sensitivity of ridge type estimation methods to condition number an analysis of ridge type estimation methods and their performance in response to different levels of ill conditioning is presented by adjusting the observation accuracy and the sampling rate the amount of ill conditioning in a linear estimation problem is altered the effectiveness of the ridge type methods in response to these changes is evaluated by comparing the solution accuracy with those of the standard minimum variance techniques results show the improved performance of the ridge type estimation method for various levels of ill conditioning in addition the amount of improvement increases as the level of ill conditioning present in the problem is increased

a survey of the physical optics inverse scattering identity the physical optics approximation is applied to the acoustic and electromagnetic direct scattering integral representation yielding an inverse scattering identity which relates the characteristic function of a scatterer to the three dimensional spatial fourier transform of the augmented far field scattering amplitude this identity requires full scattering information for all frequencies and aspect angles an integral equation for incomplete scattering information for this identity is developed this integral equation is for the unknown characteristic function of the scatterer in terms of the known incomplete scattering information the kernel of this integral equation is the three dimensional spatial fourier transform of the known characteristic function of the scattering information aperture a regularized analytic closed form solution to this integral equation is obtained synthesized numerico experimental results verifying this solution are presented the details of some special cases consisting of a priori knowledge about the scatterer or the scattering information aperture are presented

error of linear estimation of lost samples in an oversampled band limited signal a finite number of lost samples from an oversampled band limited signal can be restored from the remaining samples this paper explores the noise sensitivity of a linear algorithm that performs such restoration even though the problem is well posed restoration noise level can become prohibitively high for a sampling rates close to the nyquist rate and b too many lost samples numerical results of restoration noise level are given for the cases of one lost sample two not necessarily adjacent samples and a sequence of m adjacent lost samples the effects of both truncation and noise are evaluated for the case of a single lost sample in a stochastic signal the results are compared with the corresponding minimum mean square error of the lost sample although suboptimal the truncated lost sample sampling estimate is more straightforward computationally and does not require detailed knowledge of the signal or noise second order statistics

application of the tikhonov regularization technique to the equivalent magnetic currents near field technique the equivalent magnetic currents method can be used to characterize radiating structures and to obtain information about the current distribution on the radiating device under test dut in order to do so the system is assumed to be linear and inversion from near field measurements can be carried out using numerical techniques such as the singular value decomposition however this approach is very sensitive to modeling and measurement errors which is a consequence of the ill conditioned nature of the inversion process here we propose to account for the ill conditioning by using a tikhonov regularization technique to perform the inversion this technique requires a regularization parameter to be set to an appropriate value and we show that a generalized cross validation approach yields adequate determination of the regularization parameter directly from the measured data the proposed method can be tailored to account for specific characteristics of the dut this point is illustrated by the estimation of the current distribution of a bidimensional radiating structure for which prior information about the orientation of radiating edges is incorporated into the inversion method

on design orthogonality maximin distance and projection uniformity for computer experiments space filling designs are widely used in both computer and physical experiments column orthogonality maximin distance and projection uniformity are three basic and popular space filling criteria

the backus gilbert method and their minimum norm solution abstractthis paper has two objectives one is to review the backus gilbert bg method backus and gilbert investigate continuous inverse problems in a radially symmetric earth using an approach completely different from that of standard inversion methods if m is an earth property of interest the bg method provides average values of m over some radial intervals if an interval w is relatively short and centered near a particular radius r0 the bg average will be a local average of m near r0 with a resolving length of w backus and gilbert also introduce the concept of trade off between resolution and error which is essential in inverse theory regardless of the inversion method in spite of its importance inverse theory texts neither describe the bg method in full nor show how to apply it in all its generality because the three papers that introduce the bg method are mathematically difficult this paper provides background material and a detailed derivation of the method as well as two completely wor

