twenty five years of multifractals in fully developed turbulence a tribute to giovanni paladin the paper on the multifractal nature of fully developed turbulence and chaotic systems by benzi et al 1984 j phys a math gen 17 3521 has been a starting point of many investigations on the different faces of self similarity and intermittency in turbulent phenomena since then the multifractal model has become a useful tool for the study of small scale turbulence in particular for detailed predictions of different eulerian and lagrangian statistical properties on the occasion of the 50th birthday of our unforgettable friend and colleague giovanni paladin 1958 1996 we review here the basic concepts and some applications of the multifractal model for turbulence

the sensitivity of muscle force predictions to changes in physiologic cross sectional area abstract the mechanical effects of a muscle are related in part to the size of the muscle and to its location relative to the joint it crosses for more than a century researchers have expressed muscle size by its physiological cross sectional area pcsa researchers mathematically calculating muscle and joint forces typically use some expression of a muscle s pcsa to constrain the solution to one which is reasonable i e a solution in which small muscles may not have large forces and large muscles have large forces when expected or when there is significant electromyographic activity it is obvious that muscle mass and therefore any expression of pcsa varies significantly from person to person even in individuals of similar weight and height since it is not practical to predict the pcsa of each muscle in a living subject s limb or trunk it is important to generally understand the sensitivity of muscle force solutions to possible variations in pcsa we used nonlinear optimization techniques to predict 47 muscle forces and hip contact forces in a living subject the pcsa volume muscle fiber length of each of 47 lower limb muscle elements from two cadaver specimens and the 47 pcsa s reported by pierrynowski were input into an optimization algorithm to create three solution sets the three solutions were qualitatively similar but at times a predicted muscle force could vary as much as two to eight times in contrast the joint force solutions were within 11 of each other and therefore much less variable when using optimization techniques to predict muscle forces it must be recognized that the solution is sensitive to many assumptions and variables such as pcsa the muscle force solutions are therefore best used to determine relative values i e trends in parametric studies on the other hand the joint force solutions are less sensitive to such variations and the absolute values are more reliable

thermodynamic versus statistical nonequivalence of ensembles for the mean field blume emery griffiths model abstract we illustrate a novel characterization of nonequivalent statistical mechanical ensembles using the mean field blume emery griffiths beg model as a test model the novel characterization takes effect at the level of the microcanonical and canonical equilibrium distributions of states for this reason it may be viewed as a statistical characterization of nonequivalent ensembles which extends and complements the common thermodynamic characterization of nonequivalent ensembles based on nonconcave anomalies of the microcanonical entropy by computing numerically both the microcanonical and canonical sets of equilibrium distributions of states of the beg model we show that for values of the mean energy where the microcanonical entropy is nonconcave the microcanonical distributions of states are nowhere realized in the canonical ensemble moreover we show that for values of the mean energy where the microcanonical entropy is strictly concave the equilibrium microcanonical distributions of states can be put in one to one correspondence with equivalent canonical equilibrium distributions of states our numerical computations illustrate general results relating thermodynamic and statistical equivalence and nonequivalence of ensembles proved by ellis et al j stat phys 101 2000 999

mixed effects nonlinear regression for unbalanced repeated measures repeated measures data such as clinical pharmacokinetic data growth data and dose response data are often inherently nonlinear with respect to a given response function and are frequently incomplete and or unbalanced nonlinear random effects models together with a variety of estimation procedures have been proposed for the analysis of such data this paper is concerned with a straightforward procedure for estimating and comparing the parameters of a generalized mixed effects nonlinear regression model the asymptotic properties of the proposed estimators are given and large sample tests of hypothesis provided the results are applied to in vitro data on the water transport kinetics of hemodialyzers used in the treatment of patients with chronic renal failure

