A METHOD FOR ASSESSING NITROGEN NUTRITIONAL STATUS IN PLANTS BY VISIBLE-TO-SHORTWAVE INFRARED REFLECTANCE SPECTROSCOPY OF CARBOHYDRATES
20230078617 · 2023-03-16
Inventors
- Tarin PAZ-KAGAN (Meitar, IL)
- Or SPERLING (Beit Kama, IL)
- Ze'ev SCHMILOVITCH (Yehud, IL)
- Uri YERMIYAHU (Yavne, IL)
- Tal RAPAPORT (Lehavim, IL)
Cpc classification
G01N21/31
PHYSICS
G01N1/4044
PHYSICS
International classification
Abstract
The present disclosure discloses a method for evaluating the nutritional status in plants, using visible-to-shortwave (VIS-SWIR) infrared reflectance spectroscopy of carbohydrates, particularly in almond trees. The method comprises obtaining a dry plant sample (i.e. leaves, branches and roots), digesting and grinding it to a powder, capturing predetermined spectral data of the ground plant sample, correlating said spectral data to predetermined materials and evaluating said nitrogen status of said plants according to predetermined multivariate statistical models. The data obtained from this method facilitates crop management and fertilization by providing the nitrogen status of the plants based on non-structural carbohydrates.
Claims
1. A method for assessing nitrogen status in a plant comprising steps of: a. obtaining a sample from different plant parts or tissues; b. drying, digesting, and grinding said plant parts or tissues to a powder; c. capturing predetermined spectral data of said dried, powdered, and digested plant parts or tissues; d. correlating said spectral data to predetermined materials; and e. evaluating said nitrogen status of said plants according to predetermined multivariate statistical models.
2. The method of claim 1, wherein said plant is a tree selected from the group consisting of Magnoliophyta, Eudicotidae, Liliopsida, Magnolianae, Pinophyte, Ginkgophyte, Cycadophyte, and any combination thereof.
3. The method of claim 2, wherein said tree is a fruit tree.
4. The method of claim 3, wherein said tree is an almond tree.
5. The method of claim 1, wherein said tissues or parts are selected from the group consisting of roots, stems, branches, leaves, fruits, seeds, flowers, inflorescences, and any combination thereof.
6. The method of claim 1 further comprising a step of treating said plant with fertilizers.
7. The method of claim 6, wherein said fertilizers comprise nitrogen.
8. The method of claim 1, wherein said capturing of said predetermined spectral data is carried out using reflectance spectroscopy based on a spectrometer.
9. The method of claim 8, wherein said spectrometer is configured to capture said predetermined spectral data in the visible, near-infrared and shortwave infrared spectral regions.
10. The method of claim 1, wherein said predetermined spectral data are reflectance signals at the 400-2,500 nm spectral range.
11. The method of claim 1, wherein said multivariate statistical models are selected from a group consisting of partial least squares-regression, partial least squares discriminant analysis and any combination thereof.
12. The method of claim 11, wherein predicting said partial least squares-regression is evaluated by statistical parameters selected from a group consisting of a number of latent variables, root mean square error of calibration and cross-validation, coefficient of determination values of the relation between the predicted and observed samples and any combination thereof.
13. The method of claim 1, wherein said predetermined materials are selected from the group consisting of non-structural carbohydrates, soluble carbohydrates, starch, nitrogen, potassium, phosphorus, and any combination thereof.
14. The method of claim 1, further comprising a step of applying a computer-implemented non-transitory software on said predetermined spectral data.
15. The method of claim 14, wherein said computer-implemented non-transitory software is selected from a group consisting of PLS toolbox in Matlab environment, R, python and any combination thereof.
16. The method of claim 1, further comprising a step of conducting pre-processing transformations on said predetermined spectral data.
17. The method of claim 16, wherein said pre-processing transformations are selected from the group consisting of generalized least squares weighting, auto-scaling, Savitzky Golay algorithm, second derivatives, and multiplicative signal correction, and any combination thereof.
Description
BRIEF DESCRIPTION OF THE FIGURES
[0008] The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.
