Components Of Vector Research Articles

Distributed debiased estimation of high-dimensional partially linear models with jumps

In this paper, we focus on the estimations of both parameter vector and nonparametric component in a high-dimensional partially linear model with jumps within the framework of divide and conquer strategy. We find that a three-stage estimation procedure works well in this setting. Applying the lasso penalty and projected spline approximation, first a profiled estimator for the linear part and a projected spline estimator for the nonparametric part are obtained on each local machine. In the second stage, an efficient jump detection algorithm is developed to obtain the new knot sequence, and then based on this, the estimate of the nonparametric function is obtained and averaged after plugging in the linear part estimate on each local machine. The aggregated estimate of the nonparametric function is then computed by pooling these local estimates. In the third stage, a debiased lasso estimator is averaged to obtain a distributed debiased estimator of the linear part after plugging in the aggregated estimate of nonparametric function. Asymptotic properties of resultant estimators are established under some mild assumptions. Some simulations are conducted to illustrate the empirical performances of our proposed method.

Intra-grain orientation distributions in deformed aluminium: Synchrotron X-ray diffraction experiment and crystal-plasticity finite-element simulation

The development of intra-grain orientation distributions is analyzed for 446 individual grains of an aluminium polycrystal deformed in tension to successive strains of 1, 1.5, 2, 2.5 and 4.5%. In the experiment, diffraction contrast tomography (DCT) and far-field 3D X-ray diffraction microscopy (3DXRD) were used, and a reduced-order representation of the intra-grain orientation distributions was determined from the broadening of the 3DXRD diffraction spots. A high-resolution finite-element simulation (700 elements/grain on average) was conducted on the same polycrystal, providing detailed information on orientation evolution. Several metrics were considered to analyze the experimental and simulated orientation distributions, including the average disorientation angles and the preferential disorientation axes. The average disorientation angles were found to increase almost linearly with strain, and to be in appreciable correlation between experiment and simulation (albeit evolving faster in simulation). It was shown that the preferential disorientation axes are distributed perpendicular to the tensile direction (Z) and perpendicular to the X–Y component of the Rodrigues orientation vector. Detailed crystal plasticity analyses showed that the distribution of preferential disorientation axes is related to the presence of larger slip variabilities on particular slip systems. Using a simplified approach, it was shown that accurate knowledge of the average stress of a grain is necessary in order to predict the preferential disorientation axis, which is well-captured by the finite-element simulation. The intra-grain stress distribution appears to have comparatively less influence.

Dynamic Properties of Remote Sensing Algorithm in Digital Resistance Elements

In microprocessor-based distance protection of lines, digital resistance elements are used as measuring instruments for determining the components of the input resistance vector and their subsequent mathematical comparison with the boundaries of the selected response characteristics. The values of the resistance vector components are calculated from the voltages and currents measured at the installation site of the protection. The most common are algorithms for remote measurements of input resistance based on: two samples of instantaneous values of line voltage and current; line models; using orthogonal voltage components and current. In the resistance elements of modern microprocessor line protections for remote measurements, the last of the above algorithms is most widely used. Its dynamic properties are determined mainly by the implemented method of generating the orthogonal components of the input signals. In distance protection measuring device, non-recursive digital Fourier filters are predominantly used for this purpose. To improve the dynamic properties of the remote measurement algorithm based on them, it is proposed to correct additionally dynamic errors in transient modes. In the dynamic modeling environment MATLAB-Simulink-SimPowerSystems, digital model is implemented that allows for a comparative assessment of the dynamic properties of the proposed algorithm for remote measurements of input resistance based on the results of a computational experiment. The research results have shown that the proposed algorithm for remote measurements of input resistance has higher dynamic properties compared to the known ones.