sensitivity of dynamic simulations of gait and dynamometer experiments to hill muscle model parameters of knee flexors and extensors we assessed and compared sensitivities of dynamic simulations to musculotendon mt parameters for gait and dynamometer experiments our aim with this comparison was to investigate whether dynamometer experiments could provide information about mt parameters that are important to reliably study mt function during gait this would mean that dynamometer experiments could be used to estimate these parameters muscle contribution to the joint torque mt torque rather than relative mt force primarily affects the resulting gait pattern and torque measured by the dynamometer in contrast to recent studies therefore we assessed the sensitivity of the mt torque rather than the sensitivity of the relative mt force based on sensitivity of the mt torque to a parameter perturbation mt parameters of the knee flexors and extensors were classified in three categories low medium and high for gait classification was based on the average sensitivity during a gait cycle for isometric and isokinetic dynamometer experiments classification was based on the highest sensitivity found in the experiments the calculated muscle contributions to the knee torque during gait and dynamometer experiments had a high sensitivity to only a limited number of mt parameters of the knee flexors and extensors suggesting that not all mt parameters need to be estimated in general the highest sensitivity was found for tendon slack length however for some muscles the sensitivity to the optimal fibre length or the maximal isometric muscle force was also high or medium the classification of the individual mt parameters for gait and dynamometer experiments was largely similar we therefore conclude that dynamometer experiments provide information about mt parameters important to reliably study mt function during gait so that subject specific estimates of mt parameters could be made based on dynamometer experiments

the theory of large deviations from boltzmann s 1877 calculation to equilibrium macrostates in 2d turbulence abstract after presenting some basic ideas in the theory of large deviations this paper applies the theory to a number of problems in statistical mechanics these include deriving the form of the gibbs state for a discrete ideal gas describing probabilistically the phase transition in the curie weiss model of a ferromagnet and deriving variational formulas that describe the equilibrium macrostates in models of two dimensional turbulence a general approach to the large deviation analysis of models in statistical mechanics is also formulated

statistical equilibrium measures and coherent states in two dimensional turbulence the equilibrium statistics of the euler equations in two dimensions are studied and a new continuum model of coherent or organized states is proposed this model is defined by a maximum entropy principle similar to that governing the miller robert model except that the family of global vorticity invariants is relaxed to a family of inequalities on all convex enstrophy integrals this relaxation is justified by constructing the continuum model from a sequence of lattice models defined by gibbs measures whose invariants are derived from the exact vorticity dynamics not a spectral truncation or spatial discretization of it the key idea is that the enstrophy integrals can be partially lost to vorticity fluctuations on a range of scales smaller than the lattice microscale while energy is retained in the larger scales a consequence of this relaxation is that many of the convex enstrophy constraints can be inactive in equilibrium leading to a simplification of the mean field equation for the coherent state specific examples of these simplified theories are established for vortex patch dynamics in particular a universal relation between mean vorticity and stream function is obtained in the dilute limit of the vortex patch theory which is different from the sinh relation predicted by the montgomery joyce theory of point vortices 1999 john wiley sons inc

large deviations for the empirical field of a gibbs measure on applique le principe de contraction pour obtenir un principe de grande deviation pour la distribution des distributions empiriques on donne une description detaillee de la fonction de taux resultante

a simple probabilistic construction yielding generalized entropies and divergences escort distributions and q gaussians abstract we give a simple probabilistic description of a transition between two states which leads to a generalized escort distribution when the parameter of the distribution varies it defines a parametric curve that we call an escort path the renyi divergence appears as a natural by product of the setting we study the dynamics of the fisher information on this path and show in particular that the thermodynamic divergence is proportional to jeffreys divergence next we consider the problem of inferring a distribution on the escort path subject to generalized moment constraints we show that our setting naturally induces a rationale for the minimization of the renyi information divergence then we derive the optimum distribution as a generalized q gaussian distribution

lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers we give asymptotic formulas for the multiplicities of weights and irreducible summands in high tensor powers v n l of an irreducible representation vl of a compact connected lie group g the weights are allowed to depend on n and we obtain several regimes of pointwise asymptotics ranging from a central limit region to a large deviations region we use a complex steepest descent method that applies to general asymptotic counting problems for lattice paths with steps in a convex polytope r 2004 published by elsevier inc

optimal two period repeated measurement designs with two or more treatments summary for two period repeated measurement designs for comparing t 2 treatments we discuss universally optimal designs when the number of subjects n is a multiple of t2 and some cases when n is a multiple of t we examine efficiencies of balanced designs and other symmetric designs relative to strongly balanced designs in addition efficiencies of the universally optimal designs obtained by hedayat zhao 1990 are examined under both fixed subject and random subject effect model assumptions

