Vector Operations Research Articles

Image edge detection based on singular value feature vector and gradient operator.

This paper presents an edge detection algorithm based on singular value eigenvector and gradient operator. In the proposed algorithm, the singular values of image blocks are first calculated, and the Sobel gradient template is extended to eight other directions. Then the gradient values of image pixels are determined according to the stability of the singular values of image blocks. The determination of gradient threshold is considered from both global and local aspects. After calculating the global and local gradient thresholds of the original image, the gradient threshold of the whole image is determined by weighting function. Then the edge pixels of the image are filtered according to the gradient threshold, and the edge information image of the original image is obtained. The experimental data show that the proposed algorithm can resist a certain degree of noise interference, and the accuracy and efficiency of edge extraction are better than other similar algorithms.

Robust and Efficient Adaptive Beamforming Using Nested Subarray Principles

In this paper, we propose an adaptive beamforming algorithm for large uniform linear arrays (ULAs), where only a nested subarray is utilized to calculate the beamforming coefficients for the original ULA. In this algorithm, the steering vectors and powers of the signal-of-interest (SOI) and interferences are firstly estimated using the Capon spatial spectrum and known array structure, and the interference-plus-noise covariance matrix (INCM) is then constructed. Subsequently, an augmented INCM is formed via vectorization and spatial smoothing operations. Finally, the beamformer weight vector is determined by the augmented INCM and the estimated SOI steering vector. Our proposed algorithm exploits the enhanced degrees of freedom of the nested array, and thus can be applied to a large ULA to reduce the implementation complexity. Moreover, it fundamentally eliminates the SOI component. Numerical results demonstrate that the proposed algorithm performs better than the existing approaches.

Accelerating Revised Simplex Method Using GPU-Based Basis Update

Optimization problems lie at the core of scientific and engineering endeavors. Solutions to these problems are often compute-intensive. To fulfill their compute-resource requirements, graphics processing unit (GPU) technology is considered a great opportunity. To this end, we focus on linear programming (LP) problem solving on GPUs using revised simplex method (RSM). This method has potentially GPU-friendly tasks, when applied to large dense problems. Basis update (BU) is one such task, which is performed in every iteration to update a matrix called basis-inverse matrix. The contribution of this paper is two-fold. Firstly, we experimentally analyzed the performance of existing GPU-based BU techniques. We discovered that the performance of a relatively old technique, in which each GPU thread computed one element of the basis-inverse matrix, could be significantly improved by introducing a vector-copy operation to its implementation with a sophisticated programming framework. Second, we extended the adapted element-wise technique to develop a new BU technique by using three inexpensive vector operations. This allowed us to reduce the number of floating-point operations and conditional processing performed by GPU threads. A comparison of BU techniques implemented in double precision showed that our proposed technique achieved 17.4% and 13.3% average speed-up over its closest competitor for randomly generated and well-known sets of problems, respectively. Furthermore, the new technique successfully updated basis-inverse matrix in relatively large problems, which the competitor was unable to update. These results strongly indicate that our proposed BU technique is not only efficient for dense RSM implementations but is also scalable.

On fractional vector analysis

In this paper, we introduce fractional vector operators: the gradient, the divergence and the curl operators. Further we discuss fractional line integral and prove a fractional form of Green’s Theorem, using conformable derivative.

Dynamic Performance of PV Array fed Vector Drive Unit

In emerging applications of solar powered units the significance of its operation and control plays vital role. Industries to home, in all applications need induction motors due to its robust, simple and reliable.so this type of machines used widely in variable speed applications. In the scenario this paper presents the operation and dynamic performance of vector drive fed by PV array. Any drive unit equipped with power management unit, signal conditioning, drivers and controllers and control unit. This system powered by the excitation from PV array with MPPT controller and the load here is a vector drive. Vector control is advantageous over scalar control due to its low speed regulation, low maintenance and minimum speed at Rated torque and wide base speed range. The proposed system consists of PV array, MPPT Controller, vector controlled drive. Solar panel output boosted using Dc-Dc converter with Maximum power point tracking controller Using Incremental Conductance method and the performance curves(P-V, I-V,V-I) presented. Dynamic modelling and analysis of Individual units and the respective performance curves presented here and the simulations done in MATLAB/SIMULINK Platform.

