Six-dimensional Vector Research Articles

Subject-based feature extraction by using fisher WPD-CSP in brain–computer interfaces

Background and objectiveFeature extraction of electroencephalogram (EEG) plays a vital role in brain–computer interfaces (BCIs). In recent years, common spatial pattern (CSP) has been proven to be an effective feature extraction method. However, the traditional CSP has disadvantages of requiring a lot of input channels and the lack of frequency information. In order to remedy the defects of CSP, wavelet packet decomposition (WPD) and CSP are combined to extract effective features. But WPD-CSP method considers less about extracting specific features that are fitted for the specific subject. So a subject-based feature extraction method using fisher WPD-CSP is proposed in this paper. MethodsThe idea of proposed method is to adapt fisher WPD-CSP to each subject separately. It mainly includes the following six steps: (1) original EEG signals from all channels are decomposed into a series of sub-bands using WPD; (2) average power values of obtained sub-bands are computed; (3) the specified sub-bands with larger values of fisher distance according to average power are selected for that particular subject; (4) each selected sub-band is reconstructed to be regarded as a new EEG channel; (5) all new EEG channels are used as input of the CSP and a six-dimensional feature vector is obtained by the CSP. The subject-based feature extraction model is so formed; (6) the probabilistic neural network (PNN) is used as the classifier and the classification accuracy is obtained. ResultsData from six subjects are processed by the subject-based fisher WPD-CSP, the non-subject-based fisher WPD-CSP and WPD-CSP, respectively. Compared with non-subject-based fisher WPD-CSP and WPD-CSP, the results show that the proposed method yields better performance (sensitivity: 88.7±0.9%, and specificity: 91±1%) and the classification accuracy from subject-based fisher WPD-CSP is increased by 6–12% and 14%, respectively. ConclusionsThe proposed subject-based fisher WPD-CSP method can not only remedy disadvantages of CSP by WPD but also discriminate helpless sub-bands for each subject and make remaining fewer sub-bands keep better separability by fisher distance, which leads to a higher classification accuracy than WPD-CSP method.

Hybrid dual-tree complex wavelet transform and support vector machine for digital multi-focus image fusion

This study proposed a new method for multi-focus image fusion using hybrid wavelet and classifier. The image fusion process was formulated as a two-class classification problem: in and out-of-focus classes. First, a six-dimensional feature vector was extracted using sub-bands of dual-tree complex wavelet transform (DT-CWT) coefficients from the source images, which were then projected by a trained two-class support vector machine (SVM) to the class labels. A bacterial foraging optimization algorithm (BFOA) was developed to obtain the optimal parameters of the SVM. The output of the classification system was used as a decision matrix for fusing high-frequency wavelet coefficients from multi-focus source images in different directions and decomposition levels of the DT-CWT. After the high and low-frequency coefficients of the source images were fused, the final fused image was obtained using the inverse DT-CWT. Several existing methods were compared with the proposed method. Experimental results showed that our presented method outperformed the existing methods, in visual effect and in objective evaluation.

Surface Defect Detection on Optical Devices Based on Microscopic Dark-Field Scattering Imaging

Methods of surface defect detection on optical devices are proposed in this paper. First, a series of microscopic dark-field scattering images were collected with a line-scan camera. Translation transformation between overlaps of adjacent microscopic dark-field scattering images resulted from the line-scan camera’s imaging feature. An image mosaic algorithm based on scale invariance feature transform (SIFT) is proposed to stitch dark-field images collected by the line-scan camera. SIFT feature matching point-pairs were extracted from regions of interest in the adjacent microscopic dark-field scattering images. The best set of SIFT feature matching point-pairs was obtained via a parallel clustering algorithm. The transformation matrix of the two images was calculated by the best matching point-pair set, and then image stitching was completed through transformation matrix. Secondly, a sample threshold segmentation method was used to segment dark-field images that were previously stitched together because the image background was very dark. Finally, four different supervised learning classifiers are used to classify the defect represented by a six-dimensional feature vector by shape (point or line), and the performance of linear discriminant function (LDF) classifier is demonstrated to be the best. The experimental results showed that defects on optical devices could be detected efficiently by the proposed methods.

