Actual Error Research Articles

Research on spectral reconstruction algorithm for snapshot microlens array micro-hyperspectral imaging system.

Snapshot microlens array microscopic hyperspectral imaging systems do not require a scanning process and obtain (x,y,λ) three-dimensional data cubes in one shot. Currently, the three-dimensional spectra image data are interleaved on a charge-coupled device detector, which increases subsequent data processing difficulty. The optical design software cannot simulate actual engineering installation and adjustment results accurately and the tracking results cannot guide precise rapid online calibration of the snapshot microlens array microscopic hyperspectral imaging system. To solve these problems, we propose an accurate spectral image reconstruction model based on optical tracing, derive spatial dispersion equations for the prisms and gratings, establish an algorithm model for the correspondence between the microlens array's surface dispersion spectral distribution and its imaging position, and propose a three-dimensional spectral image reconstruction algorithm. Experimental results show that this algorithm's actual spectral calibration error is better than 0.2 nm. This meets the image processing requirements of snapshot microlens array microscopic hyperspectral systems.

Application of an indocyanine green-mediated fluorescence imaging navigation system in detecting mice tumors.

BackgroundSurgical operation plays an important role in the treatment of cancer. The success of the operation lies in the complete removal of the primary and disseminated tumor tissue while preserving the normal tissue. The development of optical molecular image navigation technology has provided a new option for intraoperative tumor visualization. In this study, a fluorescence imaging navigation system was used to detect the diameter of mice tumors and provide experimental evidence for the further development of digital diagnosis and treatment equipment.MethodsThe minimum detection concentration in vitro of the fluorescence imaging navigation system for indocyanine green (ICG) was first detected, then 120 female Institute of Cancer Research (ICR) mice and 120 female BALB/c nude mice were randomly divided into three groups by weight, high-dose (H, 4 mg/kg), middle-dose (M, 2 mg/kg), and low-dose (L, 1 mg/kg) groups of ICG solution. After inoculating solid tumors, high, medium, and low doses of ICG were injected via the tail vein, and the tumor diameter was measured by a fluorescence imaging navigation system and vernier caliper within 24 hours of injection.ResultsThe minimum detectable diameter of the system could reach 0.2 mm compared with the vernier caliper, and the actual measurement error was within 0.2 mm.ConclusionsA fluorescence imaging navigation system has high accuracy and sensitivity in the application of tumor detection, which may assist the clinical diagnosis and treatment of tumors.

Robust time‐varying estimator for descriptor system with random one‐step measurement delay

AbstractFor the linear stochastic descriptor system with random one‐step measurement delay and uncertain‐variance correlated noises, the robust estimation problem is addressed. Applying the singular value decomposition method, augmented state approach and fictitious noise approach, the original descriptor system is transformed to new standard system only with uncertain‐variance fictitious noises. Based on Kalman filtering and the minimax robust estimation principle, the actual Kalman estimator for the proposed standard system with actual measurement and the upper bounds of the variances is presented, including the Kalman predictor, filter, smoother and white noise deconvolution estimator. According to the relation of the new standard system and the original system, the actual estimator of original state of descriptor system and actual estimation error variance are presented. Further, the robustness of the actual estimator is proved by the Lyapunov equation approach, that is, the actual estimation error variance is guaranteed to have minimal upper bound for all admissible uncertainties. A simulation example about circuits system verifies the correctness and effectiveness of the proposed results.

Fault-Tolerant Control for N-Link Robot Manipulator via Adaptive Nonsingular Terminal Sliding Mode Control Technology

An adaptive nonsingular terminal sliding mode control (ANTSMC) scheme for the n-link robot manipulator is presented in this study, which can achieve faster convergence and higher precision tracking compared with the linear hyperplane-based sliding mode control. Novel adaptive updating laws based on the actual tracking error are employed to online adjust the upper bound of uncertainty, which comprehensively consider both the tracking performance and chattering eliminating problem. The stability analysis of the proposed ANTSMC is verified using the Lyapunov method with the existence of the parameter uncertainty and the actuator faults. Numerical simulation studies the comparison of performance between ANTSMC and the conventional nonsingular terminal sliding mode control (NTSMC) scheme to validate the advantages of the proposed control algorithm.

