Projection Of Vector Research Articles

A Sparse Framework for Robust Possibilistic K-Subspace Clustering

Clustering noisy, high-dimensional, and structurally complex data have always been a challenging task. As most existing clustering methods are not able to deal with both the adverse impact of noisy samples and the complex structures of data, in this article, we propose a novel robust and sparse possibilistic K-subspace (RSPKS) clustering algorithm to integrate subspace recovery and possibilistic clustering algorithms under a unified sparse framework. First, the proposed method sparsifies the membership matrix and the subspace projection vector under a dual-sparse framework to handle high-dimensional noisy data. This unifies dimensionality reduction and clustering using one objective function for which the optimization can be realized through synchronous iteration. Second, the reconstruction error of each sample in the local subspace is used as the distance metric for classification. That is, each sample itself is treated as a clustering prototype so as not to be affected by the structure of the overall data distribution. Therefore, the clustering prototype construction problem of the data with complex structures can be better addressed. Finally, to deal with nonlinear regions, our RSPKS method is further extended into a kernelized version, namely the kernelized RSPKS clustering algorithm. The experimental results on both synthetic and real-world datasets demonstrate that our proposed method outperforms state-of-the-art algorithms in terms of clustering accuracy.

A constant plunge depth control strategy for robotic FSW based on online trajectory generation

Robotic friction stir welding (RFSW) usually comes with a huge upsetting force, and the stiffness of the welding system distributes unevenly over the position, which leads to a large deviation of the plunge depth of the tool at the end of the robot. The conventional constant distance tracking control suffers from the problem of unsmooth compensation leading to the vibration of the robot and thus degrading the weld quality. For this problem, a constant plunge depth control based on online trajectory generation for RFSW is studied, which can generate an accurate welding trajectory according to the rough initial reference path and smoothly compensate for the plunge deviation. Initially, three laser-ranging sensors are utilized to measure the pose deviation of the tool in real-time and generate the ideal welding trajectory according to the projection vector method. Then, a deformation compensation model is established to realize the real-time prediction of the correct value. To ensure the smoothness and rapidity of the dynamic tracking process of displacement deviation, we adopt an online trajectory generator as the core of optimization control to meet the process constraints such as speed, acceleration, and jerk during the compensation process. Finally, simulation and experiment are carried out. The results show that the proposed method can effectively reduce the vibration caused by compensation during the welding process and reduce flash, which can improve the welding quality.

Three-Dimensional Geometry Reconstruction Method from Multi-View ISAR Images Utilizing Deep Learning

The three-dimensional (3D) geometry reconstruction method utilizing ISAR image sequence energy accumulation (ISEA) shows great performance on triaxial stabilized space targets but fails when there is unknown motion from the target itself. The orthogonal factorization method (OFM) can solve this problem well under certain assumptions. However, due to the sparsity and anisotropy of ISAR images, the extraction and association of feature points become very complicated, resulting in the reconstructed geometry usually being a relatively sparse point cloud. Therefore, combining the advantages of the above methods, an extended factorization framework (EFF) is proposed. First, the instance segmentation method based on deep learning is used for the extraction and association of a number of key points on multi-view ISAR images. Then, the projection vectors between the 3-D geometry of the space target and the multi-view ISAR images are obtained, using the improved factorization method. Finally, the 3D geometry reconstruction problem is transformed into an unconstrained optimization problem and solved via the quantum-behaved particle swarm optimization (QPSO) method. The proposed framework uses discretely observed multi-view range–Doppler ISAR images as an input, which can make full use of the long-term data of space targets from multiple perspectives and which is non-sensitive to movement. Therefore, the proposed framework shows high feasibility in practical applications. Experiments on simulated and measured data show the effectiveness and robustness of the proposed framework.

