Vector Operations Research Articles

Application of the Subsidiary Fields Method to the Modeling of $$\boldsymbol{tW+t}\bar{\boldsymbol{t}}$$ Processes with the Anomalous $$\boldsymbol{Wtb}$$ Interactions

Modeling of the pair and single top quark production are discussed in the context of searches for the anomalous $$Wtb$$ couplings. For the simulation of the anomalous $$Wtb$$ couplings in the top quark production and/or decay, the Subsidiary Fields method allows to generate a minimal number of event samples to cover all possible values of the couplings. In the paper the Subsidiary Fields method is applied to simulate the full $$t\bar{t}+tW$$ process with $$tWb$$ final state including the subsequent top quark and $$W$$ boson decays. Correctness of the differential cross sections for arbitrary values of the $$Wtb$$ couplings is demonstrated for the case of the simultaneous presence of the left- and right-handed vector operators in the Wtb vertex.

On Moment Methods in Krylov Subspaces

Moment methods in Krylov subspaces for solving symmetric systems of linear algebraic equations (SLAEs) are considered. A family of iterative algorithms is proposed based on generalized Lanczos orthogonalization with an initial vector $${{v}^{0}}$$ chosen regardless of the initial residual. By applying this approach, a series of SLAEs with the same matrix, but with different right-hand sides can be solved using a single set of basis vectors. Additionally, it is possible to implement generalized moment methods that reduce to block Krylov algorithms using a set of linearly independent guess vectors $$v_{1}^{0},...,v_{m}^{0}.$$ The performance of algorithm implementations is improved by reducing the number of matrix multiplications and applying efficient parallelization of vector operations. It is shown that the applicability of moment methods can be extended using preconditioning to various classes of algebraic systems: indefinite, incompatible, asymmetric, and complex, including non-Hermitian ones.

Approximation of the Contour of an Object in an Image Using Vector Operations

Introduction. One of the directions associated with identification, analysis of the shape of objects, their size, orientation, marking and other geometric characteristics is contour analysis. Various methods for contour approximation are described in the literature. The proposed method is based on a well-known method. Its essence lies in the sequential search for possible directions and end points of approximating straight line segments belonging to the contour. The number of approximation nodes should be as small as possible. The calculation is carried out only for the next point of the contour, without returning to check the criterion of approximation to all previous points. The computational complexity of the algorithm is proportional to the number of points in the contour. The purpose of the paper to propose a method of piecewise linear approximation of the contours of objects in images, which will allow to use the parallel computations at all stages of computer processing using vector operations. Results. The paper proposes an improved method for piecewise linear approximation of a closed contour of an object in an image by a polygon, the vertices of which are directly the points of this contour. Approximation criterion: the distance from each point of the approximated section of the contour to the approximating segment should not exceed the approximation error. The method is focused on parallel computing using vector operations. A method for parallel computation of integral vectors of extreme values of a sequence of numbers for the implementation of parallel computations using vector operations at all stages of approximation is also proposed. Conclusions. Methods are proposed that are implemented using vector operations and provide an opportunity to speed up the solution of contour analysis problems, as well as other similar problems in real time. The gain in computing speed is proportional to the amount of data that a vector processor can simultaneously process. The presence of developed subsystems of vector instructions in Intel and ARM processors makes it possible to use the proposed computation methods in practice. Keywords: image, object contour, piecewise linear approximation, parallel computations, vector operations.