A New Adaptive Sparse Pseudospectral Approximation Method and its Application for Stochastic Power Flow

With the increasing integration of various renewable energy resources into electric power systems, the stochastic power flow calculation, which falls into the uncertainty propagation (UP) problems, has attracted renewed interest recently. The adaptive sparse pseudospectral approximation method (A-SPAM) is highly efficient to solve UP problems. However, there still exist two major drawbacks: 1) its global error estimate is not accurate enough to evaluate the actual approximation error; and 2) it is intended for single-output systems and there is no efficient method for its application in multi-output systems. In order to overcome these two defects, in this study a new adaptive sparse pseudospectral approximation method (NA-SPAM) is proposed based on two improvements on A-SPAM. First, a new global error estimate is presented which features much higher estimation accuracy. Second, a revised version of error estimates is given based on unification of the index set, which apparently improves the calculation efficiency for multi-output problems. At last, the effectiveness of the two improvements and NA-SPAM is validated by mathematical and practical cases.

Verification and clinical translation of a newly designed "Skywalker" robot for total knee arthroplasty: A prospective clinical study.

ObjectiveTo evaluate accuracy of an innovative “Skywalker” system, a newly designed, robot-assisted operation system for orthopaedics via a clinical trial at knee joint.MethodsWe conducted a prospective analysis of the clinical data of 31 patients who underwent total knee arthroplasty assisted by the “Skywalker” robot (Microport, Suzhou, China) from June 2020 to January 2021. Five male patients and 26 female patients aged 69.68 ​± ​6.11 years (range: 57–79 years) were diagnosed with knee osteoarthritis and indicated for surgery. The “Skywalker” surgical robotic system was adopted to make a preoperative plan for knee arthroplasty. When the robotic arm reached the specified position during the operation, a single surgeon performed the osteotomy with a cutting saw through the cutting jig, and the difference between the actual and the expected resection thickness, and the preoperative and postoperative lower limb alignments were measured.ResultsThe actual error of the resection thickness was the difference between the actual and the expected resection thickness. The absolute error of the resection thickness was the absolute value of the actual error of resection thickness. The absolute errors of the resection thickness of the medial and lateral condyle of the distal femur, the medial and lateral posterior condyle of the femur, and the medial and lateral sides of the tibial plateau were 0.87 ​± ​0.63 ​mm, 1.02 ​± ​0.67 ​mm, 0.74 ​± ​0.46 ​mm, 0.98 ​± ​0.81 ​mm, 0.92 ​± ​0.66 ​mm, and 1.04 ​± ​0.84 ​mm, respectively. The absolute angle errors between the actual postoperative angles and the preoperative planned angles of the lower limb alignment angles, coronal femoral component angles, and coronal tibial component angles were 1.46° ​± ​0.95°, 1.13° ​± ​1.01°, and 1.05° ​± ​0.73°, respectively. Besides, 100% of the absolute error of the HKA angles was within 3°. In addition, compared to the preoperative lower limb alignment angle, 90.32% of the postoperative lower limb alignment angles of 31 patients were closer to 180° after the operation. All 31 patients underwent a successful surgery, and no relevant complications occurred after the operation, such as surgical site infection, deep venous thrombosis, or vascular and nerve injury.ConclusionThe “Skywalker” system has good osteotomy accuracy, can achieve the planned angles well, and is expected to assist surgeons in performing accurate bone cuts and reconstructing planned lower limb alignments in the relevant clinical applications in future.

Outcomes of the Haigis-L formula for calculating intraocular lens power in extreme long axis eyes after myopic laser in situ keratomileusis.