reconstruction of dielectric permittivity distributions in arbitrary 2 d inhomogeneous biological bodies by a multiview microwave numerical method a numerical method for microwave imaging of two dimensional inhomogeneous biological bodies illuminated by tm waves is presented it is a spatial domain multiview approach which makes use of the moment method to discretize the integral equation formulation of inverse scattering a pseudoinversion technique is applied to obtain a minimum norm solution for the equivalent current density inside the cross section of a scatterer a multi illumination angle multiview process is used the invariance of the green matrix makes it possible to perform only one pseudoinverse off line and once for all independently of the number of views thus reducing the need for computer resources a pixel representation is adopted and a look up table is utilized to fast synthesize images no plane wave illumination is required and no first order approximations are applied distortions in the dielectric reconstruction and noise effects are evaluated via some numerical simulations

analytical study of the effects of soft tissue artefacts on functional techniques to define axes of rotation abstract the accurate location of the main axes of rotation aor is a crucial step in many applications of human movement analysis there are different formal methods to determine the direction and position of the aor whose performance varies across studies depending on the pose and the source of errors most methods are based on minimizing squared differences between observed and modelled marker positions or rigid motion parameters implicitly assuming independent and uncorrelated errors but the largest error usually results from soft tissue artefacts sta which do not have such statistical properties and are not effectively cancelled out by such methods however with adequate methods it is possible to assume that sta only account for a small fraction of the observed motion and to obtain explicit formulas through differential analysis that relate sta components to the resulting errors in aor parameters in this paper such formulas are derived for three different functional calibration techniques geometric fitting mean finite helical axis and sara to explain why each technique behaves differently from the others and to propose strategies to compensate for those errors these techniques were tested with published data from a sit to stand activity where the true axis was defined using bi planar fluoroscopy all the methods were able to estimate the direction of the aor with an error of less than 5 whereas there were errors in the location of the axis of 30 40 mm such location errors could be reduced to less than 17 mm by the methods based on equations that use rigid motion parameters mean finite helical axis sara when the translation component was calculated using the three markers nearest to the axis

strong orthogonal arrays and associated latin hypercubes for computer experiments this paper introduces constructs and studies a new class of arrays called strong orthogonal arrays as suitable designs for computer experiments a strong orthogonal array of strength t enjoys better space filling properties than a comparable orthogonal array in all dimensions lower than t while retaining the space filling properties of the latter in t dimensions latin hypercubes based on strong orthogonal arrays of strength t are more space filling than comparable orthogonal array based latin hypercubes in all g dimensions for any 2 g t 1 copyright 2013 oxford university press

on the choice of expansion and weighting functions in the numerical solution of operator equations one of the objectives of this paper is to discuss the mathematical requirements that the expansion functions must satisfy in the method of moments mm solution of an operator equation a simple differential equation is solved to demonstrate these requirements the second objective is to study the numerical stability of point matching method galerkin s method and the method of least squares pocklington s integral equation is considered and numerical results are presented to illustrate the effect of various choices of weighting functions on the rate of convergence finally it is shown that certain choices of expansion and weighting functions yield numerically acceptable results even though they are not admissible from a strictly mathematical point of view the reason for this paradox is outlined

a comparison of two non invasive methods for measuring scapular orientation in functional positions identification of scapular dyskinesis and evaluation of interventions depend on the ability to properly measure scapulothoracic st motion the most widely used measurement approach is the acromion marker cluster amc which can yield large errors in extreme humeral elevation and can be inaccurate in children and patient populations recently an individualized regression approach has been proposed as an alternative to the amc this technique utilizes the relationship between st orientation humerothoracic orientation and acromion process position derived from calibration positions to predict dynamic st orientations from humerothoracic and acromion process measures during motion these individualized regressions demonstrated promising results for healthy adults however this method had not yet been compared to the more conventional amc this study compared st orientation estimates by the amc and regression approaches to static st angles determined by surface markers placed on palpated landmarks in typically developing adolescents performing functional tasks both approaches produced errors within the range reported in the literature for skin based scapular measurement techniques the performance of the regression approach suffered when applied to positions outside of the range of motion in the set of calibration positions the amc significantly underestimated st internal rotation across all positions and overestimated posterior tilt in some positions overall root mean square errors for the regression approach were smaller than the amc for every position across all axes of st motion accordingly we recommend the regression approach as a suitable technique for measuring st kinematics in functional motion

