Statistical Error Analysis Research Articles

Comparing Fiducial-Based and Intraoperative Computed Tomography-Based Registration for Frameless Stereotactic Brain Biopsy

Objective: The aim of this work was to compare fiducial-based and intraoperative computed tomography (iCT)-based registration for frameless stereotactic brain biopsy. Methods: Of 50 frameless stereotactic biopsies with the VarioGuide, 30 cases were registered as iCT based and 20 as fiducial based. Statistical analysis of the target registration error (TRE), dose length product, effective radiation dose (ED), operation time, and diagnostic yield was performed. Results: The mean TRE was significantly lower using iCT-based registration (mean ± SD: 0.70 ± 0.32 vs. 2.43 ± 0.73 mm, p < 0.0001). The ED was significantly lower when using iCT-based registration compared to standard navigational CT (mean ± SD: 0.10 ± 0.13 vs. 2.23 ± 0.34 mSv, p < 0.0001). Post-biopsy iCT was associated with a significant lower (p < 0.0001) ED compared to standard CT (mean ± SD: 1.04 ± 0.18 vs. 1.65 ± 0.26 mSv). The mean surgical time was shorter using iCT-based registration, although the mean total operating room (OR) time did not differ significantly. The diagnostic yield was 96.7% (iCT group) versus 95% (fiducial group). Post-biopsy imaging revealed severe bleeding in 3.3% (iCT group) versus 5% (fiducial group). Conclusion: iCT-based registration for frameless stereotactic biopsies increases the accuracy significantly without negative effects on the surgical time or the overall time in the OR. Appropriate scan protocols in iCT registration contribute to a significant reduction of the radiation exposure. The high accuracy of the iCT makes it the more favorable registration strategy when taking biopsies of small tumors or lesions near eloquent brain areas.

Adsorption of anionic dye on eco-friendly synthesised reduced graphene oxide anchored with lanthanum aluminate: Isotherms, kinetics and statistical error analysis

In the present study we made an effort to deploy eco-friendly synthesized reduced graphene oxide/Lanthanum Alluminate nanocomposites (RGO-LaAlO3) and Lanthanum Alluminate (LaAlO3) as adsorbents to remove dye from the synthetic media. XRD, SEM, BET surface area and EDX have been used to characterize the above-mentioned adsorbents. The impacts of different factors like adsorbent dosage, the concentration of adsorbate and PH on adsorption were studied. The best fit linear and nonlinear equations for the adsorption isotherms and kinetic models had been examined. The sum of the normalized errors and the coefficient of determination were used to determine the best fit model. The experimental data were more aptly fitted for nonlinear forms of isotherms and kinetic equations. Pseudo-second-order and Freundlich isotherm model fits the equilibrium data satisfactorily. Methyl orange (MO) has been used as model dye pollutant and maximum adsorption capacity was found to be 469.7 and 702.2 mg g−1 for LaAlO3 and RGO-LaAlO3, respectively.

Review and recommendations for univariate statistical analysis of spherical equivalent prediction error for IOL power calculations.

To provide a reference for study design comparing intraocular lens (IOL) power calculation formulas, to show that the standard deviation (SD) of the prediction error (PE) is the single most accurate measure of outcomes, and to provide the most recent statistical methods to determine P values for type 1 errors. Baylor College of Medicine, Houston, Texas, and University of Southern California, Los Angeles, California, USA. Retrospective consecutive case series. Two datasets comprised of 5200 and 13 301 single eyes were used. The SDs of the PEs for 11 IOL power calculation formulas were calculated for each dataset. The probability density functions of signed and absolute PE were determined. None of the probability distributions for any formula in either dataset was normal (Gaussian). All the original signed PE distributions were not normal, but symmetric and leptokurtotic (heavy tailed) and had higher peaks than a normal distribution. The absolute distributions were asymmetric and skewed to the right. The heteroscedastic method was much better at controlling the probability of a type I error than older methods. (1) The criteria for patient and data inclusion were outlined; (2) the appropriate sample size was recommended; (3) the requirement that the formulas be optimized to bring the mean error to zero was reinforced; (4) why the SD is the single best parameter to characterize the performance of an IOL power calculation formula was demonstrated; and (5) and using the heteroscedastic statistical method was the preferred method of analysis was shown.

