a model predicting individual shoulder muscle forces based on relationship between electromyographic and 3d external forces in static position abstract to study the potentiality for developing an emg based model for the human shoulder mapping of relations between static hand forces and electromyographic emg activity of 13 shoulder muscles were performed the procedure was to perform by the hands slowly varying isometric forces up to 20 maximum voluntary force in the three dimensional space by combining these data with literature values on muscle physiological cross sectional area and moment arm data an emg based model was developed for estimating muscle forces in the glenohumeral joint the model was validated for one standardized position by comparing joint moment calculated from emg by using the model with moments from the external force the highest correlation between these moments was found assuming a linear emg force calibration at low force level

finite size corrections and numerical calculations for long spin 1 2 heisenberg chains in the critical region leading and next to leading order finite size corrections to the ground and first excited states are calculated for the spin 1 2 anisotropic heisenberg model in the critical region the analytic results are compared to numerical data obtained for chains up to a length of n 1024 it is found that near the isotropic point the asymptotic region where the results obtained for n to infinity are applicable sets in at very large n values and for obtaining good accuracy in fitting the numerical data one has to take into account several correction terms even at large n 100 chain lengths

femoral strain during walking predicted with muscle forces from static and dynamic optimization mechanical strain plays an important role in skeletal health and the ability to accurately and noninvasively quantify bone strain in vivo may be used to develop preventive measures that improve bone quality and decrease fracture risk a non invasive estimation of bone strain requires combined musculoskeletal finite element modeling for which the applied muscle forces are usually obtained from static optimization so methods in this study we compared finite element predicted femoral strains in walking using muscle forces obtained from so to those obtained from forward dynamics fd simulation the general trends in strain distributions were similar between fd and so derived conditions and both agreed well with previously reported in vivo strain gage measurements on the other hand differences in peak maximum emax and minimum emin principal strain magnitudes were as high as 32 between fd emax emin 945 1271 e and so emax emin 752 859 e these large differences in strain magnitudes were observed during the first half of stance where so predicted lower gluteal muscle forces and virtually no co contraction of the hip adductors compared to fd the importance of these results will likely depend on the purpose application of the modeling procedure if the goal is to obtain a generalized strain distribution for adaptive bone remodeling algorithms then traditional so is likely sufficient in cases were strain magnitudes are critical as is the case with fracture risk assessment bone strain estimation may benefit by including muscle activation and contractile dynamics in so or by using fd when practical

brief equivalence of hybrid dynamical models this paper establishes equivalences among five classes of hybrid systems mixed logical dynamical mld systems linear complementarity lc systems extended linear complementarity elc systems piecewise affine pwa systems and max min plus scaling mmps systems some of the equivalences are established under rather mild additional assumptions these results are of paramount importance for transferring theoretical properties and tools from one class to another with the consequence that for the study of a particular hybrid system that belongs to any of these classes one can choose the most convenient hybrid modeling framework

mechanical output from individual muscles during explosive leg extensions the role of biarticular muscles the main result of this study is that biarticular leg muscles contribute significantly to the work done at joints due to transfer of power during explosive leg extensions in particular a net power transfer was shown from hip to knee joint during jumping and sprinting seven elite athletes performed explosive one legged jump and sprint push offs kinematics ground reaction forces and el tromyography emg of leg muscles were recorded the mechanical output of six individu muscle groups was estimated by using hill based muscle models the emg and kinematics served as input to these models for jumping as well as for sprinting the model estimated similar results for the relative work contribution done about a joint due to transfer of power by the biarticular muscles rectus femoris showed a power transfer from hip to knee joint while in contrast hamstrings showed a power transfer from knee to hip joint regardless of these opposite directions of power transfer a net transfer occurred from the hip to the knee joint the relative work contribution of hamstrings done in hip extension was 7 in jumping and 11 in sprinting for rectus femoris the relative work contribution done in knee extension was 21 in jumping and 31 in sprinting power transferring actions by gastrocnemius from knee to ankle contributed 25 in jumping and 28 in sprinting to the work done in piantar flexion these results support the hypothesis that the action of biarticular muscles contributes to a net transfer of power from proximal to distal joints during explosive leg extensions this action of the biarticular muscles causes an efficient conversion of body segment rotations into the desired translation of the body centre of gravity