muscle activities of the lower limb during level and uphill running this study aimed to compare the muscle activities of the lower limb during overground level running lr and uphill running ur by using a musculoskeletal model six male distance runners ran at three running speeds slow 3 3 m s medium 4 2 m s and high 5 0 m s on a level runway and a slope of 9 1 grade in which force platforms were mounted a musculoskeletal leg model and optimization were used to estimate the muscle activation and muscle torque from the joint torque of the lower limb calculated by the inverse dynamics approach at high speed the activation and muscle torque of the muscle groups surrounding the hip joints such as the hamstrings and iliopsoas during the recovery phase were significantly greater during ur than during lr at all the running speeds the knee extension torque by the vasti during the support phase was significantly smaller during ur further the hip flexion and knee extension torques by the rectus femoris during ur were significantly greater than those during lr at all the speeds this would play a role in compensating for the decrease in the knee extension torque by the vasti and in maintaining the trunk in a forward leaning position these results revealed that the activation and muscle torque of the hip extensors and flexors were augmented during ur at the high speed

an emg driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo this paper examined if an electromyography emg driven musculoskeletal model of the human knee could be used to predict knee moments calculated using inverse dynamics across a varied range of dynamic contractile conditions muscle tendon lengths and moment arms of 13 muscles crossing the knee joint were determined from joint kinematics using a three dimensional anatomical model of the lower limb muscle activation was determined using a second order discrete non linear model using rectified and lowpass filtered emg as input a modified hill type muscle model was used to calculate individual muscle forces using activation and muscle tendon lengths as inputs the model was calibrated to six individuals by altering a set of physiologically based parameters using mathematical optimisation to match the net flexion extension fe muscle moment with those measured by inverse dynamics the model was calibrated for each subject using 5 different tasks including passive and active fe in an isokinetic dynamometer running and cutting manoeuvres recorded using three dimensional motion analysis once calibrated the model was used to predict the fe moments estimated via inverse dynamics from over 200 isokinetic dynamometer running and sidestepping tasks the inverse dynamics joint moments were predicted with an average r 2 of 0 91 and mean residual error of b12 nm a re calibration of only the emg to activation parameters revealed fe moments prediction across weeks of similar accuracy changing the muscle model to one that is more physiologically correct produced better predictions the modelling method presented represents a good way to estimate in vivo muscle forces during movement tasks r 2003 elsevier science ltd all rights reserved

effects of hip center location on the moment generating capacity of the muscles we have developed a three dimensional biomechanical model of the human lower extremity to study how the location of the hip center affects the moment generating capacity of four muscle groups the hip abductors adductors flexors and extensors the model computes the maximum isometric force and the resulting joint moments that each of 25 muscle tendon complexes develops at any body position abduction adduction flexion and extension moments calculated with the model correspond closely with isometric joint moments measured during maximum voluntary contractions we used the model to determine 1 the hip center locations that maximize and minimize the moment generating capacity of each muscle group and 2 the effects of superior inferior anterior posterior and medial lateral displacement of the hip center on the moment arms maximum isometric muscle forces and maximum isometric moments generated by each muscle group we found that superior inferior displacement of the hip center has the greatest effect on the force and moment generating capacity of the muscles a 2 cm superior displacement decreases abduction force 44 moment arm 12 and moment 49 while a 2 cm inferior displacement increases abduction force 20 moment arm 7 and moment 26 similarly a 2 cm superior displacement decreases flexion force 27 moment arm 6 and moment 22 while inferior displacement increases all three variables anterior posterior displacement alters the moment generating capacity of the flexors and extensors considerably primarily due to moment arm changes medial lateral displacement has a large effect on the moment generating capacity of the adductors only a 2 cm medial displacement decreases adduction moment arm 20 force 26 and moment 40 these results demonstrate that the force and moment generating capacities of the muscles are sensitive to the location of the hip center

