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ABSTRACT The need to use rotations occurs very often in different domains. We present a basic extensive treatment of rotations in 3D. The results are presented and derived in a coordinate‐free setting, where no frames are required and no components of any matrix are manipulated. We start with the direct problem of establishing the finite rotation formula. Then we consider the composition and the vector decomposition of finite rotations. We conclude the paper by considering the inverse problem namely finding the axis of rotation and the angle of rotation from its effect on vectors.

This paper introduces a novel encryption framework for stereo image. Firstly, both views of a stereo image are decomposed into four plates, which are constituted into a full quaternion matrix. Followed by block-wise quaternion gyrator transform, then different parts of the interim results are shared by orthogonal matrix and spliced together. According to the conjugate symmetry of two-dimensional discrete Fourier spectrum, a real-valued ciphertext can be obtained by superposing real and imaginary parts of the half spectrum. Among them, two-dimensional logistic-Sine-coupling map is employed for generating phase masks, rotation angles and shared coefficients, which greatly enhances the security of the cryptosystem. Numerical simulation results demonstrate the feasibility and reliability of the proposed encryption scheme. [ABSTRACT FROM AUTHOR]

We proposed vector diffraction equations based on 3D Huygens-Fresnel principle and vector decomposition in Cartesian coordinate. Our expression should more accurate than classical Richards-Wolf diffraction, because the deduction of Richards-Wolf diffraction used a number of approximation, while our expression is based on two fundamental physical principles: vector decomposition and Huygens-Fresnel principle. Our expressions mathematical strictly satisfy conservation of energy, while Richards-Wolf’s method is based on the geometrical law of conservation of energy and RCWA(Rigorous Coupled Wave Analysis) is also an approximation. The simulated results of our vector diffraction equations with different NA (numerical aperture) are almost the same as Richards-Wolf diffraction results. Traditional Richards-Wolf vector diffraction equations, which are based on angular spectrum of plane wave, have no clear geometrical meaning, while our vector diffraction equations here have clear geometrical meaning. Our approach of vector diffraction to scalar diffraction is much simpler than Richards-Wolf’s approach. The generation of x/y/z components and their properties in the image plane can be investigated clearly by vector decomposition and synthesis. Their intensity ratios can be explained using paraxial approximation very well. The integral region of exit pupil could be reduced because of the symmetric property of the light vector decomposition and synthesis, thus our expressions have advantages on numerical simulation. Our analysis also indicate that light must ‘polarize’ in other extra dimensions and photon spin is a ‘polarize/resonate’ state in extra dimensions. Also, there is a potential convenient ability to study vector optical transfer function (OTF) analytically in Cartesian coordinate.

Purpose: The normalized filtered-x least mean square (NFxLMS) algorithm adopts a normalized step size to improve the convergence and reduce the gradient noise caused by the high-power input signal. However, this normalization would introduce an even larger misadjustment than the FxLMS algorithm when this high-power noise is in a low-frequency range. To improve the performance of the NFxLMS algorithm in such an environment, a novel vector-decomposition-based structure (VDBS) is proposed in the paper. Methods: In this study, the filter weight vector is decomposed into two sub-vectors that are updated by different algorithms. The first sub-vector is updated by the NFxLMS algorithm, whereas the second one is updated by the FxLMS algorithm. In this way, the total misadjustment can be minimized by setting relevant parameters appropriately, while a faster convergence rate and smaller round-off errors can also be reached. Results: The stability analysis proves that the proposed structure can enlarge the convergence range of the step size in the first sub-vector. The results of simulations and experiments justify that the VDBS can improve the performance of the NFxLMS algorithm for high-power low-frequency noise. Conclusion: The proposed structure can make the traditional NFxLMS algorithm perform better in a high-power low-frequency noise environment. [ABSTRACT FROM AUTHOR]