On Doppler Shifts of Breaking Waves

Field-tower-based observations were used to estimate the Doppler velocity of deep water plunging breaking waves. About 1000 breaking wave events observed by a synchronized video camera and dual-polarization Doppler continuous-wave Ka-band radar at incidence angles varying from 25 to 55 degrees and various azimuths were analyzed using computer vision methods. Doppler velocities (DVs) associated with breaking waves were, for the first time, directly compared to whitecap optical velocities measured as the line-of-sight projection of the whitecap velocity vector (LOV). The DV and LOV were found correlated; however, the DV was systematically less than the LOV with the ratio dependent on the incidence angle and azimuth. The largest DVs observed at up-wave and down-wave directions were accompanied by an increase of the cross-section polarization ratio, HH/VV, up to 1, indicating a non-polarized backscattering mechanism. The observed DV was qualitatively reproduced in terms of a combination of fast specular (coherent) and slow non-specular (incoherent) returns from two planar sides of an asymmetric wedge-shaped breaker. The difference in roughness and tilt between breaker sides (the front face was rougher than the rear face) explained the observed DV asymmetry and was consistent with previously reported mean sea surface Doppler centroid data and normalized radar cross-section measurements.

Shelling the \(m=1\) amplituhedron

The amplituhedron $\mathcal{A}_{n,k,m}$ was introduced by Arkani-Hamed and Trnka (2014) in order to give a geometric basis for calculating scattering amplitudes in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory. It is a projection inside the Grassmannian $\text{Gr}_{k,k+m}$ of the totally nonnegative part of $\text{Gr}_{k,n}$. Karp and Williams (2019) studied the $m=1$ amplituhedron $\mathcal{A}_{n,k,1}$, giving a regular CW decomposition of it. Its face poset $R_{n,l}$ (with $l := n-k-1$) consists of all projective sign vectors of length $n$ with exactly $l$ sign changes. We show that $R_{n,l}$ is EL-shellable, resolving a problem posed by Karp and Williams. This gives a new proof that $\mathcal{A}_{n,k,1}$ is homeomorphic to a closed ball, which was originally proved by Karp and Williams. We also give explicit formulas for the $f$-vector and $h$-vector of $R_{n,l}$, and show that it is rank-log-concave and strongly Sperner. Finally, we consider a related poset $P_{n,l}$ introduced by Machacek (2019), consisting of all projective sign vectors of length $n$ with at most $l$ sign changes. We show that it is rank-log-concave, and conjecture that it is Sperner.

Properties of Pb208 predicted from the relativistic equation of state in the full Dirac space

Relativistic Brueckner-Hartree-Fock (RBHF) theory in the full Dirac space allows one to determine uniquely the momentum dependence of scalar and vector components of the single-particle potentials. In order to extend this new method from nuclear matter to finite nuclei, as a first step, properties of $^{208}\mathrm{Pb}$ are explored by using the microscopic equation of state for asymmetric nuclear matter and a liquid droplet model. The neutron and proton density distributions, the binding energies, the neutron and proton radii, and the neutron skin thickness in $^{208}\mathrm{Pb}$ are calculated. In order to further compare the charge densities predicted from the RBHF theory in the full Dirac space with the experimental charge densities, the differential cross sections and the electric charge form factors in the elastic electron-nucleus scattering are obtained by using the phase-shift analysis method. The results from the RBHF theory are in good agreement with the experimental data. In addition, the uncertainty arising from variations of the surface term parameter ${f}_{0}$ in the liquid droplet model is also discussed.

