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Leaf area measurements are used in agronomic studies to evaluate plant growth, light interception, photosynthetic rates, and plant transpiration. It constitute an important indicator of crop productivity, for which the evaluation method must be fast, accurate, and of low cost. The objective of this study was to compare different indirect methods to estimate leaf area in pornunça (Manihot sp.). The research was carried out under field conditions from August 2017 to January 2019 in the semiarid region of Pernambuco State, Northeastern Brazil. Three methods were tested: linear dimensions of leaf (length, width, and the number of lobes), digital image, and leaf scanned image, analyzing 150 healthy leaves from 120 plants of pornunça at different growth stages. The criteria used to determine the best model(s) were a high coefficient of determination, low Akaike information criterion, low sum of squares of residuals, and high Willmott index. Independent of the method of determination, the power models showed the best criteria of adequacy for estimating the leaf area of the pornunça. The digital image, using the power model (Y=LW0.77NL0.49, where L and W are the leaf length and width, and NL is the number of lobes in the leaf) was the best non-destructive method for estimating the leaf area in pornunça plants.

Forests have been constantly growing with their dynamic structure. In order for this dynamic structure must be managed based on sustainable perspective. Diameter, height, age, stand structure, etc. parameters are used in the inventory stage of the planning. The easiest to measure among these parameters is the diameter. Therefore, the developed models are usually aimed at reaching other forest parameters from the diameter. In this article, 9 different height-diameter models were fitted using regression models, and feed-forward backpropagation artificial neural network model methods for uneven-aged fir (Abies nordmanniana subsp. equi-trojani) stands in Kokez, Bolu region of Turkey. The models compared based on adjusted R², bias, absolute bias, and root mean square error (RMSE). It was observed that the best result was obtained from the artificial neural network model, and the worst result was obtained from the power model.

Turnera subulata e uma planta medicinal que tem demostrado associacao com o processo de cicatrizacao. A determinacao da area foliar e importante parâmetro em estudos agronomicos, fisiologicos e morfologicos das diversas especies vegetais. Essa determinacao pode ser feita de forma destrutiva ou nao destrutiva. Dentre os metodos nao destrutivos se destaca a uso de equacoes matematicas que relacionam a area foliar e as medidas lineares das folhas como o comprimento, largura e sua combinacao. Desta forma, objetivou-se com este estudo ajustar e validar uma equacao matematica que estima a area foliar de T. subulata de forma nao destrutiva. Assim, com base em 350 folhas, foram ajustadas equacoes de modelo lineares de primeiro grau, quadratico e potencia, em que a area foliar observada foi utilizada como variavel dependente em funcao das medidas lineares do comprimento, largura e produto da multiplicacao do comprimento com a largura. Todas as equacoes ajustadas foram validadas atraves de criterios apropriados a partir de uma amostra de 100 folhas separadas unicamente para esta finalidade. Desse modo, a equacao de modelo quadratico obtida a partir do produto da multiplicacao do comprimento com a largura e a mais adequada para estimar a area foliar de T. subulata de maneira simples e precisa. Turnera subulata is a medicinal plant that has been shown to be associated with the healing process. The determination of leaf area is an important parameter in agronomic, physiological and morphological studies of different plant species. This determination can be made in a destructive or non-destructive way. Among the non-destructive methods, the use of mathematical equations that relate the leaf area and the linear measurements of the leaves, such as length, width and their combination, stands out. Thus, the objective of this study was to adjust and validate a mathematical equation that estimates the leaf area of T. subulata in a non-destructive way. based on 350 leaves, linear first-degree, quadratic and power model equations were adjusted, in which the observed leaf area was used as a dependent variable depending on the linear measures of length (L), width (W) and product of the multiplication of length with width (LW). All adjusted equations were validated using appropriate criteria from a sample of 100 sheets separated solely for this purpose. In this way, the quadratic model equation obtained from the product of the multiplication of the length with the width is the most adequate to estimate the leaf area of T. subulata in a simple and precise way

Papaya (Carica papaya L.) is a typical plant with a tropical climate, but also grown in subtropical regions. Using mathematical models well-adjusted allows with good precision to estimate characteristics of interest. The objective was to adjust an equation that estimates the fruit mass for each cultivar of papaya, Alianca and THB, using only one measure, length or width. The experiment was conducted in the municipality of Linhares in the state of Espirito Santo, Brazil. Seedlings were planted on the same day, spaced 3.6 × 1.5 m and in rows side by side. Initially, the equations were modeled, they were linearized and then the covariance analysis was performed in order to verify the possibility of an equation that would serve both cultivars. As the covariance was significant, it was necessary to develop equations for each cultivar. To obtain the growth equations, 350 fruits of cultivar Alianca and 550 of THB were used. The validation was performed with 50 fruits of each. The characteristics evaluated were the largest width (W in mm), the longest fruit length (L, in mm) and the observed mass (OM in g). The equations that best fit were those of the power model that use width (W) as an independent variable.

In this study cut, pineapple slices of 1 cm thick were packaged and stored at different temperatures and equilibrium modified atmosphere packages (EMAPs) to determine changes of color and firmness over time to represent physicochemical shelf life. From the experimental data, a variance analysis was performed to determine the effect of temperature and O2 level on the evolution of color (CIELAB coordinates) and firmness. It was observed that the evolution in L* , a* , and b* coordinates is independent on O2 concentration in the EMAP system. After that, suitable models were adjusted to represent the change of the quality properties as a function of temperature by using first-order models to represent color and a power model for firmness. Likewise, a modified normal distribution function was adjusted to represent the coefficient of firmness loss depending on the O2 level besides the temperature effect. The firmness model was used to obtain a suitable equation to predict shelf life of the pineapple slices for different EMAP systems. Finally, a validation experiment was performed at 8 °C obtaining a high capacity of prediction (R2 adj > 0.90) compared with the experimental data. The adjusted model can be used to configure a satisfactory EMAP system for the best preservation of minimally processed pineapple from the predicted evolution of color, firmness, and shelf life depending on temperature and O2 concentration. PRACTICAL APPLICATION: In this work, we built a mathematical model to simulate the shelf life of pineapple cut into slices based on changes in color and firmness and as a function of temperature and oxygen level. These properties are truly relevant because they are very clear evidence of the fruit deterioration, and for that reason, we chose them for the model. The model we developed can be applied in retail and supermarket systems to determine precisely how long the product on the shelf can last before being disposed of, reducing material losses.