Coherent elastic neutrino-nucleus scattering: EFT analysis and nuclear responses

The cross section for coherent elastic neutrino-nucleus scattering (CE$\nu$NS) depends on the response of the target nucleus to the external current, in the Standard Model (SM) mediated by the exchange of a $Z$ boson. This is typically subsumed into an object called the weak form factor of the nucleus. Here, we provide results for this form factor calculated using the large-scale nuclear shell model for a wide range of nuclei of relevance for current CE$\nu$NS experiments, including cesium, iodine, argon, fluorine, sodium, germanium, and xenon. In addition, we provide the responses needed to capture the axial-vector part of the cross section, which does not scale coherently with the number of neutrons, but may become relevant for the SM prediction of CE$\nu$NS on target nuclei with nonzero spin. We then generalize the formalism allowing for contributions beyond the SM. In particular, we stress that in this case, even for vector and axial-vector operators, the standard weak form factor does not apply anymore, but needs to be replaced by the appropriate combination of the underlying nuclear structure factors. We provide the corresponding expressions for vector, axial-vector, but also (pseudo-)scalar, tensor, and dipole effective operators, including two-body-current effects as predicted from chiral effective field theory. Finally, we update the spin-dependent structure factors for dark matter scattering off nuclei according to our improved treatment of the axial-vector responses.

Efficient high-order accurate explicit time-marching procedures for dynamic analyses

In this paper, η-order accurate truly-explicit time-marching procedures are proposed for dynamic analyses. In these new techniques, just η–1 stiffness matrix–vector operations are required for solution, per time-step, providing more efficient approaches than standard high-order time-marching procedures, which demand η matrix–vector operations per time-step. In addition, as illustrated along this work, the novel formulations are also more accurate than equivalent standard techniques, providing very effective time-domain solution procedures. Three truly-explicit time-marching procedures are discussed here, describing second-, third- and fourth-order accurate methodologies.

Closed Forms of General Solutions for Rectangular Systems of Coupled Generalized Sylvester Matrix Differential Equations

We investigate a rectangular system of coupled generalized Sylvester matrix differential equations in both nonhomogeneous and homogeneous cases. In order to obtain a closed form of its general solution, we transform it to an equivalent vector differential equation. This is done by using the vector operator and the Kronecker product. An explicit form of its general solution is given in terms of matrix series concerning Mittag-Leffler functions, exponentials, and hyperbolic functions. The main system includes certain systems of coupled matrix/vector differential equations, and single matrix differential equations as special cases.

A Vector Operation to Extract Second-Order Terrain Derivatives from Digital Elevation Models

Terrain derivatives exhibit surface morphology in various aspects. However, existing spatial change calculation methods for terrain derivatives are based on a mathematical scalar operating system, which may disregard the directional property of the original data to a certain extent. This situation is particularly true in second-order terrain derivatives, in which original data can be terrain derivatives with clear directional properties, such as slope or aspect. Thus, this study proposes a mathematical vector operation method for the calculation of second-order terrain derivatives. Given the examples of the first-order terrain derivatives of slope and aspect, their second-order terrain derivatives are calculated using the proposed vector method. Directional properties are considered and vectorized using the following steps: rotation-type judgment, standardization of initial direction, and vector representation. The proposed vector method is applied to one mathematical Gaussian surface and three different ground landform areas using digital elevation models (DEMs) with 5 and 1 m resolutions. Comparison analysis results between the vector and scalar methods show that the former achieves more reasonable and accurate second-order terrain derivatives than the latter. Moreover, the vector method avoids overexpression or even exaggeration errors. This vector operation concept and its expanded methods can be applied in calculating other terrain derivatives in geomorphometry.

Arithmetics of Vectors of Fuzzy Sets

The arithmetic operations of fuzzy sets are completely different from the arithmetic operations of vectors of fuzzy sets. In this paper, the arithmetic operations of vectors of fuzzy intervals are studied by using the extension principle and a form of decomposition theorem. These two different methodologies lead to the different types of membership functions. We establish their equivalences under some mild conditions. On the other hand, the α-level sets of addition, difference and scalar products of vectors of fuzzy intervals are also studied, which will be useful for the different usage in applications.