a non invasive protocol to determine the personalized moment arms of knee and ankle muscles one difficulty that comes with predicting muscular forces is the accuracy of experimental data particularly the assessment of muscle moment arms with respect to each joint rotation axis this paper presents a non invasive experimental protocol to obtain the personalized muscle moment arms with respect to the ankle and knee joints a specific pointer is used by a specialist of lower limb anatomy in order to define the local portion of the line of action of the different muscles closed to the joint on the standing subject s lower limb with this pointer the three dimensional coordinates of several points representing the line of action of 12 ankle and knee muscles are collected by a motion analysis system the collection is done five times by the same operator and one time by two different operators from this data the intra and inter operator repeatabilities are tested relative icc and absolute sem reliabilities are determined in order to evaluate the intra operator repeatability of this non invasive protocol the icc values obtained are higher than 0 91 for 10 among 12 muscles the intra operator repeatability is thus confirmed from the records realized by the two operators the differences are negligible thus the inter operator repeatability is also confirmed the moments arms obtained using this non invasive experimental protocol are compared with those calculated from origin and insertion points reported in the literature according to the work of whites pierrynowskis and kepples respectively the estimations obtained using the non invasive experimental protocol are found for some muscles more realistic than those calculated using the literature data and are always coherent with the role of the muscles described in anatomical books

likelihood analysis of power spectra and generalized moment problems we develop an approach to the spectral estimation that has been advocated by a ferrante et al time and spectral domain relative entropy a new approach to multivariate spectral estimation ieee trans autom control vol 57 no 10 pp 2561 2575 oct 2012 and in the context of the scalar valued covariance extension problem by p enqvist and j karlsson minimal itakura saito distance and covariance interpolation in proc 47th ieee conf decision control 2008 pp 137 142 the aim is to determine the power spectrum that is consistent with given moments and minimizes the relative entropy between the probability law of the underlying gaussian stochastic process to that of a prior the approach is analogous to the framework of earlier work by byrnes georgiou and lindquist and can also be viewed as a generalization of the classical work by burg and jaynes on the maximum entropy method in this paper we present a new fast algorithm in the general case i e for general gaussian priors and show that for priors with a specific structure the solution can be given in closed form

large deviations for gibbs random fields a large deviation principle for gibbs random fields on zd is proven and a corresponding large deviations proof of the gibbs variational formula is given a generalization of the lanford theory of large deviations is also obtained

likelihood inference for mixtures geometrical and other constructions of monotone step length algorithms summary this paper considers algorithms for the maximum likelihood estimator of the mixing distribution of a family of parametric densities specific interest is devoted to the monotonicity of the step length of the solution in 2 we introduce the idea of estimating the area above the second derivative curve and in theorem 1 we relate area overestimation to the monotonicity of the associated algorithm in 3 we apply theorem 1 to the monotonicity analysis of well known algorithms as well as to the construction of a new class of monotone step length choices which is particularly simple in the mixture setting numerical comparisons and refinements in keeping the monotonic step length from becoming too conservative are given theorem 3 characterizes conditions under which the newton raphson step is monotonic and if these conditions fail to hold states that the regula falsi step is monotonic

limit theorems for levy walks in d dimensions rare and bulk fluctuations we consider super diffusive levy walks in dimensions when the duration of a single step i e a ballistic motion performed by a walker is governed by a power law tailed distribution of infinite variance and finite mean we demonstrate that the probability density function pdf of the coordinate of the random walker has two different scaling limits at large times one limit describes the bulk of the pdf it is the d dimensional generalization of the one dimensional levy distribution and is the counterpart of the central limit theorem clt for random walks with finite dispersion in contrast with the one dimensional levy distribution and the clt this distribution does not have a universal shape the pdf reflects anisotropy of the single step statistics however large the time is the other scaling limit the so called infinite density describes the tail of the pdf which determines second dispersion and higher moments of the pdf this limit repeats the angular structure of the pdf of velocity in one step a typical realization of the walk consists of anomalous diffusive motion described by anisotropic d dimensional levy distribution interspersed with long ballistic flights described by infinite density the long flights are rare but due to them the coordinate increases so much that their contribution determines the dispersion we illustrate the concept by considering two types of levy walks with isotropic and anisotropic distributions of velocities furthermore we show that for isotropic but otherwise arbitrary velocity distributions the d dimensional process can be reduced to a one dimensional levy walk we briefly discuss the consequences of non universality for the d 1 dimensional fractional diffusion equation in particular the non uniqueness of the fractional laplacian