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SUMMARY OF THE INVENTION:
[0025] It is one object of the present invention to disclose a method for assessing nitrogen status in a plant comprising steps of: [0026] a. obtaining a sample from different plant tissues parts (roots, branches, and leaves); [0027] b. drying, digesting, and grinding the plant tissues and parts thereof to a powder; [0028] c. capturing predetermined spectral data of the dried, powdered, and digested plant tissues; [0029] d. correlating the spectral data to predetermined materials; and [0030] e. evaluating the plants' nitrogen status according to predetermined multivariate statistical models to predict plant nutritional values.
[0031] It is another object of the present invention to disclose the method as defined above, wherein the plant is a tree selected from the group consisting of Magnoliophyta, Eudicotidae, Liliopsida, Magnolianae, Pinophyte, Ginkgophyte, Cycadophyte, and any combination thereof.
[0032] It is another object of the present invention to disclose the method as defined above, wherein the tree is a fruit tree.
[0033] It is another object of the present invention to disclose the method as defined above, wherein the tree is an almond tree.
[0034] It is another object of the present invention to disclose the method as defined above, wherein the tissues and parts are selected from the group consisting of roots, stems, branches, leaves, fruits, seeds, flowers, inflorescences, and any combination thereof.
[0035] It is another object of the present invention to disclose the method as defined above, further comprising a step of treating the plant with fertilizers.
[0036] It is another object of the present invention to disclose the method as defined above, wherein the fertilizers comprise nitrogen.
[0037] It is another object of the present invention to disclose the method as defined above, wherein the capturing of the predetermined spectral data is carried out using reflectance spectroscopy based on a spectrometer.
[0038] It is another object of the present invention to disclose the method as defined above, wherein the spectrometer captures the predetermined spectral data in the visible, near-infrared, and shortwave infrared spectral regions.
[0039] It is another object of the present invention to disclose the method as defined above, wherein the predetermined spectral data are reflectance signals at the 400-2,500 nm spectral range.
[0040] It is another object of the present invention to disclose the method as defined above, wherein the multivariate statistical models are selected from a group consisting of partial least squares-regression, partial least squares discriminant analysis.
[0041] It is another object of the present invention to disclose the method as defined above, wherein predicting the partial least squares-regression is evaluated by statistical parameters selected from a group consisting of a number of latent variables, root mean square error of calibration and cross-validation, coefficient of determination values of the relation between the predicted and observed samples and any combination thereof.
[0042] It is another object of the present invention to disclose the method as defined above, wherein the predetermined materials are selected from the group consisting of non-structural carbohydrates, soluble carbohydrates, starch, nitrogen, potassium, phosphorus, and any combination thereof.
[0043] It is another object of the present invention to disclose the method as defined above, further comprising a step of applying a computer-implemented non-transitory software on the predetermined spectral data.
[0044] It is another object of the present invention to disclose the method as defined above, wherein the computer-implemented non-transitory software is selected from a group consisting of PLS toolbox in Matlab environment, R, python and any combination thereof.
[0045] It is another object of the present invention to disclose the method as defined above, further comprising a step of conducting pre-processing transformations on the predetermined spectral data.
[0046] It is another object of the present invention to disclose the method as defined above, wherein the pre-processing transformations are selected from the group consisting of generalized least squares weighting, auto-scaling, Savitzky Golay algorithm, second derivatives, multiplicative signal correction, and any combination thereof.