Deep generative modeling for mechanistic-based learning and design of metamaterial systems

Metamaterials are emerging as a new paradigmatic material system to render unprecedented and tailorable properties for a wide variety of engineering applications. However, the inverse design of metamaterial and its multiscale system is challenging due to high-dimensional topological design space, multiple local optima, and high computational cost. To address these hurdles, we propose a novel data-driven metamaterial design framework based on deep generative modeling. A variational autoencoder (VAE) and a regressor for property prediction are simultaneously trained on a large metamaterial database to map complex microstructures into a low-dimensional, continuous, and organized latent space. We show in this study that the latent space of VAE provides a distance metric to measure shape similarity, enable interpolation between microstructures and encode meaningful patterns of variation in geometries and properties. Based on these insights, systematic data-driven methods are proposed for the design of microstructure, graded family, and multiscale system. For microstructure design, the tuning of mechanical properties and complex manipulations of microstructures are easily achieved by simple vector operations in the latent space. The vector operation is further extended to generate metamaterial families with a controlled gradation of mechanical properties by searching on a constructed graph model. For multiscale metamaterial systems design, a diverse set of microstructures can be rapidly generated using VAE for target properties at different locations and then assembled by an efficient graph-based optimization method to ensure compatibility between adjacent microstructures. We demonstrate our framework by designing both functionally graded and heterogeneous metamaterial systems that achieve desired distortion behaviors.

Examining Grade 11 science students’ difficulties in learning about vector operations

Studies on student learning of scientific concepts have shown that students often experience various difficulties in understanding basic physics concepts such as vector quantities, as a result of formal and informal learning. The purpose of the present study is to document Grade 11 students’ difficulties in understanding vectors and their associated concepts. Specifically, the study tried to find answers to questions about the overall level of difficulty experienced by Grade 11 students about vectors, the nature of these difficulties, and their association with operations, such as scalars, adding vectors graphically, determining vector magnitude and direction, and multiplying vectors by numbers. Altogether, 58 Grade 11 students participated in this study. The study employed a specifically adapted test to assess participants’ understanding of vectors in relation to: (1) identifying whether students can distinguish between vectors and scalars, (2) adding vectors graphically, (3) determining the vector magnitude and direction, and (4) multiplying vectors by numbers. The findings suggested that, although most students were able to distinguish between vectors and scalars, they had experienced various difficulties in understanding operations in relation to adding vectors, graphically and mathematically, determining vector magnitudes and directions, and multiplying vectors by numbers. The findings were discussed within the recent UAE educational reform policy.

Near‐optimal hybrid precoding for millimeter wave massive MIMO systems via cost‐efficient Sub‐connected structure

Millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) is a promising technology for next generation wireless communications. The utilisation of traditional full digital precoding techniques for mmWave massive MIMO systems is too costly. Fortunately, the hybrid (analogue/digital) precoding is a better choice. In this study, the authors investigate a near-optimal iterative approximation hybrid precoding algorithm via cost-efficient sub-connected structure for mmWave massive MIMO systems. Based on the minimum mean square error (MSE) criterion, the optimal design of the proposed hybrid precoders is non-convex. The original problem is reformulated as two optimisation sub-problems, where one of the sub-problems is convex and another is non-convex. First, the authors convert the non-convex sub-problem into a convex problem by relaxing the constant modulus constraint from beampattern with interference control method, and eliminating the block diagonal constraint from vector operation with the properties of Kronecker product. Then the two convex sub–problems are solved iteratively. The proposed algorithm can achieve a highly approximate optimal solution, which can be theoretically demonstrated to converge to a Karush-Kuhn-Tucker point of the original problem. Simulation results show that the proposed algorithm via both sub–connected and fully connected structure gets favourable performance in terms of MSE and achievable rate.

