the application of segment axial density profiles to a human body inertia model the intention of this study was to construct segment density profiles and compare segment inertias calculated when uniform densities and profile densities are used in a mathematical model axial densities from computerized tomography ct slices for the body segments of a sample of chinese females zheng et al proceedings of the beijing asian games scientific congress 1990 were used to form profiles which could be employed in body segment models polynomials based on proportion of segment length were fitted to the reported mean slice densities these profiles were then used with five widely divergent samples n 10 young adult females young adult males infants male children and elderly adults the mathematical model used is based on an assumption that all segments can be represented by stacked elliptic cylinders the results show that when the profile densities were substituted for average cadaver densities the increase in the estimated total body mass was less than 0 85 for the individual segments use of the profile rather than average density increased the average segment mass estimate by up to 2 7 the centres of mass and the principal moments were affected by the variations in density along the axis as well as the magnitudes by up to 0 54 and 3 8 respectively although the effects of using the profiles appear to be small the differences for individual samples segments and parameters ranged up to 22 5 it is not possible to decide if average or profile densities produce more accurate estimates of inertia but the profile allows for axial variation in density and is therefore recommended

robust stochastic approximation approach to stochastic programming in this paper we consider optimization problems where the objective function is given in a form of the expectation a basic difficulty of solving such stochastic optimization problems is that the involved multidimensional integrals expectations cannot be computed with high accuracy the aim of this paper is to compare two computational approaches based on monte carlo sampling techniques namely the stochastic approximation sa and the sample average approximation saa methods both approaches the sa and saa methods have a long history current opinion is that the saa method can efficiently use a specific say linear structure of the considered problem while the sa approach is a crude subgradient method which often performs poorly in practice we intend to demonstrate that a properly modified sa approach can be competitive and even significantly outperform the saa method for a certain class of convex stochastic problems we extend the analysis to the case of convex concave stochastic saddle point problems and present in our opinion highly encouraging results of numerical experiments

accelerated gradient methods for nonconvex nonlinear and stochastic programming in this paper we generalize the well known nesterov s accelerated gradient ag method originally designed for convex smooth optimization to solve nonconvex and possibly stochastic optimization problems we demonstrate that by properly specifying the stepsize policy the ag method exhibits the best known rate of convergence for solving general nonconvex smooth optimization problems by using first order information similarly to the gradient descent method we then consider an important class of composite optimization problems and show that the ag method can solve them uniformly i e by using the same aggressive stepsize policy as in the convex case even if the problem turns out to be nonconvex we demonstrate that the ag method exhibits an optimal rate of convergence if the composite problem is convex and improves the best known rate of convergence if the problem is nonconvex based on the ag method we also present new nonconvex stochastic approximation methods and show that they can improve a few existing rates of convergence for nonconvex stochastic optimization to the best of our knowledge this is the first time that the convergence of the ag method has been established for solving nonconvex nonlinear programming in the literature

trunk density profile estimates from dual x ray absorptiometry accurate body segment parameters are necessary to estimate joint loads when using biomechanical models geometric methods can provide individualized data for these models but the accuracy of the geometric methods depends on accurate segment density estimates the trunk which is important in many biomechanical models has the largest variability in density along its length therefore the objectives of this study were to 1 develop a new method for modeling trunk density profiles based on dual x ray absorptiometry dxa and 2 develop a trunk density function for college aged females and males that can be used in geometric methods to this end the density profiles of 25 females and 24 males were determined by combining the measurements from a photogrammetric method and dxa readings a discrete fourier transformation was then used to develop the density functions for each sex the individual density and average density profiles compare well with the literature there were distinct differences between the profiles of two of participants one female and one male and the average for their sex it is believed that the variations in these two participants density profiles were a result of the amount and distribution of fat they possessed further studies are needed to support this possibility the new density functions eliminate the uniform density assumption associated with some geometric models thus providing more accurate trunk segment parameter estimates in turn more accurate moments and forces can be estimated for the kinetic analyses of certain human movements