whole body reaching movements formulated by minimum muscle tension change criterion it is well known that planar reaching movements of the human shoulder and elbow joints have invariant features roughly straight hand paths and bell shaped velocity profiles the optimal control models with the criteria of smoothness or precision which determine a unique movement pattern predict such features of hand trajectories in this letter on expanding the research on simple arm reaching movements we examine whether the smoothness criteria can be applied to whole body reaching movements with many degrees of freedom determining a suitable joint trajectory in the whole body reaching movement corresponds to the optimization problem with constraints since body balance must be maintained during a motion task first we measured human joint trajectories and ground reaction forces during whole body reaching movements and confirmed that subjects formed similar movements with common characteristics in the trajectories of the hand position and body center of mass second we calculated the optimal trajectories according to the criteria of torque and muscle tension smoothness while the minimum torque change trajectories were not consistent with the experimental data the minimum muscle tension change model was able to predict the stereotyped features of the measured trajectories to explore the dominant effects of the extension from the torque change to the muscle tension change we introduced a weighted torque change cost function considering the maximum voluntary contraction mvc force of the muscle as the weighting factor of each joint torque we formulated the weighted torque change cost as a simplified version of the minimum muscle tension change cost the trajectories owing to the minimum weighted torque change criterion also showed qualitative agreement with the common features of the measured data proper estimation of the mvc forces in the body joints is essential to reproduce human whole body movements according to the minimum muscle tension change criterion

large deviation techniques applied to systems with long range interactions we discuss a method to solve models with long range interactions in the microcanonical and canonical ensemble the method closely follows the one introduced by r s ellis physica d 133 106 1999 which uses large deviation techniques we show how it can be adapted to obtain the solution of a large class of simple models which can show ensemble inequivalence the model hamiltonian can have both discrete ising potts and continuous hmf free electron laser state variables this latter extension gives access to the comparison with dynamics and to the study of non equilibrium effects we treat both infinite range and slowly decreasing interactions and in particular we present the solution of the ising model in one dimension with 0 1

sensitivity of predicted muscle forces to parameters of the optimization based human leg model revealed by analytical and numerical analyses there are different opinions in the literature on whether the cost functions the sum of muscle stresses squared and the sum of muscle stresses cubed can reasonably predict muscle forces in humans one potential reason for the discrepancy in the results could be that different authors use different sets of model parameters which could substantially affect forces predicted by optimization based models in this study the sensitivity of the optimal solution obtained by minimizing the above cost functions for a planar three degrees of freedom dof model of the leg with nine muscles was investigated analytically for the quadratic function and numerically for the cubic function analytical results revealed that generally the non zero optimal force of each muscle depends in a very complex non linear way on moments at all three joints and moment arms and physiological cross sectional areas pcsas of all muscles deviations of the model parameters moment arms and pcsas from their nominal values within a physiologically feasible range affected not only the magnitude of the forces predicted by both criteria but also the number of non zero forces in the optimal solution and the combination of muscles with non zero predicted forces muscle force magnitudes calculated by both criteria were similar they could change several times as model parameters changed whereas patterns of muscle forces were typically not as sensitive it is concluded that different opinions in the literature about the behavior of optimization based models can be potentially explained by differences in employed model parameters

spatializing random measures doubly indexed processes and the large deviation principle the main theorem is the large deviation principle for the doubly indexed sequence of random measures w r q dx dy dx 1 dr k x l q k dy k 1 here is a probability measure on a polish space x d r k k 1 2 r is a dyadic partition of x hence the use of 2 r summands satisfying d r k 1 2 r and l q 1 l q 2 l q 2 r is an independent identically distributed sequence of random probability measures on a polish space y such that l q k q n satisfies the large deviation principle with a convex rate function a number of related asymptotic results are also derived the random measures w have important applications to the statistical mechanics of turbulence in a companion paper the large deviation principle presented here is used to give a rigorous derivation of maximum entropy principles arising in the well known miller robert theory of two dimensional turbulence as well as in a modification of that theory recently proposed by turkington

large deviation theory for coin tossing and turbulence large deviations play a significant role in many branches of nonequilibrium statistical physics they are difficult to handle because their effects though small are not amenable to perturbation theory even the gaussian model which is the usual initial step for most perturbation theories fails to be a starting point while discussing intermittency in fluid turbulence where large deviations dominate our contention is in the large deviation theory the central role is played by the distribution associated with the tossing of a coin and the simple coin toss is the gaussian model of problems where rare events play significant role we illustrate this by applying it to calculate the multifractal exponents of the order structure factors in fully developed turbulence