Solving optimal reactive power problem by enhanced fruit fly optimization algorithm and status of material algorithm

<div data-canvas-width="397.2735184438622">This paper proposes enhanced fruit fly optimization algorithm (EFF) and status of material algorithm (SMA) to solve the optimal reactive power problem. Fruit fly optimization algorithm is based on the food finding behavior of the fruit fly. There are two steps in food finding procedure of fruit fly: At first it smells the food source by means of osphresis organ and it flies in that direction; afterwards, when it gets closer to the food site, through its sensitive vision it will find the food. At the beginning of the run by diminishing the inertia weight from a large value to a small value, will lead to enhance the global search capability and more local search ability will be in process the end of the run of the EFF algorithm. Then SMA is projected to solve the problem. Three state of material are solid, liquid, and gas. For evolution procedure direction vector operator assign a direction to every molecule consecutively to guide the particle progression. Collision operator imitates the collisions factor in which molecules are interacting to each other. Proposed enhanced EFF, SMA has been tested in standard IEEE 30 bus test system and simulation results show the projected algorithms reduced the real power loss considerably.</div>

Deep Learning Methods in Classification of Myocardial Infarction by employing ECG Signals

Background/Objectives: To automatically classify and detect the Myocardial Infarction using ECG signals. Methods/Statistical analysis: Deep Learning algorithms Convolutional Neural Network(CNN), Long Short Term Memory(LSTM) and Enhanced Deep Neural Network(EDN) were implemented. The proposed model EDN, comprises the techniques CNN and LSTM. Vector operations like matrix multiplication and gradient decent were applied to large matrices of data that are executed in parallel with GPU support. Because of parallelism EDN faster the execution time of process. Findings: Proposed model EDN yields better accuracy (88.89%) than other state-of-art methods for PTB database. Novelty/Applications: The proposed classification algorithm for analyzing the ECG signals is obtained by comprising the Convolutional Neural Network(CNN)and Long short-term memory networks(LSTM). Also, it is identified that the novel classification technique based on deep learning decreases the misdiagnosis rate of MI. Keywords: Classification; CNN; deep learning; deep neural network; EDN; LSTM; Myocardial Infarction(MI)

Modeling the influence of injection parameters on powder efficiency in laser cladding

For lateral powder injection, adjustments of defocusing distance, powder feeding angle, and molten pool width are set as input variables, and the powder transport vector, powder outflow position vector, and the injection offset vector are determined. The powder transport model involving above adjustment parameters is constructed based on operation of such vectors, which have been verified in experiments. Then, powder transport ratios of three variables with 13 × 13 × 5 levels are calculated to reflect the effect of injection parameters, which increases with the molten pool width, and maintains a high level as the defocusing distance and powder feeding angle are both adjusted positively (clockwise) or negatively (anti-clockwise). In addition, the powder transport ratio corresponding to an arbitrary combination of injection parameters can be calculated and its process window could be extended to determine a better process combination.

Lepton flavor violation and dilepton tails at the LHC

Starting from a general effective Lagrangian for lepton flavor violation (LFV) in quark-lepton transitions, we derive constraints on the effective coefficients from the high-mass tails of the dilepton processes pp rightarrow ell _k ell _l (with kne l). The current (projected) limits derived in this paper from LHC data with 36~mathrm {fb}^{-1} (3~mathrm {ab}^{-1}) can be applied to generic new physics scenarios, including the ones with scalar, vector and tensor effective operators. For purely left-handed operators, we explicitly compare these LHC constraints with the ones derived from flavor-physics observables, illustrating the complementarity of these different probes. While flavor physics is typically more constraining for quark-flavor violating operators, we find that LHC provides the most stringent limits on several flavor-conserving ones. Furthermore, we show that dilepton tails offer the best probes for charm-quark transitions at current luminosities and that they provide competitive limits for tauonic brightarrow d transitions at the high-luminosity LHC phase. As a by-product, we also provide general numerical expressions for several low-energy LFV processes, such as the semi-leptonic decays Krightarrow pi ell ^{pm }_k ell ^{{mp }}_l, Brightarrow pi ell ^{pm }_k ell ^{{mp }}_l and Brightarrow K^{(*)} ell ^{pm }_k ell ^{{mp }}_l.