Investigation of polarization transformations performed with a refractive bi-conical axicon using the FDTD method

We investigate polarization transformations carried out with a refractive bi-conical axicon using the FDTD method. The approach is based on the transformation of a circularly polarized optical beam into an azimuthally polarized beam due to the use of a single refractive element with two conical surfaces. On the inner surface of the element, polarization conversion occurs due to the reflection and refraction of rays at the Brewster angle, while the outer surface operates as a converted beam collimator. The distributions of the components of the electric field vector and the polarization vector at different distances from the optical element are considered as criteria for a successful polarization transformation. By numerical simulation of the performance of a bi-conical axicon made of glass with a refractive index of n = 1.4958, the efficiency of the proposed approach for a circularly polarized Gaussian beam with a wavelength of λ = 1.5 µm is shown. The proposed element is shown to be immune to chromatic aberrations in a significant range of changes in the refractive index of the element material and incident wavelengths (1.5 ≤ n ≤ 1.7; 1 μm ≤ λ ≤ 1.5 μm).

Features of the formation of the nutation line in nuclear magnetic magnetometers and flow meters with flowing liquid.

The mechanism of formation of a nutation line in a flowing liquid is considered. New ones have been developed equations of motion of the longitudinal and transverse components of the magnetization vector in the nutation coil, which take into account the inhomogeneity of the magnetic field ΔH_0 in the zone of influence of the radio frequency field H_1 on the flowing liquid. The equations also take into account the nature of the change in the value of the magnetic field inhomogeneity ΔH_0 when the fluid moves along the nutation coil. The results of experimental studies of the shape of the nutation line are presented. Theoretical calculations are compared with experimental data.

A Note on Fractional Curl Operator

In this letter, we demonstrate that the fractional curl operator, widely used in electromagnetics since 1998, is essentially a rotation operation of components of the complex Riemann-Silberstein vector representing the electromagnetic field. It occurs that after the wave decomposition into circular polarisations, the standard duality rotation with the angle depending on the fractional order is applied to the left-handed basis vector whilst the right-handed basis vector stems from the complex conjugation of the left-handed counterpart. Therefore, the fractional curl operator describes another representation of rotations of the electromagnetic field decomposed into circular polarisations. Finally, we demonstrate that this operator can describe a single-qubit phase-shift gate in quantum computing.

Generation of Light Fields with Controlled Non-Uniform Elliptical Polarization When Focusing on Structured Laser Beams

We study the sharp focusing of the input structured light field that has a non-uniform elliptical polarization: the parameters of the ellipse depend on the position in the input plane (we limited ourselves to the dependence only on the angular variable). Two types of non-uniformity were considered. The first type corresponds to the situation when the semi-axes of the polarization ellipse are fixed while the slope of the major semi-axis changes. The second type is determined by the situation when the slope of the major semi-axis of the polarization ellipse is constant, and the ratio between the semi-axis changes (we limited ourselves to the trigonometric dependence of this ratio on the polar angle). Theoretical and numerical calculations show that in the case of the first type of non-uniformity, if the tilt angle is a multiple of the polar angle with an integer coefficient, then the intensity distribution has rotational symmetry, and the energy flow is radially symmetric and has the negative direction near the optical axis. In this second case, the intensity symmetry is not very pronounced, but with an odd dependence of the ratio of the semi-axes of the polarization ellipse, the focused field at each point has a local linear polarization, despite the rather complex form of the input field. In addition, we investigate the distribution of the longitudinal component of the Poynting vector. The obtained results may be used for the formation of focused light fields with the desired distributions of polarization, Poynting vector density, or spin angular momentum density in the field of laser manipulation and laser matter interaction.

Experimental and numerical study of flow structure in a model of distal anastomosis of femoral artery

