Support vector regression and multilayer feed forward neural networks for non-exercise prediction of VO2max

The purpose of this study is to develop non-exercise (N-Ex) VO₂max prediction models by using support vector regression (SVR) and multilayer feed forward neural networks (MFFNN). VO₂max values of 100 subjects (50 males and 50 females) are measured using a maximal graded exercise test. The variables; gender, age, body mass index (BMI), perceived functional ability (PFA) to walk, jog or run given distances and current physical activity rating (PA-R) are used to build two N-Ex prediction models. Using 10-fold cross validation on the dataset, standard error of estimates (SEE) and multiple correlation coefficients (R) of both models are calculated. The MFFNN-based model yields lower SEE (3.23 ml kg^?1 min^?1) whereas the SVR-based model yields higher R (0.93). Compared with the results of the other N-Ex prediction models in literature that are developed using multiple linear regression analysis, the reported values of SEE and R in this study are considerably more accurate. Therefore, the results suggest that SVR-based and MFFNN-based N-Ex prediction models can be valid predictors of VO₂max for heterogeneous samples.     

ANN based simulation and experimental verification of analytical four- and five-parameters models of PV modules

In this article, artificial neural network (ANN) is adopted to predict photovoltaic (PV) panel behaviors under realistic weather conditions. ANN results are compared with analytical four and five parameter models of PV module. The inputs of the models are the daily total irradiation, air temperature and module voltage, while the outputs are the current and power generated by the panel. Analytical models of PV modules, based on the manufacturer datasheet values, are simulated through Matlab/Simulink environment. Multilayer perceptron is used to predict the operating current and power of the PV module. The best network configuration to predict panel current had a 3–7–4–1 topology. So, this two hidden layer topology was selected as the best model for predicting panel current with similar conditions. Results obtained from the PV module simulation and the optimal ANN model has been validated experimentally. Results showed that ANN model provide a better prediction of the current and power of the PV module than the analytical models. The coefficient of determination (R²), mean square error (MSE) and the mean absolute percentage error (MAPE) values for the optimal ANN model were 0.971, 0.002 and 0.107, respectively. A comparative study among ANN and analytical models was also carried out. Among the analytical models, the five-parameter model, with MAPE = 0.112, MSE = 0.0026 and R² = 0.919, gave better prediction than the four-parameter model (with MAPE = 0.152, MSE = 0.0052 and R² = 0.905). Overall, the 3–7–4–1 ANN model outperformed four-parameter model, and was marginally better than the five-parameter model.     

A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: Validation

Accurate assessment of phytoplankton chlorophyll-a (chla) concentrations in turbid waters by means of remote sensing is challenging due to the optical complexity of case 2 waters. We have applied a recently developed model of the form [R_rs^? 1(λ₁) ? R_rs^? 1(λ₂)] × R_rs(λ₃) where R_rs(λ_i) is the remote-sensing reflectance at the wavelength λ_i, for the estimation of chla concentrations in turbid waters. The objectives of this paper are (a) to validate the three-band model as well as its special case, the two-band model R_rs^? 1(λ₁) × R_rs(λ₃), using datasets collected over a considerable range of optical properties, trophic status, and geographical locations in turbid lakes, reservoirs, estuaries, and coastal waters, and (b) to evaluate the extent to which the three-band model could be applied to the Medium Resolution Imaging Spectrometer (MERIS) and two-band model could be applied to the Moderate Resolution Imaging Spectroradiometer (MODIS) to estimate chla in turbid waters.The three-band model was calibrated and validated using three MERIS spectral bands (660–670 nm, 703.75–713.75 nm, and 750?757.5 nm), and the 2-band model was tested using two MODIS spectral bands (λ₁ = 662–672, λ₃ = 743–753 nm). We assessed the accuracy of chla prediction in four independent datasets without re-parameterization (adjustment of the coefficients) after initial calibration elsewhere. Although the validation data set contained widely variable chla (1.2 to 236 mg m^? 3), Secchi disk depth (0.18 to 4.1 m), and turbidity (1.3 to 78 NTU), chla predicted by the three-band algorithm was strongly correlated with observed chla (r² > 0.96), with a precision of 32% and average bias across data sets of ? 4.9% to 11%. Chla predicted by the two-band algorithm was also closely correlated with observed chla (r² > 0.92); however, the precision declined to 57%, and average bias across the data sets was 18% to 50.3%. These findings imply that, provided that an atmospheric correction scheme for the red and NIR bands is available, the extensive database of MERIS and MODIS imagery could be used for quantitative monitoring of chla in turbid waters.     