dynamic stochastic approximation for multi stage stochastic optimization in this paper we consider multi stage stochastic optimization problems with convex objectives and conic constraints at each stage we present a new stochastic first order method namely the dynamic stochastic approximation dsa algorithm for solving these types of stochastic optimization problems we show that dsa can achieve an optimal mathcal o 1 epsilon 4 rate of convergence in terms of the total number of required scenarios when applied to a three stage stochastic optimization problem we further show that this rate of convergence can be improved to mathcal o 1 epsilon 2 when the objective function is strongly convex we also discuss variants of dsa for solving more general multi stage stochastic optimization problems with the number of stages t 3 the developed dsa algorithms only need to go through the scenario tree once in order to compute an epsilon solution of the multi stage stochastic optimization problem as a result the memory required by dsa only grows linearly with respect to the number of stages to the best of our knowledge this is the first time that stochastic approximation type methods are generalized for multi stage stochastic optimization with t ge 3

the stark ladder and other one dimensional external field problems for a certain class of analytic potentialsv x matrix elements of the resolvent ofh f d 2 dx 2 fx v x with entire vectors of the translation group have meromorphic continuations from imz 0 to the whole complex plane the poles of these continuations are restricted to a discrete set independent of the analytic vectors chosen certain random potentials corresponding to an infinite number of particles distributed on the points of a poisson set lie in this class with probability one as do a large class of periodic potentials

multi stage stochastic optimization applied to energy planning this paper presents a methodology for the solution of multistage stochastic optimization problems based on the approximation of the expected cost to go functions of stochastic dynamic programming by piecewise linear functions no state discretization is necessary and the combinatorial explosion with the number of states the well known curse of dimensionality of dynamic programming is avoided the piecewise functions are obtained from the dual solutions of the optimization problem at each stage and correspond to benders cuts in a stochastic multistage decomposition framework a case study of optimal stochastic scheduling for a 39 reservoir system is presented and discussed

evaluating policies in risk averse multi stage stochastic programming we consider a risk averse multi stage stochastic program using conditional value at risk as the risk measure the underlying random process is assumed to be stage wise independent and a stochastic dual dynamic programming sddp algorithm is applied we discuss the poor performance of the standard upper bound estimator in the risk averse setting and propose a new approach based on importance sampling which yields improved upper bound estimators modest additional computational effort is required to use our new estimators our procedures allow for significant improvement in terms of controlling solution quality in sddp style algorithms in the risk averse setting we give computational results for multi stage asset allocation using a log normal distribution for the asset returns

absolute continuity of the integrated density of states of the quantum lorentz gas for a class of repulsive potentials for a class of repulsive potentials for instance of the type phi x mod x mod kappa 1 x2 lambda kappa lambda positive in a certain range in the random schrodinger operators h omega p2 v x omega p2 sigma j phi x xj acting in l2 rd with poisson distributed xjs the quantum lorentz gas we show that the integrated density of states n e is absolutely continuous for e zeta rho phi here is phi the integral of phi over rd rho the averaged density of points xj and zeta 0 depends on phi and d in the above example zeta d kappa 2 our method makes use of a fock space representation for the poisson random system recently developed by maassen and the author 1993 within this fock space formalism the mourre commutator method is then employed to obtain the announced result

influence of body segment parameter estimation on calculated ground reaction forces in highly dynamic movements the effect of body segment parameter estimation bsp on the inverse dynamics modelling results has not yet been demonstrated in specific groups during athletic movements with high segment accelerations therefore the purpose of this study was to analyse this effect in ski jumpers as representatives of a specific group i e low body mass index by comparing calculated and measured ground reaction forces during ski jumping imitation jumps full body kinematics and vertical ground reaction forces were recorded of 9 ski jumpers performing three imitation jumps each bsp were estimated using three previously published one individually optimized and one ski jumper group specific model vertical ground reaction forces were calculated using the vertical acceleration of the segments as well as the bsp of the single models in a top down approach statistical analysis revealed a main model effect concerning the root mean square error between the calculated and the measured ground reaction force with deviations between the models of 53 individual optimization and the application of the ski jumper group specific model increased the accuracy of the calculated ground reaction forces by 11 and 7 respectively compared to the best performing published model the results of inverse dynamics modelling are very sensitive to the bsp estimation for specific groups like ski jumpers during movements incorporating high segment accelerations this emphasizes the importance of selecting adequate bsp estimation models or methods when analysing specific groups in highly dynamic movements in order to increase the accuracy of the inverse dynamics analyses results

