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We introduce a novel online (or sequential) nonlinear prediction approach that incorporates the residuals, i.e., prediction errors in the past observations, as additional features for the current data. Including the past error terms in an online prediction algorithm naturally improves prediction performance significantly since this information is essential for an algorithm to adjust itself based on its past errors. These terms are well exploited in many linear statistical models such as ARMA, SES, and Holts-Winters models. However, the past error terms are rarely or in a certain sense not optimally exploited in nonlinear prediction models since training them requires complex nonlinear state-space modeling. To this end, for the first time in the literature, we introduce a nonlinear prediction framework that utilizes not only the current features but also the past error terms as additional features, thereby exploiting the residual state information in the error terms, i.e., the model's performance on the past samples. Since the new feature vectors contain error terms that change with every update, our algorithm jointly optimizes the model parameters and the feature vectors simultaneously. We achieve this by introducing new update equations that handle the effects resulting from the changes in the feature vectors in an online manner. We use soft decision trees and neural networks as the nonlinear prediction algorithms since these are the most widely used methods in highly publicized competitions. However, as we show, our methods are generic and any algorithm supporting gradient calculations can be straightforwardly used. We show through our experiments on the well-known real-life competition datasets that our method significantly outperforms the state-of-the-art. We also provide the implementation of our approach including the source code to facilitate reproducibility (https://github.com/ahmetberkerkoc/SDT-ARMA). [ABSTRACT FROM AUTHOR]

We obtain the clean semi-analytical solutions with method of directly defining inverse mapping (MDDiM) to the system of nonlinear equations arising in the magnetohydrodynamic (MHD) convection motion of Molybdenum disulfide (MoS2) engine-oil intrinsic nanofluid in a circumnavigatethe structure is considered for analysis. Finding the solutions by using MDDiM is a novel idea and first time solving for the system of nonlinear partial differential equations. We have chosen inverse linear mapping for the five-term solution and it emphasizes by residual error and this gives the low error (10−2 to 10−17) and can easily derive deformation terms by spending very low CPU time. Based on the proposed method, the convergence rate, accuracy, and efficiency of the governing equations are demonstrated, and result outputs shown in tabular and graphically, which exhibit meaningful structures and advantages in science and engineering. [ABSTRACT FROM AUTHOR]

A precise and efficient edge-controlled method is of importance to ensure the final performance of the optical system. The authors put forward a novel method to reduce the edge effect in the magnetorheological finishing (MRF) process through further analyzing the stability of the MRF edge tool influence function (TIF) and correcting the post-edge algorithm of dwell time. To demonstrate the feasibility and advantage of this edge-controlled theory, two mirror substrates are taken as the experimental samples. The Φ 200 mm, R-200 mm concave sphere mirror (fused silica) is removed about 3 μm uniformly and the experimental results indicate that the edge error region can be effectively suppressed below 1.5 mm. Another Φ 610 mm, R-2100, K-1 lightweighting parabolic mirror is verified about the actual practicability. The residual error reaches RMS 6.5 nm from original RMS 182 nm after two run iterations; meanwhile, the edge effect is well controlled to a large extent. The simulations of edge error coincide well with the corresponding experimental results, which strongly verify the feasibility of the edge-suppressing theory presented in this paper. [ABSTRACT FROM AUTHOR]

Deep learning methods have been employed in gravitational-wave astronomy to accelerate the construction of surrogate waveforms for the inspiral of spin-aligned black hole binaries, among other applications. We face the challenge of modeling the residual error of an artificial neural network that models the coefficients of the surrogate waveform expansion (especially those of the phase of the waveform) which we demonstrate has sufficient structure to be learnable by a second network. Adding this second network, we were able to reduce the maximum mismatch for waveforms in a validation set by 13.4 times. We also explored several other ideas for improving the accuracy of the surrogate model, such as the exploitation of similarities between waveforms, the augmentation of the training set, the dissection of the input space, using dedicated networks per output coefficient and output augmentation. In several cases, small improvements can be observed, but the most significant improvement still comes from the addition of a second network that models the residual error. Since the residual error for more general surrogate waveform models (when e.g., eccentricity is included) may also have a specific structure, one can expect our method to be applicable to cases where the gain in accuracy could lead to significant gains in computational time. • Use of neural networks for improved surrogate modeling of gravitational waveforms. • The residual errors can be learnable by a second neural networks. • Bag-of-tricks learning for improving the accuracy of the surrogate model. [ABSTRACT FROM AUTHOR]

In case of coordinate machines that use CAA correction matrix, the issue of kinematic errors analysis may be based on the determination of residual error distribution. Temperature changes have an impact on CMM kinematic structure, which may cause the differences in the map of residual errors. As for today, the residual errors were analysed only for the reference temperature. No research was undertaken on the residual errors changes depending on the temperature variations. This paper presents the experiment aimed at residual errors analysis and resulting errors distributions for different temperatures.