ensemble inequivalence in random graphs we present a complete analytical solution of a system of potts spins on a random k regular graph in both the canonical and microcanonical ensembles using the large deviation cavity method ldcm the solution is shown to be composed of three different branches resulting in a non concave entropy function the analytical solution is confirmed with numerical metropolis and creutz simulations and our results clearly demonstrate the presence of a region with negative specific heat and consequently ensemble inequivalence between the canonical and microcanonical ensembles

macroscopic determinism in interacting systems using large deviation theory we consider the quasi deterministic behavior of systems with a large number n of deterministically interacting constituents this work extends the results of a previous paper j statist phys 99 1225 1249 2000 to include vector valued observables on interacting systems the approach used here however differs markedly in that a level 1 large deviation principle ldp on joint observables rather than a level 2 ldp on empirical distributions is employed as before we seek a mapping t on the set of possibly vector valued macrostates such that when the macrostate is given to be a0 at time zero the macrostate at time t is t a0 with a probability approaching one as n tends to infinity we show that such a map exists and derives from a generalized dynamic free energy function provided the latter is everywhere well defined finite and differentiable we discuss some general properties of t relevant to issues of irreversibility and end with an example of a simple interacting lattice for which an exact macroscopic solution is obtained

microcanonical distributions for lattice gases in this article a large deviation principle cf theorem 1 3 for the empirical distribution functional is applied to prove a rather general version of boltzmann s principle cf theorem 3 5 for models with shift invariant finite range potentials the final section contains an application of these considerations to the two dimensional ising model at sub critical temperature

a physiologically based criterion of muscle force prediction in locomotion abstract the inversely nonlinear relationship of muscle contraction force and the possible contraction duration i e endurance is utilized in a method to mathematically predict individual muscle forces the method uses a nonlinear optimization scheme to solve the redundant distribution problem at the joints of interest the method is demonstrated at the elbow during isometric contraction and in the lower extremity during locomotion during gait the observed muscle activity pattern in the lower extremity as determined by emg shows substantial agreement with that activity pattern predicted when endurance is used as the optimization criterion the importance of selecting muscle prediction criteria based on sound physiological bases rather than on an arbitrary or mathematically convenient basis is emphasized

about weight factors in the non linear objective functions used for solving indeterminate problems in biomechanics a lot of non linear objective criteria are applied for solving the indeterminate problems formulated for di erent biomechanical models most of them can be covered by the expression c i dfo i dn it might be noted however that most of the suggested criteria are not applicable if considerable antagonistic co contractions exist this could be an e ect of treating the agonistic muscles and their respective antagonists in one and the same manner in the objective function using a completely inverse approach the muscle forces are supposed to be known quantities and a simple 1dof model actuated by three agonistic muscles and one corresponding antagonist it has been shown which values of the weight factors c i may predict di erent levels of muscle forces from the two antagonistic groups three hypothetical border variants for magnitudes of the muscle forces are considered exor muscles are only active extensor muscles are only active considerable co contraction of exors and extensors exists the main conclusions are the signs of c i at agonistic muscles have to be opposite to the c i signs at their antagonists the signs of the weight factors depend on the direction of the net external joint moment the closer c i to zero the bigger force will be predicted in the ith muscle 1999 elsevier science ltd all rights reserved

biomechanical modeling and optimal control of human posture the present work describes the biomechanical modeling of human postural mechanics in the saggital plane and the use of optimal control to generate open loop raising up movements from a squatting position the biomechanical model comprises 10 equivalent musculotendon actuators based on a 40 muscles model and three links shank thigh and hat head arms and trunk optimal control solutions are achieved through algorithms based on the consistent approximations theory schwartz and polak 1996 where the continuous non linear dynamics is represented in a discrete space by means of a runge kutta integration and the control signals in a spline coefficient functional space this leads to non linear programming problems solved by a sequential quadratic programming sqp method due to the highly non linear and unstable nature of the posture dynamics numerical convergence is difficult and specific strategies must be implemented in order to allow convergence results for control muscular excitations and angular trajectories are shown using two final simulation times as well as specific control strategies are discussed