on the o 1 n convergence rate of the douglas rachford alternating direction method alternating direction methods adms have been well studied in the literature and they have found many efficient applications in various fields in this note we focus on the douglas rachford adm scheme proposed by glowinski and marrocco and we aim at providing a simple approach to estimating its convergence rate in terms of the iteration number the linearized version of this adm scheme which is known as the split inexact uzawa method in the image processing literature is also discussed

a fock space representation for the quantum lorentz gas a fock space representation is given for the quantum lorentz gas i e for random schrodinger operators of the form h p2 v p2 x xj acting in h l2 rd with poisson distributed xjs an operator h is defined in k h p h l2 p d l2 p d h by the action of h on its fibers in a direct integral decomposition the stationarity of the poisson process allows a unitarily equivalent description in terms of a new family h k k rd where each h k acts in p a tip j math phys 35 113 1994 the space p is then unitarily mapped upon the symmetric fock space over l2 rd dx with the intensity of the poisson process the average number of points xj per unit volume the scatterer density and the equivalent of h k is determined averages now become vacuum expectation values and a further unitary transformation removing in dx is made which leaves the former invariant the resulting operator hf k has an interesting structure on the nth fock layer we encounter a single particle mo

random time evolution and direct integrals constants of the motion and the mass operator the members h p2 v x of ergodic families of random operators defined in h l2 rd are considered as acting in fibers in a direct integral decomposition of k l2 p d h p being the underlying probability space such a formulation may turn out to be useful in providing a rigorous background for theoretical physical methods employed in treating random systems as an example a rigorous definition of the mass operator z is presented and the formulation of transport equations in a functional analytic setting is briefly indicated in case there is translational invariance in the probability law the operator h is shown to be unitarily equivalent to an operator h which can be decomposed h h k in a way that diagonalizes p thus problems about averaged time evolution can be formulated entirely in terms of h k in l2 p

scenarios and policy aggregation in optimization under uncertainty a common approach in coping with multiperiod optimization problems under uncertainty where statistical information is not really enough to support a stochastic programming model has been to set up and analyze a number of scenarios the aim then is to identify trends and essential features on which a robust decision policy can be based this paper develops for the first time a rigorous algorithmic procedure for determining such a policy in response to any weighting of the scenarios the scenarios are bundled at various levels to reflect the availability of information and iterative adjustments are made to the decision policy to adapt to this structure and remove the dependence on hindsight

random hamiltonians ergodic in all but one direction letv 1 andv 2 be two ergodic random potentials on d we consider the schrodinger operatorh h0 v withh0 and forx x1 x2 v omega x left begin array 20 c v omega 1 x if x 1 over smash scriptstyle vphantom x 0 end array right we prove certain ergodic properties of the spectrum for this model and express the integrated density of states in terms of the density of states of the stationary potentialsv 1 andv 2 finally we prove the existence of the density of surface states forh

stochastic compositional gradient descent algorithms for minimizing compositions of expected value functions classical stochastic gradient methods are well suited for minimizing expected value objective functions however they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected value functions i e the problem min x mathbf e v left f v big mathbf e w g w x big right minxevfv ew gw x in order to solve this stochastic composition problem we propose a class of stochastic compositional gradient descent scgd algorithms that can be viewed as stochastic versions of quasi gradient method scgd update the solutions based on noisy sample gradients of f v g w fv gw and use an auxiliary variable to track the unknown quantity mathbf e w left g w x right ewgw x we prove that the scgd converge almost surely to an optimal solution for convex optimization problems as long as such a solution exists the convergence involves the interplay of two iterations with different time scales for nonsmooth convex problems the scgd achieves a convergence rate of mathcal o k 1 4 o k 1 4 in the general case and mathcal o k 2 3 o k 2 3 in the strongly convex case after taking k samples for smooth convex problems the scgd can be accelerated to converge at a rate of mathcal o k 2 7 o k 2 7 in the general case and mathcal o k 4 5 o k 4 5 in the strongly convex case for nonconvex problems we prove that any limit point generated by scgd is a stationary point for which we also provide the convergence rate analysis indeed the stochastic setting where one wants to optimize compositions of expected value functions is very common in practice the proposed scgd methods find wide applications in learning estimation dynamic programming etc