The unsteady flow and heat transfer characteristics of electrically conducting water based thin liquid film non-Newtonian (Casson and Williamson) nanofluids dispensed with graphene nanoparticles past a stretching sheet are considered in the presence of transverse magnetic field and non-uniform heat source/sink. Embedding the graphene nanoparticles effectively amplifies the thermal conductivity of Casson and Williamson nanofluids. Ordinary differential equations together with the boundary conditions are obtained through similarity variables from the governing equations of the problem, which are solved by the HAM (Homotopy Analysis Method). The solution is expressed through graphs and illustrated which show the influences of all the parameters. The convergence of the HAM solution for the linear operators is obtained. Favorable comparison with previously published research paper is performed to show the correlation for the present work. Skin friction coefficient and Nusselt number are presented through Tables and graphs which show the validation for the achieved results demonstrating that the thin liquid films results from this study are in close agreement with the results reported in the literature. Results achieved by HAM and residual errors are evaluated numerically, given in Tables and also depicted graphically which show the accuracy of the present work. [ABSTRACT FROM AUTHOR]

Chemical reaction in mixed convection magnetohydrodynamic second grade nanoliquid thin film flow through a porous medium containing nanoparticles and gyrotactic microorganisms is considered with entropy generation. The stratification phenomena, heat and mass transfer simultaneously take place within system. Microorganisms are utilized to stabilize the suspended nanoparticles through bioconvection. For the chemical reaction of species, the mass transfer increases. The governing equations of the problem are transformed to nonlinear differential equations through similarity variables, which are solved through a well known scheme called homotopy analysis method. The solution is expressed through graphs and illustrations which show the influences of all the parameters. The residual error graphs elucidate the authentication of the present work.

The corrective calibration of the removal function plays an important role in the magnetorheological finishing (MRF) high-accuracy process. This paper mainly investigates the asymmetrical characteristic of the MRF removal function shape and further analyzes its influence on the surface residual error by means of an iteration algorithm and simulations. By comparing the ripple errors and convergence ratios based on the ideal MRF tool function and the deflected tool function, the mathematical models for calibrating the deviation of horizontal and flowing directions are presented. Meanwhile, revised mathematical models for the coordinate transformation of an MRF machine is also established. Furthermore, a Ø140-mm fused silica plane and a Ø196  mm, f/1∶1, fused silica concave sphere samples are taken as the experiments. After two runs, the plane mirror final surface error reaches PV 17.7 nm, RMS 1.75 nm, and the polishing time is 16 min in total; after three runs, the sphere mirror final surfer error reaches RMS 2.7 nm and the polishing time is 70 min in total. The convergence ratios are 96.2% and 93.5%, respectively. The spherical simulation error and the polishing result are almost consistent, which fully validate the efficiency and feasibility of the calibration method of MRF removal function error using for the high-accuracy subaperture optical manufacturing. [ABSTRACT FROM AUTHOR]