A Detailed Description of Preferred Embodiments
[0047] Reflectance spectroscopy (RS) grants the ability to assess various aspects of plant biochemistry in relatively inexpensive, straightforward, and cost-effective techniques. RS is based on hyperspectral data with a hundred spectral bands, including the spectral regions of the visible (VIS), near-infrared (NIR), and shortwave infrared (SWIR), ranging from 400-2500 nm. RS is an advantageous method and high-throughput technique for the rapid detection of light reflectance that resonates with plants' physiological status. RS techniques allow the analysis of a large number of samples by measuring light at a specific wavelength for identifying different molecular chemical bonds mainly related to nitrogen, carbon, or oxygen to hydrogen (C—H, N—H, and O—H) bonds, which are the major organic components of plant tissues. RS is influenced by the combination of overtones related to minerals and organic companies in the plant tissues that related to their electronic transitions. The molecular mechanisms of electromagnetic radiation in RS involve excisions of non-fundamental vibration, overtones, and combination modes, which affect the prediction ability of non-structural carbohydrates (NSC). So far, RS has been a well-established method for indirect quantifications of nitrogen, phosphorus, and carbon in plant tissues. An additional advantage of RS is the estimation of various parameters, such as nitrogen, cellulose, and lignin, complimentary with biochemical analysis to calibrate their relations. However, presumably, accurate NSC prediction in plant tissues requires a combination of multiple spectral features and much higher spectral resolution, mainly in the SWIR spectral region. The spectral band that is known to be especially sensitive to starch, soluble carbohydrates (SC), and pectin concentrations is located primarily in the SWIR spectral region (e.g., 1450, 1490, 1510-1580, 1780, 1900, 1960, and 2070-2100 nm). The main complexity of applying RS is interpolating such wide range spectral signals and identifying the most relevant spectral wavelengths. Therefore, multivariable statistical methods are required to reduce data dimensionality and associate only the most essential spectral signals to targeted chemical combinations that would improve NSC quantification and to evaluate plant nutritional status. However, spectroscopy-based NSC analysis has been usually limited to several plant species and specific plant tissue, mainly to leaf tissues. Nevertheless, the modern computing capacities should extend the ability to assess plants' nutritional status by advancing precise farming applications. Hence, the present application aims to harness said computing capacities and multivariate statistical approaches to characterize nitrogen nutrition in the VIS-NIR-SWIR spectral region in different plant tissues (such as roots, leaves and branches) and nutritional status (mainly sugars and carbohydrates). The data obtained by the method of the present application is primarily meant to facilitate management of crop irrigation and fertilization.
[0048] As used herein after, the term “about” refers to any value being up to 25% lower or greater the defined measure.
[0049] As used herein after, the capitalized letter “N” refers to nitrogen.
[0050] As used herein after, the capitalized letter “K” refers to potassium.
[0051] As used herein after, the capitalized letter “P” refers to phosphorus.
[0052] As used herein after, the term “non-structural carbohydrates (NSC)” refers mainly to sugars (in the form of monosaccharides, disaccharides, oligosaccharides, or polysaccharides) and starch which fulfil distinct functional roles in plants, including transport, energy metabolism and osmoregulation, and provide substrates for the synthesis of different compounds in the plant.
[0053] As used herein after, the term “total non-structural carbohydrates (TNC)” refers to the sum of total glucose, free fructose and free sucrose in a plant tissue.
[0054] As used herein after, the term “soluble carbohydrates (SC)” refers to carbohydrates which are soluble in water. SC are one of the most fundamental metabolic pool in plants. SC are a universal component of most living organisms and a fundamental building block in biosynthetic processes. The qualitative and quantitative changes in carbohydrates often accompany plant's responses to stress. Carbohydrates in plant can be classified into three general groups: soluble, storage, and structural carbohydrates. SC are soluble in water and can be found in most cellular compartments.
[0055] As used herein after, the term “reflectance spectroscopy (RS)” refers to a spectroscopic technique based on near-infrared reflectance spectroscopy. This technique uses the electromagnetic spectrum region of 350-2500 nm for physiological diagnostics application.
[0056] As used herein after, the term “crop” refers to any type of plant, either a monocot or a dicot plant, an annual, biennial or a perennial plant. The crop can be for instance an agricultural crop, such as tomato or pepper, an ornamental crop or a tree.
[0057] The present application discloses a method for assessing nitrogen status in trees, comprising steps of: (i) fertilizing plants with nitrogen at varying concentrations; (ii) reading nitrogen-treated, dried, and ground plant tissues using reflectance spectroscopy (RS); (iii) linking between the spectral reflectance signals and data to nitrogen nutrition and carbohydrate concentrations of said plant tissues, including the powder form of leaves, branches, and roots; and (iv) parameterizing an RS model, by applying multivariate statistical approaches (partial least square regression and discriminant analysis) to characterize nitrogen nutrition in the VIS-NIR-SWIR spectral region in different plant tissues and nutritional status.
[0058] The present invention relates, in a non-limiting way, to almond trees, which are cultivated by intensive irrigation and fertilization applications. These conditions expose the surrounding habitats to contamination from leakage and runoffs and stipulate the sustainability of almond production on precise nutrients applications. Nonetheless, the present invention can be applied to various types of trees and plants.