To evaluate the accuracy of refractive prediction by the Haigis-L formula compared to four other IOL power calculation formulas in eyes with extremely long axial lengths (AL > 29.0 mm) after LASIK. Shanghai Eye Disease and Prevention Treatment Center, Shanghai, China. Retrospective case series. Twenty-nine eyes from 19 patients were available for analysis. The primary outcome measure was the arithmetic refractive prediction error (RPE), defined as the difference between the actual postoperative refractive error and the intended formula-derived refractive target. The main outcome measure was the median absolute refraction prediction error (MedAE). The accuracy of the Haigis-L was compared with Barrett True K No History, Shammas-PL, SRK/Tcorrected K, and Holladay 2corrected K methods to calculate IOL power. The Haigis-L formula had a significantly larger MedAE than Shammas-PL and SRK/Tcorrected K formulas (P = 0.005 and P = 0.015, respectively), a smaller percentage of eyes within ±1.50 diopter (D) of predicted error in refraction compared with Shammas-PL and SRK/Tcorrected K formulas (P = 0.014 and P = 0.005, respectively). The refractive prediction errors of 6 eyes with corneal keratometry of less than 35 D by Haigis-L all had more than 1.95 D of myopic overestimation, while none of the other four methods resulted in an absolute error over 1.95 D. The Haigis-L formula was relatively accurate in predicting extreme long axis (>29.0 mm) eyes after myopic LASIK surgery but less accurate for eyes with extremely flat corneas (<35 D). SRK/Tcorrected K and Shammas-PL performed better than the other methods for refractive prediction in this type of eyes. Haigis-L performed worse than SRK/Tcorrected K and Shammas-PL in predicting IOL power in extremely long axis (>29.0 mm) eyes after myopic LASIK, especially with extremely flat corneas (K < 35 D).

Comparison of Single-Site Ionospheric Delays Derived from Geometry-Free and Geometry-Based Approaches with an Analysis of Orbit and Clock Error Effects

The reparameterization of the geometry-free and geometry-based approaches to derive single-site ionospheric delays using Global Navigation Satellite System (GNSS) measurements is described. Kalman filtering is used to compute the geometry-free and geometry-based ionospheric delays in a forward computation procedure, aiming for a real-time application case. The numerical similarity and differences between the geometry-free and geometry-based ionospheric delays are assessed in terms of both formal and experimental errors (precision). The differences between geometry-free and geometry-based ionospheric delays are derived using two types of precise orbit and clock products. The effects of the precise orbit and clock residual errors are analyzed. The correlation coefficients between the L1 and L2 wide-lane ambiguities with the ionospheric delay are derived and analyzed. It is discovered that the geometry-based ionospheric delay is negatively correlated with geometry-based wide-lane ambiguities, while the geometry-free ionospheric delay and wide-lane ambiguities are much less correlated. A simulation analysis indicates that the impacts on geometry-based ionospheric delay estimates are partly coincided with the actual time-variant errors of the used orbit and clock in the line-of-sight direction.

Wavelet and power spectrum analysis of global navigation satellite system multipath error modeling and mitigation

SummaryThis study investigates the multipath error modeling and mitigation for triple‐frequency global navigation satellite system (GNSS) signals inside South Korea. Multifrequency global positioning system (GPS), globalnaya navigatsionnaya sputnikovaya sistema (GLONASS), and Galileo data are collected in an environment where the receiver must track these three constellations in both low and high multipath scenarios. First, an advanced power spectrum analysis technique known as Welch method is performed using experimental data, and its benefits and drawbacks are described. In the second attempt, the spectrogram method is utilized to perform multipath feature time–frequency analysis. Although the abnormal frequency peak presented by the spectrogram is stable, the spectrogram does not support the precise recognition of the multipath error peak occurrence. Hence, in the third attempt, continuous wavelet transforms (CWT) are applied to highlight this type of peak resolution. The CWT function successfully indicated the maximum and minimum peak resolutions and exhibited a clear wavelet energy spread. In the final stage, experimental data are reconstructed by inverse CWT (ICWT), and comparative results in terms of root mean square before and after the ICWT are estimated. After implementing the inverse wavelet method in high and low multipath error of experimental data, overall average percentages of multipath mitigation reduction compared to actual multipath error are estimated to be 95.74% and 98.79%, respectively. This study demonstrates the high efficiency of the wavelet method as well as the effectiveness as a multipath error reduction approach. These improvements can be considered as significant in achieving high‐precision positioning accuracy.