Reliable and precise probabilistic prediction of daily catchment-scale streamflow requires statistical characterization of residual errors of hydrological models. This study focuses on approaches for representing error heteroscedasticity with respect to simulated streamflow, i.e., the pattern of larger errors in higher streamflow predictions. We evaluate eight common residual error schemes, including standard and weighted least squares, the Box-Cox transformation (with fixed and calibrated power parameter λ) and the log-sinh transformation. Case studies include 17 perennial and 6 ephemeral catchments in Australia and the United States, and two lumped hydrological models. Performance is quantified using predictive reliability, precision, and volumetric bias metrics. We find the choice of heteroscedastic error modeling approach significantly impacts on predictive performance, though no single scheme simultaneously optimizes all performance metrics. The set of Pareto optimal schemes, reflecting performance trade-offs, comprises Box-Cox schemes with λ of 0.2 and 0.5, and the log scheme ( λ = 0, perennial catchments only). These schemes significantly outperform even the average-performing remaining schemes (e.g., across ephemeral catchments, median precision tightens from 105% to 40% of observed streamflow, and median biases decrease from 25% to 4%). Theoretical interpretations of empirical results highlight the importance of capturing the skew/kurtosis of raw residuals and reproducing zero flows. Paradoxically, calibration of λ is often counterproductive: in perennial catchments, it tends to overfit low flows at the expense of abysmal precision in high flows. The log-sinh transformation is dominated by the simpler Pareto optimal schemes listed above. Recommendations for researchers and practitioners seeking robust residual error schemes for practical work are provided. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamic thin film nanofluid sprayed on a stretching cylinder with heat transfer is explored. The spray rate is a function of film size. Constant reference temperature is used for the motion past an expanding cylinder. The sundry behavior of the magnetic nano liquid thin film is carefully noticed which results in to bring changes in the flow pattern and heat transfer. Water-based nanofluids like Al2O3-H2O and CuO-H2O are investigated under the consideration of thin film. The basic constitutive equations for the motion and transfer of heat of the nanofluid with the boundary conditions have been converted to nonlinear coupled differential equations with physical conditions by employing appropriate similarity transformations. The modeled equations have been computed by using HAM (Homotopy Analysis Method) and lead to detailed expressions for the velocity profile and temperature distribution. The pressure distribution and spray rate are also calculated. The comparison of HAM solution predicts the close agreement with the numerical method solution. The residual errors show the authentication of the present work. The CuO-H2O nanofluid results from this study are compared with the experimental results reported in the literature showing high accuracy especially, in investigating skin friction coefficient and Nusselt number. The present work discusses the salient features of all the indispensable parameters of spray rate, velocity profile, temperature and pressure distributions which have been displayed graphically and illustrated. [ABSTRACT FROM AUTHOR]

In forest management surveys, the mean of a variable of interest (Y) in a population composed ofNequal area spatial compact elements is increasingly estimated from a model linkingYto an auxiliary vectorXknown for all elements in the population. It is also desired to have synthetic estimates of the mean ofYin spatially compact domains (forest stands) with no or at most one sample-based observation ofY. We develop three alternative estimators of mean-squared errors (MSE) that reduce the risk of a serious underestimation of the uncertainty in a synthetic estimate of a domain mean in cases where the employed model does not accounts for domain effects nor spatial autocorrelation in unobserved residual errors. Expansions of the estimators including anticipated effects of a spatial autocorrelation in residual errors are also provided. Simulation results indicate that the conventional model-dependent (MD) population-level estimator of variance in a synthetic estimate of a domain mean underestimates uncertainty by a wide margin. Our alternative estimators mitigated, in settings with weak to moderate domain effects and relatively small sample sizes, to a large extent, the problem of underestimating uncertainty. We demonstrate applications with examples from two actual forest inventories. [ABSTRACT FROM AUTHOR]

Mediterranean catchments are characterized by strong nonlinearities in their hydrological behaviour. Properly simulating those nonlinearities still represents a great challenge and, at the same time, an important issue in order to improve our knowledge of their hydrological behaviour. The main aim of this work is find out diverse modelling approaches to reproduce the observed nonlinear hydrological behaviour in a small Mediterranean catchment, Can Vila (Vallcebre, NE Spain). To this end, three hydrological models were considered: two lumped models called LU3 and LU4 of increasing complexity, and a distributed model called TETIS. The structures of these different models were used as hypotheses, which could explain and reproduce the observed nonlinear behaviour at the outlet. Four analyses were carried out: (i) goodness-of-fit criteria analysis, (ii) residual errors analysis, (iii) sensitivity analysis and (iv) multicriteria analysis based on the concept of Pareto Optimal. These analyses showed the higher capability and robustness of the distributed model to reproduce the observed complex hydrological behaviour in this catchment. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Objective: To evaluate three-dimensional translational setup errors and residual errors in image-guided radiosurgery, comparing frameless and frame-based techniques, using an anthropomorphic phantom. Materials and Methods: We initially used specific phantoms for the calibration and quality control of the image-guided system. For the hidden target test, we used an Alderson Radiation Therapy (ART)-210 anthropomorphic head phantom, into which we inserted four 5- mm metal balls to simulate target treatment volumes. Computed tomography images were the taken with the head phantom properly positioned for frameless and frame-based radiosurgery. Results: For the frameless technique, the mean error magnitude was 0.22 ± 0.04 mm for setup errors and 0.14 ± 0.02 mm for residual errors, the combined uncertainty being 0.28 mm and 0.16 mm, respectively. For the frame-based technique, the mean error magnitude was 0.73 ± 0.14 mm for setup errors and 0.31 ± 0.04 mm for residual errors, the combined uncertainty being 1.15 mm and 0.63 mm, respectively. Conclusion: The mean values, standard deviations, and combined uncertainties showed no evidence of a significant differences between the two techniques when the head phantom ART-210 was used. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamic thin film nanofluid sprayed on a stretching cylinder with heat transfer is explored. The spray rate is a function of film size. Constant reference temperature is used for the motion past an expanding cylinder. The sundry behavior of the magnetic nano liquid thin film is carefully noticed which results in to bring changes in the flow pattern and heat transfer. Water-based nanofluids like Al 2 O 3 -H 2 O and CuO-H 2 O are investigated under the consideration of thin film. The basic constitutive equations for the motion and transfer of heat of the nanofluid with the boundary conditions have been converted to nonlinear coupled differential equations with physical conditions by employing appropriate similarity transformations. The modeled equations have been computed by using HAM (Homotopy Analysis Method) and lead to detailed expressions for the velocity profile and temperature distribution. The pressure distribution and spray rate are also calculated. The comparison of HAM solution predicts the close agreement with the numerical method solution. The residual errors show the authentication of the present work. The CuO-H 2 O nanofluid results from this study are compared with the experimental results reported in the literature showing high accuracy especially, in investigating skin friction coefficient and Nusselt number. The present work discusses the salient features of all the indispensable parameters of spray rate, velocity profile, temperature and pressure distributions which have been displayed graphically and illustrated.