Considering the lack of the literature and the need for developing a valid method to measure the texture sensitivity, in this study, we investigated the individual sensitivity to discriminate among different levels of graininess. With this purpose, five samples of cocoa-based creams were prepared, by changing the refining time. Samples were first characterized in terms of particles size distribution, by means of laser diffraction. Then, 59 subjects evaluated the cream sample graininess intensity, by using gLM scales, and their liking, by using LAM scales. The graininess scores of each subject were fitted with a power model, already observed with the instrumental results, estimating both the power law exponent and the R2 coefficient, and using them as clustering parameters. Subjects were then clustered into three groups: high sensitivity; moderate sensitivity; low sensitivity. First, as it was hypothesized, results showed a significant difference between the three groups in terms of perceived graininess. Second, even though results showed a significant difference between the three groups in terms of perceived graininess, only little differences were found in terms of liking scores. Indeed, all the samples were equally liked for both the moderate and low sensitivity groups, whereas a significant trend was observed for the highly sensitive subjects who liked more the most refined samples. No significant relationships were found with age, and only a little trend was observed with gender: females seemed to be more sensitive than males. Texture attributes discrimination ability, as for example sensitivity to graininess, could affect food rejection or preferences and choice, but it is poorly investigated. This exploratory study, proposes a method to cluster consumers, based on their sensitivity. A statistical methodology has been developed to discriminate among consumer sensitivity levels. The results provide useful information about graininess sensitivity suggesting that the used methodologies could be applied to other texture properties resulting in a valid tool for the industry in the development and optimization of tailored new products.

The objective of this study was to obtain mathematical equations through the leaf dimensions to estimate the area leaf of Cordia myxa L. 392 leaves of plants were collected, located in the municipality of Sao Mateus, North of the State of Espirito Santo, Brazil, 300 of which were used to adjust the equations and 92 for validation. Of all the leaves, the largest length (L) and maximum width (W) were measured, product of multiplying the length with the width (LW) and the real leaf area (RLA). Models equation first degree linear, quadratic and power were fitted, where RLA was the dependent variable as a function of L, W and LW as an independent variable. All equations were validated according to appropriate criterion. Thus, the power model ELA = 0.84(LW)0.9749, based on the product of multiplication of length with width (LW) is the most suitable for estimating the leaf area of Cordia myxa L.

The vegetative clonal teak is fast-growing, exhibits relatively uniform growth, and is sensitive to crown competition. The crown width dimension correlates positively with the size of the diameter (CW allometry). We investigated the effects of competition on CW allometry for dominant trees on good sites and the prediction accuracy of CW allometry. The data were measured during 2015–2017. The Hegyi index with a fixed 30° search cone method was used to measure competition. The scatter plot of all observations was used to identify the general pattern of CW over diameter, and competition index with both diameter and CW. The data were classified into three groups, ignored, free, and occurred competition data sets. Moreover, the occurred competition data set was categorized into three levels: low, medium, and heavy. The power model was used for parameterization of CW allometry. The dispersion of CW over diameter for all observations exhibited a moderate positive correlation, as well as the competition index with both diameter and CW. For the ignored-competition data set, the CW allometry was able to describe approximately 37.2% of observed CW. Interestingly, however, the prediction accuracy increased to 44.6% for the free competition data set. In contrast, the capability of the CW allometry for the occurred competition data set declined sharply to 9.1%. Among the occurred competition data sets, the heavier the subject trees competed, the lower the CW allometry explained the variations. However, the CW allometry was completely not able to describe the observed CW in the heavy competition level.

Accurate estimation of global solar radiation (Rs) is essential to the design and assessment of solar energy utilization systems. Existing empirical and machine learning models for estimating Rs from sunshine duration were comprehensively reviewed. The performances of 12 empirical model forms and 12 machine learning algorithms for estimating daily Rs were further evaluated in different climatic zones of China as a case study, i.e. the temperate continental zone (TCZ), temperate monsoon zone (TMZ), mountain plateau zone (MPZ) and (sub)tropical monsoon zone (SMZ). The best-performing model at each station and the overall best model for each climatic zone were selected based on six statistical indictors, a global performance index (GPI) and computational costs (computational time and memory usage). The results revealed that the machine learning models (RMSE: 2.055–2.751 MJ m−2 d−1; NRMSE: 12.8–21.3%; R2: 0.839–0.936) generally outperformed the empirical models (RMSE: 2.118–3.540 MJ m−2 d−1; NRMSE: 12.1–27.5%; R2: 0.834–0.935) in terms of prediction accuracy. The cubic model (M3), modified linear-logarithmic model (M5) and power model (M10) attained generally better ranks among empirical models based on GPI. M3 was the top-ranked model in TMZ and MPZ, while general best performance was obtained by M5 and M2 in SMZ and TCZ, respectively. ANFIS, ELM, LSSVM and MARS obtained generally better performance among machine learning models, with the overall best ranking by ANFIS in TCZ and SMZ and by ELM in MPZ and SMZ. XGBoost (8.1 s and 74.2 MB), M5Tree (11.3 s and 29.7 MB), GRNN (12.3 s and 295.3 MB), MARS (14.4 s and 42.6 MB), MLP (22.4 s and 41.3 MB) and ANFIS (29.8 s and 23.1 MB) showed relatively small computational time and memory usage. Comprehensively considering both the prediction accuracy and computational costs, ANFIS is highly recommended, while MARS and XGBoost are also promising models for daily Rs estimation.

Cycling races contain a multitude of motorcycles for various activities including television broadcasting. During parts of the race, these motorcycles can ride in close proximity of cyclists. Earlier studies focused on the impact of a nearby motorcycle on cyclist drag for in-line arrangements. It was shown that not only a motorcycle in front of a cyclist but also a motorcycle closely behind a cyclist can substantially reduce cyclist drag. However, there appears to be no information in the scientific literature about the impact of the motorcycle on cyclist drag for parallel and staggered arrangements. This paper presents wind tunnel measurements of cyclist drag for 32 different parallel and staggered cyclist-motorcycle arrangements. It is shown that the parallel arrangement leads to a drag increase for the cyclist, in the range of 5 to about 10% for a lateral distance of 2 to 1 m. The staggered arrangement can lead to either a drag increase or a drag decrease, where the latter is about 2% for most positions analyzed. For one of the parallel arrangements, computational fluid dynamics simulations were performed to provide insight into the reasons for the drag increase. A cyclist power model was used to convert the drag changes into potential time gains or losses. Compared to a lone cyclist riding at a speed of 46.8 km/h (13 m/s) on level road in calm weather, the time loss by a drag increase of 10%, 4% and − 2% was 2.16, 0.76 s and − 0.80 s per km, respectively. These time differences are large enough to influence the outcome of cycling races.

