Projection Equations Research Articles

DEM Generation With a Scale Factor Using Multi-Aspect SAR Imagery Applying Radargrammetry

Digital elevation model (DEM) generation using multi-aspect synthetic aperture radar (SAR) imagery applying radargrammetry has become a hotspot. The traditional radargrammetric method is to solve the rigorous radar projection equations to obtain the three dimensional coordinates of targets. In this paper, we propose a new DEM generation method based on the offset between multi-aspect images formed on ground plane. The ground object will be projected to different positions from different viewing aspect angles if the height of object is not equal to the height of imaging plane. The linear relationship between the offset of imaging positions and height of the object is derived and scale factor is obtained finally. Height information can be retrieved from offset of imaging positions directly through the DEM extraction model presented in this paper. Thus the solution to nonlinear equations point by point can be avoided. Real C band airborne circular SAR images is used to verify the proposed approach. When extracted DEM applied in multi-aspect imaging process, superimposition of multi-aspect images will no longer be defocusing and can achieve finer observation of the scanned scene.

Метод прогнозирования электропотребления бытовыми потребителями в условиях Республики Таджикистан

This paper presents analysis based on data of electricity consumption and urban grid conditions in Tajikistani cities in terms of electricity loss; it also invokes consumption breakdown by user groups standardized in Tajikistan for such analysis. The authors propose a method for projecting the electricity consumption and fin­ding the average power at peak loads for households, which is further adjusted for local conditions in the Republic of Tajikistan. To derive the projection equation, the paper proposes a maximum load time coefficient, , which depends on the location and climate/weather conditions of Tajikistan; as such, it may vary depending on the local conditions. The proposed electricity consumption projection method has been tested on a single feeder of the 110/35/6-kV Vostochnaya substation in Dushanbe. The paper shows how the location and the climate/weather conditions of Tajikistani cities affect the grid operations, in particular the 0.4-kV nodes.

Explicit solutions of the (2 + 1)-dimensional Hirota–Maccari system arising in nonlinear optics

In this paper, new exact traveling wave solutions of the [Formula: see text]-dimensional Hirota–Maccari system arising in nonlinear optics are successfully obtained by using two methods, namely, Improved [Formula: see text]-expansion method and general projective Riccati equation method. The considered methods have been successfully implemented to find exact traveling wave solutions for nonlinear evaluation equations (NLEE) coming for describing nonlinear optics. The results obtained by these methods are straightforward and concise mathematical tool to set up the exact solutions of NLEE.

Solitons and complexitons to the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain model

This paper investigates the ([Formula: see text])-dimensional Heisenberg ferromagnetic spin chain (HMF) model. The model describes the nonlinear spin dynamics of HMF. By adopting the modified [Formula: see text]-Expansion and projective Riccati equation methods, we report the dark, combined dark-bright and envelope optical solitons, complexitons singular solutions of the equation along with the conditions that must be satisfied for solitons to exist. The physical structure of the obtained solutions are shown by graphic illustration in order to give a better understanding on the dynamics of optical solitons.

The application of artificial neural networks in metabolomics: a historical perspective.

Metabolomics data, with its complex covariance structure, is typically modelled by projection-based machine learning (ML) methods such as partial least squares (PLS) regression, which project data into a latent structure. Biological data are often non-linear, so it is reasonable to hypothesize that metabolomics data may also have a non-linear latent structure, which in turn would be best modelled using non-linear equations. A non-linear ML method with a similar projection equation structure to PLS is artificial neural networks (ANNs). While ANNs were first applied to metabolic profiling data in the 1990s, the lack of community acceptance combined with limitations in computational capacity and the lack of volume of data for robust non-linear model optimisation inhibited their widespread use. Due to recent advances in computational power, modelling improvements, community acceptance, and the more demanding needs for data science, ANNs have made a recent resurgence in interest across research communities, including a small yet growing usage in metabolomics. As metabolomics experiments become more complex and start to be integrated with other omics data, there is potential for ANNs to become a viable alternative to linear projection methods. We aim to first describe ANNs and their structural equivalence to linear projection-based methods, including PLS regression. We then review the historical, current, and future uses of ANNs in the field of metabolomics. Is metabolomics ready for the return of artificial neural networks?