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

verification of infinite state dynamic systems using approximate quotient transition systems this paper deals with computational methods for verifying properties of labeled infinite state transition systems using quotient transition system qts a qts is a conservative approximation to the infinite state transition system based on a finite partition of the infinite state space for universal specifications positive verification for a qts implies the specification is true for the infinite state transition system we introduce the approximate qts or aqts the paper presents a sufficient condition for an aqts to be a bisimulation of the infinite state transition system an aqts bisimulation is essentially equivalent to the infinite state system for the purposes of verification it is well known however that finite state bisimulations do not exist for most hybrid systems of practical interest therefore the use of the aqts for verification of universal specifications is proposed and illustrated with an example this approach has been implemented in a tool for computer aided verification of a general class of hybrid systems

knee and ankle joint torque angle relationships of multi joint leg extension abstract the force length relation f l r is an important property of skeletal muscle to characterise its function whereas for in vivo human muscles torque angle relationships t a r represent the maximum muscular capacity as a function of joint angle however since in vivo force torque length data is only available for rotational single joint movements the purpose of the present study was to identify torque angle relationships for multi joint leg extension therefore inverse dynamics served for calculation of ankle and knee joint torques of 18 male subjects when performing maximum voluntary isometric contractions in a seated leg press measurements in increments of 10 knee angle from 30 to 100 knee flexion resulted in eight discrete angle configurations of hip knee and ankle joints for the knee joint we found an ascending descending t a r with a maximum torque of 289 5 43 3 n m which closely matches literature data from rotational knee extension in comparison to literature we observed a shift of optimum knee angle towards knee extension in contrast the t a r of the ankle joint vastly differed from relationships obtained for isolated plantar flexion for the ankle t a r derived from multi joint leg extension subjects operated over different sections of the force length curve but the ankle t a r derived from isolated joint efforts was over the ascending limb for all subjects moreover mean maximum torque of 234 7 56 6 n m exceeded maximal strength of isolated plantar flexion 185 7 27 8 n m from these findings we conclude that muscle function between isolated and more physiological multi joint tasks differs this should be considered for ergonomic and sports optimisation as well as for modelling and simulation of human movement

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

are the maximum shortening velocity and the shape parameter in a hill type model of whole muscle related to activation abstract mathematical models of the inter relationship of muscle force velocity and activation are useful in forward dynamic simulations of human movement tasks the objective of this work was to determine whether the parameters maximum shortening velocity v max and shape parameter k of a hill type muscle model interrelating muscle force velocity and activation are themselves dependent on the activation to fulfill this objective surface emg signals from four muscles as well as the kinematics and kinetics of the arm were recorded from 14 subjects who performed rapid release elbow extension tasks at 25 50 75 and 100 activation mvc the experimental elbow flexion angle was tracked by a forward dynamic simulation of the task in which v max and k of the triceps brachii were varied at each activation level to minimize the difference between the simulated and experimental elbow flexion angle because a preliminary analysis demonstrated no dependency of k on activation additional simulations were performed with constant k values of 0 15 0 20 and 0 25 the optimized values of v max normalized to the average value within a subject were then regressed onto the activation normalized v max depended significantly on the activation p k furthermore the estimated v max values were not sensitive to the selected k value the results support the use of hill type models in which v max depends on activation in forward dynamic simulations modeling muscles with mixed fiber type composition recruited in the range of 25 100 activation the use of more accurate models will lend greater confidence to the results of forward dynamic simulations