Leaf area is an important growth variable in agricultural crops and the leaf is the main variable of interest in the tobacco industry. So, the aim of this scientific research was to estimate the Burley tobacco leaf area by linear dimensions of the leaves and to determine which mathematical model is more adequate for this purpose. Two experiments were carried out with Burley tobacco, cultivar DBH 2252, in 2016/2017 and 2018/2019 agricultural years, respectively, in the municipalities of Itaqui and Vanini - RS - Brazil. In 600 leaves were measured length (L), width (W), length×width product (LW), length/width ratio (L/W) and determined the real leaf area (LA). Four hundred and fifty leaves were separated to generate models of the leaf area as a function of linear dimension and the other 150 leaves were used for model’s validation. The power model LA = 0.5037LW1.04435 (R² = 0.9960) is the most adequate for Burley tobacco ‘DBH 2252’ leaf area estimation. Alternatively, the models LA=2.0369W1.8619 (R²=0.9796) and LA=0.1222L2.2771 (R²=0.9738) based on width and length, respectively, can be used when only one leaf dimension is measured.

Key message: The crown volume of Pinus nigra trees can be modelled as a function of the total crown length and the crown radius at crown base to support forest management practices. Context: The crown volume of trees is rarely considered in forest management practices and is often approximated to a simple cone or paraboloid whose volume can be broadly derived from costly measurements. Aims: We developed two equations to predict single-tree crown volumes for Pinus nigra plantations in Italy based on the analysis of a database with 3578 trees. Methods: Two key crown parameters (total length of the crown and crown radius at crown base) were here modelled using directly measurable mensurational data using Generalise Additive Mixed-effect Model. Afterwards, two functions were then proposed to predict single-tree crown volumes. Results: The fitted models were statistically significant and explaining 57.6% for crown radius at crown base and 87.1% for crown length of the total variance. The power model for single-tree crown volumes calculation showed a mean absolute error around 4.1 m for the upper portion of the crown and 12.1 m for the lower part for a mean absolute relative error of 12.5% and 32.0% respectively for a global value of 16.4%. Conclusion: Single-tree and stand-level data are fundamental to balance forest management trajectories. The provided functions may be used in external dataset to derive indication on the single-tree or stand-level crown volume to be used as indicators of ground coverage.

The forage palm is one of the main forages of ruminants in semiarid regions. Measurements of leaf area are required in agronomic studies because they are one of the main parameters used to evaluate plant growth. The objective of this study was to validate and define the best models for estimating the area and weight of Giant Sweet clone (Nopalea cochenillifera) forage cladodes in a non-destructive way based on the linear dimensions of length, width and thickness. There were 432 randomly measured cladodes at 550 days after planting. The length, width and thickness of each cladode were measured using a digital calliper. The cladodes were weighed individually. The cladode area was calculated by the gravimetric method. The power regression model was the most efficient method to explain the cladode area as a function of the product of length by width, while the gamma model was the most efficient method to explain the weight of cladodes as a function of the product of length by width and thickness. The power model, and gamma model, = 0.536T + 0.028LW, were used to determine the area and weight of Nopalea cochenillifera Giant Sweet clone cladodes, respectively, based on the values of linear dimensions measured independently of the order of the cladode. The forage palm is one of the main forages of ruminants in semiarid regions. Measurements of leaf area are required in agronomic studies because they are one of the main parameters used to evaluate plant growth. The objective of this study was to validate and define the best models for estimating the area and weight of Giant Sweet clone (Nopalea cochenillifera) forage cladodes in a non-destructive way based on the linear dimensions of length, width and thickness. There were 432 randomly measured cladodes at 550 days after planting. The length, width and thickness of each cladode were measured using a digital calliper. The cladodes were weighed individually. The cladode area was calculated by the gravimetric method. The power regression model was the most efficient method to explain the cladode area as a function of the product of length by width, while the gamma model was the most efficient method to explain the weight of cladodes as a function of the product of length by width and thickness. The power model, and gamma model, = 0.536T + 0.028LW, were used to determine the area and weight of Nopalea cochenillifera Giant Sweet clone cladodes, respectively, based on the values of linear dimensions measured independently of the order of the cladode.

Background Xenograft mouse tumor models are used to study mechanisms of tumor growth and metastasis formation and to investigate the efficacy of different therapeutic interventions. After injection the engrafted cells form a local tumor nodule. Following an initial lag period of several days, the size of the tumor is measured periodically throughout the experiment using calipers. This method of determining tumor size is error prone because the measurement is two-dimensional (calipers do not measure tumor depth). Primary tumor growth can be described mathematically by suitable growth functions, the choice of which is not always obvious. Growth parameters provide information on tumor growth and are determined by applying nonlinear curve fitting. Methods We used self-generated synthetic data including random measurement errors to research the accuracy of parameter estimation based on caliper measured tumor data. Fit metrics were investigated to identify the most appropriate growth function for a given synthetic dataset. We studied the effects of measuring tumor size at different frequencies on the accuracy and precision of the estimated parameters. For curve fitting with fixed initial tumor volume, we varied this fixed initial volume during the fitting process to investigate the effect on the resulting estimated parameters. We determined the number of surviving engrafted tumor cells after injection using ex vivo bioluminescence imaging, to demonstrate the effect on experiments of incorrect assumptions about the initial tumor volume. Results To select a suitable growth function, measurement data from at least 15 animals should be considered. Tumor volume should be measured at least every three days to estimate accurate growth parameters. Daily measurement of the tumor volume is the most accurate way to improve long-term predictability of tumor growth. The initial tumor volume needs to have a fixed value in order to achieve meaningful results. An incorrect value for the initial tumor volume leads to large deviations in the resulting growth parameters. Conclusions The actual number of cancer cells engrafting directly after subcutaneous injection is critical for future tumor growth and distinctly influences the parameters for tumor growth determined by curve fitting.