Arbitrarily oriented object detection is one of the most-popular research fields in remote sensing image processing. In this paper, we propose an approach to predict object angles indirectly, thereby avoiding issues related to angular periodicity and boundary discontinuity. Our method involves representing the long edge and angle of an object as a vector, which we then decompose into horizontal and vertical components. By predicting the two components of the vector, we can obtain the angle information of the object indirectly. To facilitate the transformation between angle-based representation and the proposed vector-decomposition-based representation, we introduced two novel techniques: angle-to-vector encode (ATVEncode) and vector-to-angle decode (VTADecode). These techniques not only improve the efficiency of data processing, but also accelerate the training process. Furthermore, we propose an adaptive coarse-to-fine positive–negative-sample-selection (AdaCFPS) method based on the vector-decomposition-based representation of the object. This method utilizes the Kullback–Leibler divergence loss as a matching degree to dynamically select the most-suitable positive samples. Finally, we modified the YOLOX model to transform it into an arbitrarily oriented object detector that aligns with our proposed vector-decomposition-based representation and positive–negative-sample-selection method. We refer to this redesigned model as the vector-decomposition-based object detector (VODet). In our experiments on the HRSC2016, DIOR-R, and DOTA datasets, VODet demonstrated notable advantages, including fewer parameters, faster processing speed, and higher precision. These results highlighted the significant potential of VODet in the context of arbitrarily oriented object detection. [ABSTRACT FROM AUTHOR]

Vector decomposition of P- and S-wave modes from elastic seismic wavefields is a key step in elastic reverse-time migration (ERTM) to effectively improve the multi-wave imaging accuracy. Most previously developed methods based on the apparent velocities or the polarization characteristics of different wave modes are unable to accurately achieve the vector decomposition of P- and S-wave modes. To effectively overcome the shortcomings of conventional methods, we develop a vector decomposition method of P- and S-wave modes using self-attention deep convolutional generative adversarial networks (SADCGANs) to effectively separate the horizontal and vertical components of P- and S-wave modes from elastic seismic wavefields and accurately preserve their amplitude and phase characteristics for isotropic elastic media. For an elastic model, we use many time slices for a given source position to train the neural network, and use other time slices not in this training dataset to test the neural network. Numerical examples of different models demonstrate the effectiveness and feasibility of our developed method and indicate that it provides an effective intelligent data-driven vector decomposition method of P- and S-wave modes. [ABSTRACT FROM AUTHOR]

Vector decomposition of P- and S-wave modes from elastic seismic wavefields is a key step in elastic reverse-time migration (ERTM) to effectively improve the multi-wave imaging accuracy. Most previously developed methods based on the apparent velocities or the polarization characteristics of different wave modes are unable to accurately achieve the vector decomposition of P- and S-wave modes. To effectively overcome the shortcomings of conventional methods, we develop a vector decomposition method of P- and S-wave modes using self-attention deep convolutional generative adversarial networks (SADCGANs) to effectively separate the horizontal and vertical components of P- and S-wave modes from elastic seismic wavefields and accurately preserve their amplitude and phase characteristics for isotropic elastic media. For an elastic model, we use many time slices for a given source position to train the neural network, and use other time slices not in this training dataset to test the neural network. Numerical examples of different models demonstrate the effectiveness and feasibility of our developed method and indicate that it provides an effective intelligent data-driven vector decomposition method of P- and S-wave modes.

This paper proposes a novel modulation algorithm based on vector decomposition and model predictive control for 5-level active neutral-point-clamped (5 L-ANPC) inverter. Firstly, the control of 5-level inverter is transformed into that of 3-level inverter by vector decomposition, which reduces the control complexity. Secondly, based on the framework of 3-level inverter, the optimal zero sequence voltage and switch state sequence are selected by multi-objective optimisation of model predictive control to balance the neutral point voltage and floating capacitors voltages simultaneously. Finally, according to the optimal choice, single-carrier comparison is used to generate the drive signal, which does not require traditional dual-carrier or vector synthesis, and is relatively easy to implement. Experimental results verify the validity of the method. [ABSTRACT FROM AUTHOR]

This paper presents two novel neural network models for radio-frequency (RF) power amplifiers (PAs): vector decomposed time-delay neural network (VDTDNN) model and augmented vector decomposed time-delay neural network (AVDTDNN) model. In contrast to conventional neural network-based models, VDTDNN and AVDTDNN comply with the physical characteristics of RF PAs by employing carefully designed network structures. In particular, the nonlinear operations are conducted only on the magnitude of the input signals, while the phase information is recovered with the linear weighting. Linear terms with shortcut connection, as well as high-order terms, can be used to further boost the modeling performance. The complexity analysis shows that the proposed models have significantly lower complexity than the existing neural network models. A wideband GaN RF PA excited by the 40- and 60-MHz OFDM signals were employed to evaluate the performance. The extensive experimental results reveal that the proposed VDTDNN and AVDTDNN models can achieve better linearization performance with lower computational complexity compared with the existing neural network-based models.