Scattering of an elastic wave by a rigid sphere in a semi-bounded domain

The problem of scattering of plane elastic waves by a rigid sphere near a rigid boundary is considered. This leads to the appearance of multiply re-reflected dilatation and shear waves, which generate strong oscillations of the wave field. The problem for a vector operator of the shear waves is reduced to the definition of scalar functions as a consequence of symmetry. Approximate formulas for the far field and the long-wave Rayleigh approximation are presented. The construction of multiply re-reflected waves by the image method is presented and analyzed. Calculations of the scattered wave fields are plotted in the form of scattering diagrams.

Superintegrability of the Dunkl–Coulomb problem in three-dimensions

The superintegrability of the Dunkl–Coulomb model in three-dimensions is studied. The symmetry operators generalizing the Runge–Lenz vector operator are given. Together with the Dunkl angular momentum operators and reflection operators they generate the symmetry algebra of the Dunkl–Coulomb Hamiltonian which is a deformation of by reflections for bound states and is a deformation of by reflections for positive energy states. The spectrum of the Hamiltonian is derived algebraically using this symmetry algebra. The analog of the functional relation between the Coulomb Hamiltonian, Runge–Lenz operator and the angular momentum is given.

CP asymmetry in τ→KSπντ decays within the standard model and beyond

Motivated by the $2.8\sigma$ discrepancy observed between the BaBar measurement and the Standard Model prediction of the CP asymmetry in $\tau\to K_S\pi\nu_\tau$ decays, as well as the prospects of future measurements at Belle II, we revisit this observable in this paper. Firstly, we reproduce the known CP asymmetry due to $K^0 -\bar{K}^0$ mixing by means of the reciprocal basis, which is convenient when a $K_{S(L)}$ is involved in the final state. As the $K\pi$ tensor form factor plays a crucial role in generating a non-zero direct CP asymmetry that can arise only from the interference of vector and tensor operators, we then present a dispersive representation of this form factor, with its phase obtained in the context of chiral theory with resonances, which fulfills the requirements of unitarity and analyticity. Finally, the $\tau\to K_S\pi\nu_\tau$ decays are analyzed both within a model-independent low-energy effective theory framework and in a scalar leptoquark scenario. It is observed that the CP anomaly can be accommodated in the model-independent framework, even at the $1\sigma$ level, together with the constraint from the branching ratio of $\tau^-\to K_S\pi^-\nu_\tau$ decay; it can be, however, marginally reconciled only at the $2\sigma$ level, due to the specific relation between the scalar and tensor operators in the scalar leptoquark scenario. Once the combined constraints from the branching ratio and the decay spectrum of this decay are taken into account, these possibilities are however both excluded, even without exploiting further the stronger bounds from the (semi-)leptonic kaon decays under the assumption of lepton-flavour universality, as well as from the neutron electric dipole moment and $D-\bar{D}$ mixing under the assumption of $SU(2)$ invariance of the weak interactions.

Two-Step Sparse Representation Based 2D DOA Estimation with Single Moving Acoustic Vector Sensor

This paper investigates the two dimensional direction of arrival (2D DOA) estimation problem of multiple sources with one single moving acoustic vector sensor (AVS). We first use one single moving AVS to construct a synthetic nested AVS array, which is later shown that is equivalent to the physical nested AVS array. Then the vectorization and row extraction operations are performed to obtain the observation vector that behaves like signals received by a virtual uniform AVS array. Finally, the 2D DOA estimation is obtained via a two-step sparse representation (SR) method, which transforms the 2D grid search to a computationally efficient 1D grid search. The Cramer-Rao bound comparison between the synthetic and physical nested AVS arrays shows that these two arrays are equivalent for DOA estimation. Based on the property of the nested arrays and the full utilization of the array aperture via SR, the proposed method can achieve better estimation performance than spatial smoothing methods with nested AVS arrays and methods with uniform AVS arrays. Simulations validate the effectiveness of the proposed synthetic array method.

