in vivo estimation of the glenohumeral joint rotation center from scapular bony landmarks by linear regression in this paper a method is described for in vivo prediction of the glenohumeral joint rotation center gh r necessary for the construction of a humerus local coordinate system in shoulder kinematic studies the three dimensional positions of five scapula bony landmarks as well as a large number of data points on the surface of the glenoid and humeral head were collected at 36 sets of cadaver scapulae and adjacent humeri the position of gh r in each scapula was estimated by mathematically fitting spheres to the glenoid and humeral head gh r prediction from scapula geometry parameters by linear regression resulted in a rmse between measured and predicted gh r of 2 32 mm for the x coordinate 2 69 mm for the y coordinate and 3 04 mm for the z coordinate application in vivo revealed a random humerus orientation error due to measurement inaccuracies of 1 35 0 29 and 1 26 degrees standard deviation per rotation angle the estimated total humerus orientation error including the offset error due to the regression model inaccuracy was 2 86 0 84 and 2 69 degrees standard deviation as these errors were about 15 and 20 of respectively the intra and inter subject variability of the humerus orientations measured it is concluded that the method described in this paper allows for an adequate construction of a humerus local coordinate system

sub riemannian heat kernels and mean curvature flow of graphs abstract we introduce a sub riemannian analogue of the bence merriman osher algorithm merriman et al 1992 42 and show that it leads to weak solutions of the horizontal mean curvature flow of graphs over sub riemannian carnot groups the proof follows the nonlinear semi group theory approach originally introduced by l c evans 1993 27 in the euclidean setting and is based on new results on the relation between sub riemannian heat flows of characteristic functions of subgraphs and the horizontal mean curvature of the corresponding graphs

on the exponential decay of the n point correlation functions and the analyticity of the pressure the goal of this paper is to provide estimates leading to a direct proof of the exponential decay of the n point correlation functions for certain unbounded models of kac type the methods are based on estimating higher order derivatives of the solution of the witten laplacian equation on 1 forms associated with the hamiltonian of the system we also provide a formula for the taylor coefficients of the pressure that is suitable for a direct proof of the analyticity

tangent bundle elastica and computer vision visual curve completion an early visual process that completes the occluded parts between observed boundary fragments a k a inducers is a major problem in perceptual organization and a critical step toward higher level visual tasks in both biological and machine vision most computational contributions to solving this problem suggest desired perceptual properties that the completed contour should satisfy in the image plane and then seek the mathematical curves that provide them alternatively few studies including by the authors have suggested to frame the problem not in the image plane but rather in the unit tangent bundler 2 s 1 the space that abstracts the primary visual cortex where curve completion allegedly occurs combining both schools here we propose and develop a biologically plausible theory of elastica in the tangent bundle that provides not only perceptually superior completion results but also a rigorous computational prediction that inducer curvatures greatly affects the shape of the completed curve as indeed indicated by human perception

cluster expansion for abstract polymer models a new direct proof of convergence of cluster expansions for polymer contour models is given in an abstract setting it does not rely on kirkwood salsburg type equations or combinatorics of trees a distinctive feature is that at all steps the considered clusters contain every polymer at most once

isotropic hypoellipticity and trend to equilibrium for the fokker planck equation with a high degree potential we consider the fokker planck equation with a confining or anti confining potential which behaves at infinity like a possibly high degree homogeneous function hypoellipticity techniques provide the well posedness of the weak cauchy problem in both cases as well as instantaneous smoothing and exponential trend to equilibrium lower and upper bounds for the rate of convergence to equilibrium are obtained in terms of the lowest positive eigenvalue of the corresponding witten laplacian with detailed applications

on homogenization and scaling limit of some gradient perturbations of a massless free field we study the continuum scaling limit of some statistical mechanical models defined by convex hamiltonians which are gradient perturbations of a massless free field by proving a central limit theorem for these models we show that their long distance behavior is identical to a new homogenized continuum massless free field we shall also obtain some new bounds on the 2 point correlation functions of these models

adjustments to zatsiorsky seluyanov s segment inertia parameters zatsiorsky et al in contemporary problems in biomechanics pp 272 291 crc press massachusetts 1990a obtained by means of a gamma ray scanning technique the relative body segment masses center of mass cm positions and radii of gyration for samples of college aged caucasian males and females although these data are the only available and comprehensive set of inertial parameters regarding young adult caucasians they have been rarely utilized for biomechanical analyses of subjects belonging to the same or a similar population the main reason is probably that zatsiorsky et al used bony landmarks as reference points for locating segment cms and defining segment lengths some of these landmarks were markedly distant from the joint centers currently used by most researchers as reference points the purpose of this study was to adjust the mean relative cm positions and radii of gyration reported by zatsiorsky et al in order to reference them to the joint centers or other commonly used landmarks rather than the original landmarks the adjustments were based on a number of carefully selected sources of anthropometric data

correlation at low temperature ii asymptotics the present paper is a continuation of ref 4 where the truncated two point correlation function for a class of lattice spin systems was proved to have exponential decay at low temperature under a weak coupling assumption in this paper we compute the asymptotics of the correlation function as the temperature goes to zero this paper thus extends ref 3 in two directions the hamiltonian function is allowed to have several local minima other than a unique global minimum and we do not require translation invariance of the hamiltonian function we are in particular able to handle spin systems on a general lattice

pde with random coefficients and euclidean field theory in this paper a new proof of an identity of giacomin olla and spohn is given the identity relates the 2 point correlation function of a euclidean field theory to the expectation of the green s function for a pde with random coefficients the euclidean field theory is assumed to have convex potential an inequality of brascamp and lieb therefore implies gaussian bounds on the fourier transform of the 2 point correlation function by an application of results from random pde the previously mentioned identity implies pointwise gaussian bounds on the 2 point correlation function

remarks on decay of correlations and witten laplacians brascamp lieb inequalities and semiclassical limit as it appears in recent articles by helffer or sjostrand and naddaf spencer the analysis in the context of the statistical mechanics of measures of the type exp x dxis connected with the analysis of suitable witten laplacians on 1 forms for illustrating this point of view we present here remarks about the brascamp lieb inequalities and its extensions and prove the decay of the correlation in some cases when is weakly non convex