The stock market of any country indicates the health of a country. It also indicates the confidence of the population of the country in its economy. India, being an emerging country, has exhibited a substantial rate of growth over past years. One of the parameters that determine the growth rate and health of the economy of a nation is its stock market. The aim of this research is to find the volatility in the global oil price, its impact on various sectoral indices listed on the Indian Stock Exchange. BSE SENSEX and other sectoral Indices listed on the Bombay Stock Exchange (BSE) such as BSE Realty, BSE Power, BSE Oil and Gas, BSE Metal, BSE Consumer Durables, BSE Capital Goods, BSE BANKEX, BSE AUTO, BSE Utilities, BSE telecom, BSE Information Technology, BSE Industrials, BSE Finance, BSE Fast Moving Consumer Goods, BSE Energy, BSE Basic Materials are considered to determine the impact of fluctuation of oil price in the stocks of various sectors. The index BSE SENSEX has been considered to determine the performance of the Indian Equity market with respect to the oil price fluctuations. Log normal of the daily closing prices of each of the stock indices and the oil prices have been considered to carry out the research. Techniques such as unit root test, Jarque beta test, correlation test, Granger Causality test, Impulse response and Vector decomposition test have been applied on the closing prices of indices between 1st April, 2010 to 31st December 2017 (1st Financial quarter of the year 2010, in India to the 3rd Financial quarter of the year 2017). The tests show that the average stock returns for the sectors Auto, Bankex, Basic Materials, Capital Goods, Energy, Finance, FMCG, IT, Oil and Gas, Sensex, Industrials is positive whereas for others sectors, average return is negative. Although oil is one of the largest consumers of oil in the world, its stock market returns does not depend on the fluctuation in the oil prices.

The cascaded H-bridge multilevel converter (CHMC) is a promising topology for medium- and high-voltage applications, as it features modularity and scalability. In this letter, a simplified space vector modulation (SVM)-based reconfiguration strategy is proposed to enable fault-tolerant operation of a CHMC. Assuming that the faulty power cells are bypassed, the proposed strategy decomposes the asymmetric CHMC into two parts, i.e., healthy part with healthy modules and unhealthy part with faulty modules. Consequently, the basic reference vector (BRV) and the remainder reference vector (RRV) are generated from the reference vector (RV) to achieve balanced line-to-line voltages and currents with optimized harmonic performance. The proposed strategy can be easily implemented online. Performance and effectiveness of the proposed strategy is verified by experimental results. [ABSTRACT FROM AUTHOR]

Pseudo inverse matrix research, as well as related issue of their application, is in focus of scientific literature recently. Moreover, the field of applications of pseudo inverse matrices is expanding and obtained theoretical results are successfully used to solve practical problems. Interest in the pseudo inverse matric problem is large due to their various applications: in control theory, identification problems, approximation theory, statistical problems, theory of recurrent filtration and others. We investigate a linear operator equation, where the operator is a linear combination of matrices. We obtain solution using the pseudo inverse operation and small parameter method. [ABSTRACT FROM AUTHOR]

We propose a new multiple image encryption scheme based on a pixel exchange operation and a basic vector decomposition in Fourier domain. In this algorithm, original images are imported via a pixel exchange operator, from which scrambled images and pixel position matrices are obtained. Scrambled images encrypted into phase information are imported using the proposed algorithm and phase keys are obtained from the difference between scrambled images and synthesized vectors in a charge-coupled device (CCD) plane. The final synthesized vector is used as an input in a random phase encoding (DRPE) scheme. In the proposed encryption scheme, pixel position matrices and phase keys serve as additional private keys to enhance the security of the cryptosystem which is based on a 4- f system. Numerical simulations are presented to demonstrate the feasibility and robustness of the proposed encryption scheme. [ABSTRACT FROM AUTHOR]