an open source lower limb model hip joint validation musculoskeletal lower limb models have been shown to be able to predict hip contact forces hcfs that are comparable to in vivo measurements obtained from instrumented prostheses however the muscle recruitment predicted by these models does not necessarily compare well to measured electromyographic emg signals in order to verify if it is possible to accurately estimate hcfs from muscle force patterns consistent with emg measurements a lower limb model based on a published anatomical dataset klein horsman et al 2007 clinical biomechanics 22 239 247 has been implemented in the open source software opensim a cycle to cycle hip joint validation was conducted against hcfs recorded during gait and stair climbing trials of four arthroplasty patients bergmann et al 2001 journal of biomechanics 34 859 871 hip joint muscle tensions were estimated by minimizing a polynomial function of the muscle forces the resulting muscle activation patterns obtained by assessing multiple powers of the objective function were compared against emg profiles from the literature calculated hcfs denoted a tendency to monotonically increase their magnitude when raising the power of the objective function the best estimation obtained from muscle forces consistent with experimental emg profiles was found when a quadratic objective function was minimized average overestimation at experimental peak frame 10 1 for walking 7 8 for stair climbing the lower limb model can produce appropriate balanced sets of muscle forces and joint contact forces that can be used in a range of applications requiring accurate quantification of both the developed model is available at the website https simtk org home low limb london

exact and optimum tests in unbalanced split plot designs under mixed and random models abstract unbalanced split plot designs are considered where the whole plot treatments could be replicated an unequal number of times in the design but each split plot treatment occurs exactly once in every whole plot analysis of such designs is provided when the various effects could be fixed or random in each case valid exact tests and optimum invariant tests whenever they exist are derived for testing the significance of the various effects in some cases optimum tests exist only under additional conditions on the design and these conditions are specified for the various setups

optimum experimental designs for properties of a compartmental model summary three properties of interest in bioavailability studies using compartmental models are the area under the concentration curve the maximum concentration and the time to maximum concentration methods are described for finding designs that minimize the variance of the estimates of these quantities in such a model these methods use prior information both prior estimates and prior distributions are used the designs for an open one compartment model are compared with the corresponding d optimum design for all parameters and also with designs that minimize the sum of the scaled variances of the individual properties

extension of a state of the art optimization criterion to predict co contraction most studies concerned with the prediction of muscle forces have tried to predict a physiologically reasonable synergistic muscle behavior in addition to the load sharing of synergistic muscles co contraction of antagonistic muscles also occurs an extension to a standard quadratic criterion for the calculation of muscle forces is presented in this study this extension however is not limited to quadratic optimization the extension is applied to a planar one degree of freedom model of the human knee for this model an analytical solution is presented with the extended criterion it was possible to predict and control the amount of co contraction for the knee model the enforced antagonistic muscle activity led to higher agonistic muscle activity in the absence of an external load flexor and extensor muscles were activated as a consequence the knee joint was preloaded this might indicate that antagonistic muscle activity is generated to maintain or improve joint stability in conclusion this study presents a novel approach to predict co contraction when using optimization techniques to determine muscle forces by introducing a shift parameter for the optimization criterion

beyond boltzmann gibbs statistics maximum entropy hyperensembles out of equilibrium what is the best description that we can construct of a thermodynamic system that is not in equilibrium given only one or a few extra parameters over and above those needed for a description of the same system at equilibrium here we argue the most appropriate additional parameter is the nonequilibrium entropy of the system moreover we should not attempt to estimate the probability distribution of the system directly but rather the metaprobability or hyperensemble that the system is described by a particular probability distribution the result is an entropic distribution with two parameters one a nonequilibrium temperature and the other a measure of distance from equilibrium this dispersion parameter smoothly interpolates between certainty of a canonical distribution at equilibrium and great uncertainty as to the probability distribution as we move away from equilibrium we deduce that in general large rare fluctuations become far more common as we move away from equilibrium

optimal design in random effects regression models summary an approach is proposed to optimal design of experiments for estimating randomeffects regression models the population designs are defined by the number of subjects and the individual designs to be performed cost functions associated with individual designs are incorporated for a given maximal cost an algorithm is proposed for finding the statistical population design that maximises the determinant of the fisher information matrix of the population parameters the fisher information matrix is formulated for linear models and normal distributions the approach is applied to the design of an optimal experiment in toxicokinetics using a first order linearisation of the model several cost functions and designs of various orders are studied an example illustrates the optimal population designs and the increased efficiency of some optimal designs over more standard designs