deconvolution and total least squares in finding the impulse response of an electromagnetic system from measured data total least squares tls is a method of solving over determined sets of linear equations ax spl ap b when there are errors both in the observation vector b m spl times 1 and in the data matrix a m spl times n this method is particularly useful when the data matrix a is singular or highly ill conditioned we present the method of finding the tls by applying the singular value decomposition to the discrete deconvolution problem numerical results are presented for finding the impulse response of a transmission line from experimental data the advantage of this approach is that this method can be automated based on the signal to noise ratio of the measured data

estimation of the axis of a screw motion from noisy data a new method based on plucker lines the problems of estimating the motion and orientation parameters of a body segment from two n point set patterns are analyzed using the plucker coordinates of a line plucker lines the aim is to find algorithms less complex than those in conventional use and thus facilitating more accurate computation of the unknown parameters all conventional techniques use point transformation to calculate the screw axis in this paper we present a novel technique that directly estimates the axis of a screw motion as a plucker line the plucker line can be transformed via the dual number coordinate transformation matrix this method is compared with schwartz and rozumalski 2005 a new method for estimating joint parameters from motion data journal of biomechanics 38 107 116 in simulations of random measurement errors and systematic skin movements simulation results indicate that the methods based on plucker lines plucker line method are superior in terms of extremely good results in the determination of the screw axis direction and position as well as a concise derivation of mathematical statements this investigation yielded practical results which can be used to locate the axis of a screw motion in a noisy environment developing the dual transformation matrix dtm from noisy data and determining the screw axis from a given dtm is done in a manner analogous to that for handling simple rotations a more robust approach to solve for the dual vector associated with dtm is also addressed by using the eigenvector and the singular value decomposition

a survey of formal methods for determining the centre of rotation of ball joints abstract the determination of an accurate centre of rotation cor from segment marker positions is of interest across a wide range of applications but particularly for clinical gait analysis and for estimating the hip joint centre during surgical intervention of the knee for limb alignment purposes for the first time in this survey of formal methods we classify analyse and compare different methods geometric algebraic bias compensated algebraic and pratt sphere fit methods as well as the centre transformation technique the holzreiter approach the helical pivot technique the schwartz transformation techniques the minimal amplitude point method and the stoddart approach for the determination of spherical joint centres from marker position data in addition we propose a new method the symmetrical cor estimation or score in which the coordinates of the joint centre must only remain constant relative to each segment thus not requiring the assumption that one segment should remain at rest for each method 1000 cor estimations were analysed with the application of isotropic independent and identically distributed gaussian noise standard deviation 0 1 cm to each of the marker positions to all markers on the segment simultaneously and the two in combination for the test conditions used here most techniques were capable of determining the cor to within 0 3 cm as long as the spherical range of motion rom of the joint was 45 or more under the most stringent conditions tested however the score was capable of best determining the cor to within approximately 1 2 mm with a rom of 20 the correct selection and application of these methodologies should help improve the accuracy of surgical navigation and clinical kinematic measurement

a connection between uniformity and aberration in regular fractions of two level factorials summary we show a link between the two apparently unrelated areas of uniformity and minimum aberration with reference to regular fractions of two level factorials we derive an expression for the centred l2 discrepancy measure for uniformity in terms of the word length pattern this result indicates in particular excellent behaviour of minimum aberration designs with regard to uniformity and provides further justification for the popular criterion of minimum aberration

new least squares solutions for estimating the average centre of rotation and the axis of rotation a new method is proposed for estimating the parameters of ball joints also known as spherical or revolute joints and hinge joints with a fixed axis of rotation the method does not require manual adjustment of any optimisation parameters and produces closed form solutions it is a least squares solution using the whole 3d motion data set we do not assume strict rigidity but only that the markers maintain a constant distance from the centre or axis of rotation this method is compared with other methods that use similar assumptions in the cases of random measurement errors systematic skin movements and skin movements with random measurement noise simulation results indicate that the new method is superior in terms of the algorithm used the closure of the solution consistency and minimal manual parameter adjustment the method can also be adapted to joints with translational movements

