software to estimate the parameters of the equation because mixed models were employed. The mean squared error, the coefficient of determination, and Akaike’s information criterion were used to evaluate the quality of fit of the models. The studied models converged for the description of the growth of the birds at the different densities studied, showing that they were appropriate for estimating the growth of white-egg layers housed at different population densities. The Gompertz model showed a better fit than the Logistic model.

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Allometric equations for crown fuel biomass of Aleppo pine (Pinus halepensis Mill.) in Greece

International Journal of Wildland Fire ◽

10.1071/wf06038 ◽

2007 ◽

Vol 16 (5) ◽

pp. 642 ◽

Cited By ~ 21

Author(s):

I. D. Mitsopoulos ◽

A. P. Dimitrakopoulos

Keyword(s):

Pinus Halepensis ◽

Allometric Equation ◽

Aleppo Pine ◽

Allometric Equations ◽

Fuel Load ◽

Coefficient Of Determination ◽

Regression Equations ◽

Diameter At Breast Height ◽

Breast Height ◽

Average Load

Allometric equations for the estimation of crown fuel weight of Aleppo pine (Pinus halepensis Mill.) trees in the Mediterranean Basin were developed. Forty trees were destructively sampled and their crown fuels were weighed separately for each fuel category. Crown fuel components, both living and dead, were separated into size classes and regression equations that estimate crown fuel load by diameter class were derived. The allometric equation y = axb with diameter at breast height as the single predictor was chosen, because the addition of other parameters did not decrease the residual sum of squares significantly. The adjusted coefficient of determination (R2adj) values were high (R2adj = 0.82–0.88) in all cases. Diameter at breast height was the most significant determinant of crown fuel biomass. The aerial fuels that are consumed during crown fires (i.e. needles and twigs with diameter less than 0.63 cm) comprised 29.3% of the total crown weight. Live fuels constituted ~96.3% of total crown biomass, distributed as follows: needles 16.7% (average load 12.07 kg), branches with 0.0–0.63-cm diameter 12.6% (average load 9.18 kg), 0.64–2.5-cm diameter 37.3% (27.99 kg), 2.51–7.5-cm diameter 25.4% (18.59 kg), and >7.5-cm diameter 3.7% (2.65 kg). The equations provide quantitative fuel biomass attributes for use in crown fire behaviour models, fire management and carbon assessment in Aleppo pine stands.

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