comparing different approaches for determining joint torque parameters from isovelocity dynamometer measurements strength or maximum joint torque is a fundamental factor governing human movement and is regularly assessed for clinical and rehabilitative purposes as well as for research into human performance this study aimed to identify the most appropriate protocol for fitting a maximum voluntary torque function to experimental joint torque data three participants performed maximum isometric and concentric eccentric knee extension trials on an isovelocity dynamometer and a separate experimental protocol was used to estimate maximum knee extension angular velocity a nine parameter maximum voluntary torque function which included angle angular velocity and neural inhibition effects was fitted to the experimental torque data and three aspects of this fitting protocol were investigated using an independent experimental estimate of maximum knee extension angular velocity gave lower variability in the high concentric velocity region of the maximum torque function compared to using dynamometer measurements alone a weighted root mean square difference rmsd score function that forced the majority 73 92 of experimental data beneath the maximum torque function was found to best account for the one sided noise in experimental torques resulting from sub maximal effort by the participants the suggested protocol an appropriately weighted rmsd score function and an independent estimate of maximum knee extension angular velocity gave a weighted rmsd of between 11 and 13 nm 4 5 of maximum isometric torque it is recommended that this protocol be used in generating maximum voluntary joint torque functions in all torque based modelling of dynamic human movement

the relation between the resultant moments at a joint and the moments measured by an isokinetic dynamometer isokinetic dynamometers have frequently been used to determine in vivo properties of human skeletal muscles in these investigations the moments recorded by the dynamometer were often implicitly assumed to be the same as the joint moments produced by muscles this assumption may have contributed to the conflicting results about in vivo muscle properties of human skeletal muscles that are reported in the literature the purpose of this paper is to present a method for calculating the resultant joint moments from the moments recorded using a cybex ii dynamometer and to determine the differences between these two moments for some typical exercise conditions the differences between these these moments are shown to be due to a gravitational effects b inertial effects and c non rigidity of the cybex arm shank foot system the results obtained suggest that the moments recorded using the dynamometer should not be used to derive muscle properties without taking into account the relationship between the resultant joint moments and the moments measured using an isokinetic dynamometer

a fully automated framework for control of linear systems from temporal logic specifications we consider the following problem given a linear system and a linear temporal logic ltl formula over a set of linear predicates in its state variables find a feedback control law with polyhedral bounds and a set of initial states so that all trajectories of the closed loop system satisfy the formula our solution to this problem consists of three main steps first we partition the state space in accordance with the predicates in the formula and construct a transition system over the partition quotient which captures our capability of designing controllers second using a procedure resembling model checking we determine runs of the transition system satisfying the formula third we generate the control strategy illustrative examples are included

formal analysis of piecewise affine systems through formula guided refinement we present a computational framework for identifying a set of initial states from which all trajectories of a piecewise affine pwa system with additive uncertainty satisfy a linear temporal logic ltl formula over a set of linear predicates in its state variables our approach is based on the construction and refinement of finite abstractions of infinite systems we derive conditions guaranteeing the equivalence of an infinite system and its finite abstraction with respect to a specific ltl formula and propose a method for the construction of such formula equivalent abstractions while provably correct the overall method is conservative and expensive a tool for pwa systems implementing the proposed procedure using polyhedral operations and analysis of finite graphs is made available examples illustrating the analysis of pwa models of gene networks are included

a comparison of muscle energy models for simulating human walking in three dimensions the popular hill model for muscle activation and contractile dynamics has been extended with several different formulations for predicting the metabolic energy expenditure of human muscle actions these extended models differ considerably in their approach to computing energy expenditure particularly in their treatment of active lengthening and eccentric work but their predictive abilities have never been compared in this study we compared the predictions of five different hill based muscle energy models in 3d forward dynamics simulations of normal human walking in a data tracking simulation that minimized muscle fatigue the energy models predicted metabolic costs that varied over a three fold range 2 45 7 15 j m kg with the distinction arising from whether or not eccentric work was subtracted from the net heat rate in the calculation of the muscle metabolic rate in predictive simulations that optimized neuromuscular control to minimize the metabolic cost all five models predicted similar speeds step lengths and stance phase durations however some of the models predicted a hip circumduction strategy to minimize metabolic cost while others did not and the accuracy of the predicted knee and ankle angles and ground reaction forces also depended on the energy model used the results highlights the need to clarify how eccentric work should be treated when calculating muscle energy expenditure the difficulty in predicting realistic metabolic costs in simulated walking even with a detailed 3d musculoskeletal model the potential for using such models to predict energetically optimal gait modifications and the room for improvement in existing muscle energy models and locomotion simulation frameworks