In case of coordinate machines that use CAA correction matrix, the issue of kinematic errors analysis may be based on the determination of residual error distribution. Temperature changes have an impact on CMM kinematic structure, which may cause the differences in the map of residual errors. As for today, the residual errors were analysed only for the reference temperature. No research was undertaken on the residual errors changes depending on the temperature variations. This paper presents the experiment aimed at residual errors analysis and resulting errors distributions for different temperatures. [ABSTRACT FROM AUTHOR]

Multibeam bathymetric system (MBS) has been widely applied in the marine surveying for providing high-resolution seabed topography. However, some factors degrade the precision of bathymetry, including the sound velocity, the vessel attitude, the misalignment angle of the transducer and so on. Although these factors have been corrected strictly in bathymetric data processing, the final bathymetric result is still affected by their residual errors. In deep water, the result usually cannot meet the requirements of high-precision seabed topography. The combined effect of these residual errors is systematic, and it's difficult to separate and weaken the effect using traditional single-error correction methods. Therefore, the paper puts forward a new method for weakening the effect of residual errors based on the frequency-spectrum characteristics of seabed topography and multibeam bathymetric data. Four steps, namely the separation of the low-frequency and the high-frequency part of bathymetric data, the reconstruction of the trend of actual seabed topography, the merging of the actual trend and the extracted microtopography, and the accuracy evaluation, are involved in the method. Experiment results prove that the proposed method could weaken the combined effect of residual errors on multibeam bathymetric data and efficiently improve the accuracy of the final post-processing results. We suggest that the method should be widely applied to MBS data processing in deep water. [ABSTRACT FROM AUTHOR]

• A method of near-infrared spectroscopy is proposed to detect Pb-polluted mussels. • Optimum wavelengths are selected by algorithms of information measures in NRS. • A sparse ELM based on residual errors is established as a classifier for detecting. • For class imbalance problems and mislabeled samples, the performance is analysed. • The results show that REELM model is superior to traditional and randomly pruned ELMs. It is toxic to consume mussels polluted by heavy metal Pb for humans. A quick, accurate, and non-destructive method based on near-infrared reflection spectroscopy (NIRS) has been investigated for the detection of Pb-polluted mussels in this paper. The spectral data of non-polluted and Pb-polluted mussels in the range of 950–1700 nm is acquired. A wavelength selection algorithm based on information measures of neighborhood rough set is applied to select optimal wavelengths. A sparse extreme learning machine (ELM) based on residual errors (REELM) is established as a classifier to detect Pb-polluted mussels. The average accuracy of 50 randomly assigned test datasets reaches 99.27% for detecting Pb-polluted mussels. For the class imbalance problem and mislabeled samples in the presence of practical applications, the detection performance of the proposed model has been analysed. The experimental results show that, compared with the traditional ELM and randomly pruned ELM, the REELM model is proven to be superior. The results indicate that NIRS combined with pattern recognition method has great potential to detect Pb pollution in mussels. This research is of significant importance in terms of the evaluation of edible quality and safety of mussels. [ABSTRACT FROM AUTHOR]