Quantization error in stereo imaging system with noise distributions

The problem of estimating quantization error in 2D images is an inherent problem in computer vision. The outcome of this problem is directly related to the error in reconstructed 3D position coordinates of an object. Thus estimation of quantization error has its own importance in stereo vision. Although the quantization error cannot be controlled fully, still statistical error analysis helps us to measure the performance of stereo systems that relies on the imaging parameters. Generally, it is assumed that the quantization error in 2D images is distributed uniformly that need not to be true from a practical aspect. In this paper, we have incorporated noise distributions (Triangular and Trapezoidal) for the stochastic error analysis of the quantization error in stereo imaging systems. For the validation of the theoretical analysis, the detailed simulation study is carried out by considering different cases.

Intelligent prediction of engine failure through computational image analysis of wear particle

The present study is focused on studying the morphological characteristics of wear particles. The raw image captured from the CCD microscope is processed through a series of image processing techniques to obtain the final image. Fractal computation is performed to estimate the surface roughness of the particle boundary, which indicates the wear rate failure. An intelligence-based ANN model has been created using feed-forward backpropagation to predict outputs such as Form Factor, Convexity, Aspect Ratio, Solidity, and Roundness with respect to Running Hour, Engine RPM and Engine Oil temperature. The propound ANN model is seen as equipped to map the input-output patterns of failure under the engine parameter platform. Statistical analysis of combined error and correlation factor provides a powerful mapping tool for failure prediction. Subsequent ANN models have been seen as practical tools for predicting the performance of wear properties with the nominal inspection.

Beyond the EU Structural Funds’ Absorption Rate: How Do Regions Really Perform?

Although the EU structural funds aim to alleviate disparities through supporting regional development, their impact on local economies and societies is considered as uneven. As existing studies explore the absorption rate of the EU share of contribution as a point-in-time indicator at the end of the policy cycle, evidence about regional co-finance and the factors dynamically affecting absorption performance is lacking. To that end, this paper aims to provide a new longitudinal investigation of the absorption time series and develop an original indicator, supported by a statistical error analysis, for offering a transparent view of the total funds’ absorption. The analysis highlights that undesired regional strategies due to low administrative capacity may increase the absorption rate, though without supporting regional growth. The proposed approach could further facilitate the equitable allocation of political accountability regarding the structural funds’ absorption to the EU and the regions. Overall, it is anticipated that this research will support the EU in monitoring actual regional performance for prompting local managing authorities to improve their administrative capacity.

A new correlation for estimation of minimum miscibility pressure (MMP) during hydrocarbon gas injection

The satisfactory recovery of the hydrocarbon gases has made them a reliable choice for gas injection-based enhanced oil recovery (EOR) techniques. The minimum miscibility pressure (MMP) is a pivotal parameter governing the recovery factor during gas injection processes. Therefore, the determination of the authentic MMP is of a crucial importance. Due to the drawback of the experimental techniques (time and cost), empirical correlations are valuable tools in MMP determination. In this study, a multi-gene genetic programming and another software known as LINGO as an optimization tool are applied to offer a dependable MMP formula based on a comprehensive MMP dataset (a total of 108 MMP data). The independent parameters of reservoir temperature, pseudocritical temperature of the injection gas, molecular weight of C5+ components of the reservoir fluid and the intermediate (H2S, CO2, C2–C4)-to-volatile (N2 and C1) ratio are considered as input variables. A comprehensive set of experimental data covers wide span of primary parameters. Furthermore, in order to judge the accuracy of the suggested model and assess the precision and compare the predicted MMP by the current model with those estimated by preexisting correlations, the statistical and graphical error analyses have been employed. Based on the results, the proposed model can estimate MMP of the associated gas with an average absolute relative error of 9.86%. Also, the proposed correlation is more trustworthy and precise than the preexisting models in an extensive spectrum of thermodynamic circumstances. Eventually, the relevancy factor has depicted that the pseudocritical temperature of the injected gas has the most severe role in miscibility achievement.

