analytical and bootstrap approximations to estimator distributions in l 1 regression abstract edgeworth and bootstrap approximations to estimator distributions in l1 regression are described analytic approximations based on edgeworth expansions that mix lattice and nonlattice components and allow for an intercept term in the regression are developed under mild conditions which do not even require a density for the error distribution under stronger assumptions on the error distribution the edgeworth expansion assumes a simpler form bootstrap approximations are described and the consistency of the bootstrap in the l 1 regression setting is established we show how the slow rate n 1 4 of convergence in this context of the standard unsmoothed bootstrap that resamples for the raw residuals may be improved to rate n 2 5 by two methods a smoothed bootstrap approach based on resampling from an appropriate kernel estimator of the error density and a normal approximation that uses a kernel estimator of the error density at a particular point its median 0 both of these methods require ch

is a single or double arm technique more advantageous in triple jumping triple jumpers employ either an asymmetrical single arm action or symmetrical double arm action in the takeoff of each phase of the jump this study investigated which technique is more beneficial in each phase using computer simulation kinematic data were obtained from an entire triple jump using a vicon automatic motion capture system a planar 13 segment torque driven subject specific computer simulation model was evaluated by varying torque generator activation timings using a genetic algorithm in order to match performance data the matching produced a close agreement between simulation and performance with differences of 3 8 2 7 and 3 1 for the hop step and jump phases respectively each phase was optimised for jump distance and an increase in jump distance beyond the matched simulations of 3 3 11 1 and 8 2 was obtained for the hop step and jump respectively the optimised technique used symmetrical shoulder flexion whereas the triple jumper had used an asymmetrical arm technique this arm action put the leg extensors into slower concentric conditions allowing greater extensor torques to be produced the main increases in work came at the joints of the stance leg but the largest increases in angular impulse came at the shoulder joints indicating the importance of both measures when assessing the impact of individual joint actions on changes in technique possible benefits of the double arm technique include cushioning the stance leg during impact raising the centre of mass of the body at takeoff facilitating an increase in kinetic energy at takeoff allowing a re orientation of the body during flight

different methods to estimate total power and its components during lifting abstract a more fundamental understanding about the act of manual lifting can be provided by the assessment of the total production of power and the power generated in joints the present study is concerned with the validity of the estimations of these parameters four subjects lifted an 18 8 kg load while they were filmed and ground reaction forces were measured the total generated power was calculated in three ways 1 by summation of joint powers 2 on the basis of the rate of change of the summed energy contents of human body segments and 3 on the basis of the rate of change of the body energy estimated from ground reaction forces the results were compared furthermore at a segmental level the power supplied to or absorbed from a segment was compared to the rate of change of its energy content the resulting instantaneous power curves from the three different methods showed a high level of agreement which supports their validity however some minor discrepancies were observed the major cause of the observed difference between the rate of change of the summed segmental energy contents and the summed joint powers was found at a segmental level it was observed that segmental link lengths i e distances between proximal and distal markers changed during movement which yielded discrepancies between the power flow to or from a segment and the rate of change of its energy content

approximation of optimal filter for ornstein uhlenbeck process with quantised discrete time observation abstractquantisation of signals is a ubiquitous property of digital processing in many cases it introduces significant difficulties in state estimation and in consequence control popular approaches either do not address properly the problem of system disturbances or lead to biased estimates our intention was to find a method for state estimation for stochastic systems with quantised and discrete observation that is free of the mentioned drawbacks we have formulated a general form of the optimal filter derived by a solution of fokker planck equation we then propose the approximation method based on galerkin projections we illustrate the approach for the ornstein uhlenbeck process and derive analytic formulae for the approximated optimal filter also extending the results for the variant with control operation is illustrated with numerical experiments and compared with classical discrete continuous kalman filter results of comparison are substantially in favour of our approach with over 20 times