Revisiting performance of BiCGStab methods for solving systems with multiple right-hand sides

The paper discusses the efficiency of the classical BiCGStab method and several of its modifications for solving systems with multiple right-hand side vectors. These iterative methods are widely used for solving systems with large sparse matrices. The paper presents execution time analytical model for the time to solve the systems. The BiCGStab method and several modifications including the Reordered BiCGStab and Pipelined BiCGStab methods are analysed and the range of applicability for each method providing the best execution time is highlighted. The results of the analytical model are validated by the numerical experiments and compared with results of other authors. The presented results demonstrate an increasing role of the vector operations when performing simulations with multiple right-hand side vectors. The proposed merging of vector operations allows to reduce the memory traffic and improve performance of the calculations by about 30%.

A 2.92-Gb/s/W and 0.43-Gb/s/MG Flexible and Scalable CGRA-Based Baseband Processor for Massive MIMO Detection

Communication systems’ development requires service customization in aspects, such as standards, multiple-input multiple-output (MIMO) scales, and algorithms. The existing hardware designs for massive MIMO detection have difficulty in achieving both high flexibility and scalability with high hardware efficiency. This article proposes a baseband processor based on a dynamic coarse-grained reconfigurable array (CGRA) for massive MIMO detection. To efficiently support various algorithm features and requirements, three optimization techniques are proposed to achieve high flexibility and scalability. First, an on-demand matrix–vector systolic array is proposed to enable flexible and scalable matrix and vector operations, reducing memory accesses by 82%. Second, distributed multi-interaction data storage is designed for flexible data access and reusability. Finally, a continuable adaptive context information format is proposed to support different bit widths, operations, and extensions of MIMO systems, reducing context information by 67%. These techniques achieve the improvements of 1.33 $\times $ , 1.34 $\times $ , and 1.29 $\times $ in energy efficiency and 1.21 $\times $ , 1.18 $\times $ , and 1.18 $\times $ in area efficiency, evaluated by removing one technique at a time from the proposed architecture. Fabricated in a 28-nm CMOS technology, the chip achieves high flexibility and scalability in supporting various detection algorithms; various MIMO scales, such as $4\,\,\times $ 4, 32 $\times $ 32, and 128 $\times $ 8; and baseband processing tasks, such as filtering and fast Fourier transformation. When benchmarked on various detection algorithms, the processor achieves 1.64–2.92-Gb/s/W energy efficiency and 0.25–0.43-Gb/s/MG area efficiency, which are 2.78–28.54 $\times $ and 2.05–14.43 $\times $ those of state-of-the-art programmable designs, respectively. To our knowledge, this is the first flexible and scalable CGRA-based baseband processor for massive MIMO detection.

Lepton flavor violating Lambda _brightarrow Lambda ell _1ell _2 decay

Inspired by the recent hints of lepton flavor universality violation in brightarrow sell ell and brightarrow cell nu transitions, we study lepton flavor violating exclusive Lambda _brightarrow Lambda ell _1^+ell _2^- (ell _1ne ell _2) decay, which is forbidden in the Standard Model. Starting from a general effective Hamiltonian for a brightarrow sell _1^+ell _2^- transition that includes vector and axial-vector operators, and scalar and pseudo-scalar operators, we derive a two-fold decay distribution of Lambda _brightarrow Lambda ell _1^+ell _2^-. The distribution helps us to construct the differential branching ratio and the lepton-side forward–backward asymmetry, which are studied in a vector leptoquark model. The parameter space of the vector leptoquark model is constrained by low energy observables.