regularization of the moment matrix solution by a nonquadratic conjugate gradient method inspired by tikhonov regularization a nonlinear conjugate gradient method is proposed with the purpose of simultaneously regularizing and solving the moment matrix equation the procedure is based on a nonquadratic conjugate gradient algorithm with exact line search restart and rescale applied to the problem of tm scattering by perfectly conducting rectangular cylinders the method is shown to exhibit a fast convergence rate

robust estimation of dominant axis of rotation a simple method is developed for robustly estimating a fixed dominant axis of rotation aor of anatomical joints from surface marker data previous approaches which assume a model of circular marker trajectories use plane fitting to estimate the direction of the aor however when there is limited joint range of motion and rotation due to a second degree of freedom minimizing only the planar error can give poor estimates of the aor direction optimizing a cost function which includes the error component within a plane instead of only the component orthogonal to a plane leads to improved estimates of the aor direction for joints which exhibit additional rotational motion from a second degree of freedom results from synthetic data validation show the ranges of motion where the new method has lower estimation error compared to plane fitting techniques estimates of the flexion extension aor from empirical motion capture data of the knee and index finger joints were also more anatomically plausible

constrained least squares optimization for robust estimation of center of rotation this paper presents a new direct method for estimating the average center of rotation cor an existing least squares ls solution has been shown by previous works to have reduced accuracy for data with small range of motion rom alternative methods proposed to improve the cor estimation use iterative algorithms however in this paper we show that with a carefully chosen normalization scheme constrained least squares solutions can perform as well as iterative approaches even for challenging problems with significant noise and small rom in particular enforcing the normalization constraint avoids poor fits near plane singularities that can affect the existing ls method our formulation has an exact solution accounts for multiple markers simultaneously and does not depend on manually adjusted parameters simulation tests compare the method to four published cor estimation techniques the results show that the new approach has the accuracy of the iterative methods as well as the short computation time and repeatability of a least squares solution in addition application of the new method to experimental motion capture data of the thumb carpometacarpal cmc joint yielded a more plausible cor location compared to the previously reported ls solution and required less time than all four alternative techniques

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

construction of orthogonal and nearly orthogonal latin hypercubes we propose a method for constructing orthogonal or nearly orthogonal latin hypercubes the method yields a large latin hypercube by coupling an orthogonal array of index unity with a small latin hypercube it is shown that the large latin hypercube inherits the exact or near orthogonality of the small latin hypercube thus effort for searching for large latin hypercubes that are exactly or nearly orthogonal can be focussed on finding small latin hypercubes with the same property we obtain a useful collection of orthogonal or nearly orthogonal latin hypercubes which have a large factor to run ratio and the results are often much more economical than existing methods

a new method for estimating the axis of rotation and the center of rotation a new method is presented for estimating the parameters of two different models of a joint the two models are 1 a rotational joint with a fixed axis of rotation also referred to as a hinge joint and 2 a ball and socket model corresponding to a spherical joint given the motion of a set of markers it is shown how the parameters can be estimated utilizing the whole data set the parameters are estimated from motion data by minimizing two objective functions the method does not assume a rigid body motion but only that each marker rotates around the same fixed axis of rotation or center of rotation simulation results indicate that in situations where the rigid body assumption is valid and when measurement noise is present the proposed method is inferior to methods that utilize the rigid body assumption however when there are large skin movement artefacts simulation results show the proposed method to be more robust

two nonparametric methods for identifying the impulse response of linear systems this paper addresses the problem of impulse response identification using nonparametric methods although the techniques developed herein apply to the truncated untruncated and circulant models we focus on the truncated model which is useful in certain applications two methods of impulse response identification will be presented the first is based on the minimization of the c l statistic which is an estimate of the mean square prediction error the second is a bayesian approach for both of these methods we consider the effects of using both the identity matrix and the laplacian matrix as weights on the energy in the impulse response in addition we present a method for estimating the effective length of the impulse response estimating the length is particularly important in the truncated case finally we develop a method for estimating the noise variance at the output which is needed in the approach involving the c l statistic often prior information on the noise variance is not available and a good estimate is crucial to the success of estimating the impulse response with a nonparametric technique