Construction of 6D supersymmetric field models in [formula omitted] harmonic superspace

We consider the six-dimensional hypermultiplet, vector and tensor multiplet models in (1,0) harmonic superspace and discuss the corresponding superfield actions. The actions for free (2,0) tensor multiplet and for interacting vector/tensor multiplet system are constructed. Using the superfield formulation of the hypermultiplet coupled to the vector/tensor system we develop an approach to calculation of the one-loop superfield effective action and find its divergent structure.

Motor Imagery EEG Recognition Based on WPD-CSP and KF-SVM in Brain Computer Interfaces

A recognition method based on Wavelet Packet Decomposition - Common Spatial Patterns (WPD-CSP) and Kernel Fisher Support Vector Machine (KF-SVM) is developed and used for EEG recognition in motor imagery brain–computer interfaces (BCIs). The WPD-CSP is used for feature extraction and KF-SVM is used for classification. The presented recognition method includes the following steps: (1) some important EEG channels are selected. The 'haar' wavelet basis is used to take wavelet packet decomposition. And some decomposed sub-bands related with motor imagery for each EEG channel are reconstructed to obtain the relevant frequency information. (2) A six-dimensional feature vector is obtained by the CSP feature extraction to the reconstructed signal. And then the within-class scatter is calculated based on the feature vector. (3) The scatter is added into the radical basis function to construct a new kernel function. The obtained new kernel is integrated into the SVM to act as its kernel function. To evaluate effectiveness of the proposed WPD-CSP + KF-SVM method, the data from the 2008 international BCI competition are processed. A preliminary result shows that the proposed classification algorithm can well recognize EEG data and improve the EEG recognition accuracy in motor imagery BCIs.

Hyper-Jerk Analysis of Robot Manipulators

In this work the hyper-jerk analysis of robot manipulators is addressed by means of the theory of screws. The reduced hyper-jerk state of a rigid body as observed from another body or reference frame is obtained as a six-dimensional vector by applying the concept of helicoidal vector field. Moreover, this contribution demonstrates that the reduced hyper-jerk state of a rigid body can be considered, similar to the velocity state, as a twist about a screw. Furthermore, the reduced hyper-jerk state is systematically obtained in pure screw form. Finally, a case study, which is verified with the aid of commercially available software, that consists of solving the kinematics, up to the hyper-jerk analysis, of a zero-torsion parallel manipulator is included in order to show the application of the method of kinematic analysis.

6D vector orthogonal transformation and its application in multiview video coding

Multiview video (MVV) is multiple video sequences that integrated different viewpoints data of the same three-dimensional (3D) scene. Each viewpoint data are taken from the ordinary video camera. Thus, the data are very large for the MVV. So compression is necessary in order to store and transmit effectively. Based on the theory of multi-dimensional vector matrix (MDVM), we propose a six-dimensional (6D) vector orthogonal transform nuclear matrix, and prove its orthogonality and energy concentration. We apply the theory to multiview video coding (MVC). This transformation is based on discrete cosine transform (DCT), which has the optimal performance for video data. We represent MVV data with a multi-dimensional (MD) mathematical model. The chosen MVV is earlier eight frames in YUV format from two viewpoints. We divide the Y, U and V components into cubes respectively, and combine the two views data into one cube, on which the transformation is conducted. Good results are obtained in terms of energy concentration. This paper provides a new method for handling MVV, and prepare for the next quantisation and coding.

Words-of-wisdom search system based on user's desired sentiment

Many search systems exist on the Internet. However, no system searches for information based on a query related to a user's sentiment. We propose a system that searches for information based on a user's sentiment. In this paper, we propose a words-of-wisdom search system as a first step of that research. Specifically, we propose a six-dimensional sentiment vector for words-of-wisdom. Next, we propose a method for calculating the value of sentiment words that consist of words-of-wisdom based on our experiment. Subsequently, we calculate sentiment values of words-of-wisdom using the value of sentiment words. We developed a prototype system and conducted experiments.