Mason: morphological simplification

The traditional rounding and filleting morphological filters are biased. Hence, as r grows, the rounding R_r (S) of S shrinks and the filleting F_r (S) grows. A shape S is r-regular when R_r (S) = F_r (S) = S. The combinations F_r (R_r (S)) and R_r (F_r (S)) produce nearly r-regular shapes, but retain a bias: F_r (R_r (S)) is usually smaller than S and R_r (F_r (S)) is larger. To overcome this bias, we propose a new filter, called Mason. The r-mortar M_r (S) of S is F_r (S)–R_r (S), and the stability of a point P with respect to S is the smallest value of r for which P belongs to M_r (S). Stability provides important information about the shape’s imbedding that cannot be obtained through traditional topological or differential analysis tools. F_r (R_r (S)) and R_r (F_r (S)) only affect space in M_r (S). For each maximally connected component of M_r (S), Mason performs either F_r (R_r (S)) or R_r (F_r (S)), choosing the combination that alters the smallest portion of that component. Hence, Mason acts symmetrically on the shape and on its complement. Its output is guaranteed to have a smaller symmetric difference with the original shape than that of either combination F_r (R_r (S)) or R_r (F_r (S)). Many previously proposed shape simplification algorithms were focused on reducing the combinatorial storage or processing costs of a shape at the expense of the smoothness and regularity or altered the shape in regular portions that did not exhibit any high frequency complexity. Mason is the first shape simplification operator that is independent of the particular representation and offers the advantage of preserving portions of the boundary of S that are regular at the desired scale.     

Performance of radial basis and LM-feed forward artificial neural networks for predicting daily watershed runoff

This study investigated the effects of upstream stations’ flow records on the performance of artificial neural network (ANN) models for predicting daily watershed runoff. As a comparison, a multiple linear regression (MLR) analysis was also examined using various statistical indices. Five streamflow measuring stations on the Cahaba River, Alabama, were selected as case studies. Two different ANN models, multi layer feed forward neural network using Levenberg–Marquardt learning algorithm (LMFF) and radial basis function (RBF), were introduced in this paper. These models were then used to forecast one day ahead streamflows. The correlation analysis was applied for determining the architecture of each ANN model in terms of input variables. Several statistical criteria (RMSE, MAE and coefficient of correlation) were used to check the model accuracy in comparison with the observed data by means of K-fold cross validation method. Additionally, residual analysis was applied for the model results. The comparison results revealed that using upstream records could significantly increase the accuracy of ANN and MLR models in predicting daily stream flows (by around 30%). The comparison of the prediction accuracy of both ANN models (LMFF and RBF) and linear regression method indicated that the ANN approaches were more accurate than the MLR in predicting streamflow dynamics. The LMFF model was able to improve the average of root mean square error (RMSE_ave) and average of mean absolute percentage error (MAPE_ave) values of the multiple linear regression forecasts by about 18% and 21%, respectively. In spite of the fact that the RBF model acted better for predicting the highest range of flow rate (flood events, RMSE_ave/RBF = 26.8 m³/s vs. RMSE_ave/LMFF = 40.2 m³/s), in general, the results suggested that the LMFF method was somehow superior to the RBF method in predicting watershed runoff (RMSE/LMFF = 18.8 m³/s vs. RMSE/RBF = 19.2 m³/s). Eventually, statistical differences between measured and predicted medians were evaluated using Mann-Whitney test, and differences in variances were evaluated using the Levene's test.     