Teaching the Law of Cosines in Advanced 10th Grade Geometry Textbook by Way of Problem-Based Learning in Vietnam

The law of Cosines is an essential theorem in mathematics in particular and in science in general. The Cosine Rule allows us to calculate the length of one side of a triangle when we know two sides and the angle between the other two sides. This theorem is one of the first theorems when people want to build trigonometric systems. Because of such importance, many people studied the Law of Cosines. In Vietnam, they taught the Law of Cosines in the 10 th -grade Geometry program. It appears in Basic and Advanced sections, after having learned some concepts about vector operations. Although it is a famous theorem, there are not many documents mentioning how to teach the Law of Cosines effectively. We need to understand the relationship between mathematics and other fields expressed by the Law of Cosines, as well as to apply the method of problem-based learning in teaching this theorem. https://doi.org/10.26803/ijlter.18.11.24

An unsupervised framework for comparing graph embeddings

Abstract Graph embedding is the transformation of vertices of a graph into set of vectors. A good embedding should capture the graph topology, vertex-to-vertex relationship and other relevant information about the graph, its subgraphs and vertices. If these objectives are achieved, an embedding is a meaningful, understandable and compressed representations of a network. Finally, vector operations are simpler and faster than comparable operations on graphs. The main challenge is that one needs to make sure that embeddings well describe the properties of the graphs. In particular, a decision has to be made on the embedding dimensionality which highly impacts the quality of an embedding. As a result, selecting the best embedding is a challenging task and very often requires domain experts. In this article, we propose a ‘divergence score’ that can be assigned to embeddings to help distinguish good ones from bad ones. This general framework provides a tool for an unsupervised graph embedding comparison. In order to achieve it, we needed to generalize the well-known Chung-Lu model to incorporate geometry which is an interesting result in its own right. In order to test our framework, we did a number of experiments with synthetic networks as well as real-world networks, and various embedding algorithms.

Additive neural network for forest fire detection

In this paper, we introduce a video-based wildfire detection scheme based on a computationally efficient additive deep neural network, which we call AddNet. This AddNet is based on a multiplication-free vector operator, which performs only addition and sign manipulation operations. In this regard, we construct a dot product-like operation from the mf-operator and use it to define dense and convolutional feed-forwarding passes in AddNet. We train AddNet on images taken from forestry surveillance cameras. Our experiments show that AddNet can achieve a time-saving by 12.4% when compared to an equivalent regular convolutional neural network (CNN). Furthermore, the smoke recognition performance of AddNet is as good as regular CNNs and substantially better than binary-weight neural networks.

Finding buckling points for nonlinear structures by dynamic relaxation scheme

Dynamic Relaxation Method (DRM) is an explicit approach for solving the simultaneous systems of equations. In this tactic, the fictitious mass and damping are added to the static governing equations, and an artificial dynamic system is constructed. By using DRM for nonlinear analysis, the structural static equilibrium path is obtained. This outcome is extremely valuable, since it leads to the behavior of structures. Among the finding related to the structural static path are the critical and buckling points for nonlinear structures. In this paper, a new way for calculating the load factor is proposed by setting the external work zero. Mixing the dynamic relaxation scheme with external work technique has not been formulated so far. In all incremental-iterative methods, the load factor increment sign should be determinated by extra calculations. This sign leads to increase or decrease of the load increment. It is worth emphasizing that sign of the load factor increment changes at the load limit points. Therefore, the sign determinations are required in the common work control methods. These disadvantages are eliminated in the proposed algorithm. In fact, the suggested load factor depends only on the Dynamic Relaxation (DR) fictitious parameters. Besides, all DR calculations are performed via vector operation. Moreover, the load factor is calculated only by one formula, and it has the same relation in the all solution processes. In contrast to the arc length techniques, which requires the sign determined, the proposed scheme does not need any sign finding. It is shown that author’s technique is quicker than the other dynamic relaxation strategies. To prove the capability and efficiency of the presented scheme, several numerical tests are performed. The results indicate that the suggested approach can trace the complex structural static paths, even in the snap-back and snap-through parts.