An efficient representation of Euclidean gravity I

We explore how the topology of spacetime fabric is encoded into the local structure of Riemannian metrics using the gauge theory formulation of Euclidean gravity. In part I, we provide a rigorous mathematical foundation to prove that a general Einstein manifold arises as the sum of SU(2)_L Yang-Mills instantons and SU(2)_R anti-instantons where SU(2)_L and SU(2)_R are normal subgroups of the four-dimensional Lorentz group Spin(4) = SU(2)_L x SU(2)_R. Our proof relies only on the general properties in four dimensions: The Lorentz group Spin(4) is isomorphic to SU(2)_L x SU(2)_R and the six-dimensional vector space of two-forms splits canonically into the sum of three-dimensional vector spaces of self-dual and anti-self-dual two-forms. Consolidating these two, it turns out that the splitting of Spin(4) is deeply correlated with the decomposition of two-forms on four-manifold which occupies a central position in the theory of four-manifolds.

Spatio-temporal coupling of random electromagnetic pulses interacting with reflecting gratings

Matrix optics is applied to a class of random, in time and space, electromagnetic pulsed beam-like (REMPB) radiation interacting with linear optical elements. A 6×6 order matrix describing transformation of a six-dimensional state vector including four spatial and two temporal positions within the field is used to derive conditions for spatio-temporal coupling. An example is included which deals with a spatio-temporal coupling in a typical REMPB on reflection from a reflecting grating. Electromagnetic nature of such interaction is explored via considering dependence of the degree of polarization of the reflected REMPB on its source and on the structure of the grating.

A Beginner's Guide to 6-D Vectors (Part 1)

A rigid body has six degrees of motion freedom, so why not use six-dimensional (6-D) vectors to describe its motions and the forces acting upon it? In fact, some roboticists already do this, and the practice is becoming more common. The purpose of this tutorial is to present a beginner's guide to 6-D vectors in sufficient detail that a reader can begin to use them as a practical problem-solving tool right away. This tutorial covers the basics, and Part 2 will cover the application of 6-D vectors to a variety of robot kinematics and dynamics calculations.

Role of electronic nematicity in the interplay between s- and d-wave broken-symmetry states

To understand the role of electronic nematic order in the interplay between s- and d-wave particle–particle or particle–hole condensate states, relations between various s- and d-wave order parameters are studied. We find that the nematic operator transforms two independent six-dimensional vectors. The d-wave superconducting, d-density wave, and antiferromagnetic orders are organized into one vector, and the s-wave superconducting, charge density wave, and spin-triplet d-density wave orders into the other vector. Each vector acts as a superspin and transforms under the action of SO(6) where charge, spin, η- and π-pairing, spin-triplet nematic operators satisfy the SO(6) Lie algebra. Electronic nematic order is not a part of the SO(6) group. It commutes with all 15 generators. Our findings imply that nematic order does not affect the competition among the order parameters within the same superspin, while it strongly interferes the interplay between two order parameters that belong to different superspins. For example, nematicity allows a linear coupling between d- and s-wave superconducting order parameters which modifies the superconducting transition temperature. A generalized Ginzburg-Landau theory and further physical implications are discussed.

A geometric interpretation of coherent structures in Navier–Stokes flows

The pressure in the incompressible three-dimensional Navier–Stokes and Euler equations is governed by Poisson's equation: this equation is studied using the geometry of three-forms in six dimensions. By studying the linear algebra of the vector space of three-forms Λ 3 W * where W is a six-dimensional real vector space, we relate the characterization of non-degenerate elements of Λ 3 W * to the sign of the Laplacian of the pressure—and hence to the balance between the vorticity and the rate of strain. When the Laplacian of the pressure, Δ p , satisfies Δ p >0, the three-form associated with Poisson's equation is the real part of a decomposable complex form and an almost-complex structure can be identified. When Δ p <0, a real decomposable structure is identified. These results are discussed in the context of coherent structures in turbulence.