Alternative continuous- and discrete-time neural networks for image restoration

ABSTRACTThis paper presents alternative continuous- and discrete-time neural networks for image restoration in real time by introducing new vectors and transforming its optimization conditions into a system of double projection equations. The proposed neural networks are shown to be stable in the sense of Lyapunov and convergent for any starting point. Compared with the existing neural networks for image restoration, the proposed models have the least neurons, a one-layer structure and the faster convergence, and is suitable to parallel implementation. The validity and transient behaviour of the proposed neural network is demonstrated by numerical examples.

System integration of a fluoroscopic image calibration using robot assisted surgical guidance for distal locking process in closed intramedullary nailing of femur

<span>Distal locking procedure is one of the most complex tasks in close intramedullary nailing operation which requires fluoroscopic image to interpret 2-D distal locking position on image related to 3-D distal locking position on the patient site. Hence the surgeon has to perform the distal locking process by using multiple fluoroscopic images which causes a lot of x-ray exposure to the patient and surgeon and is a time consuming task. This paper presents the system integration of a fluoroscopic image calibration using robot assisted surgical guidance. The system integration consists of three parts; distal locking recovery, fluoroscopic calibration and tracking, and robot assisted surgical guidance. The distal locking-hole recovery algorithm is based on characteristic information of the major and minor axes of distal locking hole. The fluoroscopic calibration and tracking is modeled as pin-hole projection model to estimate a projection equation based on optical tracking system. The robot-assisted surgical guidance is developed to overlay a trajectory path using a laser beam for reducing the problem of hand – eye coordination on most surgical navigation system. We integrate each part to complete a surgical navigation system for distal locking process. The experiment of system integration is conducted to validate the accuracy of distal locking axis position and orientation. The results of the system integration shows a mean angular error of 1.10 and mean Euclidean distance in X-Y plane error of 3.65 mm.</span>

Multiple vehicle tracking and classification system with a convolutional neural network

This paper proposes a traffic monitoring system that detects, tracks, and classifies multiple vehicles on the road in real time using various digital image processing techniques and the process of machine learning based on a convolutional neural network (CNN). With this system, a video camera is installed on the road, and calibration is used to obtain the projection equation of the actual road on the image plane. Several image processing techniques, such as background modeling, background extraction, edge detection, and object tracking, are used to develop and implement a prototype system. The proposed system also uses a transfer learning process that is more efficient than starting CNN from scratch. This maximizes training efficiency and increases prediction accuracy in vehicle classification. Preliminary experimental results demonstrate that multiple vehicle tracking and classification are possible while calculating vehicle speed. The ultimate goal of this study is to develop a single digital video camera system with embedded machine learning process that can monitor and distinguish multiple vehicles simultaneously in multiple lanes.

Three-dimensional reconstruction for space targets with multistatic inverse synthetic aperture radar systems

In this paper, a three-dimensional (3D) reconstruction algorithm is proposed for space targets with multistatic inverse synthetic aperture radar (ISAR) systems. In the proposed algorithm, target 3D geometry can be obtained by solving the projection equations between the target 3D geometry and ISAR images. Specially, it is no need to perform cross-range scaling. To obtain the projection equations, the algorithm consists of two steps: establishing projection matrix and associating scattering centers. Firstly, observation angles of sensor can be estimated by kinematic formulas and coordinate systems transformation. Using azimuth and elevation angles of sensor relative to target, the projection matrix from target 3D geometry to ISAR images is established. Secondly, an association cost function based on projective transform and epipolar geometry is developed. As the cost function is an assignment with 0–1 linear programming, the Jonker-Volgenant algorithm is used to build a one-to-one correspondence between two scattering centers. Numerical results show the efficiency of the proposed algorithm.

