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Today, remote sensing is widely used to estimate soil properties. Because it is an easy and accessible way to estimate soil properties that are difficult to estimate in the field. Based on this, to evaluate the soil fertility (SF), soil sampling was performed irregularly from the surface depth of 0–30 cm in 216 points, 11 soil properties were measured, and the soil fertility index (SFI) was calculated by soil properties. Simultaneously, we combined satellite images of Landsat 8 and Sentinel-2 using the Gram-Schmidt algorithm. Finally, multiple linear regression SFI was calculated using satellite data, as well as the spatial distribution of SFI was obtained in very low, low, moderate, high, and very high classes. Our findings showed that the combination of Landsat 8 and Sentinel-2 data using the Gram-Schmidt algorithm has a higher correlation with SFI than when these data are individually. Therefore, combined Landsat 8 and Sentinel 2 data were used for SFI modeling. Using model selection procedure indices (including Cp, AIC, and ρc criteria), the visible range bands, notably blue (r = 0.65), green (r = 0.63), and red (r = 0.61), provide the best model for estimating SFI (R2 = 0.43, Cp = 3.34, AIC = -277.4, and ρc = 0.44). Therefore, these bands were used to estimate the SFI index. Also, the spatial distribution of the SIF index showed that the most significant area was related to the low class, and the lowest area belonged to the high and very high fertility classes. According to these results, it can be concluded that using the combination of Landsat 8 and Sentinel 2 bands to estimate soil fertility index in agricultural lands can increase the accuracy of soil fertility estimation. [ABSTRACT FROM AUTHOR]

In order to protect the digital image copyright, it is necessary to design a robust watermarking algorithm. To achieve this purpose, a novel color image watermarking scheme based on an improved QR decomposition is proposed in this paper. The proposed method gives a new algorithm to find elements of Q and R matrices instead of using the Gram–Schmidt algorithm for QR factorization. First, the R matrix is performed by solving a set of linear equations where diagonal elements of R are checked and modified if they are zero or negative. After that, the Q matrix is computed based on the R matrix. In addition, a novel formula is proposed to improve the extracting time where the first element R(1, 1) of the R matrix is found instead of computing QR decomposition as the previous proposals. Experimental results show that the proposed method outperforms other considered methods in this paper in terms of the quality of the watermarked images. Furthermore, the execution time is significantly improved, and the extracted watermark is more robust against almost tested attacks. [ABSTRACT FROM AUTHOR]

Based on Orthogonal Chaotic Vector Shift Keying (OCVSK) system and Multilevel Code-Shifted Differential Chaos Shift Keying (MCS-DCSK) system, a new Multilevel Code-Shifted Differential Chaos Shift Keying (OMCS-DCSK) modulation system is proposed and designed in this paper. New orthogonal chaotic signal sets are generated using Gram-Schmidt algorithm and Walsh code function then these signals are used for bearing information bits to achieve higher data rate and better bandwidth efficiency compared with the conventional DCSK communication system. The bit error rate (BER) analysis of the OMCS-DCSK system over additive white Gaussian noise (AWGN) and multipath Rayleigh fading channel is derived and compared with the simulation results. Also, the spectral and complexity analysis of the system are presented and compared with the conventional DCSK systems. The results show that the proposed system outperforms OCVSK and MCS-DCSK in BER performance and spectral efficiency

Based on Orthogonal Chaotic Vector Shift Keying (OCVSK) system and Multilevel Code-Shifted Differential Chaos Shift Keying (MCS-DCSK) system, a new Multilevel Code-Shifted Differential Chaos Shift Keying (OMCS-DCSK) modulation system is proposed and designed in this paper. New orthogonal chaotic signal sets are generated using Gram-Schmidt algorithm and Walsh code function then these signals are used for bearing information bits to achieve higher data rate and better bandwidth efficiency compared with the conventional DCSK communication system. The bit error rate (BER) analysis of the OMCS-DCSK system over additive white Gaussian noise (AWGN) and multipath Rayleigh fading channel is derived and compared with the simulation results. Also, the spectral and complexity analysis of the system are presented and compared with the conventional DCSK systems. The results show that the proposed system outperforms OCVSK and MCS-DCSK in BER performance and spectral efficiency. [ABSTRACT FROM AUTHOR]

In this paper we consider the variants of Gram-Schmidt such as Classical Gram-Schmidt and Modified Gram-Schmidt algorithms. It is shown that for problems of dimension more than two the round-off error of operation q1Tq2 has more propagation in both of algorithms. To cure this difficulty we will present an algorithm, namely Optimized Modified Gram-Schmidt algorithm. Numerical examples indicate the accuracy of this algorithm. We show that this method can improve the loss of orthogonality of the orthogonalization in some ill-conditioned cases. [ABSTRACT FROM AUTHOR]

This paper proposes a new simple precoding solution based on the Gram-Schmidt orthonormalization to be used at the relay station of a multirelay wireless networks where the different mobile stations belong to the same network, in order to mitigate the multiuser interference at each mobile station. The strength of this method is that it only requires the knowledge of all channel impulse responses from a given relay to all the mobile stations. In other words, to compute its precoding vectors, each relay does not need to know the channel impulse responses of the channels of other relays. Unlike the centralized reference method where each mobile station benefits from the same diversity gain, using this algorithm, some mobile stations will improve their diversity gain at the cost of a loss in the diversity gain of other users. This constitutes a simple solution to supply different qualities of service in the case of a multiservices network. Furthermore, this work proposes an optimized power allocation between the relays. Analytical and accurate performance analyses for the different studied contexts are provided. [ABSTRACT FROM AUTHOR]