A Screw Theory of Timoshenko Beams

In this work, the classic theory of Timoshenko beams is revisited using screw theory. The theory of screws is familiar from robotics and the theory of mechanisms. A key feature of the screw theory is that translations and rotations are treated on an equal footing and here this means that bending, torsion, and extensions can all be considered together in a particularly simple manner. By combining forces and torques into a six-dimensional vector called a wrench, Hooke’s law for the Timoshenko beam can be written in a very simple form. From here simple expressions can be found for the kinetic and potential energy densities of the beam. Hence equations of motion for small vibrations of the beam can be easily derived. The screw theory also leads to a new understanding of the boundary conditions for beams. It is demonstrated that simple boundary conditions are closely related to mechanical joints. In order to set up the boundary conditions for a beam attached to a joint, a system of wrenches dual to the screws representing the freedoms of the joint must be found. Finally, a screw version of the Rayleigh–Ritz numerical method is introduced. An example is investigated in which the boundary conditions on the beam lead to vibrational modes of the beam involving bending, torsion, and extension at the same time.

A Dynamical State Space Representation and Performance Analysis of a Feedback-Controlled Rotary Left Ventricular Assist Device

The left ventricular assist device (LVAD) is a mechanical device that can assist an ailing heart in performing its functions. The latest generation of such devices is comprised of rotary pumps which are generally much smaller, lighter, and quieter than the conventional pulsatile pumps. The rotary pumps are controlled by varying the rotor (impeller) speed. If the patient is in a health care facility, the pump speed can be adjusted manually by a trained clinician to meet the patient's blood needs. However, an important challenge facing the increased use of these LVADs is the desire to allow the patient to return home. The development of an appropriate feedback controller for the pump speed is therefore crucial to meet this challenge. In addition to being able to adapt to changes in the patient's daily activities by automatically regulating the pump speed, the controller must also be able to prevent the occurrence of excessive pumping (known as suction) which may cause collapse of the ventricle. In this paper we will discuss some theoretical and practical issues associated with the development of such a controller. As a first step, we present and validate a state-space mathematical model, based on a nonlinear equivalent circuit flow model, which represents the interaction of the pump with the left ventricle of the heart. The associated model is a six-dimensional vector of time varying nonlinear differential equations. The time variation occurs over four consecutive intervals representing the contraction, ejection, relaxation, and filling phases of the left ventricle. The pump in the model is represented by a nonlinear differential equation which relates the pump rotational speed and the pump flow to the pressure difference across the pump. Using this model, we discuss a feedback controller which adjusts the pump speed based on the slope of the minimum pump flow signal, which is one of the model state variables that can be measured. The objective of the controller is to increase the speed until the envelope of the minimum pump flow signal reaches an extreme point and maintain it afterwards. Simulation results using the model equipped with this feedback controller are presented for two different scenarios of patient activities. Performance of the controller when measurement noise is added to the pump flow signal is also investigated.

Geometric phases and Bloch-sphere constructions forSU(N)groups with a complete description of the SU(4) group

A two-sphere (``Bloch'' or ``Poincare'') is familiar for describing the dynamics of a spin-$1∕2$ particle or light polarization. Analogous objects are derived for unitary groups larger than SU(2) through an iterative procedure that constructs evolution operators for higher-dimensional $\mathrm{SU}(N)$ in terms of lower-dimensional ones. We focus, in particular, on the SU(4) of two qubits which describes all possible logic gates in quantum computation and entangled states in quantum-information sciences. For a general Hamiltonian of SU(4) with 15 parameters, and for Hamiltonians of its various subgroups so that fewer parameters suffice, we derive Bloch-like rotation of unit vectors analogous to the one familiar for a single spin in a magnetic field. The unitary evolution of a quantal spin pair is thereby expressed as rotations of real, many-dimensional vectors. Correspondingly, the manifolds involved are Bloch two-spheres along with higher dimensional manifolds such as a four-sphere for the SO(5) subgroup and an eight-dimensional Grassmannian manifold for the general SU(4). The latter may also be viewed as two, mutually orthogonal, real six-dimensional unit vectors moving on a five-sphere with an additional phase constraint. This geometrical picture for two spins provides the extension and generalization of the Bloch sphere that has proved invaluable for the understanding of the dynamics of a single spin.