the simulation of aerial movement i the determination of orientation angles from film data abstract quantitative mechanical analyses of human movement require the time histories of the angles which specify body configuration and orientation when these angles are obtained from a filmed performance they may be used to evaluate the accuracy of a simulation model this paper presents a method of determining orientation angles and their rates of change from film data the stages used comprise the synchronization of data obtained from two camera views the determination of three dimensional coordinates of joint centres the calculation of an angle from a sequence of sine and cosine values and the curve fitting of angles using quintic splines for each state other possible approaches are discussed original procedures are presented for obtaining individual error estimates of both the film data and the calculated angles to permit the automatic fitting of quintic splines for interpolation and differentiation and for deriving the time history of an angle as a continuous function from a sequence of sine and cosine values the method is applied to a forward somersault with 1 1 2 twists and the average error estimate of 17 orientation angles is obtained as 2 1 degrees

measurement of body segment parameters using dual energy x ray absorptiometry and three dimensional geometry an application in gait analysis abstract body segment parameters bsp are essential input for the computations in kinetics of motion applied in the field of biomechanics these data are usually obtained from population specific predictive equations which present limitations in being representative of the population under study more recently medical imaging techniques have been adopted but are limited to two dimensional 2 d measurements or required extensive tomographic images for three dimensional 3 d reconstruction we proposed an in vivo method to measure 3 d bsp using x ray imaging and 3 d exterior geometry criterion values of the bsp were determined using magnetic resonance imaging mri which has previously been validated errors for all bsp values were less than 2 when values derived from our method were compared to the criterion values we found no significant difference between our method and four selected bsp models in both stance and swing phase significant phase effects were observed for our method and other bsp models between stance and swing phase significant differences p

kinematics estimation of straddled movements on high bar from a limited number of skin markers using a chain model to reduce the effects of skin movement artefacts and apparent joint dislocations in the kinematics of whole body movement derived from marker locations global optimisation procedures with a chain model have been developed these procedures can also be used to reduce the number of markers when self occlusions are hard to avoid this paper assesses the kinematics precision of three marker sets 16 11 and 7 markers for movements on high bar with straddled piked posture a three dimensional person specific chain model was defined with 9 parameters and 12 degrees of freedom and an iterative procedure optimised the gymnast posture for each frame of the three marker sets the time histories of joint angles obtained from the reduced marker sets were compared with those from the 16 marker set by means of a root mean square difference measure occlusions of medial markers fixed on the lower limb occurred when the legs were together and the pelvis markers disappeared primarily during the piked posture despite these occlusions reconstruction was possible with 16 11 and 7 markers the time histories of joint angles were similar the main differences were for the thigh mediolateral rotation and the knee flexion because the knee was close to full extension when five markers were removed the average angles difference was about 3 this difference increased to 9 for the seven marker set it is concluded that kinematics of sports movement can be reconstructed using a chain model and a global optimisation procedure for a reduced number of markers

segment inertial parameter evaluation in two anthropometric models by application of a dynamic linked segment model the estimation of segment inertial parameters sips is an important source of error in inverse dynamic analysis in most individual cases sips are derived from extrapolation of known sips of a certain population through regression equations proportional models another well known method is the use of mathematical approximation of the shape of human body segments combined with estimations of segment densities geometric models in the current study five males and five females performed four different lifting movements in the sagittal plane a full body linked segment model was applied twice to the same data set once using a proportional and once using a geometric anthropometric model as a full body linked segment model is an overdetermined system of equations four equations could be formed to test the summed effect of sip errors on the inverse dynamic analysis the overall performance in terms of coefficients of correlation was better for the geometric model as compared to the proportional model when a back lifting movement was performed the equations indicated systematic errors in the proportional model however when a leg lifting movement was performed the equations indicated systematic errors in the geometric model therefore analyzing only one kind of movement does not suffice to draw conclusions with respect to the reliability of an anthropometric model

the effect of increasing strength and approach velocity on triple jump performance the triple jump is an athletic event comprising three phases in which the optimal phase ratio the proportion of each phase to the total distance jumped is unknown this study used a planar whole body torque driven computer simulation model of the ground contact parts of all three phases of the triple jump to investigate the effect of strength and approach velocity on optimal performance the strength and approach velocity of the simulation model were each increased by up to 30 in 10 increments from baseline data collected from a national standard triple jumper increasing strength always resulted in an increased overall jump distance increasing approach velocity also typically resulted in an increased overall jump distance but there was a point past which increasing approach velocity without increasing strength did not lead to an increase in overall jump distance increasing both strength and approach velocity by 10 20 and 30 led to roughly equivalent increases in overall jump distances distances ranged from 14 05m with baseline strength and approach velocity up to 18 49m with 30 increases in both optimal phase ratios were either hop dominated or balanced and typically became more balanced when the strength of the model was increased by a greater percentage than its approach velocity the range of triple jump distances that resulted from the optimisation process suggests that strength and approach velocity are of great importance for triple jump performance