Physical and numerical simulation of the steady blood flow was carried out focusing on the distal end-to-side anastomosis of a graft to the femoral artery. The angle between the graft and the artery was 60°. Two Reynolds numbers were considered that corresponded to the physiological range when estimated using the average (Re = 240) and maximum (Re = 1640) blood flow through the human femoral artery over a single cardiac cycle. The experiment included flow visualization and measurements of instantaneous vector fields of velocity using an optical SIV (Smoke Image Velocimetry) technique. Direct numerical simulation (DNS) was employed for numerical study. The distribution of blood flows through the branches of the main artery was 80 % in the antegrade and 20 % in the retrograde direction. Main patterns in the distribution of velocity and its root-mean-square fluctuations in both branches of the main artery were revealed. Flow separation regions were observed in the branching area. Additionally, secondary flows (Prandtl’s vortices of the first kind) were revealed. The flow in the branching area was still laminar Re = 240, while the signs of transition to turbulence were documented within separation regions at Re = 1640. Distributions of streamwise and circumferential components of skin friction vector were estimated. In some regions of flow, these components were shown to be comparable in size. The location of regions was revealed in which the friction magnitude in the considered flow regimes was lower than the one in an unimpaired artery (developed laminar flow in a circular pipe) at appropriate Reynolds numbers.

Epidemiological Model for Conventional Tobacco Control Measures and Tobacco Endgame Policies.

Epidemiological models, also known as host-agent-vector-environment models, are utilized in public health to gain insights into disease occurrence and to formulate intervention strategies. In this paper, we propose an epidemiological model that incorporates both conventional measures and tobacco endgame policies. Our model suggests that conventional measures focus on relationships among agent-vector-host-environment components, whereas endgame policies inherently aim to change or eliminate those components at a fundamental level. We also found that the vector (tobacco industry) and environment (physical and social surroundings) components were insufficiently researched or controlled by both conventional measures and tobacco endgame policies. The use of an epidemiological model for tobacco control and the tobacco endgame is recommended to identify areas that require greater effort and to develop effective intervention measures.

Helicopter radio system for low altitudes and flight speed measuring with pulsed ultra-wideband stochastic sounding signals and artificial intelligence elements

The subject matter of this study is algorithms for measuring the components of an aircraft speed vector and altitude. The goal of this study is to improve algorithms for processing wideband stochastic pulse signals in helicopter low-altitude and flight-speed radio systems by introducing secondary signal processing based on artificial intelligence elements. The tasks to be solved are as follows: to develop an optimal algorithm for determining the speed and altitude of flight for a helicopter radio complex; to supplement the signal processing algorithm with an artificial intelligence-based processor to determine the "safety" of the current trajectory; provide the pilot with relevant information about possible options for further actions based on an analysis of the current position of the helicopter and flight parameters; and to analyse the efficiency of the proposed complex when using various artificial intelligence-based algorithms. The methods used are as follows: methods of mathematical statistics and optimal solutions for solving problems of statistical synthesis of active radio complex structure; methods of machine learning; and methods of computer simulation. The following results were obtained. The algorithms for signal processing in a helicopter radio complex are obtained by the method of maximum likelihood, and the use of three radio channels to calculate the full vector of speed and altitude is argued. The structure of a secondary information processing system, using algorithms based on artificial intelligence is proposed. The effectiveness of determining the safety of the current landing trajectory using various algorithms based on artificial intelligence (LinearSVC, GaussianNB, DecisionTreeClassifier, RandomForestClassifier, KNeighborsClassifier, MLPClassifier and RidgeClassifier) was analysed. Conclusions. The simulation results show that in the presence of accurate (noise-free) information on the current location of the helicopter, its axial velocities, and a map of the terrain with defined areas dangerous for landing, the DecisionTreeClassifier and RandomForestClassifier algorithms can provide a high probability of correctly determining the safety of the current landing trajectory. At the same time, in the presence of instability in the measurements of helicopter movement parameters, only the RandomForestClassifier algorithm maintains high accuracy.