Computer-based analysis of explicit approximations to the implicit Colebrook–White equation in turbulent flow friction factor calculation

The implicit Colebrook–White equation has been widely used to estimate the friction factor for turbulent fluid-flow in rough-pipes. In this paper, the state-of-the-art review for the most currently available explicit alternatives to the Colebrook–White equation, is presented. An extensive comparison test was established on the 20 × 500 grid, for a wide range of relative roughness (ε/D) and Reynolds number (R) values (1 × 10^?6 ? ε/D ? 5 × 10^?2; 4 × 10³ ? R ? 10⁸), covering a large portion of turbulent flow zone in Moody’s diagram. Based on the comprehensive error analysis, the magnitude points in which the maximum absolute and the maximum relative error are occurred at the pair of ε/D and R values, are observed. A limiting case of the most of these approximations provided friction factor estimates that are characterized by a mean absolute error of 5 × 10^?4, a maximum absolute error of 4 × 10^?3 whereas, a mean relative error of 1.3% and a maximum relative error of 5.8%, over the entire range of ε/D and R values, respectively. For practical purposes, the complete results for the maximum and the mean relative errors versus the 20 sets of ε/D value, are also indicated in two comparative figures. The examination results for error properties of these approximations gives one an opportunity to practically evaluate the most accurate formula among of all the previous explicit models; and showing in this way its great flexibility for estimating turbulent flow friction factor. Comparative analysis for the mean relative error profile revealed, the classification for the best-fitted six equations examined was in a good agreement with those of the best model selection criterion claimed in the recent literature, for all performed simulations.     

Calibration and validation of hyperspectral indices for the estimation of broadleaved forest leaf chlorophyll content,leaf mass per area,leaf area index and leaf canopy biomass

This article aims at finding efficient hyperspectral indices for the estimation of forest sun leaf chlorophyll content (CHL, µg cm_leaf^? 2), sun leaf mass per area (LMA, g_{dry matter} m_leaf^? 2), canopy leaf area index (LAI, m²_leaf m_soil^? 2) and leaf canopy biomass (B_leaf, g_{dry matter} m_soil^? 2). These parameters are useful inputs for forest ecosystem simulations at landscape scale. The method is based on the determination of the best vegetation indices (index form and wavelengths) using the radiative transfer model PROSAIL (formed by the newly-calibrated leaf reflectance model PROSPECT coupled with the multi-layer version of the canopy radiative transfer model SAIL). The results are tested on experimental measurements at both leaf and canopy scales. At the leaf scale, it is possible to estimate CHL with high precision using a two wavelength vegetation index after a simulation based calibration. At the leaf scale, the LMA is more difficult to estimate with indices. At the canopy scale, efficient indices were determined on a generic simulated database to estimate CHL, LMA, LAI and Bleaf in a general way. These indices were then applied to two Hyperion images (50 plots) on the Fontainebleau and Fougères forests and portable spectroradiometer measurements. They showed good results with an RMSE of 8.2 µg cm^? 2 for CHL, 9.1 g m^? 2 for LMA, 1.7 m² m^? 2 for LAI and 50.6 g m^? 2 for Bleaf. However, at the canopy scale, even if the wavelengths of the calibrated indices were accurately determined with the simulated database, the regressions between the indices and the biophysical characteristics still had to be calibrated on measurements. At the canopy scale, the best indices were: for leaf chlorophyll content: ND_chl = (ρ₉₂₅ ? ρ₇₁₀)/(ρ₉₂₅ + ρ₇₁₀), for leaf mass per area: ND_LMA = (ρ₂₂₆₀ ? ρ₁₄₉₀)/(ρ₂₂₆₀ + ρ₁₄₉₀), for leaf area index: D_LAI = ρ₁₇₂₅ ? ρ₉₇₀, and for canopy leaf biomass: ND_Bleaf = (ρ₂₁₆₀ ? ρ₁₅₄₀)/(ρ₂₁₆₀ + ρ₁₅₄₀).     