adaptive filtering using quantized output measurements a normalized stochastic gradient adaptive filtering algorithm based on a finite impulse response fir model is discussed the algorithm identifies the system exactly given only coarsely quantized output measurements a description of the quantizer is included in the overall input output model and the scheme exploits an approximation of the derivative of the quantizer using an associated differential equation global convergence is established to a zero output error except for possible colored measurement disturbances parameter setting or to the boundary of the model set

recursive state estimation for two dimensional shift varying systems with random parameter perturbation and dynamical bias abstract in this paper the state estimation problem is investigated for a class of two dimensional 2 d stochastic systems with shift varying parameters the stochasticity with the underlying system comes from three sources namely random parameter perturbations dynamical biases and additive white noises the measurement output is subject to the uniform quantization as a result of communication constraints on the sensors the purpose of the addressed problem is to recursively estimate the system states with prescribed estimation performance in spite of the stochastic disturbances and the uniform quantizations an augmented model is first constructed to combine the information about the state and the bias and the dynamical evolution is subsequently discussed furthermore through stochastic analysis and mathematical induction the estimator design algorithm is developed to acquire certain upper bound on the estimation error variance and such an upper bound is then minimized in the matrix trace sense moreover the boundedness issue of the estimation errors is investigated via matrix inversion lemma and inductive analysis technique finally the effectiveness of the proposed state estimation algorithm is validated on a typical 2 d system modeled by the well known darboux equation with extensive application potentials in industrial processes

optimal estimation theory for dynamic systems with set membership uncertainty an overview in many problems such as linear and nonlinear regressions parameter and state estimation of dynamic systems state space and time series prediction interpolation smoothing and functions approximation one has to evaluate some unknown variable using available data the data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables typically the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory an interesting alternative approach referred to as set membership or unknown but bounded ubb error description has been investigated since the late 1960s in this approach uncertainty is described by an additive noise which is known only to have given integral typically l2 of l1 or componentwise l bounds in this paper we review the main results of this theory with special attention to the most recent advances obtained in the case of componentwise bounds

on edgeworth expansions in the mixture cases where denotes transpose in the lattice case where each univariate population assigns its entire mass to countably many equidistant points the expansion is different and an explicit form is known only for a restricted class of sets a consider an univariate statistic of the form h zn for a smooth function h bhattacharya and ghosh 1978 used the expansion for zn to establish the validity of the formal edgeworth expansion for vn h zn h e zn in the nonlattice case in the lattice case an explicit form of the expansion is typically not available for nonlinear univariate statistics see yarnold 1972 for instance where an explicit expansion for pn a is given when a is an ellipsoid in this paper we consider edgeworth expansions for h zn when x has a lattice distribution and y has a continuous distribution situations like this do arise in statistical experiments as a simple example x could be the age of a plant or animal in years and y could be its weight h zn yjxn in this article we establish that no correction factor is needed for the lattice character of x in the one term edgeworth expansion beyond one term the answer is not known to us at present our approach for establishing the above mentioned fact is as follows let q be a symmetric random variable having finite third moment and whose characteristic function vanishes outside a compact interval it is first shown that in the

optimal recursive state estimation with quantized measurements a set of exact nonlinear filters is derived and analyzed the filters perform recursive state estimation when only coarsely quantized output signals are available a system with the dynamics given by n integrators together with a uniform prior on the state vector form the model assumptions in the case with one integrator properties of the quantizer allows the construction of an exact recursive algorithm for the updating of the probability density function p d f using only the corners of a convex polygon defining the region where the p d f is nonzero it is also shown how to generalize the algorithm to handle multiple measurements quantized with vector quantizers