Generalized Finsler Geometry and the Anisotropic Tearing of Skin

A continuum mechanical theory with foundations in generalized Finsler geometry describes the complex anisotropic behavior of skin. A fiber bundle approach, encompassing total spaces with assigned linear and nonlinear connections, geometrically characterizes evolving configurations of a deformable body with the microstructure. An internal state vector is introduced on each configuration, describing subscale physics. A generalized Finsler metric depends on the position and the state vector, where the latter dependence allows for both the direction (i.e., as in Finsler geometry) and magnitude. Equilibrium equations are derived using a variational method, extending concepts of finite-strain hyperelasticity coupled to phase-field mechanics to generalized Finsler space. For application to skin tearing, state vector components represent microscopic damage processes (e.g., fiber rearrangements and ruptures) in different directions with respect to intrinsic orientations (e.g., parallel or perpendicular to Langer’s lines). Nonlinear potentials, motivated from soft-tissue mechanics and phase-field fracture theories, are assigned with orthotropic material symmetry pertinent to properties of skin. Governing equations are derived for one- and two-dimensional base manifolds. Analytical solutions capture experimental force-stretch data, toughness, and observations on evolving microstructure, in a more geometrically and physically descriptive way than prior phenomenological models.

METHODOLOGY FOR MODELING THE SPREAD OF RADIOACTIVE SUBSTANCES IN CASE OF AN EMERGENCY RELEASE AT A NUCLEAR POWER PLANT

The methodology for modeling the propagation of accidental releases of radionuclides from a power unit of a nuclear power plant has been developed. The calculation method takes into account the most critical factors propagation cloud - wind direction and speed, the intensity of the release radionuclides change: semi-continuous release, long-term release, instantaneous release. Diffuse processes and the presence of interference in the form of buildings were also taken into account. To solve the modeling equation of the aerodynamic model, the velocity potential equation is solved. The use of this equation instead of the traditional Novier-Stokes equation makes it possible to rationalize the calculation process in terms of the speed obtaining simulated data. To build a numerical model, a rectangular difference grid is used. The velocity potential and the quantities values of volumetric activity are determined at the centers of difference cells. The value of the airflow velocity vector component is determined on the sides of the difference cells. A finite-difference splitting scheme is used for numerical integration of the equation convective-diffusion transfer radionuclides. A computer code was developed on the basis of the constructed numerical model, the programming language Fortran was used. The approach used makes it possible to reduce the time for obtaining one scenario of an accident development. The cloud propagation dynamics determining is carried out almost in real time. This allows you to quickly respond to changing situations and make adequate decisions.

Complex Dependence of Escherichia coli-based Cell-Free Expression on Sonication Energy During Lysis.

Cell lysis─by sonication or bead beating, for example─is a key step in preparing extracts for cell-free expression systems. To create high protein-production capacity extracts, standard practice is to lyse cells sufficiently to thoroughly disrupt the membrane and thus extract expression machinery but without degrading that machinery. Here, we investigate the impact of different sonication energy inputs on the protein-production capacity of Escherichia coli extracts. While the existence of operator-specific optimal sonication energy inputs is widely known, our findings show that the sonication energy input that yields maximal protein output from a given expression template may depend on plasmid concentration, transcriptional and translational features (e.g., promoter), and other expression vector components (e.g., origin of replication). These results indicate that sonication protocols cannot be standardized to a single optimum, suggest strategies for improving protein yields, and more broadly highlight the need for better metrics and protocols for characterizing cell extracts.

Polarization Sensitivity in Scattering-Type Scanning Near-Field Optical Microscopy—Towards Nanoellipsometry

Electric field enhancement mediated through sharp tips in scattering-type scanning near-field optical microscopy (s-SNOM) enables optical material analysis down to the 10-nm length scale and even below. Nevertheless, the out-of-plane electric field component is primarily considered here due to the lightning rod effect of the elongated s-SNOM tip being orders of magnitude stronger than any in-plane field component. Nonetheless, the fundamental understanding of resonantly excited near-field coupled systems clearly allows us to take profit from all vectorial components, especially from the in-plane ones. In this paper, we theoretically and experimentally explore how the linear polarization control of both near-field illumination and detection can constructively be implemented to (non-)resonantly couple to selected sample permittivity tensor components, e.g., explicitly to the in-plane directions as well. When applying the point-dipole model, we show that resonantly excited samples respond with a strong near-field signal to all linear polarization angles. We then experimentally investigate the polarization-dependent responses for both non-resonant (Au) and phonon-resonant (3C-SiC) sample excitations at a 10.6 µm and 10.7 µm incident wavelength using a tabletop CO2 laser. Varying the illumination polarization angle thus allows one to quantitatively compare the scattered near-field signatures for the two wavelengths. Finally, we compare our experimental data to simulation results and thus gain a fundamental understanding of the polarization’s influence on the near-field interaction. As a result, the near-field components parallel and perpendicular to the sample surface can be easily disentangled and quantified through their polarization signatures, connecting them directly to the sample’s local permittivity.