Consistent Right-Invariant Fixed-Lag Smoother with Application to Visual Inertial SLAM

State estimation problems without absolute position measurements routinely arise in navigation of unmanned aerial vehicles, autonomous ground vehicles, etc., whose proper operation relies on accurate state estimates and reliable covariances. Unaware of absolute positions, these problems have immanent unobservable directions. Traditional causal estimators, however, usually gain spurious information on the unobservable directions, leading to over-confident covariance inconsistent with actual estimator errors. The consistency problem of fixed-lag smoothers (FLSs) has only been attacked by the first estimate Jacobian (FEJ) technique because of the complexity to analyze their observability property. But the FEJ has several drawbacks hampering its wide adoption. To ensure the consistency of a FLS, this paper introduces the right invariant error formulation into the FLS framework. To our knowledge, we are the first to analyze the observability of a FLS with the right invariant error. Our main contributions are twofold. As the first novelty, to bypass the complexity of analysis with the classic observability matrix, we show that observability analysis of FLSs can be done equivalently on the linearized system. Second, we prove that the inconsistency issue in the traditional FLS can be elegantly solved by the right invariant error formulation without artificially correcting Jacobians. By applying the proposed FLS to the monocular visual inertial simultaneous localization and mapping (SLAM) problem, we confirm that the method consistently estimates covariance similarly to a batch smoother in simulation and that our method achieved comparable accuracy as traditional FLSs on real data.

S-Guard: Multisensor Embedded Obstructive Sleep Apnea and Bruxism Real-Time Data Transmission Intraoral Appliance Device

Obstructive sleep apnea (OSA) and bruxism are widely recognized as common forms of sleep obstruction in modern everyday life. The most representative and conventional treatment method using continuous positive airway pressure has a critical problem owing to its high inconvenience. A relatively modern alternative solution is the mandibular advancement device, but it still has no monitoring function for patient compliance. Therefore, this research proposes Sleep Guard (s-Guard), a multisensor embedded OSA monitoring intraoral appliance device based on Internet-of-Things technology. Relevant health information monitoring sensors, such as temperature, gyroscope, accelerometer, and SpO2 sensors, were embedded for real-time health monitoring. Results showed an average transmission speed of 91,870.19 bytes per second, a successful connection check rate of 100%, and a wireless data stream error rate of 0.1%. Overall, the actual speed, connection, and error test results revealed the robust functioning of s-Guard in real monitoring scenarios. This research is envisioned to greatly enhance patient compliance when treating OSA or bruxism and is also expected to motivate other sensors to be embedded in our proposed model for the application of other disease areas.

Application of Bayesian Vector Autoregressive Model in Regional Economic Forecast

The Bayesian vector autoregressive (BVAR) model introduces the statistical properties of variables as the prior distribution of the parameters into the traditional vector autoregressive (VAR) model, which can overcome the problem of too little freedom. The BVAR model established in this paper can overcome the problem of short time series data by using prior statistical information. In theory, it should have a good effect in China’s regional economic forecasting. Most regional forecasting model literature lacks out-of-sample forecasting error evaluation research in the real sense, but our early forecasts of major economic indicators provide an excellent opportunity for this paper to evaluate the actual forecast errors of the BVAR model in detail. The analysis in this paper shows that the prediction error of the BVAR model is very small and the prediction ability is very satisfactory. At the same time, this article also analyzes and points out the direction of efforts to further improve the prediction accuracy of the BVAR model.

Modul Front-End Sistem Informasi Geospasial Patroli Terpadu Kebakaran Hutan dan Lahan

To prevent and handle forest and land and forest fire (karhutla), the Ministry of Environment and Forestry assembled a patrol team that conducts a daily task to observe directly to the hotspot location as an indication for land fire. Currently, the patrol team reported the investigation result into a group chat. This method consumed many storage spaces and not suitable for formal reporting. This study aims to develop a front-end module for a web GIS application that visualizes the patrol team's daily report. The application has its data recapitulation method and able to create a formal report. The data used in this study are a set of the report that collected in 2016 by Sumatera and Kalimantan patrol team. The steps to build this application include communication, integrate with the API from the back-end system, developing functional needs, software testing, and the last is software release. The application was build using HTML and CSS for its interface and Javascript and API from the back-end module for its content management. The system uses Google Maps services and library to support the functionalities of the application. The unit testing method's test result shows that the module runs well and can afford all of the required functionality. In addition, the system testing result that the ratio between actual error and expected error is equal to 1. This result indicates the functions of the system are working properly according to the use cases of the system.&#x0D;

Confidence in action: Differences between perceived accuracy of decision and motor response

Each of our decisions is associated with a degree of confidence. This confidence can change once we have acted because we might start doubting our choice or even become convinced that we have made a mistake. In this study, we explore the relations between action and our confidence that our decision was correct or erroneous. Fifty-four volunteers took part in a perceptual decision task in which their decisions could either lead to action or not. At the end of each trial, participants rated their confidence that their decision was correct, or they reported that they had made an error. The main results showed that when given after a response, confidence ratings were higher and more strongly related to decision accuracy, and post-response reports of errors more often indicated actual errors. The results support the view that error awareness and confidence might be partially based on postaction processing.