An improved mathematical prediction of the time evolution of the Covid-19 pandemic in Italy, with a Monte Carlo simulation and error analyses

We present an improved mathematical analysis of the time evolution of the Covid-19 pandemic in Italy and a statistical error analyses of its evolution, including a Monte Carlo simulation with a very large number of runs to evaluate the uncertainties in its evolution. A previous analysis was based on the assumption that the number of nasopharyngeal swabs would be constant. However, the number of daily swabs is now more than five times what it was when we did our previous analysis. Therefore, here we consider the time evolution of the ratio of the new daily cases to number of swabs, which is more representative of the evolution of the pandemic when the number of swabs is increasing or changing in time. We consider a number of possible distributions representing the evolution of the pandemic in Italy, and we test their prediction capability over a period of up to 6 weeks. The results show that a distribution of the type of Planck black body radiation law provides very good forecasting. The use of different distributions provides an independent possible estimate of the uncertainty. We then consider five possible trajectories for the number of daily swabs and we estimate the potential dates of a substantial reduction in the number of new daily cases. We then estimate the spread in a substantial reduction, below a certain threshold, of the daily cases per swab among the Italian regions. We finally perform a Monte Carlo simulation with 25,000 runs to evaluate a random uncertainty in the prediction of the date of a substantial reduction in the number of diagnosed daily cases per swab.

Super-Resolution of Thermal Images Using an Automatic Total Variation Based Method

The relatively poor spatial resolution of thermal images is a limitation for many thermal remote sensing applications. A possible solution to mitigate this problem is super-resolution, which should preserve the radiometric content of the original data and should be applied to both the cases where a single image or multiple images of the target surface are available. In this perspective, we propose a new super-resolution algorithm, which can handle either single or multiple images. It is based on a total variation regularization approach and implements a fully automated choice of all the parameters, without any training dataset nor a priori information. Through simulations, the accuracy of the generated super-resolution images was assessed, in terms of both global statistical indicators and analysis of temperature errors at hot and cold spots. The algorithm was tested and applied to aerial and terrestrial thermal images. Results and comparisons with state-of-the-art methods confirmed an excellent compromise between the quality of the high-resolution images obtained and the required computational time.

Features of application of sensitivity theory for analysis of influence of parametric disturbances on dynamic properties electromechanical converters

At the design and testing stage of electromechanical converters, the analysis of the influence of parametric perturbations on the dynamic properties of an object using sensitivity theory, which allows to evaluate the quality of operation of electrical machines depending on operating conditions, is relevant. Based on the system of differential equations of a DC motor, the sensitivity equations of the corresponding coordinates were obtained in three parameters. A vector structural scheme of the sensitivity model has been formed, as well as the Simulink-model, with the help of which sensitivity function plots were obtained, which determine the additional motion of the object of study when parameters change within specified limits. It is shown that the largest steady-state values of the sensitivity functions correspond to changes in the moment of inertia. It is revealed that the influence of the moment of inertia on the coordinates of the object of study is the most significant. Where in the coordinate most sensitive to variations in parameters is the rotation speed of the electromechanical converter. The problem of statistical analysis of errors of the output coordinates of a DC motor under the assumption of normal distribution of parametric disturbances was also solved. Simulations were carried out and dispersions and relative estimates of the influence of variable parameters were calculated, and graphs were obtained to estimate the degree of influence of parametric disturbances.

Identification of Physical Helicopter Models Using Subspace Identification

Subspace identification is a powerful tool due to its well-understood techniques based on linear algebra (orthogonal projections and intersections of subspaces) and numerical methods like singular value decomposition. However, the state space model matrices, which are obtained from conventional subspace identification algorithms, are not necessarily associated with the physical states. This can be an important deficiency when physical parameter estimation is essential. This holds for the area of helicopter flight dynamics, where physical parameter estimation is mainly conducted for mathematical model improvement, aerodynamic parameter validation, and flight controller tuning. The main objective of this study is to obtain helicopter physical parameters from subspace identification results. To achieve this objective, the subspace identification algorithm is implemented for a multirole combat helicopter using both FLIGHTLAB simulation and real flight-test data. After obtaining state space matrices via subspace identification, constrained nonlinear optimization methodologies are utilized for extracting the physical parameters. The state space matrices are transformed into equivalent physical forms via the "sequential quadratic programming" nonlinear optimization algorithm. The required objective function is generated by summing the square of similarity transformation equations. The constraints are selected with physical insight. Many runs are conducted for randomly selected initial conditions. It can be concluded that all of the significant parameters can be obtained with a high level of accuracy for the data obtained from the linear model. This strongly supports the idea behind this study. Results for the data obtained from the nonlinear model are also evaluated to be satisfactory in the light of statistical error analysis. Results for the real flight-test data are also evaluated to be good for the helicopter modes that are properly excited in the flight tests.