Propagation of scalar and tensor gravitational waves in Horndeski theory

Gravitational waves travel through the distributions of matter and dark energy during propagation. For this reason, gravitational waves emitted from binary compact objects serve as a useful tool especially to probe the nature of dark energy. The geometrical optics approximation is a conventional way of investigating wave propagation. However, the approximation becomes less accurate as the wavelength approaches the curvature radius of the background, which can occur in generic situations. In this paper, we suggest a formulation for higher-order corrections of the geometrical optics expansion, applied to Horndeski theory which accommodates many dark energy models. At the level of the background, assuming that the derivative of the scalar field is non-vanishing and timelike, we choose the time slices to coincide with the contours of the scalar field. This choice of the background time slices is advantageous as the sound cones of both scalar and tensor gravitational waves are upright with respect to the background time slices whenever the scalar field behaves as a perfect fluid. We then analyze the equations of motion for scalar and tensor components of gravitational waves at the leading and next-to-leading order in the geometrical optics expansion, deriving the evolution equations for their amplitudes under certain conditions. In particular, for Generalized Brans-Dicke theories, we find a simple description of equations for gravitational waves in terms of an effective metric.

Fuzzy RDF Knowledge Graph Embeddings Through Vector Space Model

Resource description framework (RDF) is a World Wide Web consortium recommendation and has been widely accepted for semantic data models (e.g., knowledge graphs). As such, a large amount of RDF data is readily available. Information in the real world is often uncertain, and uncertain RDF data models have been proposed and received increasing attention. Knowledge graph embedding is an effective way to perform vector projection of structured knowledge, after which we can infer a large-scale knowledge graph. Nowadays, knowledge graph embedding models are widely proposed, but most of them can only handle crisp information. In this article, we concentrate on modeling fuzzy RDF graphs in the vector space. We propose a fuzzy RDF knowledge graph embedding model (FRKGE), which can project the fuzzy entities and fuzzy relations with membership degree to the vector space. Our proposed model preserves the structure of the fuzzy RDF knowledge graph and the explicit expression of membership degree in the vector space, which provides a natural expression of fuzzy RDF tuples. Our experimental results demonstrate that the FRKGE model is competent for the task of representation learning for fuzzy RDF knowledge graphs.

A Semiblind PCA-based Foreground Subtraction Method for 21 cm Intensity Mapping

The principal component analysis (PCA) method and the singular value decomposition (SVD) method are widely used for foreground subtraction in 21 cm intensity mapping experiments. We show their equivalence, and point out that the condition for completely clean separation of foregrounds and cosmic 21 cm signal using the PCA/SVD is unrealistic. We propose a PCA-based foreground subtraction method, dubbed the “singular vector projection (SVP)” method, which exploits a priori information of the left and/or right singular vectors of the foregrounds. We demonstrate with simulation tests that this new, semiblind method can reduce the error of the recovered 21 cm signal by orders of magnitude, even if only the left and/or right singular vectors in the largest few modes are exploited. The SVP estimators provide a new, effective approach for 21 cm observations to remove foregrounds and uncover the physics in the cosmic 21 cm signal.

Identification of deformed configurations of segmental tunnel rings based on measured convergences

If convergences grow so large that the serviceability of a tubbing ring is lost, remedial measures must be taken. In this context, it is useful to reconstruct the displacement history of the tunnel ring in order to gain insight into the evolution of the structural behavior that has led to the current configuration. This challenge is tackled with the help of measured convergences and rigid body kinematics. The latter are sufficient, because the deformations of tubbings, resulting from normal forces and bending moments, do not contribute significantly to the displacements of segmental rings. The analysis is focused on convergences measured during a real-scale test of a symmetric tunnel ring. It consists of six tubbings and has three kinematic degrees of freedom. Deformed configurations are reproduced by optimizing the three scalar components of one symmetric and two antisymmetric modes of rigid body displacements. This problem is under-determined, because convergences are routinely measured in two directions only. Its solution is obtained in two steps. At first, the component of the symmetric mode of rigid body displacements is identified such that the measured convergences are reproduced in the best-possible fashion. Thereafter, the remaining differences between measured and modeled convergences are reduced to zero by optimizing the components of the two antisymmetric modes. This kind of structural analysis starts with the most recent set of measured convergences. It proceeds, in a step-by-step manner backwards in time to older sets of monitored data. It is shown that the developed method allows for a satisfactory reproduction of the displacement history of the tested tubbing ring, making use of measured vertical and horizontal convergences. The obtained visualization of the displacement history of the entire tunnel ring provides more insight into the structural behavior than diagrams showing only the evolution of single convergences.