Camera pose estimation based on global structure from motion

In this paper, a new global camera pose estimation algorithm WTLS-IRLS is proposed, which can effectively solve the global rotation when there are outliers. Firstly, according to the relationship between the rotation vector and the rotation matrix, we simplify the product operation of the rotation matrix into the subtraction operation of the rotation vector, which reduces the complexity of the algorithm. Secondly, the weighted total least squares (WTLS) and the iteratively reweighted least squares (IRLS) are used to average relative rotations. As the initialization of IRLS, WTLS provides a good initial guess by correcting the linearization equation and adding weight information to the relative rotations. IRLS continues to add weight information to the relative rotation matrices to optimize the global rotations. We demonstrate the performance of our approach by a number of large-scale data sets, the results show that our method has been greatly improved in efficiency, accuracy and iteration. In order to verify the correctness of our proposed method, we completed the complete reconstruction process, the experimental results show that our proposed WTLS-IRLS rotation averaging algorithm can obtain dense point clouds with more three-dimensional points.

A Simple Quantum Integro-Differential Solver (SQuIDS)

Simple Quantum Integro-Differential Solver (SQuIDS) is a C++ code designed to solve semi-analytically the evolution of a set of density matrices and scalar functions. This is done efficiently by expressing all operators in an SU(N) basis. SQuIDS provides a base class from which users can derive new classes to include new non-trivial terms from the right hand sides of density matrix equations. The code was designed in the context of solving neutrino oscillation problems, but can be applied to any problem that involves solving the quantum evolution of a collection of particles with Hilbert space of dimension up to six. New version program summaryProgram Title: SQuIDSCPC Library link to program files:http://dx.doi.org/10.17632/hnchbtnybs.1Developer’s respository link:https://github.com/jsalvado/SQuIDSLicensing provisions: GNU Lesser General Public License, version 3.Programming language: C++11.External routines: GNU Scientific Library (http://www.gnu.org/software/gsl/).Journal reference of previous version: Comput. Phys. Commun. 196 (2015) 569–591Does the new version supersede the previous version?: Yes.Nature of problem: Solve the evolution of open quantum systems of Hilbert space dimension N with self interactions and interaction with classical fields.Solution method: The algebra is implemented as a C++ object and is embedded into the GSL ordinary differential equation solver.Reasons for the new version: Added new features and improved runtime.Summary of revisions:•Library names have been moved into the ‘squids’ namespace.•Support for extraction of SU vectors and basis transformations to GSL matrices.•Implementation of matrix exponentiation for use cases like evolution with non-diagonalized Hamiltonians.•Implementation of a number of useful matrix operations on SU vectors, including applying arbitrary unitary transformations, extracting real and imaginary components, transposition, and generalized, weighted rotations.•Support for obtaining the eigensystem which diagonalizes an SU_vector.•Explicit disallowance of creating or manipulating SU(1) vectors, which are degenerate with scalars.•A fix to a severe issue in the use of the GSL ODE interface, now giving good output for much less stringent tolerance values.•Optimization of element-wise operations on SU vectors without the need to allocate temporary storage.•Redesign of SU vector operations for vectorizability, including optimized allocation of element storage with optimal alignment.•Implementation of a more efficient version of SU vector time evolution which can share initialization costs across multiple evolutions by the same operator over the same time interval.•A more precise definition of the meter.•Improvements to configuration and build system.•Clean up of capitalization for file and class names.•Rearrangement of project files to a more standard layout.•Elimination of memory leaks.•Limited support for the Intel and Portland Group compilers. These should not be considered guaranteed to work, but have been given minimal testing and appear compile the library correctly.•Added additional unit conversions to SQuIDS constants.Additional comments including restrictions and unusual features: The code is only implemented up to Hilbert spaces of dimension six, but a Mathematica notebook is provided in order to generate higher dimensional solutions. Furthermore, only ordinary differential equation solution methods that require only the first derivative can be used. Acknoledgements CAA is supported by NSF grant PHY-1912764. JS acknowledges financial support from EU Networks FP10ITN ELUSIVES (H2020-MSCA-ITN-2015-674896) and INVISIBLES-PLUS (H2020-MSCA-RISE2015-690575), by the MINECO grant FPA2016-76005-C2-1-P and by the Maria de Maeztu grant MDM-2014-0367 of ICCUB.