EXAMPLE 1
[0059] In order to establish the method of the present invention, 24 almond saplings were planted in 1 cubic meter lysimeters filled with inert soil-less media throughout April 2016 at the Gilat Research Center, Israel. Since April 2017, the trees were irrigated with the necessary microelements, 10 mg of P L.sup.−1, 60 mg of K L.sup.−1, and 0, 10, 30, 60, 100, or 150 mg of N L.sup.−1 (4 trees per treatment). The irrigation amounts were set by potential evapotranspiration (ETp) and maintained a 0.3 leaching to ensure the roots zone's adequate flushing. Further information concerning the experimental setup is available at Sperling et al. (“Excessive Nitrogen Impairs Hydraulics, Limits Photosynthesis, and Alters the Metabolic Composition of Almond Trees”, Plant Physiology and Biochemistry 143: 265-74, 20192019). From April to October 2017, diurnal irrigation (I) and drainage (D) quantities were recorded monthly for each lysimeter. Then, the irrigation N concentration [Ni] and drainage N concentration [Nd] were analyzed using a Gallery 152 Plus Automated Photometric Analyzer (Thermo Fischer Scientific Inc., MA, USA). Finally, daily evapotranspiration (ET) and N uptake (NU) were computed by Eq. 1 and 2).
ET=I−D Equation 1
N.sub.U=[N.sub.I].Math.I−[N.sub.D].Math.D Equation 2
[0060] As depicted in
[0061] Symbols depicted in
EXAMPLE 2
[0062] To investigate the effects of nitrogen concentrations in the irrigation water on almond trees' metabolic profile and nitrogen status, trees were grown and irrigated as described in Example 1. Plant tissues (leaves, branches, and roots) were collected on Sep. 1, 2018, dried, powdered, and digested with sulfuric acid and hydrogen peroxide. Then, the liquidized nitrogen was detected by an automated photometric analyzer (Thermo Scientific Gallery 152 Plus). Roots (25 cm deep and 5 mm in diameter), branches (5 cm of current year's growth), and leaves (fully developed young leaves) were sampled, flash-frozen in liquid nitrogen, lyophilized, and stored at −80° C. The dried samples were later ground to a fine powder using a ball grinder (MiniBeadbeater-96, Glen Mills Inc., NJ) and analyzed for non-structural carbohydrates (NSC) using updated enzymatic and colorimetric method. First, soluble carbohydrates (SC) were extracted by dissolving 25 mg of the tissue in 1 mL of deionized water (DI), shaking for 15 minutes at 72° C., centrifuging for 10 minutes at 17,000 g, and removing 50 μL of the supernatant. Then, starch was digested by incubating the tissue in 500 μL sodium acetate buffer (0.2 M, pH 5.6), 100 μL amylglucosidase (70 units mL.sup.−1, Sigma-Aldrich), and 100 μl amylase (7 units ml.sup.−1, Sigma-Aldrich) for 4 hours at 37° C. Another 50 μL supernatant was extracted, samples were diluted (X21), mixed in a 96 well plate with 150 μL sulfuric acid and anthrone solution (0.1%), incubated at 96° C. for 10 minutes, and cooled to 22° C. Finally, light absorbance at 620 nm was measured using a spectrophotometer (Multiskan, Thermo Fischer Scientific Inc., MA), and glucose equivalent SC and starch concentrations were determined.