Versatile clinical movement analysis using statistical parametric mapping in MovementRx

Clinical gait analysis is an important biomechanics field that is often influenced by subjectivity in time-varying analysis leading to type I and II errors. Statistical Parametric Mapping can operate on all time-varying joint dynamics simultaneously, thereby overcoming subjectivity errors. We present MovementRx, the first gait analysis modelling application that correctly models the deviations of joints kinematics and kinetics both in 3 and 1 degrees of freedom; presented with easy-to-understand color maps for clinicians with limited statistical training. MovementRx is a python-based versatile GUI-enabled movement analysis decision support system, that provides a holistic view of all lower limb joints fundamental to the kinematic/kinetic chain related to functional gait. The user can cascade the view from single 3D multivariate result down to specific single joint individual 1D scalar movement component in a simple, coherent, objective, and visually intuitive manner. We highlight MovementRx benefit by presenting a case-study of a right knee osteoarthritis (OA) patient with otherwise undetected postintervention contralateral OA predisposition. MovementRx detected elevated frontal plane moments of the patient’s unaffected knee. The patient also revealed a surprising adverse compensation to the contralateral limb.

Determination of Non-Zero Initial Conditions for IIR Notch Filters Using the Vector Projection Method with Minimum Delay

In this paper, two approaches to determining the non-zero initial conditions for the difference equation of notch filters are proposed and analyzed. The vector of non-zero initial conditions is determined to reduce the transient of the considered IIR notch filters. Both presented approaches are based on the vector projection method. The first method is based on the iterative determination of the vectors of initial conditions using samples available at a given moment. The main goal of the second approach is to reduce the computational cost compared to the first method with a slight deterioration in the quality of filtration. In order to demonstrate the suitability of the proposed methods, they have been used in simulation studies of power line interference filtering from disturbed ECG signals. The use of the proposed methods allowed for a significant reduction of the transient in the filter response with a shorter delay than in the classical vector projection method.

Leukemia Detection Using Invariant Structural Cascade Segmentation Based on Deep Vectorized Scaling Neural Network

Leukemia is one of the deadliest diseases that occur in white blood cells which is identified in microscopic images from blood samples. Researchers have developed various techniques to diagnose leukemia using a machine learning approach by analyzing micro imaging blood samples. During image screening, the Damaged cells be identified based on manually counting on similar structure lymphocytes and monocytes structures, but the variant difference of both cells aren’t identified accurately. So the identification failures that occur lead to failed accurate cancer detection because feature variants project equal cell structure. To resolve this problem, we propose an Invariant Structural Cascade Segmentation (ISCS) based on Deep Vectorized Scaling Neural Network (DVSNN) is implemented to detect the Leukemia Cancer automatically from bio-blood samples micro image for early diagnosis. First, the Leukemia Cancer micro-image dataset (LCMID) was collected and preprocessed into a noise-free dataset based on adaptive median filters. Then the segmentation was carried to partition the microcells using Invariant structural cascade segmentation (ISCS) optimized with watershed to identify the features such as texture, pixel color, pixel intensity. For identifying the structural components of cells variation difference using Angular Vector Projection (AVP) was applied to find the structural variance. Then the histogram color equalizer (HCE) was applied to select the damaged cells using K-counts and their feature weight. Then the selected feature weights are trained into Deep vectorized scaling the neural network to classify the risk of the Leukemia cancer cells. This identifies the cancer cells effectively from micro image cells for detecting the risk of the patients. This improves the sensitivity, specificity rate as well in classification accuracy compared to the other methods.