Facing the increasingly serious network safety, the security of information encryption cannot be delayed to be improved. To enhance the security of image encryption, vector transformation was used to separate an original image into two matrices based on the idea of asymmetric editing and Gyrator transformation; one was served as a decryption key, and the other as a continued Gyrator transformation. Then an asymmetric encryption structure was formed. A simulation test was performed to test the performance of the encryption algorithm and a correlation coefficient was introduced to determine the similarity of the decrypted image and the original one. The obtained simulation results suggest that the proposed encryption algorithm was able to encrypt Camera MAN images and recover the encrypted ones. The encrypted images could not be recovered in the absence of any decryption key. The proposed decryption key was so sensitive that even a small disturbance could make many useful image information loss in the image decryption and can resist a chosen-plaintext attack. In conclusion, the asymmetric cryptographic algorithm based on vector decomposition and improved Gyrator transformation is reliable. The work offers a reference and assistance to the information encryption of optical images on the network. [ABSTRACT FROM AUTHOR]

A radial basis function method based on matrix-valued kernels is presented and analysed for computing two types of vector decompositions on bounded domains: one where the normal component of the divergence-free part of the field is specified on the boundary, and the other where the tangential component of the curl-free part of the field is specified. These two decompositions can then be combined to obtain a full Helmholtz-Hodge decomposition of the field, i.e., the sum of divergence-free, curl-free and harmonic fields. All decompositions are computed from samples of the field at (possibly scattered) nodes over the domain, and all boundary conditions are imposed on the vector fields, not their potentials, distinguishing this technique from many current methods. Sobolev-type error estimates for the various decompositions are provided and demonstrated with numerical examples. [ABSTRACT FROM AUTHOR]

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In the image quality assessment (IQA) research field, the structural similarity index measurement (SSIM) method and human visual system (HVS) model have received much attention. However, this paper shows that the definition of the luminance comparison function in SSIM conflicts with the Weber–Fechner law in HVS. To reconcile this contradiction, we propose a space similarity decomposition model based on the Weber–Fechner law and SSIM’s structure parameter to decompose the image into mean value, similarity, and vertical components. Experimental results show that the vertical component is the main factor of subjective perception and should be used by itself to assess image quality. This method not only can be used to independently assess image quality, it can also be combined with other IQA methods as a preprocessing step. [ABSTRACT FROM AUTHOR]

The perception of motion not only depends on the detection of motion signals but also on choosing and applying reference-frames according to which motion is interpreted. Here we propose a neural model that implements the common-fate principle for reference-frame selection. The model starts with a retinotopic layer of directionally-tuned motion detectors. The Gestalt common-fate principle is applied to the activities of these detectors to implement in two neural populations the direction and the magnitude (speed) of the reference-frame. The output activities of retinotopic motion-detectors are decomposed using the direction of the reference-frame. The direction and magnitude of the reference-frame are then applied to these decomposed motion-vectors to generate activities that reflect relative-motion perception, i.e., the perception of motion with respect to the prevailing reference-frame. We simulated this model for classical relative motion stimuli, viz., the three-dot, rotating-wheel, and point-walker (biological motion) paradigms and found the model performance to be close to theoretical vector decomposition values. In the three-dot paradigm, the model made the prediction of perceived curved-trajectories for the target dot when its horizontal velocity was slower or faster than the flanking dots. We tested this prediction in two psychophysical experiments and found a good qualitative and quantitative agreement between the model and the data. Our results show that a simple neural network using solely motion information can account for the perception of group and relative motion. [ABSTRACT FROM AUTHOR]

Common-reflection-point (CRP) gather is a bridge that connects seismic data and petrophysical parameters. Pre-stack attributes extraction and pre-stack inversion, both of them are important means of reservoir prediction. Quality of CRP gather usually has great impact on the accuracy of seismic exploration. Therefore, pre-stack CRP gathers noise suppression technology becomes a major research direction. Based on the vector decomposition principle, here we propose a method to suppress noise. This method estimates optimal unit vectors by searching in various directions and then suppresses noise through vector angle smoothing and restriction. Model tests indicate that the proposed method can separate effective signal from noise very well and suppress random noise effectively in single wavenumber case. Application of our method to real data shows that the method can recover effective signal with good amplitude preserved from pre-stack noisy seismic data even in the case of low signal to noise ratio (SNR). [ABSTRACT FROM AUTHOR]