Evaluation of three methodologies to estimate the VO2max in people of different ages

Aging and gender are factors that affect the variation of physical work capacity. The present paper highlights the importance of the metabolism used by ergonomics to establish the appropriate limits of loads at work. This study compares the aerobic capacity of people from 20 to 71 years old split in 5 different groups. The laboratory experiment tested 33 volunteers (19 women and 14 men). A submaximal step test was used to measure the VO₂ using a portable breath by breath metabolic system and a telemetric heart rate monitor. Three methods to estimate the VO_2max were compared: 1) a direct measurement of VO₂, 2) estimation by heart rate, and 3) a step test method using predetermined charts. Significant difference was encountered among the estimation methods as well as among the age ranges (F_2,92 = 6.43, p < 0.05 y F_4,92 = 7.18, p < 0.05 respectively). The method of direct measurement and the method of predetermined charts were different for the estimation of the VO_2max with a confidence level of 95%. The method of predetermined charts is better adapted for males and people younger than 30 years. The estimation through non invasive heart rate apparatus was a good appraiser of the maximal oxygen consumption considering both genders and all the age groups.     

Remote sensing of canopy light use efficiency in temperate and boreal forests of North America using MODIS imagery

Light use efficiency (LUE) is an important variable characterizing plant eco-physiological functions and refers to the efficiency at which absorbed solar radiation is converted into photosynthates. The estimation of LUE at regional to global scales would be a significant advantage for global carbon cycle research. Traditional methods for canopy level LUE determination require meteorological inputs which cannot be easily obtained by remote sensing. Here we propose a new algorithm that incorporates the enhanced vegetation index (EVI) and a modified form of land surface temperature (T_m) for the estimation of monthly forest LUE based on Moderate Resolution Imaging Spectroradiometer (MODIS) imagery. Results demonstrate that a model based on EVI × T_m parameterized from ten forest sites can provide reasonable estimates of monthly LUE for temperate and boreal forest ecosystems in North America with an R² of 0.51 (p < 0.001) for the overall dataset. The regression coefficients (a, b) of the LUE–EVI × T_m correlation for these ten sites have been found to be closely correlated with the average EVI (EVI_ave, R² = 0.68, p = 0.003) and the minimum land surface temperature (LST_min, R² = 0.81, p = 0.009), providing a possible approach for model calibration. The calibrated model shows comparably good estimates of LUE for another ten independent forest ecosystems with an overall root mean square error (RMSE) of 0.055 g C per mol photosynthetically active radiation. These results are especially important for the evergreen species due to their limited variability in canopy greenness. The usefulness of this new LUE algorithm is further validated for the estimation of gross primary production (GPP) at these sites with an RMSE of 37.6 g C m^? 2 month^? 1 for all observations, which reflects a 28% improvement over the standard MODIS GPP products. These analyses should be helpful in the further development of ecosystem remote sensing methods and improving our understanding of the responses of various ecosystems to climate change.     

Prediction of cutting temperature in orthogonal machining of AISI 316L using artificial neural network

In this study, an approach based on artificial neural network (ANN) was proposed to predict the experimental cutting temperatures generated in orthogonal turning of AISI 316L stainless steel. Experimental and numerical analyses of the cutting forces were carried out to numerically obtain the cutting temperature. For this purpose, cutting tests were conducted using coated (TiCN + Al₂O₃ + TiN and Al₂O₃) and uncoated cemented carbide inserts. The Deform-2D programme was used for numerical modelling and the Johnson–Cook (J–C) material model was used. The numerical cutting forces for the coated and uncoated tools were compared with the experimental results. On the other hand, the cutting temperature value for each cutting tool was numerically obtained. The artificial neural network model was used to predict numerical cutting temperatures by means of the numerical cutting forces. The best results in predicting the cutting temperature were obtained using the network architecture with a hidden layer which has seven neurons and LM learning algorithm. Finally, the experimental cutting temperatures were predicted by entering the experimental cutting forces into a formula obtained from the artificial neural networks. Statistical results (R², RMSE, MEP) were quite satisfactory. This demonstrates that the established ANN model is a powerful one for predicting the experimental cutting temperatures.     