A Multi-Level Simultaneous Minimization Scheme Applied to Jerk-Bounded Redundant Robot Manipulators

In this paper, a multi-level simultaneous minimization (MLSM) scheme is proposed and investigated to remedy the joint-angle drift (JAD) and non-zero final joint-velocity (NZFJV) phenomena as well as to prevent the occurrence of high joint variables of redundant robot manipulators. The proposed scheme is novelly designed within multiple levels and finally resolved at the jerk level for a jerk-bounded robot motion, which is desirable for engineering applications. More importantly, the correctness of the proposed MLSM scheme is guaranteed by the corresponding theorems. Then, the MLSM scheme is formulated as a dynamical quadratic program (DQP) that is solved by a piecewise linear projection equation neural network (PLPENN). Furthermore, the path-tracking simulations based on a 6-degrees-of-freedom (DOF) robot manipulator substantiate the effectiveness and advantage of the MLSM scheme. Comparisons between the MLSM scheme and the minimum jerk norm (MJN) scheme illustrate that the proposed scheme is superior and more applicable. Finally, the additional validation on the KUKA robot in the virtual robot experimentation platform (V-REP) is provided for reproducible engineering applications by researchers and practitioners. Note to Practitioners —This paper is motivated by the inverse kinematics problem of jerk-bounded redundant robot manipulators in practical applications. Note that the joint-angle drift (JAD) and non-zero final joint-velocity (NZFJV) phenomena as well as the occurrence of high joint variables always encountered in the traditional norm-based scheme for robot manipulators, which is not suitable for the real-time control of robots. Besides, it would be appealing and desirable to resolve the robot redundancy at the jerk level for industrial robots in engineering. Therefore, an effective, flexible, and stable solution for such robot manipulators is significant for practitioners. This paper proposes a multi-level simultaneous minimization (MLSM) scheme for practitioners interested in robot kinematics to remedy the JAD and NZFJV phenomena as well as to prevent the occurrence of high joint variables of redundant robot manipulators. Unlike traditional single-level schemes, such as the minimum jerk norm (MJN) scheme, the proposed scheme is designed within multiple levels with distinct physical nature and finally resolved at the jerk level to achieve a desirable performance for the jerk-bounded redundant robot manipulators. Besides, for better understanding of practitioners, the corresponding block diagram and principle interpretation of the MLSM scheme are presented. Simulation studies and comparisons are designed and conducted on a 6-degrees-of-freedom (DOF) robot manipulator to substantiate the effectiveness and superiority of the proposed scheme. Extensive tests with different weighting factors fully verify the flexibility and stable performance of the proposed MLSM scheme. For reproducible engineering applications by researchers and practitioners, the additional validation on the KUKA robot in the virtual robot experimentation platform (V-REP) is further presented.

New Disturbance Rejection Constraint for Redundant Robot Manipulators: An Optimization Perspective

Due to the property of multiple solutions, redundant robot manipulators are usually required to simultaneously achieve multiple objectives in complex applications. The research of robustness for scheme formulation and optimization becomes an increasingly important issue for motion planning of redundant robot manipulators. From the perspective of optimization, a robust hybrid multiobjective (RHMO) scheme with a new disturbance rejection constraint is proposed in this article to achieve simultaneously four objectives together with the suppression of external time-varying disturbances. Theoretical results on the property of disturbance rejection are shown to confirm the effectiveness and robustness of the proposed RHMO scheme with a new disturbance rejection constraint. The RHMO scheme is then reformulated as dynamical quadratic programming with its solution found via the piecewise-linear projection equation neural network. Numerical experiments, tests, and comparisons on the basis of a PA10 manipulator verify the effectiveness, robustness, and superiority of the RHMO scheme with the new constraint for the motion planning and optimization of redundant robot manipulators against time-varying disturbances.

Instruction on the construction of coherent structures based on variable separation solutions of (2+1)-dimensional nonlinear evolution equations in fluid mechanics

At first, we focus on the projective Riccati equation method again and find that many solutions of the projective Riccati equation in the literatures are not independent. We derive an exponential form solution of the projective Riccati equation, which includes many solutions reported in the literatures. Then, via the projective Riccati equation method with the exponential form solution firstly reported in this paper, we can obtain variable separation solutions of (2+1)-dimensional nonlinear evolution equations in physics and engineering. For example, we get variable separation solutions of (2+1)-dimensional generalized Burgers equation and Boiti–Leon–Pempinelli equation in fluid mechanics. At last, based on these variable separation solutions of two equations, we study coherent structure including the interaction between four-dromion structures and collision between complex wave with dromion pair structures. We find that for the same physical coherent structure of the potential, coherent structures constructed from the original field quantities exhibit physical property (for Burgers equation) and un-physical property (for Boiti–Leon–Pempinelli equation). Therefore, we must be careful with the construction of coherent structures based on variable separation solutions, and we need consider the construction of coherent structures for all field quantities at the same time lest so-called new coherent structures found by researchers which are un-physical and illusive.