In this paper, an Integral Equationbased Simplification Method (IE-SM) is presented for the efficient analysis of the symmetrical electromagnetic model. The proposed approach stems from the decomposition and recomposition of any arbitrary excitation sources into a set of independent vectors which induce a symmetrical current distribution. Compared to the Conventional Integral Equation (CIE) method for modeling an entire structure, this simplification method not only saves computation resources and time by reducing the number of unknowns, but also maintains the computation accuracy. In addition, this method has a simple integral equation formulation, so it can be easily accelerated with fast algorithms and integrated into the existing Method of Moments (MoM) codes. Numerical examples show that the proposed method demonstrates both satisfactory accuracy and efficiency with less computational complexity. [ABSTRACT FROM AUTHOR]

In the recent past, remotely sensed data with high spectral resolution has been made available and has been explored for various agricultural and geological applications. While these spectral signatures of the objects of interest provide important clues, the relatively poor spatial resolution of these hyperspectral images limits their utility and performance. In this context, hyperspectral image enhancement using multispectral data has been actively pursued to improve spatial resolution of such imageries and thus enhancing its use for classification and composition analysis in various applications. But, this also poses a challenge in terms of managing the trade-off between improved spatial detail and the distortion of spectral signatures in these fused outcomes. This paper proposes a strategy of using vector decomposition, as a model to transfer the spatial detail from relatively higher resolution data, in association with sensor simulation to generate a fused hyperspectral image while preserving the inter band spectral variability. The results of this approach demonstrates that the spectral separation between classes has been better captured and thus helped improve classification accuracies over mixed pixels of the original low resolution hyperspectral data. In addition, the quantitative analysis using a rank-correlation metric shows the appropriateness of the proposed method over the other known approaches with regard to preserving the spectral signatures. [ABSTRACT FROM AUTHOR]

Abstract: We examine interlinkages of stock return behavior for China and three emerging market neighbors from the Asia Pacific region from November 1993 to July 2008. Results are based on a VAR model. Impulse responses and vector decomposition of VAR are also utilized. Evidence suggests that the aggregate markets are mostly not interrelated. However, we observe relations between China and the other markets when foreign investor returns are specifically accounted for. In addition, a shock originating in China is significantly felt in the other equity markets. Stock market characteristics and macroeconomic conditions of these countries may help explain the observed relations. [Copyright &y& Elsevier]

How do spatially disjoint and ambiguous local motion signals in multiple directions generate coherent and unambiguous representations of object motion? Various motion percepts, starting with those of Duncker ( Induced motion, ) and Johansson ( Configurations in event perception, ), obey a rule of vector decomposition, in which global motion appears to be subtracted from the true motion path of localized stimulus components, so that objects and their parts are seen as moving relative to a common reference frame. A neural model predicts how vector decomposition results from multiple-scale and multiple-depth interactions within and between the form- and motion-processing streams in V1-V2 and V1-MST, which include form grouping, form-to-motion capture, figure-ground separation, and object motion capture mechanisms. Particular advantages of the model are that these mechanisms solve the aperture problem, group spatially disjoint moving objects via illusory contours, capture object motion direction signals on real and illusory contours, and use interdepth directional inhibition to cause a vector decomposition, whereby the motion directions of a moving frame at a nearer depth suppress those directions at a farther depth, and thereby cause a peak shift in the perceived directions of object parts moving with respect to the frame. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we attempt to distinguish the direct effect of financial development on poverty reduction from its indirect effect through economic growth. Using an efficient estimator called fixed effect vector decomposition (FEVD) we employ a set of panel data from 54 developing countries for the period 1993–2004. Our results indicate that on average financial development is conducive for poverty reduction but the instability accompanying financial development is detrimental to the poor. The major policy recommendations suggested by the paper indicate that financial sector reforms should be directed at easing credit restrictions while taking into consideration the effects of financial instability on the poor. [Copyright &y& Elsevier]

Abstract: An alternative proof for the explicit equations of motion for mechanical systems with independent non-ideal constraints is proposed in this paper. These equations are derived without the use of generalized inverse matrices and based on the decomposition of the constraint forces along the acceleration-constrained flat surface and its normal plane. [Copyright &y& Elsevier]