Interpretation and topographic compensation of conifer canopy self-shadowing

The self-shadowing of conifer canopies results from the size and arrangement of trees within a stand and is a first-order term controlling radiance from forested terrain at common pixel scales of tens of meters. Although self-shadowing is a useful attribute for forest remote-sensing classification, compensation for the topographic effects of self-shadowing has proven problematic. This study used airborne canopy LiDAR measurements of 80 Pacific Northwest, USA conifer stands ranging in development stage from pre-canopy closure to old-growth in order to model canopy self-shadowing for four solar zenith angles (SZA). The shadow data were compared to physical measurements used to characterize forest stands, and were also used to test and improve terrain compensation models for remotely sensed images of forested terrain. Canopy self-shadowing on flat terrain strongly correlates with the canopy's geometric complexity as measured by the rumple index (canopy surface area/ground surface area) (R² = 0.94–0.87 depending on SZA), but is less correlated with other stand measurements: 95th percentile canopy height (R² = 0.68), mean diameter at breast height (dbh) (R² = 0.65), basal area ha^? 1 (R² = 0.18), and canopy stem count ha^? 1 (R² = 0.18). The results in this paper support interpretation of self-shadowing as a function of canopy complexity, which is an important ecological characteristic in its own right. Modeling of canopy self-shadowing was used to assess the accuracy of the Sun-Canopy-Sensor (SCS) topographic correction, and to develop a new empirical Adaptive Shade Compensation (ASC) topographic compensation model. ASC used measured shadow (as an estimate of canopy complexity) and the SCS term (to describe the illumination geometry) as independent variables in multiple regressions to determine the topographic correction. The ASC model provided more accurate radiance corrections with limited variation in results across the full range of canopy complexities and incidence angles.     

Precipitation forecasting by using wavelet-support vector machine conjunction model

A new wavelet-support vector machine conjunction model for daily precipitation forecast is proposed in this study. The conjunction method combining two methods, discrete wavelet transform and support vector machine, is compared with the single support vector machine for one-day-ahead precipitation forecasting. Daily precipitation data from Izmir and Afyon stations in Turkey are used in the study. The root mean square errors (RMSE), mean absolute errors (MAE), and correlation coefficient (R) statistics are used for the comparing criteria. The comparison results indicate that the conjunction method could increase the forecast accuracy and perform better than the single support vector machine. For the Izmir and Afyon stations, it is found that the conjunction models with RMSE=46.5 mm, MAE=13.6 mm, R=0.782 and RMSE=21.4 mm, MAE=9.0 mm, R=0.815 in test period is superior in forecasting daily precipitations than the best accurate support vector regression models with RMSE=71.6 mm, MAE=19.6 mm, R=0.276 and RMSE=38.7 mm, MAE=14.2 mm, R=0.103, respectively. The ANN method was also employed for the same data set and found that there is a slight difference between ANN and SVR methods.     

Artificial neural networks for rapid WWTP performance evaluation: Methodology and case study

Reliable performance evaluation of wastewater treatment plants (WWTPs) can be done by simulating the plant behavior over a wide range of influent disturbances, including series of rain events with different intensity and duration, seasonal temperature variations, holiday effects, etc. Such simulation-based WWTP performance evaluations are in practice limited by the long simulation time of the mechanistic WWTP models. By moderate simplification (avoiding big losses in prediction accuracy) of the mechanistic WWTP model only a limited reduction of the simulation time can be achieved. The approach proposed in this paper combines an influent disturbance generator with a mechanistic WWTP model for generating a limited sequence of training data (4 months of dynamic data). An artificial neural network (ANN) is then trained on the available WWTP input-output data, and is subsequently used to simulate the remainder of the influent time series (20 years of dynamic data) generated with the influent disturbance generator. It is demonstrated that the ANN reduces simulation time by a factor of 36, even when including the time needed for the generation of training data and for ANN training. For repeated integrated urban wastewater system simulations that do not require repeated training of the ANN, the ANN reduces simulation time by a factor of 1300 compared to the mechanistic model. ANN prediction of effluent ammonium, BOD₅ and total suspended solids was good when compared to mechanistic WWTP model predictions, whereas prediction of effluent COD and total nitrogen concentrations was a bit less satisfactory. With correlation coefficients R² > 0.95 and prediction errors lower than 10%, the accuracy of the ANN is sufficient for applications in simulation-based WWTP design and simulation of integrated urban wastewater systems, especially when taking into account the uncertainties related to mechanistic WWTP modeling.     