on the complexity of the hybrid proximal extragradient method for the iterates and the ergodic mean in this paper we analyze the iteration complexity of the hybrid proximal extragradient hpe method for finding a zero of a maximal monotone operator recently proposed by solodov and svaiter one of the key points of our analysis is the use of new termination criteria based on the varepsilon enlargement of a maximal monotone operator the advantage of using these termination criteria is that their definition do not depend on the boundedness of the domain of the operator we then show that korpelevich s extragradient method for solving monotone variational inequalities falls in the framework of the hpe method as a consequence using the complexity analysis of the hpe method we obtain new complexity bounds for korpelevich s extragradient method which do not require the feasible set to be bounded as assumed in a recent paper by nemirovski another feature of our analysis is that the derived iteration complexity bounds are proportional to the distance of the initial point to the solution set the hpe framework is also used to obtain the first iteration complexity result for tseng s modified forward backward splitting method for finding a zero of the sum of a monotone lipschitz continuous map with an arbitrary maximal monotone operator whose resolvent is assumed to be easily computable also using the framework of the hpe method we study the complexity of a variant of a newton type extragradient algorithm proposed by solodov and svaiter for finding a zero of a smooth monotone function with lipschitz continuous jacobian

on stochastic subgradient mirror descent algorithm with weighted averaging this paper considers stochastic subgradient mirror descent method for solving constrained convex minimization problems in particular a stochastic subgradient mirror descent method with weighted iterate averaging is investigated and its per iterate convergence rate is analyzed the novel part of the approach is in the choice of weights that are used to construct the averages through the use of these weighted averages we show that the known optimal rates can be obtained with simpler algorithms than those currently existing in the literature specifically by suitably choosing the stepsize values one can obtain the rate of the order 1 k for strongly convex functions and the rate 1 sqrt k for general convex functions not necessarily differentiable furthermore for the latter case it is shown that a stochastic subgradient mirror descent with iterate averaging converges along a subsequence to an optimal solution almost surely even with the stepsize of the form 1 sqrt 1 k which was not p

body segment growth during infancy in order to better understand relationships between physical growth and motor development during infancy changes in segment inertias were examined a rationale based on dynamic systems theory and intersegmental moments was used to select the variables the segment mass and principal moments of nine segments the hypothesis was that there are differences in growth velocity between segments and these are consistent with the principles of cephalocaudal development and distal to proximal growth a mathematical model of the segments was used to examine changes of the inertia parameters twenty seven normal infants carried to full term and aged between 2 and 9 months at the beginning of the study were photographed once a month for 6 months outlines of segments from front and side 35 mm images were digitized and mass and principal moments of inertia estimates obtained polynomial regression was used to give the development curves regression coefficients for the 155 data points also linear regressions were fitted to the six growth data points of each subject most of the relationships between chronological age and segment mass and principal moments were significant and linear the differences in growth velocity between segments were significant and partially consistent with the growth principles however there were considerable differences in particular for the lower trunk and the shank where it appears that growth may be irregular until after the age of 15 months

changes in segment inertia proportions between 4 and 20 years growth between 4 and 20 yr produces an increase in body mass and a redistribution of that mass throughout the body it is the purpose of this investigation to describe changes in the segment mass radius to the mass centre and radius of gyration for a sample of males 4 20 yr and the potential effects of these changes on joint reaction forces and moments the data were collected annually over 9 yr in a mixed longitudinal study completed in 1985 elliptical zones 2 cm wide were used to model the 16 segments of the body from these and reported segment densities mass the coordinates of the mass centre and the principal moments of inertia were determined for the segments and the body the parameters reported are the inertia parameters suitable for a sagittal planar analysis with the head and neck considered one segment and values given for other fused segments the accuracy of the method was judged against the total body mass and other accuracy estimates from the literature were examined the parameters are presented as proportions of total mass or segment length it is clear from the polynomial regressions that there is a substantial redistribution of the mass between segments and this is consistent with the principles of cephalo caudal and distal to proximal development the proportions for radius and radius of gyration indicate that mass redistribution within segments is comparatively small the parameters for a 6 yr old were compared to the parameters expected at 18 24 and 54 yr and substantial differences noted abstract truncated at 250 words