predicting maximum eccentric strength from surface emg measurements the origin of the well documented discrepancy between maximum voluntary and in vitro tetanic eccentric strength has yet to be fully understood this study aimed to determine whether surface emg measurements can be used to reproduce the in vitro tetanic force velocity relationship from maximum voluntary contractions five subjects performed maximal knee extensions over a range of eccentric and concentric velocities on an isovelocity dynamometer whilst emg from the quadriceps were recorded maximum voluntary mvc force length velocity data were estimated from the dynamometer measurements and a muscle model normalised amplitude length velocity data were obtained from the emg signals dividing the mvc forces by the normalised amplitudes generated emg corrected force length velocity data the goodness of fit of the in vitro tetanic force velocity function to the mvc and emg corrected forces was assessed based on a number of comparative scores the in vitro tetanic force velocity function provided a significantly better fit to the emg corrected forces compared to the mvc forces p or 0 05 furthermore the emg corrected forces generated realistic in vitro tetanic force velocity profiles a 58 19 increase in maximum eccentric strength is theoretically achievable through eliminating neural factors in conclusion emg amplitude can be used to estimate in vitro tetanic forces from maximal in vivo force measurements supporting neural factors as the major contributor to the difference between in vitro and in vivo maximal force

the phase boundary in dilute and random ising and potts ferromagnets the authors present an approach to dilute ising and potts models based on the fortuin kasteleyn random cluster representation which is simultaneously rigorous intuitive and surprisingly simple their analysis yields with no dimensional restrictions or other caveats the following asymptotic form of the phase boundary for the regular dilute model in which bonds have constant ferromagnetic coupling j with probability p and are vacant with probability 1 p the critical temperature scales as exp j ktc p approximately mod p pc mod implying that the crossover exponent is phi 1 if the constant couplings are replaced by a distribution f j with mass near j 0 quite different crossover behaviour is observed for example if f j approximately jalpha then for p near pc tc p approximately mod p pc mod 1 alpha

do relevant shear forces appear in isokinetic shoulder testing to be implemented in biomechanical models abstract isokinetic dynamometers measure joint torques about a single fixed rotational axis previous studies yet suggested that muscles produce both tangential and radial forces during a movement so that the contact forces exerted to perform this movement are multidirectional then isokinetic dynamometers might neglect the torque components about the two other euclidean space axes our objective was to experimentally quantify the shear forces impact on the overall shoulder torque by comparing the dynamometer torque to the torque computed from the contact forces at the hand and elbow ten healthy women performed isokinetic maximal internal external concentric eccentric shoulder rotation movements the hand and elbow contact forces were measured using two six axis force sensors the main finding is that the contact forces at the hand were not purely tangential to the direction of the movement effectiveness indexes from 0 26 0 25 to 0 54 0 20 such that the resulting shoulder torque computed from the two force sensors was three dimensional therefore the flexion and abduction components of the shoulder torque measured by the isokinetic dynamometer were significantly underestimated up to 94 9 these findings suggest that musculoskeletal models parameters should not be estimated without accounting for the torques about the three space axes

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

new solutions of the bethe ansatz equations for the isotropic and anisotropic spin 1 2 heisenberg chain bethe ansatz equations bae are investigated for the isotropic spin 1 2 heisenberg chain as well as the xxz chain with real solutions characterized by identical integers in the logarithmic form of the bae such states do not belong to the usual classification scheme string hypothesis they always exist in critical sectors with respect to the total spin of the chain and the anisotropy the conception of holes has to be changed in this case because there occur more holes than expected the finite size corrections for the xxx model are calculated including complex roots and the new type of real solutions with repeating integers the tower structure predicted by the hypothesis of conformal invariance is shown to remain unchanged