moment distribution among human elbow extensor muscles during isometric and submaximal extension to understand better how the central nervous system cns distributes a joint moment among muscles moment distribution among the three heads of the triceps and the anconeus muscles during isometric elbow extension was quantified in vivo and noninvasively electrical stimulation was used to activate an individual muscle selectively at various contraction levels and the relationship between the peak m wave amplitude and peak elbow extension moment was established across various contraction levels for each muscle the relationship was then used to calibrate the corresponding emg signal and determine moment distribution among the muscles during voluntary isometric elbow extension results showed that moment distribution among muscles was not proportional to the muscles physiological cross sectional areas pcsa and the cns favored uniarticular muscles for the isometric task performed the uniarticular lateral and medial heads of the triceps were dominant contributing approximately 70 90 of the total elbow extension moment and the anconeus contributed significantly especially at the lower levels of elbow extension moment up to approximately 15 of the extension moment in contrast the two joint long head of the triceps contributed significantly less than the uniarticular heads of the triceps while the absolute contributions of all the muscles increased with the total elbow extension moment the relative contributions of the muscles may increase or decrease with the elbow extension moment cross validation using fresh data not used in determining the moment distribution showed close match between the measured and predicted elbow extension moment except for trials in which fatigue became significant

a general conditional large deviation principle given a sequence of borel probability measures on a hausdorff space which satisfy a large deviation principle ldp we consider the corresponding sequence of measures formed by conditioning on a set b if the large deviation rate function i is good and effectively continuous and the conditioning set has the property that 1 overline b circ overline b and 2 i x infty for all x in overline b then the sequence of conditional measures satisfies a ldp with the good effectively continuous rate function i b where i b x i x inf i b if x in overline b and i b x infty otherwise

individual specific muscle maximum force estimation using ultrasound for ankle joint torque prediction using an emg driven hill type model abstract emg driven models can be used to estimate muscle force in biomechanical systems collected and processed emg readings are used as the input of a dynamic system which is integrated numerically this approach requires the definition of a reasonably large set of parameters some of these vary widely among subjects and slight inaccuracies in such parameters can lead to large model output errors one of these parameters is the maximum voluntary contraction force f om this paper proposes an approach to find f om by estimating muscle physiological cross sectional area pcsa using ultrasound us which is multiplied by a realistic value of maximum muscle specific tension ultrasound is used to measure muscle thickness which allows for the determination of muscle volume through regression equations soleus gastrocnemius medialis and gastrocnemius lateralis pcsas are estimated using published volume proportions among leg muscles which also requires measurements of muscle fiber length and pennation angle by us f om obtained by this approach and from data widely cited in the literature was used to comparatively test a hill type emg driven model of the ankle joint the model uses 3 emgs soleus gastrocnemius medialis and gastrocnemius lateralis as inputs with joint torque as the output the emg signals were obtained in a series of experiments carried out with 8 adult male subjects who performed an isometric contraction protocol consisting of 10 s step contractions at 20 and 60 of the maximum voluntary contraction level isometric torque was simultaneously collected using a dynamometer a statistically significant reduction in the root mean square error was observed when us obtained f om was used as compared to f om from the literature

nonlinear mixed effects models for repeated measures data we propose a general nonlinear mixed effects model for repeated measures data and define estimators for its parameters the proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood or restricted maximum likelihood estimators for linear mixed effects models we implement newton raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed

microcanonical solution of the mean field φ 4 model comparison with time averages at finite size abstract we study the mean field 4 model in an external magnetic field in the microcanonical ensemble using two different methods the first one is based on rugh s microcanonical formalism and leads to express macroscopic observables such as temperature specific heat magnetization and susceptibility as time averages of convenient functions of the phase space the approach is applicable for any finite number of particles n the second method uses large deviation techniques and allows us to derive explicit expressions for microcanonical entropy and for macroscopic observables in the n limit assuming ergodicity we evaluate time averages in molecular dynamics simulations and using rugh s approach we determine the value of macroscopic observables at finite n these averages are affected by a slow time evolution often observed in systems with long range interactions we then show how the finite n time averages of macroscopic observables converge to their corresponding n values as n is increased as expected finite size effects scale as n 1