A clipping algorithm on non-conformal interface for heat conduction analysis

In numerical analysis of heat transfer including complicated computational domains or geometries, the domains are divided into several simple domains, and it is possible to generate cells in the simple domains easily. However, for the sake of the isolation of the domains, the methods lead the vertex mismatch between the divided regions, and become non-conformal. Because of the non-conformal meshes, it is difficult to calculate fluxes through the interface. Therefore, a computational treatment for the non-conformal mesh is required to obtain geometrical information between neighboring cells. A clipping method to find the geometrical information are developed, and applied to thermal conduction problems. The clipping method implemented in this study is advantageous in using simple vector operations only to obtain the geometrical information on the non-conformal interface. To test the accuracy of the clipping method, twelve cases with different grid configurations are presented. They show that the method has a high degree of accuracy for calculating the clipped areas. Furthermore, to validate the scheme, the heat conduction problem is performed. And then, the numerical result agrees well with the exact solution. Additionally, we apply the scheme to the fourth case in the ISO 10211 that includes two materials with different aspect ratios. In the vicinity of the interface, the high temperature gradients are presented because of the different thermal conduction coefficients. Therefore, it shows that the present methods can treat the non-conformal meshes with the different neighboring cell size properly.

Conformal Invariance and Vector Operators in the O(N) Model

It is widely expected that, for a large class of models, scale invariance implies conformal invariance. A sufficient condition for this to happen is that there exists no integrated vector operator, invariant under all internal symmetries of the model, with scaling dimension $-1$. In this article, we compute the scaling dimensions of vector operators with lowest dimensions in the $O(N)$ model. We use three different approximation schemes: $\epsilon$ expansion, large $N$ limit and third order of the Derivative Expansion of Non-Perturbative Renormalization Group equations. We find that the scaling dimensions of all considered integrated vector operators are always much larger than $-1$. This strongly supports the existence of conformal invariance in this model. For the Ising model, an argument based on correlation functions inequalities was derived, which yields a lower bound for the scaling dimension of the vector perturbations. We generalize this proof to the case of the $O(N)$ model with $N\in \left\lbrace 2,3,4 \right\rbrace$.

Color image encryption based on vector decomposition operations and secondary image phase masks

This paper presents a method aimed at encrypting color images using vector operations and secondary image phase masks (SPMs). In this encryption, the optical coherent superposition principle is used to separate and overlay the original image into two phase plates on the three channels R, G and B, respectively. Then the double random phase encoding in the Fresnel domain is performed using the SPMs to encrypt one of the phase plates. Finally, the Kronecker product of two random matrices is directly perform randomization on the encoded image, achieving multilevel encryption of color images. Computer simulations are presented to demonstrate its performance, and the feasibility and security of the proposed system are analyzed as well.

Development of Vector Representation Test Instrument for Senior High School Students in Realizing Learning Outcomes

The study was conducted to developthe vector representation ability test items for seniorhigh school students and obtain Item Curve Characteristics (ICC). Grid test instruments are arranged based on competencies and vector representation indicators which are then used to compile items. The test instrument consists of five question items related to vector representation which includes drawing vectors, determining the magnitude and direction of vectors and performing vector operations. The validated instrument was piloted in 296 students from three schools in Batang Regency, Central Java. Politomus data were analyzed using the QUEST program for classical analysis and PARSCALE 4 for modern analysis theory based on Partial Credit Model (PCM). The results of the data analysis of the trial itemsindicate that of the five item questions, only 4 questions were fit with PCM. The reliability of the test instrument is 0.72, the level of difficulty of the items is in the range of 0.79 to 1.35. The information function and Standard Error Measurement (SEM) show that test items are developed reliably to measure the vector abilities of students with the average category in -1,6< θ<+3,2 logit scale with SEM ± 0,5.