[0063]
[0064] As depicted in
[0065] Leaf nitrogen concentration bottomed at 12 mg g.sup.−1 DW in the 0 mg N L.sup.−1 irrigation group, increased to ˜20 mg g.sup.−1 DW in the 10, 30, 60, and 100 mg N L.sup.−1 irrigation treatments, and then finally increased to 25 mg g.sup.−1 DW in the 150 mg N L.sup.−1 irrigation group (as shown in the upper panel of
[0066] Symbols presented in
EXAMPLE 3
[0067] Each tissue sample (as fine powder material) was placed into a 2 mL vial for RS analysis. Spectral data were obtained for each plant tissue sample using spectrometers placed at a 45° angle, with fixed light sources. A spectrometer (Analytical Spectral Device, CO, USA) with a spectral region of VIS-NIR-SWIR (i.e., 400-2500 nm) was used, equipped with a fiber optic contact probe in reflectance mode with fix light. A Field Spec® Pro spectrometer (Analytical Spectral Device, Malvern Panalytical Technologies, Boulder, Colo., USA) that measured the spectral region of VIS-NIR-SWIR (i.e., 350-2500 nm) with 2151 channels (i.e., 350-2500 nm range at a 1 nm resolution) and 25° field of view was used. The spectrometer relied on three separate detectors—a silicon VIS-NIR detector (350-1000 nm) and two indium-gallium-arsenide (InGaAs) photodiode SWIR detectors (1001-1800 and 1801-2500 nm). The spectral acquisition was performed using the instrument's Indico™ Pro Spectral Acquisition software and was post-processed using the View-Spec-Pro software (Malvern Panalytical Technologies, Boulder, Colo., USA). In order to standardize the energy flux reading into a reflectance (ρ) base, a commercial white reference panel (Spectralon Labsphere Inc., North Sutton, N.H., USA) was used throughout the measurements. The spectral data included four spectral readings for each sample that later averaged to a final value representing the spectral sample. Averaging the spectral data was done to reduce spectral noise and overcome micro-topography and shadow effects. The spectrometer signal data was captured using the Indico™ Pro Spectral Acquisition Software (Analytical Spectral Device, CO, USA).
[0068] For developing a predictive model of carbohydrate concentrations, the reflectance values were calibrated against analytical lab-based NSCs (SC and starch) measurements by multivariate statistical regression and classification models. The inventors applied linear partial least square regression and discriminant analysis (PLS-R, and PLS-DA, respectively). PLS-R is an established and well-known statistical model for spectroscopy application that was used to predict NSC (see “PLS-Regression: A Basic Tool of Chemometrics”, Wold, Sjöström, and Eriksson, Chemometrics and Intelligent Laboratory Systems 58: 109-30, 2001). PLS-DA was applied to classify the different plant tissues (leaves, branches, and roots) and the irrigation nutritional treatments to test their effect on minerals and the metabolic composition of SC and starch. PLS-DA is a supervised multivariate classification method for spectral data, aiming to find the variability and direction in multivariate space that determine the known classes in the calibration dataset. This method makes it easier to understand, by graphical means, the spectral differences between categories (i.e., different plant tissues, irrigation nitrogen treatments) and also permits the statistical evaluation of whether the differences between the classes are significant. Before applying the PLS procedure, the dataset was randomly divided into two separate calibration and validation datasets using the Venetian blind cross-validation method, based on a 70 to 30 split ratio, respectively.
[0069] In light of the description above, a PLS-DA analysis was performed to quantify the changes in the spectral signal between the different plant tissues and classify the effect of nitrogen gradient in the supplied irrigation water and on the metabolic and mineral composition of almond trees. The results of the PLS-DA classification of the three plant tissues (branches, leaves and roots) are depicted in
EXAMPLE 4
[0070] The effect of nitrogen gradient in the supplied irrigation water on the metabolic and nitrogen accumulation of almond trees in root and leaf tissues is demonstrated in
[0071] The PLS-DA (generated according to the description in example 3) for nitrogen gradient in the supplied irrigation in leaves (
EXAMPLE 5
[0072] In addition to conducting a PLS-DA, a PLS-R (linear partial least square regression) was utilized to generate a predictive model of carbohydrate concentrations in almond trees. PLS-R is a well-known method, and it establishes a statistical model that is used to predict NSC (see “Near-infrared Spectroscopy (NIRS) Predicts Non-structural Carbohydrate Concentrations in Different Tissue Types of a Broad Range of Tree Species”, Ramirez et al., Methods in Ecology and Evolution 6(9): 1018-25, 2015). PLS-R selects factors to maximize the variation between predictor (spectral data as X-block) and response variables [laboratory carbohydrate concentrations as Y-block; (Paz-Kagan. et al. 2015)] and reduce data dimensionality.