A Minimum Variance (MV) wind speed estimator for Global Navigation Satellite System-Reflectometry (GNSS-R) is presented. The MV estimator is a composite of wind estimates obtained from five different observables derived from GNSS-R Delay-Doppler Maps (DDMs). Regression-based wind retrievals are developed for each individual observable using empirical geophysical model functions that are derived from NDBC buoy wind matchups with collocated overpass measurements made by the GNSS-R sensor on the United Kingdom-Disaster Monitoring Constellation (UK-DMC) satellite. The MV estimator exploits the partial decorrelation that is present between residual errors in the five individual wind retrievals. In particular, the RMS error in the MV estimator, at 1.65 m/s, is lower than that of each of the individual retrievals. Although they are derived from the same DDM, the partial decorrelation between their retrieval errors demonstrates that there is some unique information contained in them. The MV estimator is applied here to UK-DMC data, but it can be easily adapted to retrieve wind speed for forthcoming GNSS-R missions, including the UK's TechDemoSat-1 (TDS-1) and NASA's Cyclone Global Navigation Satellite System (CYGNSS). [ABSTRACT FROM PUBLISHER]

Residual errors of hydrological models are usually both heteroscedastic and autocorrelated. However, only a few studies have attempted to explicitly include these two statistical properties into the residual error model and jointly infer them with the hydrological model parameters. This technical note shows that applying autoregressive error models to raw heteroscedastic residuals, as done in some recent studies, can lead to unstable error models with poor predictive performance. This instability can be avoided by applying the autoregressive process to standardized residuals. The theoretical analysis is supported by empirical findings in three hydrologically distinct catchments. The case studies also highlight strong interactions between the parameters of autoregressive residual error models and the water balance parameters of the hydrological model. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents health monitoring of welded structures using acceleration time response data. Residual errors are extracted from the measured acceleration time response data using an auto-regressive model. Damage identification is done by monitoring the residual errors using Shewhart and exponentially weighted moving average control charts. The applicability of the proposed method is tested with the welded structure model. Five damage levels are investigated and the damage is introduced by cutting a slot in the weld using an electrical discharge machine. Acceleration time response data are collected using piezoelectric sensors for all damage levels. The results show that both Shewhart and exponentially weighted moving average control charts are capable of identifying the presence of damage in the welded structure model under consideration. Exponentially weighted moving average control charts are more sensitive in damage identification than Shewhart control charts. [Copyright &y& Elsevier]

Deterministic error modelling, calibration and model parameter estimation of consumer‐grade accelerometers is considered and improvement to the traditionally used measurement model is proposed. Calibration experiments on a flight motion simulator are performed for experimental verification. Model parameters are estimated using the Levenberg‐Marquardt optimisation algorithm. Residual errors are considerably reduced as a result of the improved measurement model. [ABSTRACT FROM AUTHOR]

We present a rigorous two-step analysis of systematic errors in the four-noise parameter determination of a two-port network using the cold-source technique. This analysis is based on an original model that accounts for residual errors in the source impedance measurement. The method employs two linear fractional transforms to decompose the errors into relevant factor sets affecting the parameters in different ways. Analyses performed for a low-noise pseudornorphic high-electron mobility transistor (PHEMT) and a microwave amplifier show that the noise parameters of the low-noise PREMT are highly vulnerable to such errors. [ABSTRACT FROM AUTHOR]

This letter presents a new method, called total Zero Doppler steering, to perform yaw and pitch steering for spaceborne synthetic aperture radar (SAR) systems. The new method reduces the Doppler centroid to theoretically 0 Hz, independent of the range position of interest. Residual errors are only due to pointing inaccuracy or due to approximations in the implementation of the total zero Doppler steering law. This letter compares the new method with currently applied methods. The attitude angles and the residual Doppler centroid frequencies are calculated and depicted exemplarily for the parameters of TerraSAR-X, for which the new method will be implemented and used. The new method provides a number of advantages. The low residual Doppler centroid and the reduced variation of the Doppler centroid over range allow a more accurate Doppler centroid estimation. Due to the low residual Doppler centroid, the synthetic aperture radar (SAR) processing can be alleviated, since the range cell migration is reduced and the Doppler frequencies are low. This facilitates the use of very efficient processing algorithms, which are based on approximations whose quality is better for low Doppler frequencies. The new method will furthermore optimize the overlap of the azimuth spectra of SAR image pairs for cross-track interferometry. Low Doppler centroids will also reduce the impact of coregistration errors on the interferometric phase. Furthermore, scalloping corrections in the ScanSAR processing are alleviated due to the low variation of the Doppler centroid over range. [ABSTRACT FROM PUBLISHER]