Remote sensing of the distribution and abundance of host species for spruce budworm in Northern Minnesota and Ontario

Insects and disease affect large areas of forest in the U.S. and Canada. Understanding ecosystem impacts of such disturbances requires knowledge of host species distribution patterns on the landscape. In this study, we mapped the distribution and abundance of host species for the spruce budworm (Choristoneura fumiferana) to facilitate landscape scale planning and modeling of outbreak dynamics. We used multi-temporal, multi-seasonal Landsat data and 128 ground truth plots (and 120 additional validation plots) to map basal area (BA), for 6.4 million hectares of forest in northern Minnesota and neighboring Ontario. Partial least-squares (PLS) regression was used to determine relationships between ground data and Landsat sensor data. Subsequently, BA was mapped for all forests, as well as for two specific host tree genera (Picea and Abies). These PLS regression analyses yielded estimates for overall forest BA with an R² of 0.62 and RMSE of 4.67 m² ha^? 1 (20% of measured BA), white spruce relative BA with an R² of 0.88 (RMSE = 12.57 m² ha^? 1 [20% of measured]), and balsam fir relative BA with an R² of 0.64 (RMSE = 6.08 m² ha^? 1 [33% of measured]). We also used this method to estimate the relative BA of deciduous and coniferous species, each with R² values of 0.86 and RMSE values of 9.89 m² ha^? 1 (23% of measured) and 9.78 m² ha^? 1 (16% of measured), respectively. Of note, winter imagery (with snow cover) and shortwave infrared-based indices – especially the shortwave infrared/visible ratio – strengthened the models we developed. Because ground measurements were made largely in forest stands containing spruce and fir, modeled results are not applicable to stands dominated by non-target conifers such as pines and cedar. PLS regression has proven to be an effective modeling tool for regional characterization of forest structure within spatially heterogeneous forests using multi-temporal Landsat sensor data.     

Hyperspectral remote sensing of cyanobacteria in turbid productive water using optically active pigments,chlorophyll a and phycocyanin

Nuisance blue-green algal blooms contribute to aesthetic degradation of water resources by means of accelerated eutrophication, taste and odor problems, and the production of toxins that can have serious adverse human health effects. Current field-based methods for detecting blooms are costly and time consuming, delaying management decisions. Methods have been developed for estimating phycocyanin concentration, the accessory pigment unique to freshwater blue-green algae, in productive inland water. By employing the known optical properties of phycocyanin, researchers have evaluated the utility of field-collected spectral response patterns for determining concentrations of phycocyanin pigments and ultimately blue-green algal abundance. The purpose of this research was to evaluate field spectroscopy as a rapid cyanobacteria bloom assessment method. In-situ field reflectance spectra were collected at 54 sampling sites on two turbid reservoirs on September 6th and 7th in Indianapolis, Indiana using ASD Fieldspec (UV/VNIR) spectroradiometers. Surface water samples were analyzed for in-vitro pigment concentrations and other physical and chemical water quality parameters. Semi-empirical algorithms by Simis et al. [Simis, S., Peters, S., Gons, H. (2005). Remote sensing of the cyanobacterial pigment phycocyanin in turbid inland water. American Society of Limnology and Oceanography 50(11): 237–245] were applied to the field spectra to predict chlorophyll a and phycocyanin absorption at 665 nm and 620 nm, respectively. For estimation of phycocyanin concentration, a specific absorption coefficient of 0.0070 m² mg PC^-1 for phycocyanin at 620 nm, a_PC^?(620), was employed, yielding an r² value of 0.85 (n = 48, p < 0.0001), mean relative residual value of 0.51 (σ = 1.41) and root mean square error (RMSE) of 19.54 ppb. Results suggest this algorithm could be a robust model for estimating phycocyanin. Error is highest in water with phycocyanin concentrations of less than 10 ppb and where phycocyanin abundance is low relative to chlorophyll a. A strong correlation between measured phycocyanin concentrations and biovolume measurements of cyanobacteria was also observed (r = 0.89), while a weaker relationship (r = 0.66) resulted between chlorophyll a concentration and cyanobacterial biovolume.     