[0073] Pre-processing transformations (PPTs) for classifications were used to decrease the variability within classes and increase the variability between classes, at the same time. PPT for the regression model is used for reducing noise and the variation in the dataset that cannot be managed by the modeling techniques. Several of the most frequently used PPTs in spectroscopy were selected, including auto-scaling, Savitzky Golay algorithm, second derivatives, multiplicative signal correction (MSC), and generalized least squares weighting (GLSW). Each PPT was tested separately and with different combinations. The selection of the PPTs was based on previous studies that had been found to be successful for spectroscopy applications (see “Comparing the Effect of pre-processing Transformations on Methods of Land-Use Classification Derived from Spectral Soil Measurements”, Rozenstein et al., IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 8: 2393-2404, 2015). The most accurate models were found to be the GLSW with and without autoscaling before the GLSW transformation. The prediction of the PLS-R was evaluated using several statistical parameters and included the number of latent variables (LVs), root means square error (RMSE) of calibration and cross-validation (RMSEC and RMSECV, respectively), as well as by the coefficient of determination (R.sup.2) values of the relation between the predicted and observed samples. For the classification accuracy of the PLS-DA model, the total accuracy and the Kappa statistic were calculated. All the data processing was applied by PLS-Toolbox (Eigenvector Research Inc., WA, USA) running under a Matlab environment version 9.3 (The Mathworks Inc., MA, USA).
[0074] The relevant essential wavelengths identified by the PLS-R analysis indicative of soluble carbohydrates and starch content are shown in Table 1. The statistical parameters included R.sup.2, RMSEC, and RMSECV. In order to evaluate the relative importance of each wavelength in the different PLS-R models, the variable importance in projection (VIP) statistic was computed to reveal the wavelength importance scores of each explanatory variable. Since the average of squared VIP scores equals 1, those wavelengths with a VIP score greater than one are identified as important wavelengths.
[0075] When all three plant tissues were used in the PLS-R modeling process, the R.sup.2 were 0.88 and 0.95 for the soluble carbohydrates and starch, respectively. However, omitting the branch tissues from the modeling process (i.e., leaving only the leaf and root plant tissues,
TABLE-US-00001 TABLE 1 Accuracy assessment of the partial least squares - regression (PLS-R) models in terms of the spectral range indicative of soluble carbohydrates and starch. LVs Range Mean SD R.sup.2 RMSEC RMSECV VIP (Spectral bands in nm) Soluble carbohydrates (SC) Branches 3 88.01 63.22 21.07 0.65 13.74 16.79 430, 670 Leaves 4 91.96 83.42 14.39 0.71 7.25 7.91 525, 680, 1450, 1940 Root 3 68.97 48.32 13.03 0.72 7.81 8.16 550, 680, 1000, 1450, 1780, 1940, 2000, 2080, 2330 All plant tissues 4 130.41 66.39 21.94 0.88 9.68 10.76 443 680, 1450, 1770, 1809, 1950, 2050, 2250, 2330, 2375 Leaves & Roots 3 130.41 67.9 23.38 0.87 7.25 11.65 680, 100, 1450, 1800, 1900, 2050 Starch Branches 5 49.25 31.97 11.38 0.82 5.23 8.87 425, 670, 1450, 1800, 1910, 1960, 2100, 2250-2370 Leaves 6 64.01 33.56 13.57 0.85 5.85 7.28 450, 670, 1000, 1450, 1580, 1900, 1960, 2250 Root 5 13 4.37 91.55 26.81 0.90 8.49 9.58 500, 1450, 1960, 2080, 2350 All plant tissues 4 155.156 50.42 32.41 0.95 7.59 11.65 430, 670, 1010, 1450, 1560, 2002 2080 2250, 2360 Leaves & Roots 3 155.156 59.21 32.4 0.93 6.44 9.41 1450, 1560, 1980, 2050, 2200,
[0076] The spectral bands found to be sensitive by the VIP for soluble carbohydrates and starch include the spectral regions of 1400, 1900, and 2070-2300 nm. These spectral regions are mainly related to oxygen and hydrogen chemical band and NSC content. These bands are also associated with the hydroxyl group's first overtone showing the spectral fluctuations from 1400-1600 nm spectral regions. These spectral regions are sensitive to hydrogen bonding, mainly in the starch molecule, which was predicted with higher accuracy than SC. The organic compounds identified in this study are mostly at the SWIR spectral regions (i.e., 2050, 2250 nm), which are also known to be related to the concentration of cellulose, glucose, starch, and lignin in different plant tissues.
EXAMPLE 6
[0077]
EXAMPLE 7
[0078] Reference is now made to
EXAMPLE 8
[0079] Reference is now made to