Estimation of nitrate nitrogen content in cotton petioles under drip irrigation based on wavelet neural network approach using spectral indices

Background Estimation of nitrate nitrogen (NO3−–N) content in petioles is one of the key approaches for monitoring nitrogen (N) nutrition in crops. Rapid, non-destructive, and accurate evaluation of NO3−–N contents in cotton petioles under drip irrigation is of great significance. Methods In this study, we discussed the use of hyperspectral data to estimate NO3−–N contents in cotton petioles under drip irrigation at different N treatments and growth stages. The correlations among trilateral parameters and six vegetation indices and petiole NO3−–N contents were first investigated, after which a traditional regression model for petioles NO3−–N content was established. A wavelet neural network (WNN) model for estimating petiole NO3−–N content was also established. In addition, the performance of WNN was compared to those of random forest (RF), radial basis function neural network (RBF) and back propagation neural network (BP). Results Between the blue edge amplitude (Db) and blue edge area (SDb) of the blue edge parameters was the optimal index for the estimation model of petiole NO3−–N content. We found that the prediction results of the blue edge parameters and WNN were 7.3% higher than the coefficient of determination (R2) of the first derivative vegetation index and WNN. Root mean square error (RMSE) and mean absolute error (MAE) were 25.2% and 30.9% lower than first derivative vegetation, respectively, and the performance was better than that of RF, RBF and BP. Conclusions An inexpensive approach consisting of the WNN algorithm and blue edge parameters can be used to enhance the accuracy of NO3−–N content estimation in cotton petioles under drip irrigation.

Estimation of nitrate nitrogen content in cotton petioles under drip irrigation based on spectral indices and wavelet neural network

Background: Estimating nitrate nitrogen (NO3--N) content in petioles is one of the key approaches for monitoring nitrogen (N) nutrition in crops. Rapid, non-destructive, and accurate monitoring of great NO3--N content in cotton petioles under drip irrigation is of great significance.Methods: NO3--N content in cotton petioles under drip irrigation and the corresponding canopy spectral reflectance of cotton plants grown in experimental plots under various N application levels were analyzed. The correlations among ‘trilateral parameters’ and six vegetation indices, and NO3--N content in petioles were determined. A traditional regression model of NO3--N content in cotton petioles under drip irrigation was established, and a wavelet neural network (WNN) model with different index numbers was developed. The WNN model was verified using independent data, and compared with the random forest algorithm , radial basis function neural network and back propagation neural network.Results: Based on the analyses of ‘trilateral parameters’ and petiole NO3--N content, blue edge amplitude (Db) and blue edge area (SDb) of the blue edge parameters exhibited a strong positive correlation with petiole NO3--N content, and the correlation coefficients was 0.90. Among the blue edge parameters, the coefficient of determination (R2) of the Db polynomial regression equation and petiole NO3--N content was the highest (R2 = 0.89), while the root mean square error (RMSE) of the linear regression model was the lowest (RMSE = 1.04). R2 value of the traditional regression model developed using blue edge parameters and petiole NO3--N content significantly increased, while RMSE value decreased when compared with those of the red edge and yellow edge parameters. Analyses results of the vegetation index developed using original spectral reflectance data and the vegetation index developed using the first set of derivative spectral reflectance data and petiole NO3--N content, revealed that the first derivative vegetation index, normalized difference spectral index (ND705) exhibited a strong negative correlation, with a correlation coefficient of -0.90. The first derivative vegetation index, ND705 and petiole NO3--N content index regression equation had the highest coefficient of determination (R2 = 0.83), while the first derivative vegetation index, red edge model index (CIred-edge) and petiole NO3--N content linear regression equation had the lowest RMSE = 0.92. R2 value of the traditional regression equation for the first derivative vegetation index and petiole NO3--N content significantly increased, while the RMSE value decreased when compared with the original spectral vegetation index. After conducting correlation analyses and developing traditional regression models, Db and SDb of the blue edge parameters, and the first derivative vegetation index, ND705 and CIred-edge were used to develop a WNN model. The model based on blue edge parameters had R2 of 0.88, RMSE of 0.74g/L and mean absolute error (MAE) of 0.58 g/L, the R2 value was 8.6% higher than the R2 the first derivative vegetation index model, in which RMSE and MAE reduced by 18.7% and 20.5%, respectively. The model was tested using independent verification data, and which revealed that the R2 value of the model was 0.88, RMSE was 0.65g/L, and MAE was 0.47g/L based on the blue edge parameters, predicted value of WNN, and true value of the verification model, which was superior other models. The performance of the WNN model based on the blue edge parameters improved by 7.3%, and RMSE and MAE reduced by 25.2% and 30.9%, respectively when compared with those of the vegetation index model.Conclusion: The present study demonstrated that an inexpensive approach consisting of WNN algorithm and spectrum can be used to enhance the accuracy of NO3--N content estimation in cotton petioles under drip irrigation, which reflects their practical application potential.

The Size of the Giant Joint Component in a Binomial Random Double Graph

We study the joint components in a random 'double graph' that is obtained by superposing red and blue binomial random graphs on $n$~vertices. A joint component is a maximal set of vertices that supports both a red and a blue spanning tree. We show that there are critical pairs of red and blue edge densities at which a giant joint component appears. In contrast to the standard binomial graph model, the phase transition is first order: the size of the largest joint component jumps from $O(1)$ vertices to $\Theta(n)$ at the critical point. We connect this phenomenon to the properties of a certain bicoloured branching process.