The classical Gram-Schmidt algorithm for computing the QR factorization of a matrix X requires at least one pass over the current orthogonalized matrix Q as each column of X is added to the factorization. When Q becomes so large that it must be maintained on a backing store, each pass involves the costly transfer of data from the backing store to main memory. However, if one orthogonalizes the columns of X in blocks of m columns, the number of passes is reduced by a factor of 1/m. Moreover, matrix-vector products are converted into matrix-matrix products, allowing level-3 BLAS cache performance. In this paper we derive such a block algorithm and give some experimental results that suggest it can be quite effective for large scale problems, even when the matrix X is rank degenerate. [ABSTRACT FROM AUTHOR]

Considering trajectory curves, integral of n-dimensional dynamical systems, within the framework of Differential Geometry as curves in Euclidean n-space, it will be established in this article that the curvature of the flow, i.e. the curvature of the trajectory curves of any n-dimensional dynamical system directly provides its slow manifold analytical equation the invariance of which will be then proved according to Darboux theory. Thus, it will be stated that the flow curvature method, which uses neither eigenvectors nor asymptotic expansions but only involves time derivatives of the velocity vector field, constitutes a general method simplifying and improving the slow invariant manifold analytical equation determination of high-dimensional dynamical systems. Moreover, it will be shown that this method generalizes the Tangent Linear System Approximation and encompasses the so-called Geometric Singular Perturbation Theory. Then, slow invariant manifolds analytical equation of paradigmatic Chua's piecewise linear and cubic models of dimensions three, four and five will be provided as tutorial examples exemplifying this method as well as those of high-dimensional dynamical systems. [ABSTRACT FROM AUTHOR]

An alternative spectral instead of traditional statistical approach of molecular structure-biological activity relationship is proposed. It directly provides the functional relationship among all predictor variables taken in consideration respecting the activity effects under study. [ABSTRACT FROM AUTHOR]

In many applications-latent semantic indexing, for example it is required to obtain a reduced rank approximation to a sparse matrix A. Unfortunately, the approximations based on traditional decompositions, like the singular value and QR decompositions, are not in general sparse. Stewart [(1999), 313-323] has shown how to use a variant of the classical Gram-Schmidt algorithm, called the quasi-Gram-Schmidt-algorithm, to obtain two kinds of low-rank approximations. The first, the SPQR, approximation, is a pivoted, Q-less QR approximation of the form (XR11-1)(R11 R12), where X consists of columns of A. The second, the SOB approximation, is of the form the form A ... XTYT, where X and Y consist of columns and rows A and T, is small. In this article we treat the computational details of these algorithms and describe a MATLAB implementation. [ABSTRACT FROM AUTHOR]

The ABS class for linear and nonlinear systems has been recently introduced by Abaffy, Broyden, Galantai and Spedicato. Here we consider various ways of applying these algorithms to the determination of the minimal euclidean norm solution of over-determined linear systems in the least squares sense. Extensive numerical experiments show that the proposed algorithms are efficient and that one of them usually gives better accuracy than standard implementations of the QR orthogonalization algorithm with Householder reflections. [ABSTRACT FROM AUTHOR]

Objective . In this study, a hybrid method combining hardware and software architecture is proposed to remove stimulation artefacts (SAs) and extract the volitional surface electromyography (sEMG) in real time during functional electrical stimulations (FES) with time-variant parameters. Approach . First, an sEMG detection front-end (DFE) combining fast recovery, detector and stimulator isolation and blanking is developed and is capable of preventing DFE saturation with a blanking time of 7.6 ms. The fragment between the present stimulus and previous stimulus is set as an SA fragment. Second, an SA database is established to provide six high-similarity templates with the current SA fragment. The SA fragment will be de-artefacted by a 6th-order Gram-Schmidt (GS) algorithm, a template-subtracting method, using the provided templates, and this database-based GS algorithm is called DBGS. The provided templates are previously collected SA fragments with the same or a similar evoking FES intensity to that of the current SA fragment, and the lengths of the templates are longer than that of the current SA fragment. After denoising, the sEMG will be extracted, and the current SA fragment will be added to the SA database. The prototype system based on DBGS was tested on eight able-bodied volunteers and three individuals with stroke to verify its capacity for stimulation removal and sEMG extraction. Results. The average stimulus artefact attenuation factor, SA index and correlation coefficient between clean sEMG and extracted sEMG for 6th-order DBGS were 12.77 ± 0.85 dB, 1.82 ± 0.37 dB and 0.84 ± 0.33 dB, respectively, which were significantly higher than those for empirical mode decomposition combined with notch filters, pulse-triggered GS algorithm, 1st-order and 3rd-order DBGS. The sEMG-torque correlation coefficients were 0.78 ± 0.05 and 0.48 ± 0.11 for able-bodied volunteers and individuals with stroke, respectively. Significance. The proposed hybrid method can extract sEMG during dynamic FES in real time., (© 2021 IOP Publishing Ltd.)