Estimating leaf area is essential to evaluate vegetal growth. Our study sought to obtain statistical models to allow the leaf area estimation of Palicourea racemosa, considering its length (L) and width (W). For such purpose, we collected 200 leaves of this species in the State Park Mata do Pau-Ferro, in the municipality of Areia, Paraíba, Northeast of Brazil. The regression models used were: linear, linear without intercept, power and exponential. The choice of the best equation was based on the values of the coefficient of determination (R2), root mean square error (RMSE), Akaike information criterion (AIC), Willmott concordance index (d) and BIAS ratio. All linear and power models may be used to measure the P. racemosa leaf area; however, the power model LA = 0 . 609 * ( L . W ) 0 . 995 is the most recommended to estimate this species’ leaf area.

Pasture studies require information on leaf area, as it is one of the main parameters for evaluation of plant growth. Thus, the objective of this study was to estimate the leaf blade area of pangolão grass (Digitaria pentzii Stent.) using non-destructive methods by regression model analysis. The experimental design consisted of randomized blocks, with three cutting heights (10, 15, and 20 cm) and four replications. Three hundred leaf blades of pangolão grass were randomly collected, and their respective lengths (L) and widths (W) determined using a digital caliper. The leaf blade area of pangolão grass was estimated by the gravimetric method, using linear and power regression models to explain the leaf blade area as a function of the product of L and maximum W. The real leaf blade area presented an average value of 18.64 cm², ranging from 4.29 to 45.95 cm². The leaf blade area of pangolão grass, regardless of cutting height, was estimated with greater accuracy by the power model. The power model, ?=LW1.007, can be used to estimate the leaf blade area of pangolão grass based on leaf blade L and W values. Keywords: modeling; non-destructive method; pangolão grass.

Background and objectives: To determine the head scatter factor, a formalism presented by Vadash and Bjärngard has been employed to assess collimator exchange effects. The aim of this study was to determine the best Vadash correction factor (A) by introducing a new method based on the output factor measured in air for different square and rectangular fields. Materials and Methods: A new simple mathematical method based on selection of the best dosimetric data was proposed to obtain the A value for Vadash to predict the equivalent square field size. Measurements were performed with a Farmer chamber 0.6 cc in SSD 100 cm and build up cap of Plexiglas, 1.5 and 3.5 cm equal to water, for 6 and 18 MV, respectively, with a Perimus Plus linear accelerator. The output factor in air (OFair) was measured for square and rectangular fields. MATLAB software (version R2014a) was employed for calculations and curve fitting. Results: A power model with a constant value was applied to the output factor in air as a function of square field size. The output factor in air ranged from 0.983 to 1.038 at 6MV and from 0.731 to 1.05 at 18 MV with the Y collimator having a greater effect. Obtained values for A were 1.42 and 1.55 with respect to σmin=0.98 and 2.3 for 6 and 18 MV energies, respectively. Conclusion: The proposed A values minimize the collimator exchange effect in calculating equivalent squares, which plays an important role in patient dose calculation and treatment planning.

We aimed to propose a reliable and accurate model using non-destructive measurements of leaf length (L) and/or width (W) for estimating leaf area (LA) of Surinam cherry ( Eugenia uniflora L.). For model construction, 560 leaves were randomly sampled from different levels of the tree canopies and encompassed the full spectrum of measurable leaf sizes. Power models better fit E. uniflora leaf area than linear models; but, among of then, the best fit were made when product of the L and W (LW) were used. To validate these models, independent data set of 156 leaves were used. Thus, we developed a single power model (Yi = β0 xβ1) [LA = 0.685 (LW)0.989; standard errors: β0 = 0.014, β1 = 0.005; R2 a = 0.997] with high precision and accuracy, random dispersal pattern of residuals and unbiased. A simpler linear model [LA = 0.094 + (LW * 0.655); standard errors: β0 = 0.025, β 1 = 0.001; R2 a = 0.998] also described here to estimate leaf area of E. uniflora, which are as good as the first. The simplicity of the latter model may be relevant in field studies, as it does not demand high precision or expensive instruments.

It is well known that the max-stable laws under power normalization attract more distributions than that under linear normalization. This fact practically means that the classical linear model (L-model) may fail to fit the given extreme data, while the power model (P-model) succeeds to do that. The main object of this paper is developing the modeling of extreme values via P-model by suggesting a simple technique to obtain a parallel estimator of the extreme value index (EVI) in the P-model for every known estimator to the corresponding parameter in L-mode. An application of this technique yields two classes of moment and moment ratio estimators for EVI in the P-model. The performances of these estimators are assessed via a simulation study. Moreover, an efficient criterion for comparing the L and P models is proposed to choose the best model when the two models successfully work.

Allometric models predicting aboveground woody biomass for open grown valonian oak (Q. ithaburensis subs. macrolepis L.) trees growing in a Mediterranean silvopastoral system were built based on Bayesian and classical statistical techniques. The simple power model M = aDb was used for predicting aboveground woody biomass (M), stem (MS) and branch (MB) biomass through tree diameter (D). An informative Bayesian approach (IB) based on prior information about a and b and increasing variance of predicted values in relation to D was applied on 25 destructively sampled trees for estimating M. Non-informative Bayesian (NB), log-linear regression (LR) and non-linear regression were also built for M, MS and MB. Quite similar M distribution was derived from LR and NB across the D range, totally different from IB predictions which provided biologically sound estimates. Tree height, stem length and crown length did not substantially improve predictions for M, MS and MB. Comparisons to oak trees growing in closed stands indicated that open-grown oaks sustain much less stem biomass but maintain larger branch biomass than forest-grown counterparts. Comparisons to published values for open-grown green ash trees supported the hypothesis that open grown broadleaved specimens may sustain similar M values, irrespectively of species, growth conditions and tree size. On the contrary, allocation pattern of organic matter to stem and branches seems to vary by species and/or site conditions. Finally, predictions for b = 2.67 derived from a theoretical model was not supported by this dataset.

Power is an important parameter for mechanical design, processing parameter optimization and motor design. A power model is established for medium equipment (aircraft, steamship, cutting machine, etc.) based on specific cutting energy and material removing rate (MRR). A group of turning experiments were carried out on aluminum alloy 6061 to validate the established power model. The specific turning energy varies with the rotation speed (cutting speed) undulately, and it decreases with increase in the feed per revolution and cutting depth. The MRR increases with the turning parameters. The power increases with increase in the turning parameters due to the larger MRR, although the specific turning energy decreases with the decrease in the turning parameters. The turning power can be classified as kinetics power and stress power. The power efficiency increases with the increase in the turning parameters.