PCEP: Few-Shot Model-Based Source Camera Identification

Source camera identification is an important branch in the field of digital forensics. Most existing works are based on the assumption that the number of training samples is sufficient. However, in practice, it is unrealistic to obtain a large amount of labeled samples. Therefore, in order to solve the problem of low accuracy for existing methods in a few-shot scenario, we propose a novel identification method called prototype construction with ensemble projection (PCEP). In this work, we extract a variety of features from few-shot datasets to obtain rich prior information. Then, we introduce semi-supervised learning to complete the construction of prototype sets. Subsequently, we use the prototype sets to retrain SVM classifiers, and take the posterior probability of each image sample belonging to each class as the final projection vector. Finally, we obtain classification results through ensemble learning voting. The PCEP method combines feature extraction, feature projection, classifier training and ensemble learning into a unified framework, which makes full use of image information of few-shot datasets. We conduct comprehensive experiments on multiple benchmark databases (i.e., Dresden, VISION and SOCRatES), and empirically show that our method achieves satisfactory performance and outperforms many recent methods in a few-shot scenario.

Quasi-Classical Trajectory Dynamics Study of the Reaction OH + H2S→H2O + SH and Its Isotopic Variants: Comparison with Experiment

The hydrogen abstraction reaction OH + H2S→H2O + SH plays an important role in acid rain formation, air pollution and climate change. In this work, the product energy disposals of the reaction and its isotopic variants OD + H2S and OD + D2S are calculated on a new ab-initio-based ground electronic state potential energy surface (PES) using the quasi-classical trajectory method. The PES is developed by fitting a total of 72,113 points calculated at the level of UCCSD(T)-F12a/aug-cc-pVTZ and using the fundamental invariant-neural network method, resulting in a total RMSE of 4.14 meV. The product H2O formed in the OH + H2S reaction at 298 K is found to be largely populated in the first overtone states of its symmetric and asymmetric stretching modes, while the vibrational distributions of the products HOD and D2O in the isotopically substituted reactions are visibly different. The computed product vibrational state distributions agree reasonably well with experimental results and are rationalized by the sudden vector projection model.

Virtual Stiffness: A Novel Biomechanical Approach to Estimate Limb Stiffness of a Multi-Muscle and Multi-Joint System

In recent years, different groups have developed algorithms to control the stiffness of a robotic device through the electromyographic activity collected from a human operator. However, the approaches proposed so far require an initial calibration, have a complex subject-specific muscle model, or consider the activity of only a few pairs of antagonist muscles. This study described and tested an approach based on a biomechanical model to estimate the limb stiffness of a multi-joint, multi-muscle system from muscle activations. The "virtual stiffness" method approximates the generated stiffness as the stiffness due to the component of the muscle-activation vector that does not generate any endpoint force. Such a component is calculated by projecting the vector of muscle activations, estimated from the electromyographic signals, onto the null space of the linear mapping of muscle activations onto the endpoint force. The proposed method was tested by using an upper-limb model made of two joints and six Hill-type muscles and data collected during an isometric force-generation task performed with the upper limb. The null-space projection of the muscle-activation vector approximated the major axis of the stiffness ellipse or ellipsoid. The model provides a good approximation of the voluntary stiffening performed by participants that could be directly implemented in wearable myoelectric controlled devices that estimate, in real-time, the endpoint forces, or endpoint movement, from the mapping between muscle activation and force, without any additional calibrations.

Quantum-Controlled Collisions of H2 Molecules.