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

bisimilar linear systems the notion of bisimulation in theoretical computer science is one of the main complexity reduction methods for the analysis and synthesis of labeled transition systems bisimulations are special quotients of the state space that preserve many important properties expressible in temporal logics and in particular reachability in this paper the framework of bisimilar transition systems is applied to various transition systems that are generated by linear control systems given a discrete time or continuous time linear system and a finite observation map we characterize linear quotient maps that result in quotient transition systems that are bisimilar to the original system interestingly the characterizations for discrete time systems are more restrictive than for continuous time systems due to the existence of an atomic time step we show that computing the coarsest bisimulation which results in maximum complexity reduction corresponds to computing the maximal controlled or reachability invariant subspace inside the kernel of the observations map these results establish strong connections between complexity reduction concepts in control theory and computer science

formal analysis of discrete time piecewise affine systems in this technical note we study temporal logic properties of trajectories of discrete time piecewise affine pwa systems specifically given a pwa system and a linear temporal logic formula over regions in its state space we attempt to find the largest region of initial states from which all trajectories of the system satisfy the formula our method is based on the iterative computation and model checking of finite quotients we illustrate our method by analyzing pwa models of two synthetic gene networks

bethe equation at q 0 moebius inversion formula and weight multiplicities ii x_n case the uq sl 2 bethe equation is studied at q 0 a linear congruence equation is proposed related to the string so lutions the number of its off diagonal solutions is expressed in terms of an explicit combinatorial formula and coincides with the weight multiplicities of the quantum space

deformed strings in the heisenberg model we investigate solutions to the bethe equations for the isotropic s 1 2 heisenberg chain involving complex string like rapidity configurations of arbitrary length going beyond the traditional string hypothesis of undeformed strings we describe a general procedure to construct eigenstates including strings with generic deformations discuss general features of these solutions and provide a number of explicit examples including complete solutions for all wavefunctions of short chains we finally investigate some singular cases and show from simple symmetry arguments that their contribution to zero temperature correlation functions vanishes

modelling suppressed muscle activation by means of an exponential sigmoid function validation and bounds the aim of this study was to establish how well a three parameter sigmoid exponential function difact follows experimentally obtained voluntary neural activation angular velocity profiles and how robust it is to perturbed levels of maximal activation six male volunteers age 26 3 2 73 years were tested before and after an 8 session 3 week training protocol torque angular velocity t and experimental voluntary neural drive angular velocity va datasets obtained via the interpolated twitch technique were determined from pre and post training testing sessions non linear regression fits of the product of difact and a hill type tetanic torque function and of the difact function only were performed on the pre and post training t and va datasets for three different values of the difact upper bound max 100 95 90 the determination coefficients r2 and the rms of the fits were compared using a two way mixed anova and results showed that there was no significant difference p 0 05 due to changing max values indicating the difact remains robust to changes in maximal activation mean r2 values of 0 95 and 0 96 for pre and post training sessions show that the maximal voluntary torque function successfully reproduces the t raw dataset

maximum voluntary joint torque as a function of joint angle and angular velocity model development and application to the lower limb measurements of human strength can be important during analyses of physical activities such measurements have often taken the form of the maximum voluntary torque at a single joint angle and angular velocity however the available strength varies substantially with joint position and velocity when examining dynamic activities strength measurements should account for these variations a model is presented of maximum voluntary joint torque as a function of joint angle and angular velocity the model is based on well known physiological relationships between muscle force and length and between muscle force and velocity and was tested by fitting it to maximum voluntary joint torque data from six different exertions in the lower limb isometric concentric and eccentric maximum voluntary contractions were collected during hip extension hip flexion knee extension knee flexion ankle plantar flexion and dorsiflexion model parameters are reported for each of these exertion directions by gender and age group this model provides an efficient method by which strength variations with joint angle and angular velocity may be incorporated into comparisons between joint torques calculated by inverse dynamics and the maximum available joint torques