AIM: One of the main applications of the island species–area relationship (SAR) is to predict species richness in areas of habitat too large to be sampled, but there are few clear guidelines for choosing an appropriate model for this purpose. We therefore aimed to test whether a multi‐model averaging approach could improve the accuracy of predictions made by extrapolating the ISAR. Specifically, we compared the performance of multi‐model averaging with that of the default ISAR model of choice, the power model, in predicting species richness in large habitat islands. LOCATION: Global TAXA: Vertebrates, invertebrates and plants METHODS: We removed the largest islands from 120 habitat island datasets, and fitted both the power model and a multi‐model average curve (averaging the predictions of up to 20 ISAR models) to this filtered dataset. We then assessed the accuracy of both approaches in predicting the species richness of the largest island in the original dataset using the log error of extrapolation (LEE) metric. A generalized additive regression modelling framework was used to determine whether any dataset characteristics could explain variation in the LEE values for the power model (LEE‐POW). RESULTS: The power model gave the more accurate richness predictions for 58% of the analysed datasets and the multi‐model averaged curve gave the more accurate predictions for the remaining 42%. Both the power models (61% of LEE‐POW values were positive) and the multi‐model averaged curve (60% were positive) had a slightly greater tendency to over predict the observed richness. The confidence intervals were also on average narrower for the power model predictions (median 95% confidence interval width = 18 species) than for the multi‐model averaged curve predictions (median 95% confidence interval width = 78). The range in island areas and richness values explained a small amount of the variation in LEE‐POW. MAIN CONCLUSIONS: Contrary to expectation, multi‐model averaging was less accurate than the power model in the majority of cases, and thus does not appear to be a panacea for uncertainty in model choice when extrapolating the ISAR. However, further research is urgently needed to evaluate the performance of a multi‐model averaging approach at larger spatial scales.

In this paper the sinh-power model is developed as a natural follow up to the log-linear Birnbaum-Saunders power model. The class of models resulting, incorporates the sinh-power-normal model, the ordinary sinh-normal model and the log-linear Birnbaum-Saunders model (Rieck and Nedelman, Technometrics 33:51–60, 1991). Maximum likelihood estimation is developed with the Hessian matrix used for standard error estimation. An application is reported for the data set on lung cancer studied in Kalbfleisch and Prentice (2002), where it is shown that the log-linear Birnbaum-Saunders power-normal model presents better fit than the log-linear Birnbaum-Saunders model. Another application is devoted to a fatigue data set previously analyzed in the literature. A nonlinear Birnbaum-Saunders power-normal model is fitted to the data set, with satisfactory performance.

A widely used approach in designing the phase I clinical trial is continual reassessment method (CRM). In this paper, we prove that under simple power model and logistic model, the way CRM selects the next dose level is highly efficient from the perspective of optimal design. More specifically, for simple power model, we show that the optimal design selects the dose level such that the corresponding toxicity rate is around 0.2; as for logistic model, we show that CRM is indeed optimal, which will justify the efficiency of the algorithm in theory.

A meta-analysis was conducted to study the effect of a change in the speed limit on mean driving speed and safety on interurban roads. Information from 108 research results—documented in a database collected by Elvik et al. in 2004—was analyzed. The link between accident ratio (after–before) and the mean driving speed ratio was studied by estimating the power parameter in the Nilsson power model. A modified power model was applied to estimate the link between speed limit (rather than mean driving speed) ratio and accidents ratio. When the speed limit was raised, the mean driving speed ratio (mean driving speed after to mean driving speed before) was on average 1.04 (SD = 0.04), significantly higher than 1 but smaller than the speed limit ratio (average = 1.17; SD = 0.05). The power parameters in Nilsson’s power model and in its modified version were 3.73 (SD = 2.61) and 0.99 (SD = 0.46), respectively. When speed limit was reduced, the mean driving speed ratio was 0.93 (SD = 0.04), significantly smaller than 1 but larger than the speed limit ratio (average = 0.82; SD = 0.04). The corresponding power parameters were 2.81 (SD = 0.65) and 1.24 (SD = 0.44). This paper summarizes research on the link between changes in speed limit, driving speed, and safety. It was found that the average speed changed in the same direction as the speed limit, but the magnitude of the change was smaller. As a result, the power parameters in the second version of the power model were lower than those in the original Nilsson’s model, and so the average change in safety is nearly proportional to the change in speed limit.

This study aims to determine the most suitable model to estimate the leaf area of dwarf pigeon pea in function of the leaf central leaflet dimension. Six samplings of 200 leaves were performed in the first experiment, at 36, 42, 50, 56, 64, and 72 days after emergence (DAE). In the second experiment, seven samplings of 200 leaves were performed at 29, 36, 43, 49, 57, 65, and 70 DAE, totaling 2600 leaves. The length (L) and width (W) of the central leaflet were measured in all leaves composed by left, central, and right leaflets, the product of length times width (LW) was calculated, and the leaf area (Y – sum of left, central, and right leaflet areas) was determined by digital images. Linear, power, quadratic, and cubic models of Y as function of L, W, and LW were built using data from the second experiment. Leaves from the first experiment were used to validate the models. In dwarf pigeon pea, the linear (Ŷ = – 0.4088 + 1.6669x, R2 = 0.9790) is preferable, but power (Ŷ = 1.6097x1.0065, R2 = 0.9766), quadratic (Ŷ = – 0.3625 + 1.663x + 0.00007x2, R2 = 0.9790), and cubic (Ŷ = 0.7216 + 1.522x + 0.005x2 – 5E–05x3, R2 = 0.9791) models in function of LW are also suitable to estimate the leaf area obtained by digital images. The power model (Ŷ = 5.2508x1.7868, R2 = 0.95) based on the central leaflet width is less laborious because requires only one variable, but it presents accuracy reduction.

We concentrate on characteristics of minima XN from samples of iid lognormals X1i ∼ 2pLND. We demonstrate that the distribution of XN for 2 ≤ N ≤ 1,000 may be fitted more accurately by 2pLND than by the limiting Gumbel distribution. An extended power model is established to represent the quotients CN/C1, where CN is the mean, standard deviation, or p-quantile of XN and C1 is the corresponding characteristic of X1i. Our empirical comparisons show that this model provides not only more accurate estimates than alternating approximations but it is also much simpler than its competitors.