Generalized Strong Pseudoprime Tests and Applications

We describe probabilistic primality tests applicable to integers whose prime factors are all congruent to 1 mod r where r is a positive integer;r =  2 is the Miller–Rabin test. We show that if ν rounds of our test do not find n ≠  =  (r +  1)²composite, then n is prime with probability of error less than (2 r) ^− ν. Applications are given, first to provide a probabilistic primality test applicable to all integers, and second, to give a test for values of cyclotomic polynomials.     

Assessment of grape yield and composition using the reflectance based Water Index in Mediterranean rainfed vineyards

In rainfed vineyards water deficits play a major role in determining berry yield and composition. Therefore, reliable indicators of vine water status might be of great value for the optimization of grape yield and quality. In the present study the feasibility of using hyperspectral reflectance indices related to plant biophysical properties at predicting berry yield and quality attributes in rainfed vineyards is assessed. The study was conducted on Vitis vinifera cv. Chardonnay in commercial vineyards in the D.O. Penedès region (Catalonia, Spain) over two consecutive years (2007–2008). Field measurements of fractional intercepted Photosynthetic Active Radiation (fIPAR), canopy reflectance, predawn water potential (Ψ_p) and the canopy to air temperature difference at midday (ΔT_midday) were conducted at the stage of veraison. Yield, Total Soluble Solids (TSS), Titratable Acidity (TA) and the ratio TSS/TA (maturation index, IMAD) were determined at harvest. Contrasted water availability among vineyards prompted considerable variation in berry yield and quality attributes. Across years, higher yield was accompanied by higher TA (r = 0.59, p < 0.01) and lower IMAD (r = ? 0.63, p < 0.01) while no significant relationship was observed between yield and TSS. Yield was related to canopy vigor (fIPAR) in a variable extend: in 2007, yield was positively related to fIPAR (r = 0.71, p < 0.05) while yield was found to decrease along with increasing fIPAR in 2008 (r = ? 0.62, p < 0.05). Contrastingly, NDVI provided consistent estimates of yield across years (r = 0.57, p < 0.05). These results suggest that NDVI might be more appropriate to characterize the effects of varying water availability on yield than fIPAR. In addition, yield was found to be related to ΔT_midday (r = ? 0.63 and r = ? 0.66, in 2007 and 2008, respectively). Accordingly, the Water Index (WI), an indicator of vine water status, provided robust estimates of yield across years (r = 0.61, p < 0.01). The strength of the correlation between NDVI and WI vs. yield suggests that yield was influenced by changes in both leaf area (intercepted light) and photosynthesis (stomatal aperture) in a variable extent according to the timing and severity of water deficits in the years of study. Berry quality attributes did not show significant relationships against fIPAR but were related to ΔT_midday. Accordingly, NDVI did not show significant correlation with berry quality attributes, while WI was found to be consistently related to TA (r = 0.70, p < 0.01) and IMAD (r = ? 0.71, p < 0.01) across years. The results obtained suggest that the WI might provide reliable estimates of berry quality attributes in vineyards experiencing moderate to severe water deficits with potential application in precision viticulture activities such as selective harvesting according to grape quality attributes as well as for ripening assessment.     

Curves of Genus 2 with (N,N) Decomposable Jacobians

Let C be a curve of genus 2 and ψ₁: C  −  → E ₁  a map of degree n, from C to an elliptic curveE₁ , both curves defined over C. This map induces a degree n map φ₁:P¹  −  → P ¹  which we call a Frey–Kani covering. We determine all possible ramifications for φ₁. If ψ₁:C  −  → E ₁  is maximal then there exists a maximal map ψ₂: C  −  → E ₂  , of degree n, to some elliptic curveE₂ such that there is an isogeny of degree n²from the JacobianJ_C to E₁ × E₂. We say thatJ_C is (n, n)-decomposable. If the degree n is odd the pair (ψ₂, E₂) is canonically determined. For n =  3, 5, and 7, we give arithmetic examples of curves whose Jacobians are (n, n)-decomposable.