nearly orthogonal arrays mappable into fully orthogonal arrays we develop a method for construction of arrays which are nearly orthogonal in the sense that each column is orthogonal to a large proportion of the other columns and which are convertible to fully orthogonal arrays via a mapping of the symbols in each column to a possibly smaller set of symbols these arrays can be useful in computer experiments as designs which accommodate a large number of factors and enjoy attractive space filling properties our construction allows both the mappable nearly orthogonal array and the consequent fully orthogonal array to be either symmetric or asymmetric resolvable orthogonal arrays play a key role in the construction

comparative evaluation of scapular and humeral coordinate systems based on biomedical images of the glenohumeral joint bio imaging techniques represent a powerful tool for shoulder joint biomechanical analysis however the restricted field of view may prevent the acquisition of complete scapula and humerus bone models and hence limiting the applicability of standardized anatomical coordinate system acs definitions the aim of this study was to propose acs definitions for both scapula and humerus which can be implemented when limited portions of the relevant bones are available magnetic resonance mr images of twenty right humeri and scapulae were acquired the proposed acss were assessed in terms of 1 sensitivity to bone morphological variation 2 intra and inter operator repeatability and 3 consistency with the anatomical cardinal directions a comparison with alternative acs definitions was also performed overall our acs scapular proposal and that presented in kedgley and dunning 2010 were found to be the least sensitive to the morphometric variability mean angular absolute deviation lower than 8 3 deg and they were characterized by a high intra and inter operator repeatability mean angular absolute deviation lower than 1 5 deg the humeral acs proposal showed a morphometric variability similar to amadi et al 2009b mean angular absolute deviation lower than 8 3 deg but a higher reproducibility the scapular and humeral acs mean angular deviation from the reference anatomical cardinal directions were smaller than 15 deg and 8 6 deg respectively the proposed scapular and humeral acs definitions are therefore suitable to be applied when a limited portion of the glenohumeral joint is available as it may occur in standard shoulder clinical exams

generalized minimum aberration for asymmetrical fractional factorial designs by studying treatment contrasts and anova models we propose a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs the criterion is independent of the choice of treatment contrasts and thus model free it works for symmetrical and asymmetrical designs regular and nonregular designs in particular it reduces to the minimum aberration criterion for regular designs and the minimum g 2 aberration criterion for two level nonregular designs in addition by exploring the connection between factorial design theory and coding theory we develop a complementary design theory for general symmetrical designs which covers many existing results as special cases

spinal shape changes resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation this paper reports the changes in spinal shape resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation the objective is to test the hypothesis that the type of spinal instrumentation system cotrel dubousset versus colorado does not influence these motion parameters intervertebral rotations and centers of rotation of the scoliotic spines were computed from the pre and post operative radiographs of 82 patients undergoing spinal correction the three dimensional 3d reconstruction of six anatomical landmarks was achieved for each of the thoracic and lumbar vertebrae a least squares approach based on singular value decomposition was used to calculate the rigid body transformation parameters average centers of rotation for all intervertebral levels are located in the neural canal at the mid sagittal plane and approximately at the superior endplate level of the inferior vertebra intervertebral rotations have components in all planes 6 7 degrees frontal 5 5 degrees sagittal and 4 5 degrees transverse rms for all intervertebral levels nearly all intervertebral rotations and centers of rotation are not significantly different for the two instrumentation systems various intervertebral rotations and 3d reconstruction errors were simulated on a theoretical model of a lumbar functional unit to assess the proposed method intervertebral rotation errors were 1 7 degrees when simulating 3d errors of 3mm on the position of the landmarks maximum errors for the position of centers of rotation were below 1cm in the case of intervertebral rotations larger than 2 5 degrees most cases but were larger 38 mm for small intervertebral rotations 1 degrees the type of instrumentation system did not influence intervertebral rotations and centers of rotation these results provide valuable data for the development and validation of simulation models for surgical instrumentation of idiopathic scoliosis