optimizing the determination of the body center of mass the position or trajectory of the body center of mass com is often a parameter of interest when studying posture or movement for instance in balance control studies the body com can be related to the ground reaction force or to the base of support since small displacements of the body com are important in balance control studies it is essential to obtain valid estimates of the body com the main source of error in the determination of the body com is the estimation of the masses and centers of mass of the body segments especially the determination of the trunk com is prone to error in the current study five subjects maintained three postures differing in trunk angle during a few seconds the relation between the center of pressure of the ground reaction force and the vertical projection of the body com during the postures was used to optimize the trunk com position additionally the subjects performed two lifting movements the validity of the body com trajectory estimation during the lifting movements both with and without optimized trunk com was checked by relating the external moment of the ground reaction force with respect to the body com to the rate of change of the angular momentum of the whole body it was shown that the correspondence between the external moment and the rate of change of the angular momentum improved after optimization of the trunk com this suggests that the body com trajectory estimation can be improved by the proposed optimization procedure

an algorithm for determining gravity line location from posturographic recordings abstract in posturographic recordings the center of pressure cop displacement does not accurately reflect migration of the gravity line gl the vertical line passing through the body s center of gravity cog since the horizontal ground reaction force f x is proportional to the horizontal acceleration of the cog its second integral does represent the horizontal position of the gravity line glp however the initial constants of integration initial velocity and position are not known in this note a technique for estimating these integration constants is suggested zero point to zero point integration this method is based on a postulation that when f x 0 the glp and cop coincide by integrating f x from one zero point to another zero point both the instantaneous glp and its velocity are determined a validation of the suggested algorithm was performed using optical methods to determine the glp during a one legged standing tasks cross correlation values of glp determined via videography and the suggested algorithm ranged from 0 79 to 0 96 these results suggest that the zero point to zero point integration is an acceptable technique for determining glp from posturographic recordings

the appropriate use of regression equations for the estimation of segmental inertia parameters linear regression equations are commonly used in conjunction with experimental data to provide linear relationships between quantities which are dimensionally distinct in many cases theoretical relationships between such quantities are known and can be used as a basis for non linear regression equations this study compares linear and non linear approaches for estimating the segmental moments of inertia from anthropometric measurements using the data of chandler et al chandler et al 1975 investigation of inertial properties of the human body amrl technical report 74 137 wright patterson air force base oh right limb data were used to derive the equations while left limb data were used as a cross validation sample to evaluate the inertia estimates calculated from the equations for the limb segments the standard error estimates had average values of 21 for the linear equations and 13 for the non linear equations data on a 10 yr old boy was used to compare the two approaches outside the sample range the mean percentage residuals were 286 for the linear equations and 20 for the non linear equations a set of non linear equations is provided

determination of subject specific model parameters for visco elastic elements the determination of subject specific model parameter values is necessary in order for a computer simulation model of human motion to be evaluated quantitatively this study used an optimisation procedure along with a kinematically driven simulation model of the contact phase in running jumps to determine the elastic parameters of segmental wobbling masses and the foot ground interface kinetic and kinematic data were obtained on running jumps for height and distance performed by an elite male high jumper stiffness and damping coefficients of the visco elastic elements in the model were varied until the difference between simulation and performance was minimised percentage differences of 6 and 9 between the simulated and recorded performances were obtained in the jumps for height and distance respectively when the parameters obtained from the jump for height were used in a simulation of the jump for distance and vice versa there was poor agreement with the recorded jump on the other hand a common set of visco elastic parameters were obtained using the data from both recorded jumps resulting in a mean difference of only 8 made up of 7 and 10 between simulation and performance that was almost as good as the individual matches simulations were not overly sensitive to perturbations of the common set of visco elastic parameters it is concluded that subject specific elastic parameters should be calculated from more than a single jump in order to provide a robust set of values that can be used in different simulations

partial mixing and edgeworth expansion introducing a conditional mixing property gotze and hipp s theory is generalized to a continuous time conditional markov process satisfying this property the malliavin calculus for jump processes applies to random coefficient stochastic differential equations with jumps with the aid of the support theorem to verify the non degeneracy condition i e a conditional type cramer condition