Re-observation on localized waves constructed by variable separation solutions of (1+1)-dimensional coupled integrable dispersionless equations via the projective Riccati equation method

Variable separation exponential-form solution of (1+1)-dimensional coupled integrable dispersionless equations in physics and mathematics is obtained via the projective Riccati equation method. Based on the potential function, the multi-valued loop soliton, chaotic soliton chain and fractal pattern are studied. However, the singularity structure without the physical meaning is found at the same time for the original components of the system. Actually, if suitable functions are taken in variable separation solution, the singularity for the original components can be avoided. If the singularity structure for anyone of all components appears, novel and interesting structures for the potential function will become meaningless.

Optimising recruitment into trials using an internal pilot

BackgroundRecruitment to trials can be difficult. Despite careful planning and research that outlines ways to improve recruitment, many trials do not achieve their target on time and require extensions of funding or time.MethodsWe describe a trial in which an internal pilot with embedded qualitative research was used to improve recruitment processes and inform recruitment projections for the main trial. At the end of the pilot, it was clear that the sample size would not be met on time. Three steps were taken to optimise recruitment: (1) adjustments were made to the recruitment process using information from the qualitative work done in the pilot and advice from a patient and public involvement group, (2) additional recruiting sites were included based on site feasibility assessments and (3) a projection equation was used to estimate recruitment at each site and overall trial recruitment.ResultsQualitative work during the pilot phase allowed us to develop strategies to optimise recruitment during the main trial, which were incorporated into patient information packs, the standard operating procedures and training sessions with recruiters. From our experience of feasibility assessments, we developed a checklist of recommended considerations for feasibility assessments. For recruitment projections, we developed a four-stage projection equation that estimates the number of participants recruited using a conversion rate of the number randomised divided by the number screened.ConclusionsThis work provides recommendations for feasibility assessments and an easy-to-use projection tool, which can be applied to other trials to help ensure they reach the required sample size.Trial registrationISRCTN, ISRCTN92545361. Registered on 6 September 2016.

Spherical Bounding Classifier using CGP Generated Transforms

A Cartesian Genetic Programming (CGP) approach was applied to generate data projection equations (transforms) to project original N-dimensional features space into new 3-dimensional coordinate space followed by a spherical bounding for classification. The solution finding mechanism differs slightly from conventional CGP based machine learning in four ways. Firstly, inputs were weighted to introduce more flexibility for solution finding. Secondly, a dual mutation sequence was introduced to encourage faster convergence. Thirdly, chromosome vector included a 3-dimensional coordinate point and spherical bounding mechanism for classification. Fourthly, the probability of selecting either of the input types (feature input, node sequence, or constant) are made approximately equal to ensure that the input types have equal probability to be in the active equation nodes. The best classification rate on test datasets achieved using 10 fold cross validation was 98.57% (Wisconsin Breast Cancer dataset), 87.78% (Heart disease dataset) and 80.5% (PIMA Indian diabetes dataset).

Impact of Coming Demographic Changes on the Number of Adults in Need of Care for Hypertension in Brazil, China, India, Indonesia, Mexico, and South Africa.

Over the coming decades, middle-income countries are expected to undergo substantial demographic changes. We estimated the consequences of these changes on the number of adults in need of hypertension care between 2015 and 2050 using nationally representative household-survey data collected in Brazil, China, India, Indonesia, Mexico, and South Africa (N=770 121). To reflect unmet need for healthcare, we defined hypertension as systolic blood pressure ≥140 mm Hg or diastolic blood pressure ≥90 mm Hg regardless of treatment status. Using a mathematical disease projection equation, we calculated the change in the number of individuals in need of hypertension care in each country that was due to changes in population size, age composition, and age-specific prevalence under various epidemiological scenarios. If the current age-specific prevalence schedule of hypertension remains unchanged until 2050, demographic changes alone will increase the number of adults in need of hypertension care by 319.7 million individuals, ranging from a relative growth of 55% in China to 151% in Mexico. Even if the age-specific prevalence of hypertension is reduced by 25% by 2050 among adults aged ≥40 years, the number of individuals in need of hypertension care will still increase by 145.9 million individuals, with relative increases ranging from 16% in China to 88% in Mexico. Overall, our results suggest that coming demographic changes in middle-income countries will overpower even ideal prevention efforts. Middle-income countries will need to massively expand healthcare services for aging-related diseases, such as hypertension, if they are to meet the virtually inevitable future increase in care needs for these conditions.

