Nitrogen Content Estimation of Apple Leaves Using Hyperspectral Analysis

Leaf nitrogen content (LNC) is an important factor reflecting the growth quality of plants. We estimated the nitrogen content of apple leaves using hyperspectral wavelength analysis using the differential spectrum, differential spectrum transformation, and vegetation spectrum index with different derivative gaps. We then used the characteristic wavelengths extracted via the correlation coefficient method as the input vectors to the gradient boosting decision tree (GBDT) model for analysis and performed cross-validation to optimize the inversion model parameters. We analyzed the results with different input variables and loss functions and compared the GBDT model with other mainstream algorithm models. The results show that the R2 value of the optimized GBDT inversion model is higher than that obtained using the random forest (RF) and support vector regression (SVR) models. Thus, the GBDT model is accurate, and the characteristic wavelength analysis is helpful for the tasks of real-time monitoring and detection of apple tree health.

Deciding EA-equivalence via invariants

We define a family of efficiently computable invariants for (n,m)-functions under EA-equivalence, and observe that, unlike the known invariants such as the differential spectrum, algebraic degree, and extended Walsh spectrum, in the case of quadratic APN functions over $\mathbb {F}_{2^n}$ F 2 n with n even, these invariants take on many different values for functions belonging to distinct equivalence classes. We show how the values of these invariants can be used constructively to implement a test for EA-equivalence of functions from $\mathbb {F}_{2}^{n}$ F 2 n to $\mathbb {F}_{2}^{m}$ F 2 m ; to the best of our knowledge, this is the first algorithm for deciding EA-equivalence without resorting to testing the equivalence of associated linear codes.

Differential spectra of a class of power permutations with Niho exponents

<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M1">\begin{document}$ m\geq3 $\end{document}</tex-math></inline-formula> be a positive integer and <inline-formula><tex-math id="M2">\begin{document}$ n = 2m $\end{document}</tex-math></inline-formula>. Let <inline-formula><tex-math id="M3">\begin{document}$ f(x) = x^{2^m+3} $\end{document}</tex-math></inline-formula> be a power permutation over <inline-formula><tex-math id="M4">\begin{document}$ {\mathrm {GF}}(2^n) $\end{document}</tex-math></inline-formula>, which is a monomial with a Niho exponent. In this paper, the differential spectrum of <inline-formula><tex-math id="M5">\begin{document}$ f $\end{document}</tex-math></inline-formula> is investigated. It is shown that the differential spectrum of <inline-formula><tex-math id="M6">\begin{document}$ f $\end{document}</tex-math></inline-formula> is <inline-formula><tex-math id="M7">\begin{document}$ \mathbb S = \{\omega_0 = 2^{2m-1}+2^{2m-3}-1,\omega_2 = 2^{2m-2}+2^{m-1}, \omega_4 = 2^{2m-3}-2^{m-1},\omega_{2^m} = 1\} $\end{document}</tex-math></inline-formula> when <inline-formula><tex-math id="M8">\begin{document}$ m $\end{document}</tex-math></inline-formula> is even, and <inline-formula><tex-math id="M9">\begin{document}$ \mathbb S = \{\omega_0 = \frac{7\cdot2^{2m-2}+2^m}3, \omega_2 = 3\cdot2^{2m-3}-2^{m-2}-1, \omega_6 = \frac{2^{2m-3}-2^{m-2}}3, \omega_{2^m+2} = 1\} $\end{document}</tex-math></inline-formula> when <inline-formula><tex-math id="M10">\begin{document}$ m $\end{document}</tex-math></inline-formula> is odd.</p>