the simulation of aerial movement iv a computer simulation model a computer simulation model of human airborne movement is described the body is modelled as 11 rigid linked segments with 17 degrees of freedom which are chosen with a view to modelling twisting somersaults the accuracy of the model is evaluated by comparing the simulation values of the angles describing somersault tilt and twist with the corresponding values obtained from film data of nine twisting somersaults the maximum deviations between simulation and film are found to be 0 04 revolutions for somersault seven degrees for tilt and 0 12 revolutions for twist it is shown that anthropometric measurement errors from which segmental inertia parameters are calculated have a small effect on a simulation whereas film digitization errors can account for a substantial part of the deviation between simulation and film values

influence of body segments parameters estimation models on inverse dynamics solutions during gait the purpose of the present study was to examine the in uence of anthropometric data on joint kinetics during gait we particularly focused on the sensitivity of inverse dynamics solutions to the use of models for body segment parameters bsp estimation six often used estimation models were selected to provide bsp values for the three segments of the lower limb kinematics and dynamics were sampled from seven subjects performing barefoot gait at three different speeds joint kinetics were estimated with the bottom up method using bsp values derived from each estimation model as anthropometric inputs the bsp estimates were highly sensitive to the model used with deviations ranging from at least 9 73 up to 60 maximal variations of peak values for the hip joint exion extension moment during the swing phase were 20 11 hence our ndings suggest that the in uence of bsp cannot be neglected observed deviations are especially due to the effect of varying simultaneously the mass moments of inertia and the center of mass location values according to the underlying relationship of interdependency linking each component considering both the differences found in joint kinetics and the level of accuracy of bsp models evidence is provided that using multiple regression bsp estimation functions derived from zatsiorsky and seluyanov biomechanics viii b 1983 pp 1152 1159 should be recommended to assess joint kinetics

fixed order fir approximation of linear systems from quantized input and output data the problem of identifying a fixed order fir approximation of linear systems with unknown structure assuming that both input and output measurements are subjected to quantization is dealt with in this paper a fixed order fir model providing the best approximation of the input output relationship is sought by minimizing the worst case distance between the output of the true system and the modeled output for all possible values of the input and output data consistent with their quantized measurements the considered problem is firstly formulated in terms of robust optimization then two different algorithms to compute the optimum of the formulated problem by means of linear programming techniques are presented the effectiveness of the proposed approach is illustrated by means of a simulation example

moment of inertia of whole body using an oscillating table in adolescent boys abstract this study measured the moment of inertia of the body using the oscillating table method and saw how it is affected by age and body size one hundred and seventeen subjects of junior and senior high school boys of ages 13 18 participated in this study moment of inertia was measured in two postures of supine imx and recumbent imy positions both imx and imy account for the range from 5 6 to 14 0 kg m2 and 4 2 to 13 5 kg m2 respectively and correlate linearly to body height ht and body weight w the values of i my i mx becomes 93 6 and 95 2 independent of age and body size the difference between imx and imy might be affected by projection areas on the frontal from the sagittal area of the body the multiple regression analysis of ht2 and w with regard to im was performed to obtain the following multiple regression equations i mx 3 44 ht 2 0 144 w 8 04 r 0 973 i my 3 52 ht 2 0 125 w 7 78 r 0 972 when imx and imy were estimated using these equations the standard deviation of error which calculates the percent differences between the estimated and measured values amounted to 5 in imx and imy the results suggest that with japanese boys there is a relationship between the postures and body size height or weight independent of age

second order correctness of the poisson bootstrap abstract rao pathak and koltchinskii 1997 have recently studied a sequential approach to resampling in which resampling is carried out sequentially one by one with replacement each time until the bootstrap sample contains m approximately 1 e 1 n approximately 632n distinct observations from the original sample in our previous work we have established that the main empirical characteristics of the sequential bootstrap go through in the sense of being within a distance of order o n 3 4 from those of the usual bootstrap however the theoretical justification of the second order correctness of the sequential bootstrap is somewhat difficult it is the main topic of this investigation among other things we accomplish it by approximating our sequential scheme by a resampling scheme based on the poisson distribution with mean u 1 and censored at x 0