Prediction of corneal power vectors after cataract surgery with toric lens implantation-A vector analysis.

Intraocular lenses are typically calculated based on a pseudophakic eye model, and for toric lenses (tIOL) a good estimate of corneal astigmatism after cataract surgery is required in addition to the equivalent corneal power. The purpose of this study was to investigate the differences between the preoperative IOLMaster (IOLM) and the preoperative and postoperative Casia2 (CASIA) tomographic measurements of corneal power in a cataractous population with tIOL implantation, and to predict total power (TP) from the IOLM and CASIA keratometric measurements. The analysis was based on a dataset of 88 eyes of 88 patients from 1 clinical centre before and after tIOL implantation. All IOLM and CASIA keratometric and total corneal power measurements were converted to power vector components, and the differences between preoperative IOLM or CASIA and postoperative CASIA measurements were assessed. Feedforward neural network and multivariate linear regression prediction algorithms were implemented to predict the postoperative total corneal power (as a reference for tIOL calculation) from the preoperative IOLM and CASIA keratometric measurements. On average, the preoperative IOLM keratometric / total corneal power under- / overestimates the postoperative CASIA keratometric / real corneal power by 0.12 dpt / 0.21 dpt. The prediction of postoperative CASIA real power from preoperative IOLM or CASIA keratometry shows that postoperative total corneal power is systematically (0.18 dpt / 0.27 dpt) shifted towards astigmatism against the rule, which is not reflected by keratometry. The correlation of postoperative CASIA real power to the corresponding preoperative CASIA values is better than those as compared to the preoperative IOLM keratometry. However, there is a large variation from preoperative IOLM or CASIA keratometry to the postoperative CASIA real power of up to 1.1 dpt (95% confidence interval). One of the challenges of tIOL calculation is the prediction of postoperative total corneal power from preoperative keratometry. Keratometric power restricted to a front surface measurement does not fully reflect the situation of corneal back surface astigmatism, which typically adds some extra against the rule astigmatism.

Numerical modeling of nonlinear deformation processes for shells of medium thickness

When modeling a nonlinear isotropic eight-node finite element, the main kinematic and physical relationships are determined. In particular, isoparametric approximations of the geometry and an unknown displacement increment vector, covariant and contravariant components of basis vectors, metric tensors, strain tensors (Cauchy - Green and Almansi) and true Cauchy stresses in the initial and current configuration are introduced. Next, a variational equation is introduced in the stress rates in the actual configuration without taking into account body forces and the Seth material is considered, where the Almansi strain tensor is used as the finite strain tensor. Linearization of this variational equation, discretization of the obtained relations (stiffness matrix, matrix of geometric stiffness) is carried out. The resulting expressions are written as a system of linear algebraic equations. Several test cases are considered. The problem of bending a strip into a ring is presented. This problem is solved analytically, based on kinematic and physical relationships. Examples of nonlinear deformation of cylindrical and spherical shells are also shown. The method proposed in this paper for constructing a three-dimensional finite element of the nonlinear theory of elasticity, using the Seth material, makes it possible to obtain a special finite element, with which it is quite realistic to calculate the stress state of shells of medium thickness using a single-layer approximation in thickness. The obtained results of test cases demonstrate the operability of the proposed technique.