strong orthogonal arrays of strength two plus strong orthogonal arrays were recently introduced and studied in he and tang biometrika100 2013 254 260 as a class of space filling designs for computer experiments to enjoy the benefits of better space filling properties when compared to ordinary orthogonal arrays strong orthogonal arrays need to have strength three or higher which may require run sizes that are too large for experimenters to afford to address this problem we introduce a new class of arrays called strong orthogonal arrays of strength two plus these arrays while being more economical than strong orthogonal arrays of strength three still enjoy the better two dimensional space filling property of the latter among the many results we have obtained on the characterizations and constructions of strong orthogonal arrays of strength two plus worth special mention is their intimate connection with second order saturated designs

synthesis of near field patterns of a nonuniformly spaced array a technique of synthesis of near field patterns of a nonuniformly spaced linear array of point dipoles with identical direction of current flow for each array element or a uniformly spaced array of point dipoles with variation in direction of current flow for each dipole is presented further it is described how one should prescribe the near field nf pattern and how one should sample the same while performing the nf pattern synthesis also discussed is how nf pattern synthesis should be performed so that the synthesized nf amplitude pattern closely follows a prescribed far field amplitude pattern of the same array numerical computations are performed to demonstrate the validity of the physical concepts made use of in the technique proposed for performing the nf pattern synthesis successfully

a method of constructing space filling orthogonal designs abstractthis article presents a method of constructing a rich class of orthogonal designs that include orthogonal latin hypercubes as special cases two prominent features of the method are its simplicity and generality in addition to orthogonality the resulting designs enjoy some attractive space filling properties making them very suitable for computer experiments

some mathematical considerations in dealing with the inverse problem many problems of mathematical physics can be formulated in terms of the operator equation ax y where a is an integro differential operator given a and x the solution for y is usually straightforward however the inverse problem which consists of the solution for x when given a and y is much more difficult the following questions relative to the inverse problem are explored 1 does specification of the operator a determine the set y for which a solution x is possible 2 does the inverse problem always have a unique solution 3 do small perturbations of the forcing function y always result in small perturbations of the solution 4 what are some of the considerations that enter into the choice of a solution technique for a specific problem the concept of an ill posed problem versus that of a well posed problem is discussed specifically the manner by which an ill posed problem may be regularized to a well posed problem is presented the concepts are illustrated by several examples

microwave imaging based on a markov random field model a new approach to microwave imaging of 2d inhomogeneous dielectric scatterers is presented the method is developed in the space domain and markov random fields are used to obtain a model of the distributions of dielectric features in the scattering region in this way a priori knowledge can be easily inserted in the imaging scheme this stochastic approach gives rise to a functional equation that can be minimized by using a simulated annealing algorithm an iterative scheme is derived that allows one to bypass the need for storing large matrices in the computer numerical simulation results confirming the capabilities and effectiveness of the proposed method are reported solutions have generally been obtained in few steps and seem better than those obtained by other imaging techniques in the space domain the capability of the algorithm to operate in a strongly noisy environment is also proved

a correction for axis misalignment in the joint angle curves representing knee movement in gait analysis this paper derives a simple mathematical model relating changes in the orientations of the two cartesian coordinate systems involved in recording knee movement and the varus valgus and the internal external rotation angles for describing the knee s motion rotation matrices are given for changing the orientations of the two cartesian coordinate systems in such a way that the quadratic variations in the varus valgus and in the external internal angles are minimal these estimated rotation matrices are used to correct for axis misalignment the correction is calibrated by considering the impact of the new orientation of the thigh cartesian coordinate system on the hip joint angles the procedure is applied to kinematic data collected on normal subjects the uncertainty about the specification of the thigh cartesian coordinate system is shown to explain some of the between subject variability in the varus valgus and in the internal external rotation angles curves