body segment mass radius and radius of gyration proportions of children abstract the segment inertial parameters of children are fundamental to the analysis and simulation of their movements generally it has been recognized that adult parameters cannot be extrapolated and most of the anthropometric data on children are of little or no use for determining inertias consequently there have been few studies of children s kinetics in response to this problem a longitudinal investigation the laurentian study of biomechanical development was launched and in this paper the effects of growth on selected segmental size and inertial parameters are reported for boys between the ages of 4 and 15 yr the twelve subjects representing heterogeneous body types were followed over 3 yr for a total of 36 observations elliptical zones 2 cm wide were used to model the body and segment inertias calculated using segment densities from the literature these inertias were the mass moment of inertia and mass centroid location for a fourteen segment planar representation of the body the general accuracy mean error based on body mass was 0 203 which is consistent with reports from similar studies and techniques plots of segment mass proportions with respect to age showed a decrease in the head proportion balanced by increases in the thigh shank foot and upper arm proportions in particular the trends for each segment were consistent with the trends for linear measures reported in the anthropometry literature radius proportions to the mass centroid and radius of gyration proportions were also plotted and showed smaller but consistent changes with respect to age linear regressions were then fitted to the distributions and standard errors calculated the magnitude and slope of the regressions were for the most part consistent with a reported cross sectional study of japanese children where data were available predicted parameters were compared with the reported parameters for a 12 yr old analyzed using a different mathematical model comparisons were also made between the predicted parameters at 15 yr and the reported parameters for healthy young adults who had been scanned using a gamma radiation technique for most parameters there was either good agreement or differences could be explained logically the traditionally used parameters from older cadavers were quite inconsistent with the above the variances of the 36 observations about the regression lines as indicated by the standard errors were small as an illustration of the effect of these variances the trunk parameters for a 10 yr old performing a standing jump for distance were decreased by 1 s e and this matched by increases for the thigh shank and head the changes for ankle torques and horizontal and vertical reaction force components were minimal and less than the changes produced by a 1 hz increase in cut off frequency for the digital filter on the basis of these comparisons it is suggested that where direct determination of body segment parameters for children is not possible the regression equations be used to obtain the segment inertias

reducing ground reaction forces in gymnastics landings may increase internal loading the aim of this study was to use a subject specific seven link wobbling mass model of a gymnast and a multi layer model of a landing mat to determine landing strategies that minimise ground reaction forces grf and internal forces subject specific strength parameters were determined that defined the maximum voluntary torque angle angular velocity relationship at each joint these relationships were used to produce subject specific lumped linear muscle models for each joint muscle activation histories were optimised using a simplex algorithm to minimise grf or bone bending moments for forward and backward rotating vault landings optimising the landing strategy to minimise each of the grf reduced the peak vertical and horizontal grf by 9 for the backward rotating vault and by 8 and 48 for the forward rotating vault compared to a matching simulation however most internal loading measures bone bending moments joint reaction forces and muscle forces increased compared to the matching simulation optimising the landing strategy to minimise the peak bone bending moments resulted in reduced internal loading measures and in most cases reduced grf bone bending moments were reduced by 27 during the forward rotating vault and by 2 during the backward rotating vault landings when compared to the matching simulations it is possible for a gymnast to modify their landing strategy in order to minimise internal forces and lower grf however using a reduction in grf due to a change in landing strategy as a basis for a reduction in injury potential in vaulting movements may not be appropriate since internal loading can increase