We develop a unique set of techniques to support reliable and efficient video transmission over bandwidth-limited mobile networks. The video coder is based on the H.263 coding standard, while its transmission system design is based on a joint study of combined source and channel coding, diversity reception, and pre/postprocessing techniques. In particular, a finite-state Markov model for representing a correlated fading channel with diversity is developed. Based on this model, a recursive algorithm is further devised for an efficient estimation of block-code performance. By doing so, an important means for finding proper diversity and channel coding schemes for correlated video data in correlated fading channels is obtained. In addition, robust decoding together with a combined spatial-temporal concealment is employed to mitigate the effects of decoding mismatch caused by residual errors. Simulation results confirm that the proposed system can significantly reduce the bursty error effects on the H.263 coded video data while maintaining high transmission efficiency [ABSTRACT FROM PUBLISHER]

Summary: Software reliability deals with the probability that software will not cause the failure of a system in a specified time interval. Software reliability growth models (SRGMs) are used to predict future behaviour from known characteristics of software, like historical failures. With the increasing demand to deliver quality software, more accurate SRGMs are required to estimate the software release time and cost of the testing effort. Software failure predictions at early phases also provide an opportunity for investing in proper quality assurance and upfront resource planning. Up till now, many parametric software reliability growth models (PSRGMs) have been proposed. However, several limitations of them mean that their predictive capacities differ from one dataset to others. In this paper, to enhance the prediction accuracy of existing PSRGMs, a high precision error iterative analysis method (HPEIAM) has been proposed based on the residual errors. In HPEIAM, residual errors from the estimated results of SRGMs are considered as another source of data that can combine the residual error modification with artificial neural network sign estimator. The repeated computation of residual errors by SRGMs improves and corrects the prediction accuracy up to the expected level. The performance of HPEIAM is tested with several PSRGMs using two sets of real software failure data based on three performance criteria. Moreover, we have compared the estimated failures predicted by HPEIAM with genetic algorithm (GA)‐based prediction improvement. The results demonstrate that HPEIAM gives an improvement in goodness‐of‐fit and predictive performance for every PSRGM in initial few iterations. [ABSTRACT FROM AUTHOR]

Chemical reaction in mixed convection magnetohydrodynamic second grade nanoliquid thin film flow through a porous medium containing nanoparticles and gyrotactic microorganisms is considered with entropy generation. The stratification phenomena, heat and mass transfer simultaneously take place within system. Microorganisms are utilized to stabilize the suspended nanoparticles through bioconvection. For the chemical reaction of species, the mass transfer increases. The governing equations of the problem are transformed to nonlinear differential equations through similarity variables, which are solved through a well known scheme called homotopy analysis method. The solution is expressed through graphs and illustrations which show the influences of all the parameters. The residual error graphs elucidate the authentication of the present work. [ABSTRACT FROM AUTHOR]

Objective: To evaluate three-dimensional translational setup errors and residual errors in image-guided radiosurgery, comparing frameless and frame-based techniques, using an anthropomorphic phantom., Materials and Methods: We initially used specific phantoms for the calibration and quality control of the image-guided system. For the hidden target test, we used an Alderson Radiation Therapy (ART)-210 anthropomorphic head phantom, into which we inserted four 5mm metal balls to simulate target treatment volumes. Computed tomography images were the taken with the head phantom properly positioned for frameless and frame-based radiosurgery., Results: For the frameless technique, the mean error magnitude was 0.22 ± 0.04 mm for setup errors and 0.14 ± 0.02 mm for residual errors, the combined uncertainty being 0.28 mm and 0.16 mm, respectively. For the frame-based technique, the mean error magnitude was 0.73 ± 0.14 mm for setup errors and 0.31 ± 0.04 mm for residual errors, the combined uncertainty being 1.15 mm and 0.63 mm, respectively., Conclusion: The mean values, standard deviations, and combined uncertainties showed no evidence of a significant differences between the two techniques when the head phantom ART-210 was used.