in vivo estimation of the glenohumeral joint centre by functional methods accuracy and repeatability assessment abstract several algorithms have been proposed for determining the centre of rotation of ball joints these algorithms are used rather to locate the hip joint centre few studies have focused on the determination of the glenohumeral joint centre however no studies have assessed the accuracy and repeatability of functional methods for glenohumeral joint centre this paper aims at evaluating the accuracy and the repeatability with which the glenohumeral joint rotation centre ghrc can be estimated in vivo by functional methods the reference joint centre is the glenohumeral anatomical centre obtained by medical imaging five functional methods were tested the algorithm of gamage and lasenby 2002 bias compensated halvorsen 2003 symmetrical centre of rotation estimation ehrig et al 2006 normalization method chang and pollard 2007 helical axis woltring et al 1985 the glenohumeral anatomical centre ghac was deduced from the fitting of the humeral head four subjects performed three cycles of three different movements flexion extension abduction adduction and circumduction for each test the location of the glenohumeral joint centre was estimated by the five methods analyses focused on the 3d location on the repeatability of location and on the accuracy by computing the euclidian distance between the estimated ghrc and the ghac for all the methods the error repeatability was inferior to 8 25 mm this study showed that there are significant differences between the five functional methods the smallest distance between the estimated joint centre and the centre of the humeral head was obtained with the method of gamage and lasenby 2002

orthogonal array based latin hypercubes abstract in this article we use orthogonal arrays oa s to construct latin hypercubes besides preserving the univariate stratification properties of latin hypercubes these strength r oa based latin hypercubes also stratify each r dimensional margin therefore such oa based latin hypercubes provide more suitable designs for computer experiments and numerical integration than do general latin hypercubes we prove that when used for integration the sampling scheme with oa based latin hypercubes offers a substantial improvement over latin hypercube sampling

double calibration an accurate reliable and easy to use method for 3d scapular motion analysis the most recent non invasive methods for the recording of scapular motion are based on an acromion marker am set and a single calibration sc of the scapula in a resting position however this method fails to accurately measure scapular kinematics above 90 of arm elevation due to soft tissue artifacts of the skin and muscles covering the acromion the aim of this study was to evaluate the accuracy and inter trial and inter session repeatability of a double calibration method dc in comparison with sc the sc and dc data were measured with an optoelectronic system during arm flexion and abduction at different angles of elevation 0 180 they were compared with palpation of the scapula using a scapula locator dc data was not significantly different from palpation for 5 6 axes of rotation tested y x and z in abduction and flexion where as sc showed significant differences for 5 6 axes the root mean square errors ranged from 2 96 to 4 48 for dc and from 6 to 9 19 for sc the inter trial repeatability was good to excellent for sc and dc the inter session repeatability was moderate to excellent for sc and moderate to good for dc coupling am and dc is an easy to use method which yields accurate and reliable measurements of scapular kinematics for the complete range of arm motion it can be applied to the measurement of shoulder motion in many fields sports orthopaedics and rehabilitation especially when large ranges of arm motion are required

orthogonal column latin hypercubes and their application in computer experiments abstract latin hypercubes have been frequently used in conducting computer experiments in this paper a class of orthogonal latin hypercubes that preserves orthogonality among columns is proposed applying an orthogonal latin hypercube design to a computer experiment benefits the data analysis in two ways first it retains the orthogonality of traditional experimental designs the estimates of linear effects of all factors are uncorrelated not only with each other but also with the estimates of all quadratic effects and bilinear interactions second it can facilitate nonparametric fitting procedures because one can select good space filling designs within the class of orthogonal latin hypercubes according to selection criteria

comparison between tripod and skin fixed recording of scapular motion non invasive dynamical measurements of 3d scapular motion can be performed easily by attachment of a 6 dof electromagnetic receiver onto the skin above the acromion to quantify the introduction of possible errors due to skin displacement we assessed 3d scapular positions on n 8 subjects by both tripod and skin fixed method error analysis included the variables method tripod skin fixed simultaneously with tripod separate skin fixed at 0 and 0 25hz of elevation speed plane of elevation 0 degrees and 90 degrees and observation receiver replacement n 3 inter individual group differences depended on elevation plane and showed an average underestimation of scapular rotation of 6 5 degrees worst case 13 degrees using the skin fixed method only the group rmse not the individual rmse could be successfully lowered using linear regression to about 2 degrees inter trial reliability rmse 0 94 and rmse between 0 and 0 25hz recordings about 2 5 degrees were satisfactory intra observer rmse after replacement of the skin fixed receiver was 5 degrees the skin fixed method is suitable for dynamic recordings of scapular rotations however measurements are precise only when the acromion receiver is not replaced combined with a relatively low accuracy we conclude that the skin fixed method should be used only in combination with tripod calibration