Two Efficient and Reliable a posteriori Error Estimates for the Local Discontinuous Galerkin Method Applied to Linear Elliptic Problems on Cartesian Grids

In this paper, we derive two a posteriori error estimates for the local discontinuous Galerkin (LDG) method applied to linear second-order elliptic problems on Cartesian grids. We first prove that the gradient of the LDG solution is superconvergent with order $$p+1$$ towards the gradient of Gauss-Radau projection of the exact solution, when tensor product polynomials of degree at most p are used. Then, we prove that the gradient of the actual error can be split into two parts. The components of the significant part can be given in terms of $$(p+1)$$ -degree Radau polynomials. We use these results to construct a reliable and efficient residual-type a posteriori error estimates. We further develop a postprocessing gradient recovery scheme for the LDG solution. This recovered gradient superconverges to the gradient of the true solution. The order of convergence is proved to be $$p+1$$ . We use our gradient recovery result to develop a robust recovery-type a posteriori error estimator for the gradient approximation which is based on an enhanced recovery technique. We prove that the proposed residual-type and recovery-type a posteriori error estimates converge to the true errors in the $$L^2$$ -norm under mesh refinement. The order of convergence is proved to be $$p + 1$$ . Moreover, the proposed estimators are proved to be asymptotically exact. Finally, we present a local adaptive mesh refinement procedure that makes use of our local and global a posteriori error estimates. Our proofs are valid for arbitrary regular meshes and for $$P^p$$ polynomials with $$p\ge 1$$ . We provide several numerical examples illustrating the effectiveness of our procedures.

Time-Varying Error Prediction and Compensation for Movement Axis of CNC Machine Tool Based on Digital Twin

Currently, it is a challenging issue to predict the thermal-induced time-varying error for the movement axis of the computer numerical control (CNC) machine tool. Subsequently, it is a challenge to predict the machining accuracy for a certain workpiece when the machine tool and numerical control program are determined. In order to resolve this shortcoming, the time-varying error prediction and compensation for the movement axis of the CNC machine tool was studied in this article, and the advantage of digital twin in predicting the changing trend for the physical entity was applied. The framework of time-varying error prediction and compensation for the CNC machine tool's movement axis was proposed based on the digital twin concept, which includes the physical entity layer, data transmission layer, function execution layer, and application service layer. The digital twin of the movement axis, containing a time-varying error model based on heat transfer theory and visual model, was created and packaged as a ready-to-use software for predicting and compensating time-varying error. The prediction experiment of the hole-pitch time-varying error for a workpiece was carried out. It was found that the difference between prediction error and actual error is only −0.2–2.6 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> m. The fluctuation range of hole-pitch error is reduced by 69.19% with the time-varying error compensation in real-time. The experimental results show that the method of time-varying error prediction and compensation based on a digital twin is an effective and feasible scheme.

A New Method for High Resolution Surface Change Detection: Data Collection and Validation of Measurements from UAS at the Nevada National Security Site, Nevada, USA

The use of uncrewed aerial systems (UAS) increases the opportunities for detecting surface changes in remote areas and in challenging terrain. Detecting surface topographic changes offers an important constraint for understanding earthquake damage, groundwater depletion, effects of mining, and other events. For these purposes, changes on the order of 5–10 cm are readily detected, but sometimes it is necessary to detect smaller changes. An example is the surface changes that result from underground explosions, which can be as small as 3 cm. Previous studies that described change detection methodologies were generally not aimed at detecting sub-5-cm changes. Additionally, studies focused on high-fidelity accuracy were either computationally modeled or did not fully provide the necessary examples to highlight the usability of these workflows. Detecting changes at this threshold may be critical in certain applications, such as global security research and monitoring for high-consequence natural hazards, including landslides. Here we provide a detailed description of the methodology we used to detect 2–3 cm changes in an important applied research setting—surface changes related to underground explosions. This methodology improves the accuracy of change detection data collection and analysis through the optimization of pre-field planning, surveying, flight operations, and post-processing the collected data, all of which are critical to obtaining the highest output data resolution possible. We applied this methodology to a field study location, collecting 1.4 Tb of images over the course of 30 flights, and location data for 239 ground control points (GCPs). We independently verified changes with orthoimagery, and found that structure-from-motion, software-reported root mean square errors (RMSEs) for both control and check points underestimated the actual error. We found that 3 cm changes are detectable with this methodology, thereby improving our knowledge of a rock’s response to underground explosions.