Predictive model of algal biofuel production based on experimental data

Algal biofuels are of growing interest in the quest to reduce carbon emissions in the atmosphere but the sensitivity of the fuel production to various factors is not well understood. Therefore, the effects of temperature, light intensity, carbon concentration, aeration rate, pH, and time on the CO2 biofixation rate of Chlorella vulgaris (ISC-23) were investigated using experimental, and Genetic Programming (GP) modeling techniques. The impacts of applying the cement industrial flue gas as a source of carbon, useful for the growth of microalgae, were also studied. Chlorella vulgaris (ISC-23) was cultivated in a laboratory photobioreactor on a BG-11 medium. The developed GP model was used to optimize the CO2 biofixation based on the studied variables and produce a predictive equation. By using statistical measurements and error analysis, the predictive equation was shown to agree with the experimentally obtained values. It was found that the optimum conditions occur at 26o C, and 3200 lx of light, in the existence of CO2. Applying 6% CO2 as the input with the aeration rate of 0.5 vvm in 11 days was also reported as the optimum scenario for algae production with keeping the pH close to 7.5. The results indicate that the predictions determined with the proposed equation can be of practical worth for researchers and experts in the biofuel industry.

Statistical reasoning levels and error analysis of prospective mathematics teacher students

This paper describes the level of statistical reasoning and the difficulties and errors that occur in statistical problem-solving in prospective mathematics teacher students at STKIP PGRI Jombang. This research is a qualitative study with a case study strategy, the case study in the process of solving statistical problems carried out by the subject. The research subjects were the 69 students at third-semester of Mathematics Education Program STKIP PGRI Jombang who had taken descriptive statistics. The results of this study indicate that students are not found at the idiosyncratic level, most of them are at the transitional and quantitative level, while the analytical level is still a minority

The hip joint as an egg shape: a comprehensive study of femoral and acetabular morphologies

ABSTRACT Understanding the morphological features characterising a normal femoral head and acetabular cavity is critical for a more comprehensive and updated definition of hip anatomy. Based on anatomical observations, MacConaill introduced the notion that spheroidal articular surfaces are better represented by ovoidal shapes, in comparison with the still well-established spherical shape. This work tests MacConaill’s classification by using a surface-fitting framework to assess the goodness-of-fit regarding the largest assortment of sphere-like shapes presented in a single study (i.e. a total of 10 different shapes: sphere, rotational conchoids, rotational ellipsoid, ellipsoid, superellipsoid, Barr’s superellipsoid, tapered ellipsoid, Barr’s tapered superellipsoid, ovoid, superovoid). Anatomical data of the femoral head and acetabular cavity were obtained from computed tomography scans of a gender-balanced, asymptomatic 15 population of 30 adult subjects. The framework involved image segmentation with active contour methods, mesh smoothing and decimation, and surface fitting to point clouds was performed with genetic algorithms. The statistical analysis of the surface-fitting errors revealed the superior approximation of non-spherical shapes: superovoids provided the best fit for each femoral head and acetabular cavity, whereas spheres presented the worst fitting values. We also addressed gender variability in bony 20 hip geometry as sphericity, ellipticity, conicity and squareness were measured.

Constitutive modelling of Al7075 using the Johnson–Cook model

In this paper, hot compression behaviour of Al7075 in the temperature range of 573–723 K and the strain rate range of 0.001–0.1 $$\hbox {s}^{-1}$$ , based on standard requirements, was studied. The prediction of flow stress was performed using constitutive equations based on the basic and modified-Johnson–Cook model and the accuracy of the proposed models was estimated by comparing with the experimental results by the statistical error analysis method. Based on the experimental results, flow stress is changed significantly with changes in the strain rate and temperature. However, the basic model cannot predict the correlated effects of these parameters which decrease its accuracy of model, the flow stress of the materials especially at high temperatures. During the calculation of the constants based on the modified model, the effects of hardening and softening behaviour were included in addition to considering the correlated effects of the parameters. The accuracy of the modified model increased significantly when compared with experimental results.