O®-Line Chinese Signature Veri¯cation Based on Segmentation and HMM

Automatic off-line Chinese signature verification is a very complicated problem. The difficulty lies in the fact that it is hard to find a signature model that is insusceptible to intro-classes distance and at the same time is sensitive to inter-classes distance. In this paper, a simple robust segmentation method with low computation cost is proposed which can successfully extract strokes of handwritten Chinese characters and takes into account the characteristics of signature verification. After being segmented and feature extracted, each signature is represented by a series of six-dimensional vectors quantized using an improved vector quantization method to obtain a series of observation values. Twelve genuine samples were used to train the signature DHMM of a writer and 4576 signatures are used in the test. The cross error rate is only 5.5%.

Retinal Vessel Centerline Extraction Using Multiscale Matched Filters, Confidence and Edge Measures

Motivated by the goals of improving detection of low-contrast and narrow vessels and eliminating false detections at nonvascular structures, a new technique is presented for extracting vessels in retinal images. The core of the technique is a new likelihood ratio test that combines matched-filter responses, confidence measures and vessel boundary measures. Matched filter responses are derived in scale-space to extract vessels of widely varying widths. A vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile. Vessel boundary measures and associated confidences are computed at potential vessel boundaries. Combined, these responses form a six-dimensional measurement vector at each pixel. A training technique is used to develop a mapping of this vector to a likelihood ratio that measures the "vesselness" at each pixel. Results comparing this vesselness measure to matched filters alone and to measures based on the Hessian of intensities show substantial improvements, both qualitatively and quantitatively. The Hessian can be used in place of the matched filter to obtain similar but less-substantial improvements or to steer the matched filter by preselecting kernel orientations. Finally, the new vesselness likelihood ratio is embedded into a vessel tracing framework, resulting in an efficient and effective vessel centerline extraction algorithm.

An object-based image retrieval system for digital libraries

A novel approach to clustering for image segmentation and a new object-based image retrieval method are proposed. The clustering is achieved using the Fisher discriminant as an objective function. The objective function is improved by adding a spatial constraint that encourages neighboring pixels to take on the same class label. A six-dimensional feature vector is used for clustering by way of the combination of color and busyness features for each pixel. After clustering, the dominant segments in each class are chosen based on area and used to extract features for image retrieval. The color content is represented using a histogram, and Haar wavelets are used to represent the texture feature of each segment. The image retrieval is segment-based; the user can select a query segment to perform the retrieval and assign weights to the image features. The distance between two images is calculated using the distance between features of the constituent segments. Each image is ranked based on this distance with respect to the query image segment. The algorithm is applied to a pilot database of natural images and is shown to improve upon the conventional classification and retrieval methods. The proposed segmentation leads to a higher number of relevant images retrieved, 83.5% on average compared to 72.8 and 68.7% for the k-means clustering and the global retrieval methods, respectively.

Kinematics and singularity analyses of a 4-dof parallel manipulator using screw theory

In this work, the kinematics and singularity analyses of a four degrees of freedom parallel manipulator are investigated using the theory of screws. As an initial step, the forward position analysis is carried out and forward position equations are obtained in a closed form, thanks to the simplicity of the architecture of the proposed mechanism. Afterwards, simple and compact expressions are derived for the velocity and reduced acceleration states of the moving platform w.r.t. the fixed coordinate frame of the manipulator, both in screw form, through each limb, and as six-dimensional vectors. The Klein form, a symmetrical bilinear form of the Lie algebra e(3), plays a central role in the present work. A numerical example is provided to demonstrate the efficacy of screw theory in efficiently analysing the kinematics and singularity of the parallel manipulator. The numerical results from the kinematic analysis are verified with results produced with a commercially available dynamic and kinematic simulation program.