USING GEOGEBRA IN TEACHING PLANE VECTOR

The study of geometry knowledge is an important component of high school mathematics. Plane geometry is the main thread that runs through high school geometry knowledge. Vector learning is the focus and difficulty of plane geometry. When students encounter a new knowledge, it will be difficult to overcome it, and it is difficult to form a new logical system in their minds. Therefore, when students learn the content of vectors, they will have cognitive conflicts at different levels of thinking. The calculation from planar geometry to directed line segments needs a transition. It is difficult to understand the concept and nature of vectors without the help of teachers. This study attempts to guide the application of Geogebra software in teaching plane vector by using Van Hill Theory to intuitively display abstract geometric knowledge, and guide students to perform dynamic operations and deductive reasoning , Gradually help students transition from point to surface to vector operation, improve classroom teaching efficiency, and thereby optimize geometry teaching, in order to provide some reference for front-line teachers.

Direction-of-Arrival Estimation for 2D Coherently Distributed Sources with Nested Array Based on Matrix Reconstruction

This paper has made proposition of a nested array and an estimation algorithm for direction-of-arrival (DOA) of two-dimensional (2D) coherently distributed (CD) sources. According to the difference coarray concept, double parallel hole-free virtual uniform linear arrays are generated by virtue of vectorization operation on cross-correlation matrices of subarrays. Sensor coordinates of virtual arrays are derived. Rational invariance relationships of virtual arrays are derived. According to the rotational invariance relationships, matrices satisfying rotation invariance are constructed by extracting and regrouping the receive vectors of the virtual arrays, and then an estimation of signal parameters via rotational invariance techniques- (ESPRIT-) like framework on matrix reconstruction is deduced. Optimal configuration of the nested array as well as computational complexity are analyzed. Without pair matching, the proposed method can resolve more sources than the sensor number. Simulation outcomes indicate that the proposed method tends to have a better performance as compared to the traditional uniform arrays that have similar number of sensors.

A baitbox for all seasons: temporal shifts in a vector’s propagule supply characteristics and implications for invasion ecology

Invasion dynamics are influenced by both vector operation and propagule pressure. Which propagules are entrained in a vector depends on how, where, and when a vector operates, but the timing and effects of vector operations on species delivery patterns is poorly resolved. Using the live marine baitworm trade, we tested vector selectivity across 3 boreal seasons (summer 2011, fall 2011, and spring 2012). We compared macroinvertebrate assemblages at the source (Maine, US east coast field) and in baitboxes upon delivery (Mid-Atlantic distributors, US east coast) and quantified live and dead biota to test for interactive effects of season and vector stage (i.e. source vs. destination) on per capita abundance, species richness, diversity, functional richness, and community composition. In all, we identified 46262 hitchhiking macro-organisms from 56 distinct taxa. Among live biota, taxonomic richness, functional group richness, and abundance differed by vector stage and season. Community composition showed seasonality for functional groups, but not for taxonomic groups. Vector stage affected dead community composition more than season, implying that vector operations (i.e. handling at source and during shipping) filter species transfers differentially. Dead communities were typically composed of the most abundant live organisms in the same baitboxes, emphasizing how important propagule pressure is to successful transport. Some combinations of 5 key functional traits (body size, feeding mode, growth form, modularity, and motility) were associated with increased survival during vector transfer. Successful species transfers are correlated with specific functional traits and propagule pressure, both of which are influenced by seasonal variation.