High-precision machining technology based on analytical method for integral impeller with flank milling

The paper first introduces R offset tool axis error calculation method. In order to reduce the maximum machining error, the paper presents a new geometric model of tool axis vector for flank milling non-developable ruled surfaces and machining error exact analytical solution is derived. Its main advantage is that the theoretical machining error of each point on the straight generatrix can be calculated. MATLAB software simulation and actual NC machining experiment are conducted to validate the effectiveness of the proposed algorithm. The measurement experimental results show that the actual maximum machining error is basically consistent with the theoretical calculation error, and the machining error can be reduced compared with the previous literature algorithm.

An Upper Bound on Magnitude Error of Voltage Drop Phasors in Distribution Lines Due to Phase Transposition Assumption

A renewed interest in comprehensive modeling of distribution system components arose in recent literature. This trend can be attributed to, aside from the inherent imbalance of such systems, the rapid and system-wide integration of technologies, e.g. non-linear loads and distributed generators, which further increase grid imbalance effects. Such phenomena, in turn, demand sufficiently detailed models for their proper assessment. Despite the described scenario, it remains reasonable to inquire whether approximate component models can still be used for simplifying computations without causing exceedingly high modeling error. In this context, an approximation of particular interest is assuming phase transposition for distribution lines, due to its property of impedance matrix decoupling on the symmetric component frame. In this paper, the derivation of a closed-form upper bound for voltage drop magnitude error, due to assuming transposition in a general M-phase line, is carried out. The bound is validated by means of a case study based on the IEEE 4-bus feeder considering generalized feeder geometries. Obtained results suggest that the upper bound is tight with respect to actual error and thus provides a practical means of estimating voltage drop error yielded by the assumption of distribution line transposition.

AN APPROXIMATE METHOD FOR CALCULATING GRAIN FLOW IN A VERTICAL CYLINDRICAL VIBROSIEVE

A modified hydrodynamic model of a stable grain flow of an inhomogeneous mixture over the surface of a vertical cylindrical vibrating sieve is proposed under the assumption that the porosity of the mixture in the moving annular layer depends on the velocity of movement. A linear dependence of the porosity of the mixture on the velocity of movement are accepted, where higher speed corresponds to higher porosity.. The calculation of the velocity is reduced to solving an inhomogeneous differential equation of the Bessel type. Further, by "freezing" the variable coefficient of this equation, the problem has been simplified. This simplification is permissible due to the fact that the thickness of the moving layer of the mixture is much less than the radius of the vibrating sieve. As a result, the dependence of the velocity on the radial coordinate is expressed through the elementary functions. A compact formula for determining the maximum grain flow velocity is obtained. By integrating, in elementary functions, the formula for the average velocity in the layer is obtained. An approximate formula for the performance of the vibrating sieve by the mass of the exit fraction is derived. For this, it is proposed to calculate the corresponding integral approximately by the Simpson formula, so as not to calculate the values of special functions of large argument using the asymptotic formulas. It is shown that the named productivity significantly depends on the porosity of the grain mixture. In order to obtain information about the actual errors of the approximate formulas, we additionally carried out the numerical integration of the original non-simplified Bessel-type equation on a computer. A comparative analysis of the calculation results confirmed the small errors of the simplifications introduced into the equation of motion, as well as the adequacy of the theoretical results obtained. By passing to a simplified differential equation, approximate formulas were derived and tested for calculating the main characteristics of the grain flow along a vertical cylindrical vibrating sieve, taking into account the change in porosity in the grain mixture layer from the velocity of movement. The work summarizes the known theoretical results obtained using hydrodynamic models of the motion of grain mixtures fluidized by vibrations. The generalization carried out slightly complicated the theory, because the final calculation formulas are quite compact and convenient in practical implementation.