Compact numerical solutions to the two-dimensional repulsive Hubbard model obtained via nonunitary similarity transformations

Similarity transformation of the Hubbard Hamiltonian using a Gutzwiller correlator leads to a non-Hermitian effective Hamiltonian, which can be expressed exactly in momentum-space representation, and contains three-body interactions. We apply this methodology to study the two-dimensional Hubbard model with repulsive interactions near half-filling in the intermediate interaction strength regime ($U/t=4$). We show that at optimal or near optimal strength of the Gutzwiller correlator, the similarity transformed Hamiltonian has extremely compact right eigenvectors, which can be sampled to high accuracy using the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method, and its initiator approximation. Near-optimal correlators can be obtained using a simple projective equation, thus obviating the need for a numerical optimisation of the correlator. The FCIQMC method, as a projective technique, is well-suited for such non-Hermitian problems, and its stochastic nature can handle the 3-body interactions exactly without undue increase in computational cost. The highly compact nature of the right eigenvectors means that the initiator approximation in FCIQMC is not severe, and that large lattices can be simulated, well beyond the reach of the method applied to the original Hubbard Hamiltonian. Results are provided in lattice sizes upto 50 sites and compared to auxiliary-field QMC. New benchmark results are provided in the off half-filling regime, with no severe sign-problem being encountered. In addition, we show that methodology can be used to calculate excited states of the Hubbard model and lay the groundwork for the calculation of observables other than the energy.

Acceleration-level trajectory planning for a dual-arm space robot

In order to achieve disturbance rejection of the base while realizing the pre-capturing process under joint physical constraints (such as limited joint-angle, joint-velocity, joint-acceleration), this paper proposed an acceleration-level trajectory planning method for a dual-arm space robot. Firstly, the acceleration-level kinematic models are derived by using the velocity-level kinematics and linear and angular momentum conservation law. On this basis, the joint physical constraints are reformulated as a quadratic programming (QP) problem which can be converted to a piecewise-linear projection equation. Meanwhile, the improved damped least-squares (DLS) method is applied to design trajectory planning for the balance arm which is employed to keep the base disturbance free. Finally, simulation results verify the effectiveness of the proposed acceleration-level trajectory planning method.

Spectral Unmixing of Hyperspectral Remote Sensing Imagery via Preserving the Intrinsic Structure Invariant.

Hyperspectral unmixing, which decomposes mixed pixels into endmembers and corresponding abundance maps of endmembers, has obtained much attention in recent decades. Most spectral unmixing algorithms based on non-negative matrix factorization (NMF) do not explore the intrinsic manifold structure of hyperspectral data space. Studies have proven image data is smooth along the intrinsic manifold structure. Thus, this paper explores the intrinsic manifold structure of hyperspectral data space and introduces manifold learning into NMF for spectral unmixing. Firstly, a novel projection equation is employed to model the intrinsic structure of hyperspectral image preserving spectral information and spatial information of hyperspectral image. Then, a graph regularizer which establishes a close link between hyperspectral image and abundance matrix is introduced in the proposed method to keep intrinsic structure invariant in spectral unmixing. In this way, decomposed abundance matrix is able to preserve the true abundance intrinsic structure, which leads to a more desired spectral unmixing performance. At last, the experimental results including the spectral angle distance and the root mean square error on synthetic and real hyperspectral data prove the superiority of the proposed method over the previous methods.

System of Extended General Variational Inequalities for Relaxed Cocoercive Mappings in Hilbert Space

In this manuscript, we study a system of extended general variational inequalities (SEGVI) with several nonlinear operators, more precisely, six relaxed ( α , r ) -cocoercive mappings. Using the projection method, we show that a system of extended general variational inequalities is equivalent to the nonlinear projection equations. This alternative equivalent problem is used to consider the existence and convergence (or approximate solvability) of a solution of a system of extended general variational inequalities under suitable conditions.