The amount of information that can be obtained from a scattering experiment depends upon the precision with which the quantum states are defined in the incoming channel. By precisely defining the incoming states and measuring the outgoing states in a scattering experiment, we set up the boundary condition for experimentally solving the Schrödinger equation. In this Perspective we discuss cold inelastic scattering experiments using the most theoretically tractable H2 and its isotopologues as the target. We prepare the target in a precisely defined rovibrational (v, j, m) quantum state using a special coherent optical technique called the Stark-induced adiabatic Raman passage (SARP). v and j represent the quantum numbers of the vibrational and rotational energy levels, and m refers to the projection of the rotational angular momentum vector j on a suitable quantization axis in the laboratory frame. Selection of the m quantum numbers defines the alignment of the molecular frame, which is necessary to probe the anisotropic interactions. For us to achieve the collision temperature in the range of a few degrees Kelvin, we co-expand the colliding partners in a mixed supersonic beam that is collimated to define a direction for the collision velocity. When the bond axis is aligned with respect to a well-defined collision velocity, SARP achieves stereodynamic control at the quantum scale. Through various examples of rotationally inelastic cold scattering experiments, we show how SARP coherently controls the dynamics of anisotropic interactions by preparing quantum superpositions of the orientational m states within a single rovibrational (v, j) energy state. A partial wave analysis, which has been developed for the cold scattering experiments, shows dominance of a resonant orbital that leaves its mark in the scattering angular distribution. These highly controlled cold collision experiments at the single partial wave limit allow the most direct comparison with the results of theoretical computations, necessary for accurate modeling of the molecular interaction potential.

DBSCAN-Based Automatic De-Duplication for Software Quality Inspection Data

Software quality inspection will generate too much data, and removing duplicate data can improve the efficiency of software quality inspection. This paper studies the automatic de-duplication method of software quality inspection data based on density-based spatial clustering of applications with noise (DBSCAN) clustering. Intelligent optimization algorithm is used to generate software quality inspection data by initializing individuals, calculating fitness function value, improving individuals and splitting individuals that meet the conditions. Local linear embedding algorithm is selected to extract software quality inspection data features by searching neighborhood points, calculating reconstruction weight and projection vector. The extracted features are used to select DBSCAN multi-density clustering algorithm of regional division, and the automatic de-duplication of software quality inspection data is realized by grid division, data bin dividing and grid merging. The experimental results show that the precision and recall of this method are higher than 99%, and the resource consumption rate is low, which can effectively improve the efficiency of software quality inspection.

Multicomponent Seismic Data Reconstruction via a Biquaternion-Based Vector POCS Method

Multicomponent seismic exploration as a powerful geophysical technology has attracted more and more attention in seeking and identifying subtle oil and gas reservoirs. However, like traditional single-component acquisition, multicomponent seismic data acquisition also encounters sparse and irregular sampling problems. The conventional reconstruction methods treat multicomponent data as independent components and recover the missing traces in a component-by-component manner. These componentwise approaches ignore the internal mutual relationships among different components and damage the vector characteristics of the seismic wavefield. Quaternion algebra provides an effective vector representation tool for multicomponent data. Upon that, we present a new vector Projection Onto Convex Sets (POCS) method with biquaternion Fourier transform to reconstruct the irregularly missing traces of 3-D and three-component (3-D-3C) seismic data. Compared to the current real-valued quaternion reconstruction methods implemented in the time domain, the proposed method performed in the frequency domain can fully maintain the conjugate symmetry property of the biquaternion data and only reconstruct the positive or negative frequency slices of the observed 3-D-3C data. Besides, the new method can simultaneously interpolate the 3C or 4C data with different missing patterns. We compare the proposed vector POCS method with the scalar POCS method through experiments with a synthetic 3-D-3C dataset and a field 3-D-3C volume. Both experiments demonstrate the effectiveness and superiority of the proposed method.

FRACTAL ALGEBRA A MATHEMATICAL ALLEGORY

An abstract fractal algebra is developed with structures analogous to conventional linear algebra. Focus is on group properties and symmetries forming an abstract algebraic structure over the body of real numbers. The new algebra is worked out on a sample fractal geometry. Correspondences between fractal and linear algebra are explained with numerical examples, including fractal vectors and fractal versions of the vector sum, projections, scalar product, cross product, matrix, and matrix product. We allude to possible applications of fractal vectors in physics. This fractal algebra may open novel possibilities for analysis of fractal systems.