Design of a high-spectral-resolution lidar for atmospheric temperature measurement down to the near ground.

In this paper, a high-spectral-resolution lidar (HSRL) for profiling atmospheric temperature from the ground to 10 km is proposed. A double Nd:YAG laser produces the transmitted laser at 532 nm. The backscattering lidar signal is passed through two different saturated iodine-vapor filters and thus obtains molecular scattering signals that can be employed to determine the temperature. A coaxial postposition transceiver is constructed with an off-axis aspheric reflective telescope (OART). The design of the transceiver and that of the OART are demonstrated. With this transceiver, the lidar blind zone where the overlap factor is zero can be reduced greatly, and accurate temperature measurement for full elevation can be achieved. The whole system is optimized with theoretical models based on geometrical optics and statistical error analyses. Monte Carlo simulations display the performance of the designed HSRL, showing that the all-day temperature retrieval error is better than 1.4 K from the ground to 10 km. The proposed HSRL is expected to provide more accurate atmospheric auxiliary parameters for the detection of aerosols' optical characteristics.

A new method to quantify mineral dust and other aerosol species from aircraft platforms using single-particle mass spectrometry

Abstract. Single-particle mass spectrometry (SPMS) instruments characterize the composition of individual aerosol particles in real time. Their fundamental ability to differentiate the externally mixed particle types that constitute the atmospheric aerosol population enables a unique perspective into sources and transformation. However, quantitative measurements by SPMS systems are inherently problematic. We introduce a new technique that combines collocated measurements of aerosol composition by SPMS and size-resolved absolute particle concentrations on aircraft platforms. Quantitative number, surface area, volume, and mass concentrations are derived for climate-relevant particle types such as mineral dust, sea salt, and biomass burning smoke. Additionally, relative ion signals are calibrated to derive mass concentrations of internally mixed sulfate and organic material that are distributed across multiple particle types. The NOAA Particle Analysis by Laser Mass Spectrometry (PALMS) instrument measures size-resolved aerosol chemical composition from aircraft. We describe the identification and quantification of nine major atmospheric particle classes, including sulfate–organic–nitrate mixtures, biomass burning, elemental carbon, sea salt, mineral dust, meteoric material, alkali salts, heavy fuel oil combustion, and a remainder class. Classes can be sub-divided as necessary based on chemical heterogeneity, accumulated secondary material during aging, or other atmospheric processing. Concentrations are derived for sizes that encompass the accumulation and coarse size modes. A statistical error analysis indicates that particle class concentrations can be determined within a few minutes for abundances above ∼10 ng m−3. Rare particle types require longer sampling times. We explore the instrumentation requirements and the limitations of the method for airborne measurements. Reducing the size resolution of the particle data increases time resolution with only a modest increase in uncertainty. The principal limiting factor to fast time response concentration measurements is statistically relevant sampling across the size range of interest, in particular, sizes D &lt; 0.2 µm for accumulation-mode studies and D &gt; 2 µm for coarse-mode analysis. Performance is compared to other airborne and ground-based composition measurements, and examples of atmospheric mineral dust concentrations are given. The wealth of information afforded by composition-resolved size distributions for all major aerosol types represents a new and powerful tool to characterize atmospheric aerosol properties in a quantitative fashion.

Blocking and re-arrangement of pots in greenhouse experiments: which approach is more effective?