In this paper we prove that the Minimum Latency Aggregation Scheduling (MLAS) problem in the Signal-to-Interference-Noise-Ratio (SINR) model is APX-hard in the uniform power model.

The morbidity problem of the GM(1,1) power model in parameter identification is discussed by using multiple and rotation transformation of vectors. Firstly we consider the morbidity problem of the special matrix and prove that the condition number of the coefficient matrix is determined by the ratio of lengths and the included angle of the column vector, which could be adjusted by multiple and rotation transformation to turn the matrix to a well-conditioned one. Then partition the corresponding matrix of the GM(1,1) power model in accordance with the column vector and regulate the matrix to a well-conditioned one by multiple and rotation transformation of vectors, which completely solve the instability problem of the GM(1,1) power model. Numerical results show that vector transformation is a new method in studying the stability problem of the GM(1,1) power model.

Centre pivot irrigation system is a promising and precise system, for increasing the utilization efficiency of unit water. Hence, A CPIM simulation model has been developed and validated, however, A CPIM model is based on crop type, weather data, and soil characteristics. The model comprises five sub-models for: (a) main sub-model; (b) data entry sub-model; (c) weather sub-model; (d) irrigation sub-model; and (e) results sub-model. The most important simulation outputs of the CPIM model include nozzle flow rate (m3/h), application rate (mm/h), and throw diameter (m). These outputs (outputs of 9 scenarios) were compared with observed/manufactured data for the calibration and validation of the model. Results of this comparison show that differences in model accuracy owing to different variables affecting the design and management of the center pivot were not significant. The relationships between the observed/manufactured and simulated results have a good correlation with high value of coefficient of determination and the best models are as follows: 1- Nozzle flow rate (m3/h) was in scenario 5 with R2 = 0.967 and explained by an exponential model: Q SIM = 0.1067e4.1131 (Q obs). 2- Application rate (mm/h) was in all scenarios with a very high R2 and explained by a linear model. 3- Throw diameter (m) was in scenario 1 with R2 = 0.942 and explained by a power model: Dw SIM = 3.9064 (Dw MFD)0.4361.

O gladíolo, importante flor de corte, é uma planta herbácea e suas folhas apresentam formato de lança. Os objetivos do trabalho foram determinar um modelo matemático empírico que melhor estima a área da folha do gladíolo a partir de dimensões lineares e aplicar o modelo matemático para determinar o perfil vertical da área das folhas de diferentes posições na planta. Para isso foi realizado um experimento de campo em Santa Maria com quatro cultivares de gladíolo (Peter Pears, Rose Friendship, Jester e Amsterdã), sendo coletadas 50 folhas de cada cultivar, das quais mensuraram-se o comprimento (C) e a maior largura (L). Em seguida, fotocopiou-se cada folha em um scanner, calculando-se a área individual (AF) com auxílio de um software. A relação entre área e as dimensões das folhas foi ajustada no modelo potência e a capacidade preditiva das equações foi avaliada por várias estatísticas. Resultados indicam que o modelo AF = a (C.L) é o mais indicado para a estimativa da área foliar em gladíolo, podendo-se utilizar a = 0,644 para as quatro cultivares testadas. As menores folhas estão nas posições basais e apicais e as maiores, na posição intermediária da planta. Gladiolus, an important cut flower, is a herbaceous plant that has sword-shaped leaves. The objectives of this study are to determinate an empirical model to estimate the area of gladiolus leaves from its linear dimensions and to apply this model to estimate the vertical profile of leaf area in different position on the plant. A field experiment was conducted in Santa Maria, RS, Brazil, with four gladiolus cultivars (Peter Pears, Rose Friendship, Jester and Amsterdam). A total of fifty leaves from each cultivar were collected and their width (C) and length (L) measured. Each leaves have then their area (AF) measured digitally. The relationship between area and dimensions of each leaf was fitted to a power model and the performance of the equations was evaluated by several statistics. Results indicates that the model AF = a. (C. L) is the best model to estimate leaf area in gladiolus, with a=0.664 for the four cultivars. Smaller leaves are ate the bottom and at the upper position and larger leaves are ate intermediate position on the plant.

Recent epidemiological evidence indicates that preparation of fresh produce for use as ingredients in ready-to-eat food in commercial settings has been a significant source of the norovirus (NoV) infections in the U.S. This research investigated the dissemination of NoV from a single tomato to many others via the use of an 11-horizontal blade slicer commonly found in restaurants or sandwich shops. A total of eight trials were conducted. The source of contamination in each trial was a soak-inoculated, air-dried globe tomato containing ~ 8 log10 murine norovirus (MNV). Each trial began by slicing a single un-inoculated tomato in the slicer, followed by slicing an inoculated tomato. This was then followed by slicing 9 to 27 un-inoculated tomatoes. A similar and constant hand pressure on the slicer was used in every trial. Three slices from each tomato were collected for virus elution, concentration, and extraction before RT-PCR detection of MNV. The change in MNV per sliced tomato was averaged over all eight trials, and two mathematical models were fit to the average data using a logarithmic model or a power model. Regression analysis determined that the equation that best fit the data was y = − 0.903 ∗ ln(x) + 7.945 , where y = log10 MNV per slicing and x = tomato slicing number. An acceptable fit ( R 2 = 0.913) was indicated. The MNV levels transferred ( y ) generally decreased as the number of tomatoes sliced ( x ) increased, with some exceptions. Infrequent but erratic transfers, where the MNV level of a subsequent tomato was higher than that of a preceding tomato, occurred in later transfer of some trials. In contrast, the first and second transfers of each trial were always shown to have sharply decreased levels of MNV from the inoculum. The MNV log10 reduction per slicing event changes throughout the process: with a predicted 0.63 log10 reduction from tomato 1 to tomato 2 (76% reduction); a 0.07 log10 reduction predicted from tomato 13 to tomato 14 (a 14% reduction); and 0.03 log10 reduction predicted from tomato 27 to tomato 28 (a 7% reduction). Virus transfer is clearly variable even given the consistent slicing procedure used throughout each trial. This study illustrates the complex nature of risk prediction associated with NoV cross-contamination during food preparation in commercial establishments.