Spatial audio reproduction over ad hoc loudspeaker array using near-field compensation in spherical harmonics domain

Spatial audio reproduction using the loudspeaker array introduces the curvature effect leading to a distorted listening experience when the listener is in the near field. In the near-field, the loudspeakers are approximated as point sources (spherical wave) and amplify the mode vectors. Further, the problem becomes more challenging for the irregular loudspeaker arrangement, which causes uneven energy distribution in the reproduction region. In this context, a near-field compensation is applied to the encoded ambisonics coefficients. An optimization problem is formulated, such as the loudspeaker gains encoded with spherical harmonics basis coefficients should match the target ambisonics coefficients. Further, the in-phase and quadrature components of the energy localization vector are imposed as the constraints to direct maximum energy in the reproduction region. The solution to the optimization problem is obtained using a derivative-free optimization solver. The performance of the proposed methods is evaluated for ITU-R recommended loudspeaker layouts using the technical and perceptual evaluation attributes.

Adaptive Diffusion Pairwise Fused Lasso LMS Algorithm Over Networks.

The topic of identification for sparse vector in a distributed way has triggered great interest in the area of adaptive filtering. Grouping components in the sparse vector has been validated to be an efficient way for enhancing identification performance for sparse parameter. The technique of pairwise fused lasso, which can promote similarity between each possible pair of nonnegligible components in the sparse vector, does not require that the nonnegligible components have to be distributed in one or multiple clusters. In other words, the nonnegligible components may be randomly scattered in the unknown sparse vector. In this article, based on the technique of pairwise fused lasso, we propose the novel pairwise fused lasso diffusion least mean-square (PFL-DLMS) algorithm, to identify sparse vector. The objective function we construct consists of three terms, i.e., the mean-square error (MSE) term, the regularizing term promoting the sparsity of all components, and the regularizing term promoting the sparsity of difference between each pair of components in the unknown sparse vector. After investigating mean stability condition of mean-square behavior in theoretical analysis, we propose the strategy of variable regularizing coefficients to overcome the difficulty that the optimal regularizing coefficients are usually unknown. Finally, numerical experiments are conducted to verify the effectiveness of the PFL-DLMS algorithm in identifying and tracking sparse parameter vector.

A simple mathematical method to identify optimal biplane fluoroscopic angulations for chronic total occlusion percutaneous coronary intervention using CT angiography.

The concept of three-dimensional (3D) wiring for chronic total occlusion (CTO) percutaneous coronary intervention (PCI) is now widely accepted among coronary interventionalists. The 3 axes, i.e., the 2 X-ray beams and the CTO segment, should intersect with each other at as close to a right angle as possible. However, how to specify optimal fluoroscopic angulations for a given CTO segment has not been well established. We aimed to develop a simple and practical method to identify optimal fluoroscopic angulations for CTO PCI. A CTO vector can be derived from slab maximum intensity projection (MIP) images of coronary computed tomography (CT) angiography. Using trigonometric functions, the inner product of vectors and the equation of a plane, we calculated 2 fluoroscopic vectors perpendicular to each other and to the CTO vector. We applied this method to a patient with mid-left circumflex CTO and translated the resulting fluoroscopic vectors into optimal fluoroscopic angulations. To facilitate its use, we developed a calculator using spreadsheet software that can output optimal fluoroscopic angulations within a practical range by inputting the x, y, and z components of the CTO vector. This approach also helps to minimise dead angles in biplane fluoroscopy. This method has the potential to make CTO PCI safer and easier, without requiring dedicated equipment or software. Its effectiveness should be validated in clinical practice.

On the Kinematic Description of the Motion of a Rigid Body

A system of ordinary differential equations is derived for a vector of finite rotation corresponding to Euler’s theorem: the vector of finite rotation is directed along the axis of finite rotation of a solid and its length is equal to the angle of plane rotation around this axis. The system of equations is explicitly resolved with respect to the time derivative of the components of the rotation vector. The right part of the system depends on the rotation vector and the angular velocity vector in the main axes. The equivalence of the obtained system of equations to the system of equations for quaternions is shown. The coordinates of the orts of the main axes of a rigid body in fixed axes are expressed in terms of the angles of final rotation and the components of angular velocity according to simple analytical formulas.