effect of low pass filtering on joint moments from inverse dynamics implications for injury prevention analyses of joint moments are important in the study of human motion and are crucial for our understanding of e g how and why acl injuries occur such analyses may be affected by artifacts due to inconsistencies in the equations of motion when force and movement data are filtered with different cut off frequencies the purpose of this study was to quantify the effect of these artifacts and compare joint moments calculated with the same or different cut off frequency for the filtering of force and movement data 123 elite handball players performed sidestep cutting while the movement was recorded by eight 240 hz cameras and the ground reaction forces were recorded by a 960 hz force plate knee and hip joint moments were calculated through inverse dynamics with four different combinations of cut off frequencies for signal filtering movement 10 hz force 10 hz 10 10 movement 15 hz force 15 hz movement 10 hz force 50 hz 10 50 movement 15 hz force 50 hz the results revealed significant differences especially between conditions with different filtering of force and movement mean sd peak knee abduction moment for the 10 10 and 10 50 condition were 1 27 0 53 and 1 64 0 68 nm kg respectively ranking of players based on knee abduction moments were affected by filtering condition out of 20 players with peak knee abduction moment higher than mean 1 sd with the 10 50 condition only 11 were still above mean 1 sd when the 10 10 condition was applied hip moments were very sensitive to filtering cut off mean sd peak hip flexion moment was 3 64 0 75 and 5 92 1 80 under the 10 10 and 10 50 conditions respectively based on these findings force and movement data should be processed with the same filter conclusions from previous inverse dynamics studies where this was not the case should be treated with caution

adjustments to mcconville et al and young et al body segment inertial parameters body segment inertial parameters bsips are important data in biomechanics they are usually estimated from predictive equations reported in the literature however most of the predictive equations are ambiguously applicable in the conventional 3d segment coordinate systems scss also the predictive equations reported in the literature all include two assumptions the centre of mass and the proximal and distal endpoints are assumed to be aligned and the inertia tensor is assumed to be principal in the segment axes these predictive equations restraining both position of the centre of mass and orientation of the principal axes of inertia become restrictive when computing 3d inverse dynamics when analyzing the influence of bsip estimations on joint forces and moments and when evaluating personalized 3d bsips obtained from medical imaging in the current study the extensive data from mcconville et al 1980 anthropometric relationships of body and body segment moments of inertia afamrl tr 80 119 aerospace medical research laboratory wright patterson air force base dayton ohio and from young et al 1983 anthropometric and mass distribution characteristics of the adults female technical report afamrl tr 80 119 faa civil aeromedical institute oklaoma city oklaoma are adjusted in order to correspond to joint centres and to conventional segment axes in this way scaling equations are obtained for both males and females that provide bsips which are directly applicable in the conventional scss and do not restrain the position of the centre of mass and the orientation of the principal axes these adjusted scaling equations may be useful for researchers who wish to use appropriate 3d bsips for posture and movement analysis

edgeworth expansion of a function of sample means many important statistics can be written as functions of sample means of vector variables a fundamental contribution to the edgeworth expansion for functions of sample means was made by bhattacharya and ghosh in their work the crucial cramer c condition is assumed on the joint distribution of all the components of the vector variable however in many practical situations only one or a few of the components satisfy conditionally this condition while the rest do not such a case is referred to as satisfying the partial cramer c condition the purpose of this paper is to establish edgeworth expansions for functions of sample means when only the partial cramer c condition is satisfied

the simulation of aerial movement ii a mathematical inertia model of the human body a mathematical inertia model which permits the determination of personalized segmental inertia parameter values from anthropometric measurements is described the human body is modelled using 40 geometric solids which are specified by 95 anthropometric measurements a stadium solid is introduced for modelling the torso segments using perimeter and width measurements this procedure is more accurate than the use of elliptical discs of given width and depth and permits a smaller number of such solids to be used inertia parameter values may be obtained for body models of up to 20 segments errors in total body mass estimates from this and other models are discussed with reference to the unknown lung volumes

body segment inertial parameter estimation for the general population of older adults the practical determination of accurate body segment inertial parameters for the general older adult population remains a problem especially in estimating these parameters for women and accounting for variations in body type a method is presented for determining the mass and center of mass location of the body segments of individuals within the general population of older adults effects of sex and body type on older adult mass distribution are accounted for using 32 easily obtainable body measurements the method is based on existing results from different data sources and employs a combination of validated estimation approaches including body mass and segment length proportions linear and nonlinear regression equations and a mathematical model of the trunk the method was applied to a validation sample of healthy community dwelling older adults 29 men 50 women predicted body mass was 96 7 4 8 and 95 7 3 7 of measured body mass in the men and women respectively the estimates of body segment mass and trunk center of mass location for the sample population approximate those reported in the literature supporting the validity of the described method by producing practical subject specific estimates of body segment inertial parameters the method should allow more accurate biomechanical analyses of the older adult population