SUMMARYAlthough the grey forecasting model has been successfully employed in various fields and demonstrates promising results, the literature shows that its performance could still be improved. Therefore, the aim of the present study was to continue the investigation and derive three hybrid models to predict grain production in China by combining particle swarm optimization (PSO) with the grey linear power index model, the grey logarithm power model and the grey parabola power model. In grey modelling, the use of PSO had the ability to search optimum grey parameters to construct three improved derivative grey models. The results concluded that the improved optimization models with high precision were superior to the traditional models, and PSO contributed more to precision improvement of the three grey models. Furthermore, results from the experiments demonstrated that the optimized models were reliable and valid.

Using the data presented in the accompanying paper [Hilkhuysen et al., J. Acoust. Soc. Am. 131, 531-539 (2012)], the ability of six metrics to predict intelligibility of speech in noise before and after noise suppression was studied. The metrics considered were the Speech Intelligibility Index (SII), the fractional Articulation Index (fAI), the coherence intelligibility index based on the mid-levels in speech (CSIImid), an extension of the Normalized Coherence Metric (NCM+), a part of the speech-based envelope power model (pre-sEPSM), and the Short Term Objective Intelligibility measure (STOI). Three of the measures, SII, CSIImid, and NCM+, overpredicted intelligibility after noise reduction, whereas fAI underpredicted these intelligibilities. The pre-sEPSM metric worked well for speech in babble but failed with car noise. STOI gave the best predictions, but overall the size of intelligibility prediction errors were greater than the change in intelligibility caused by noise suppression. Suggestions for improvements of the metrics are discussed.

Based on the three parameter power model, the finite element models of the extended end-plate semi-rigid connections are established by using FEA software ANSYS10.0, and the moment-rotation curve of the semi-rigid connections are obtained. By fitting the moment-rotation curve with numerical analysis method, two approximate formulas for calculating the shape coefficient of semi-rigid connections are obtained, and compared with the existing experimental data. The results shows that semi-rigid connections M-θ curves obtained by the fitted formula of shape coefficient are in consistent with the M-θ curve of FEA model and experimental data, which is based on the three parameter power model. The correctness and applicability of the approximate formula of shape coefficient are confirmed, and provides the theoretical basis for the design method of semi-rigid connections in practical engineering.

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.

The objective of this work was to propose models of equations from measurements of the linear dimensions of the last leaflet for the estimation of the leaf area of the composite leaves of Canavalia rosea. For this purpose, 441 composite leaves of 198 seedlings were used, 45 days after sowing, produced in nursery and belonging to the Federal University of Espírito Santo, Campus São Mateus, located in the municipality of São Mateus, North of the State of Espírito Santo, Brazil. The length (L) along the main midrib and the maximum leaf width (W) of the last leaflet of each composite leaf, as well as the leaf area of all leaflets, were measured. Subsequently, it was determined the product of the multiplication of the length with the width (LW) and leaf area observed (OLA) from the sum of leaf area of leaflets in front of these measures were adjusted linear and non-linear equations of linear first degree, quadratic and power models, where, OLA was used as a dependent variable in function of L, W and LW as independent variable. Based on the models tested, we obtained equations for the estimated leaf area (ELA). The mean values of ELA and OLA were compared by Student's t test 5% probability. The mean absolute error (MAE), the root mean square error (RMSE) and the Willmott d index, were determined as criteria for validation. The best adjusted equation was chosen through the non-significant values in the comparison of the means of ELA and OLA, values of MAE and RMSE closer to zero, value of the index d near the unitary and higher values of R2. Thus, the leaf area of the composite leaf of C. rosea seedlings can be estimated by the power model represented by equation ELA = 2.2951 (LW)0.9474 quickly, easily and non-destructively.

The purpose of the study aims to develop comprehensive modeling alternatives for intraproduct line pricing effect and compare the explanation power among them. The researchers want to include the highest explanation power model for Shipment Timing Support System for stored apple. Five intra-apple pricing models were developed and applied to the wholesale price data with four graded Fuji apple announced by SAMPC in Korea. Five intra-apple pricing model divided into three dichotomies: the first model for price level effect with proportional response, the second and third models for price gap effect with proportional response, and the fourth and fifth models for price gap effect with non-proportional response. The result showed that the modeling of the price gap between excellent grade and three lower grade apples with proportional response showed the highest adjusted R2 among five models. This result implies that the interdependency among apple grades has the proportional response to price difference instead of non-proportional response to price difference among apple grade.

Power model, linear model and hyperbolic model were commonly used to estimate forest biomass via stand volume, however the relative accuracy is unclear forPinus tabulaeformisforests in China. In order to compare the accuracies of these models, data from 130Pinus tabulaeformisforest stands were compiled from published literatures. Data of 100 stands were randomly selected to establish regression equations, the other 30 data were used to compare the accuracies of equations either established in this study or in previous studies. The results show that biomass ofPinus tabulaeformisforests could be well estimated by power model and linear model, while hyperbolic model is likely to result in enormous overestimation or underestimation. The mean relative errors of the power model and linear model established in this study are-0.3% and 1.8% respectively. In comparison with models established by previous studies, these two models have better prediction accuracies.

A novel grey Bass model with a power exponent (Grey Bass Power Model) was proposed, and the related parameter-packets of the model were deduced. A nonlinear programming method was employed to optimize the grey parameters and improve the accuracy of the grey Bass model. The results show that GM(1,1) model, GPM (1,1) model, grey Verhulst model and grey Bass model are the special examples of grey Bass power model. The actual example of product diffusion shows the modelling accuracy has been remarkably improved by using the new model.

In order to evaluate the security of Application Specific Integrated Circuit (ASIC) implemented cryptographic algorithms at an early design stage, a Hamming distance model based power analysis is proposed. The Data Encryption Standard (DES) algorithm is taken as an example to illustrate the threats of differential power analysis (DPA) attack against the security of ASIC chip. A DPA attack against the ASIC implementation of a DES algorithm is realized based on hamming distance power model (HD model), and it realized the attack by successfully guessing the right 48-bit subkey. This result indicates that the power analysis attack based on the HD model is simple, rapid and effective for the design and evaluation of security chips.