BackgroundObservations measured in field and greenhouse experiments always contain errors. These errors can arise from measurement error, local or positional conditions of the experimental units, or from the randomization of experimental units. In statistical analysis errors can be modelled as independent effects or as spatially correlated effects with an appropriate variance–covariance structure. Using a suitable experimental design, a part of the variance can be captured through blocking of the experimental units. If experimental units (e.g. pots within a greenhouse) are mobile, they can be re-arranged during the experiment. This re-arrangement enables a separation of variation due to time-invariant position effects and variation due to the experimental units. If re-arrangement is successful, the time-invariant positional effect can average out for experimental units moved between different positions during the experiment. While re-arrangement is commonly done in greenhouse experiments, data to quantify its usefulness is limited.ResultsA uniformity greenhouse experiment with barley (Hordeum vulgare L.) to compare re-arrangement of pots with a range of designs under fixed-position arrangement showed that both methods can reduce the residual variance and the average standard error of a difference. All designs with fixed-position arrangement, which accounted for the known north–south gradient in the greenhouse, outperformed re-arrangement. An α-design with block size four performed best across seven plant growth traits.ConclusionBlocking with a fixed-position arrangement was more efficient in improving precision of greenhouse experiments than re-arrangement of pots and hence can be recommended for comparable greenhouse experiments.

New models for prediction of reservoir rock properties in Biyad formation of Kharir oil field, Hadramout Governorate

Reservoir description is a process of describing various reservoir characteristics using all the available data. The nature of the description of reservoir properties is related to the availability of sample data and geologic complexity of reservoir. Reservoir characterization is needed for effective reservoir management studies. Reservoir rock properties can be estimated by several methods. Rock properties are determined by performing laboratory analyses on cores extracted from the reservoir. However, obtaining the properties from core analysis or well logging is time consuming and an expensive operation. For that, in this work, new models for estimating rock properties (porosity, permeability) are developed by adapting Artificial Neural network model (ANN). Models were successfully demonstrated for predicting reservoir rock properties (porosity and permeability) forBiyad formation of Kharir oil field. The models were tested against properties yielded from core laboratories using statistical error analysis. Result showed a great potential in predicting reservoir properties using artificial intelligence models.

Entropy optimized dissipative CNTs based flow with probable error and statistical declaration

BackgroundCNTs are categorized subject to their structures i.e., SWCNTs (single wall nanotubes), DWCNTs (double wall nanotubes) and MWCNTs (multi-wall nanotubes). The various structures have distinct characteristics that make the nanotubes suitable for various physical applications. It is due their unique electrical, mechanical and thermal attributes CNTs present thrilling opportunities for mechanical engineering, industrial, scientific research and commercial applications. There is fruitful potential for carbon nanotubes in the composites business and industry. Today, CNTs find utilization in frequent various products, and analyst continue to explore new applications. Currently applications comprise wind turbines, bicycle components, scanning probe microscopes, flat panel displays, marine paints, sensing devices, electronics, batteries with longer lifetime and electrical circuitry etc. Such applications in mind, entropy optimized dissipative CNTs based flow of nanomaterial by a stretched surface. Flow is caused due to stretching phenomenon and studied in 3D coordinates. Both types of CNTs are studied i.e., SWCNTs and MWCNTs. CNTs are considered for nanoparticles and water for continuous phase fluid. Special consideration is given to the analysis of statistical declaration and probable error for skin friction and Nusselt number. Furthermore, entropy rate is calculated. Entropy rate is discussed in the presence of four main irreversibilities i.e., heat transfer, Joule heating, porosity and dissipation. MethodHomotopy technique is utilized to develop the convergence series solutions. ResultsImpacts of sundry variables subject to both SWCNTs (single) and MWCNTs (multi) are graphically discussed. Statistical analysis and probable error for surface drag force and Nusselt number are numerically calculated subject to various flow variables. Numerical results for such engineering quantities are displayed through tables. In addition, comparative analysis for SWCNTs and MWCNTs are presented for the velocity, concentration and thermal fields. ConclusionsResults for entropy rate is calculated in the presence of various sundry variable through implementation of second law of thermodynamics. It is examined from the results that velocity decreases for both CNTs via higher magnetic, inertia coefficient and porosity parameters. Secondary velocity i.e., velocity in g-direction boosts up versus rotation parameter while it declines for larger slip parameter for both CNTs. thermal field intensifies for both CNTs via larger heat generation/absorption parameter. Concentration which shows the mass transfer of species increases subject to higher homogeneous parameter and Schmidt number in case of both CNTs. Entropy rate in more for larger magnetic, Reynolds number and slip parameter. Bejan number boosts up for higher Reynold number and slip parameter while it declines for magnetic parameter.