Identification of Rice Sheath Blight through Spectral Responses Using Hyperspectral Images

Sheath blight (ShB), caused by Rhizoctonia solani AG1-I, is one of the most important diseases in rice worldwide. The symptoms of ShB primarily develop on leaf sheaths and leaf blades. Hyperspectral remote sensing technology has the potential of rapid, efficient and accurate detection and monitoring of the occurrence and development of rice ShB and other crop diseases. This study evaluated the spectral responses of leaf blade fractions with different development stages of ShB symptoms to construct the spectral feature library of rice ShB based on “three-edge” parameters and narrow-band vegetation indices to identify the disease on the leaves. The spectral curves of leaf blade lesions have significant changes in the blue edge, green peak, yellow edge, red valley, red edge and near-infrared regions. The variables of the normalized index between green peak amplitude and red valley amplitude (Rg − Ro)/(Rg + Ro), the normalized index between the yellow edge area and blue edge area (SDy − SDb)/(SDy + SDb), the ratio index of green peak amplitude and red valley amplitude (Rg/Ro) and the nitrogen reflectance index (NRI) had high relevance to the disease. At the leaf scale, the importance weights of all attributes decreased with the effect of non-infected areas in a leaf by the ReliefF algorithm, with Rg/Ro being the indicator having the highest importance weight. Estimation rate of 95.5% was achieved in the decision tree classifier with the parameter of Rg/Ro. In addition, it was found that the variety degree of absorptive valley, reflection peak and reflecting steep slope was different in the blue edge, green and red edge regions, although there were similar spectral curve shapes between leaf sheath lesions and leaf blade lesions. The significant difference characteristic was the ratio index of the red edge area and green peak area (SDr/SDg) between them. These results can provide the basis for the development of a specific sensor or sensors system for detecting the ShB disease in rice.

Response of plant reflectance spectrum to simulated dust deposition and its estimation model

To quantitatively reflect the relationship between dust and plant spectral reflectance. Dust from different sources in the city were selected to simulate the spectral characteristics of leaf dust. Taking Euonymus japonicus as the research object. Prediction model of leaf dust deposition was established based on spectral parameters. Results showed that among the three different dust pollutants, the reflection spectrum has 6 main reflection peaks and 7 main absorption valleys in 350–2500 nm. A steep reflection platform appears in the 692–763 nm band. In 760–1400 nm, the spectral reflectance gradually decreases with the increase of leaf dust coverage, and the variation range was coal dust > cement dust > pure soil dust. The spectral reflectance in 680–740 nm gradually decreases with the increase of leaf dust coverage. In the near infrared band, the fluctuation amplitude and slope of its first derivative spectrum gradually decrease with the increase of leaf dust. The biggest amplitude of variation was cement dust. With the increase of dust retention, the red edge position generally moves towards short wave direction, and the red edge slope generally decreases. The blue edge position moved to the short wave direction first and then to the long side direction, while the blue edge slope generally shows a decreasing trend. The yellow edge position moved to the long wave direction first and then to the short wave direction (coal dust, cement dust), and generally moved to the long side direction (pure soil dust). The yellow edge slope increases first and then decreases. The R2 values of the determination coefficients of the dust deposition prediction model have reached significant levels, which indicated that there was a relatively stable correlation between the spectral reflectance and dust deposition. The best prediction model of leaf dust deposition was leaf water content index model (y = 1.5019x − 1.4791, R2 = 0.7091, RMSE = 0.9725).

The Ramsey Number of Fano Plane Versus Tight Path

The hypergraph Ramsey number of two $3$-uniform hypergraphs $G$ and $H$, denoted by $R(G,H)$, is the least integer~$N$ such that every red-blue edge-coloring of the complete $3$-uniform hypergraph on $N$ vertices contains a red copy of $G$ or a blue copy of $H$. The Fano plane $\mathbb{F}$ is the unique 3-uniform hypergraph with seven edges on seven vertices in which every pair of vertices is contained in a unique edge. There is a simple construction showing that $R(H,\mathbb{F}) \ge 2(v(H)-1) + 1.$ Hypergraphs $H$ for which the equality holds are called $\mathbb{F}$-good. Conlon asked to determine all $H$ that are $\mathbb{F}$-good.In this short paper we make progress on this problem and prove that the tight path of length $n$ is $\mathbb{F}$-good.

Cycle-Complete Ramsey Numbers

The Ramsey number $r(C_{\ell },K_n)$ is the smallest natural number $N$ such that every red/blue edge colouring of a clique of order $N$ contains a red cycle of length $\ell $ or a blue clique of order $n$. In 1978, Erd̋s, Faudree, Rousseau, and Schelp conjectured that $r(C_{\ell },K_n) = (\ell -1)(n-1)+1$ for $\ell \geq n\geq 3$ provided $(\ell ,n) \neq (3,3)$. We prove that, for some absolute constant $C\ge 1$, we have $r(C_{\ell },K_n) = (\ell -1)(n-1)+1$ provided $\ell \geq C\frac{\log n}{\log \log n}$. Up to the value of $C$ this is tight since we also show that, for any $\varepsilon>0$ and $n> n_0(\varepsilon )$, we have $r(C_{\ell }, K_n) \gg (\ell -1)(n-1)+1$ for all $3 \leq \ell \leq (1-\varepsilon )\frac{\log n}{\log \log n}$. This proves the conjecture of Erd̋s, Faudree, Rousseau, and Schelp for large $\ell $, a stronger form of the conjecture due to Nikiforov, and answers (up to multiplicative constants) two further questions of Erd̋s, Faudree, Rousseau, and Schelp.