This article reviews currently used approaches for establishing dose proportionality in Phase I dose escalation studies. A review of relevant literature between 2002 and 2006 found that the power model was the preferred choice for assessing dose proportionality in about one-third of the articles. This article promotes the use of the power model and a conceptually appealing extension, i.e. a criterion based on comparing the 90% confidence interval for the ratio of predicted mean values from the extremes of the dose range (R(dnm)) to pre-defined equivalence criterion (theta(L),theta(U)). The choice of bioequivalence default values of theta(L)=0.8 and theta(U)=1.25 seems reasonable for dose levels only a doubling apart but are impractically strict when applied over the complete dose range. Power calculations are used to show that this prescribed criterion lacks power to conclude dose proportionality in typical Phase I dose-escalation studies. A more lenient criterion with values theta(L)=0.5 and theta(U)=2 is proposed for exploratory dose proportionality assessments across the complete dose range.

Accelerated Lifetime Test is a method of estimation of lifetime quality characteristics under operation condition with the accelerated lifetime data obtained under accelerated stress. In this paper we propose estimation method with accelerated lifetime data using quantile regression. We apply the method to real data with Arrhenius and Inverse power model.

Leaf area estimation models based on linear leaf dimensions are an important method because their application is not destructive to the leaves. For these models to be reliable, it is important that the estimation of model parameters is accurate, and for that to occur, the models must be generated using an adequate sample size (number of leaves). The objective of this study was to determine the number of leaves necessary to accurately model the leaf area of jack beans (Y), determined by digital photos, according to the width of the central leaflet (x), by a power model (Y = ax b ) generated through an iterative process. Accordingly, an experiment was performed in a 256 m 2 area. A total of 745 leaves were randomly collected at six different crop development stages (29, 43, 57, 73, 87 and 101 days after emergence). Each leaf was comprised of a left, central and right leaflet. The width of the central leaflet (x) was measured on the 745 leaves. Leaf area (sum of the area of the left, central and right leaflets; Y) was then determined using a digital photo method. The number of leaves necessary for the estimation of the parameters a and b and the coefficient of determination (R 2 ) of the power model were determined through resampling with replacement. The power model (Ŷ = 4.2049x 1.8215 , R 2 = 0.9701), based on the width of the central leaflet was determined to be adequate for estimating jack bean leaf area. Data collected from a sample of 200 leaves were determined to be sufficient for constructing an accurate power model for the leaf area of jack beans (Y) as a function of the width of the central leaflet (x), based on determinations of leaf area using digital photos.

Two models were derived for the estimation of effective hydraulic conductivity (K e ) of a soil layer based on exponential and inverse square variation of hydraulic conductivity with soil depth. Darcy’s law was applied to a vertical soil stratum subdivided into a finite number of layers. The relationship between K e and layer thickness is of quadratic form with R 2 ≈ 1.As the layer thickness increases, the values of K e for the exponential model increases drastically, exceeding the K e estimate of the power model. The percentage difference between the two models assumes an asymptotic form to the y-axis at a percentage difference of 5%, as the size of layer approaches zero. power model gives lower estimates of K e than the exponential model within soil depth range of 1.5m ≤ D ≤ 3.2m for n = 2; 0.8m ≤ D ≤ 1.9m for n = 50; and 0.7m ≤ D ≤ 1.9m for n = 100 and above. For very shallow soil stratum (D ≤ 2), the exponential model gives better and more realistic estimates of K e than the power model; while for medium to deep soil stratum (D ≥ 2), the power model gives better estimates of K e . http://dx.doi.org/10.4314/njt.v34i3.30

The increasing number of model types that are used to predict tree biomass from diameter, height and wood density has brought questioning about the biological relevance of complex allometries (i.e. non-power models). Statistical issues such as collinearity among predictors and unreliable coefficient estimates have also been associated with complex allometric models. Using a data set of 225 trees from central Africa, we assessed the relevance of simple allometry (i.e. power model) versus complex allometry to predict tree biomass. A complex allometric model of biomass was developed based on a model of resource partition between dbh and height growths. Although being a good model for biomass prediction, the power model was outperformed by the complex allometric model. A careful examination showed that the power model could be segmented into two pieces of power models. Using tree diameter and height as separated predictors improved the biomass prediction, irrespective of the collinearity between these two predictors. A critical value of 25% for the PRSE statistic used to assess the reliability of coefficient estimates corresponded to a significance level of 10 - 5 – 10 - 4 and was thus unreasonably low. We conclude that growth theories should be developed to explain allometric models, but that the arbitration between these models should ultimately rely on observed data, not on theories.

This paper presents the regression analysis of the bearing capacity of a square footing on reinforced pond ash. A power model has been developed to estimate bearing capacity of a square footing ( q rs ) on reinforced pond ash at any settlement using all possible regression techniques based on 2088 model test data to select the significant subset of the predictors. From the regression analysis, the predictors viz., the bearing capacity of a square footing ( q s ) at the same settlement on unreinforced pond ash, settlement to width of the footing ratio ( s / B ) in percentage, number of layers (N) of reinforcement, friction ratio (f), i.e. the ratio of the pond ash—geotextile interface friction angle ( ψ ) to the direct shear friction angle of pond ash ( φ d ) , depth of the upper most layer of reinforcement from the base of the footing to width of the footing ratio ( u / B ) , length of reinforcement sheet to width of footing ratio ( L s / B ) and vertical spacing of the reinforcement to width of the footing ratio ( S v / B ) are found to be significant to the model. The adjusted coefficient of determination ( R adj 2 ) for the proposed model is found to be 0.9448 and for the regression model 72% data out of 2088 observed data have prediction with less than 15% error. The additional set of 99 data was used for validation of the model.

Leaves were sampled from Vitis labruscana Bailey cv. ‘Niagara’ and the interspecific hybrid ‘DeChaunac’ grapevines several times during a 2-year investigation of leaf area estimation. Linear measurements of leaf length and width were made and correlated with leaf area measurements made with a computerized image processing system. For each cultivar, nine regression equations were derived and compared. Most models resulted in high (R2=0.90) coefficients of determination, but the power model using leaf width provided a high R2 and relatively low standard error of the estimate (‘Niagara’: area=0.637W1.995, R2=0.9821, and S.E.=10.58; ‘DeChaunac’: area=0.672W1.963, R2=0.9632, S.E.=5.67). Use of single-variable equations facilitates simple, rapid, and accurate estimation of ‘Niagara’ and ‘DeChaunac’ leaf area.