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

validation of net joint loads calculated by inverse dynamics in case of complex movements application to balance recovery movements the joint forces and moments driving the motion of a human subject are classically computed by an inverse dynamic calculation however even if this process is theoretically simple many sources of errors may lead to huge inaccuracies in the results moreover a direct comparison with in vivo measured loads or with gold standard values from literature is only possible for very specific studies therefore assessing the inaccuracy of inverse dynamic results is not a trivial problem and a simple method is still required this paper presents a simple method to evaluate both 1 the consistency of the results obtained by inverse dynamics 2 the influence of possible modifications in the inverse dynamic hypotheses this technique concerns recursive calculation performed on full kinematic chains and consists in evaluating the loads obtained by two different recursive strategies it has been applied to complex 3d whole body movements of balance recovery a recursive newton euler procedure was used to compute the net joint loads two models were used to represent the subject bodies considering or not the upper body as a unique rigid segment the inertial parameters of the body segments were estimated from two different sets of scaling equations de leva p 1996 adjustments to zatsiorsky suleyanov s segment inertia parameters journal of biomechanics 29 1223 1230 dumas r cheze l verriest j p 2006b adjustments to mcconville et al and young et al body segment inertial parameters journal of biomechanics in press using this comparison technique it has been shown that for the balance recovery motions investigated 1 the use of the scaling equations proposed by dumas et al instead of those proposed by de leva improves the consistency of the results average relative influence up to 30 for the transversal moment 2 the arm motions dynamically influence the recovery motion in a non negligible way average relative influence up to 15 and 30 for the longitudinal force and the transversal moment respectively

supersymmetry and morse theory it is shown that the morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics hamiltonian some of the implications of modern ideas in mathematics for supersymmetric theories are discussed

on the correlation for kac like models in the convex case the aim of this paper is to stu the behavior asm tends to of a family of measures exp m x dx m on m where m is a potential on m which is a perturbation in a suitable sense of the harmonic potential j x j 2

regression equations to predict segmental moments of inertia from anthropometric measurements an extension of the data of chandler et al 1975 a set of regression equations was developed to fully utilize the data of chandler et al amrl technical report 74 137 wright patterson air force base 1975 to estimate segmental moments of inertia in living subjects using anthropometric measurements as predictors moments of inertia can be computed about both transverse and longitudinal axes passing through each segment s center of mass symmetry about segment long axes is assumed because of the small sample size upon which these equations are based it is suggested that they be used cautiously especially to avoid extrapolation to subjects having anthropometric measurements outside the range of sample values

edge universality of beta ensembles we prove the edge universality of the beta ensembles for any beta ge 1 provided that the limiting spectrum is supported on a single interval and the external potential is fancyscript c 4 and regular we also prove that the edge universality holds for generalized wigner matrices for all symmetry classes moreover our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class fancyscript c 4

a note on the decay of correlations under δ pinning we prove that for a class of massless interface models on 2 introduction of an arbitrarily small pinning self potential leads to exponential decay of correlation or in other words to creation of mass

renormalization group analysis of spectral problems in quantum field theory abstract in this paper we present a self contained and detailed exposition of the new renormalization group technique proposed in 1 2 its main feature is that the renormalization group transformation acts directly on a space of operators rather than on objects such as a propagator the partition function or correlation functions we apply this renormalization transformation to a hamiltonian describing the physics of an atom interacting with the quantized electromagnetic field and we prove that excited atomic states turn into resonances when the coupling between electrons and field is nonvanishing

spectral theory of pauli fierz operators abstract we study spectral properties of pauli fierz operators which are commonly used to describe the interaction of a small quantum system with a bosonic free field we give precise estimates of the location and multiplicity of the singular spectrum of such operators applications of these estimates which will be discussed elsewhere concern spectral and ergodic theory of non relativistic qed our proof has two ingredients the feshbach method which is developed in an abstract framework and mourre theory applied to the operator restricted to the sector orthogonal to the vacuum

mean field bounds and correlation inequalities i prove a new correlation inequality for a class ofn component classical ferromagnets 1 n 4 this inequality implies that the correlation functions decay exponentially and the spontaneous magnetization is zero above the mean field critical temperature

expansions in statistical physics on presente un traitement auto contenu du developpement polymere on axiomatise cette notion on demontre comment ces developpements permettent un traitement systematique de la plupart des developpements en amas de la physique statistique

smooth feshbach map and operator theoretic renormalization group methods abstract a new variant of the isospectral feshbach map defined on operators in hilbert space is presented it is constructed with the help of a smooth partition of unity instead of projections and is therefore called smooth feshbach map it is an effective tool in spectral and singular perturbation theory as an illustration of its power a novel operator theoretic renormalization group method is described and applied to analyze a general class of hamiltonians on fock space the main advantage of the new renormalization group method over its predecessors is its technical simplicity which it owes to the use of the smooth feshbach map

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

segment interaction in sprint start analysis of 3d angular velocity and kinetic energy in elite sprinters the aim of the present study was to measure during a sprint start the joint angular velocity and the kinetic energy of the different segments in elite sprinters this was performed using a 3d kinematic analysis of the whole body eight elite sprinters 10 30 0 14s 100 m time equipped with 63 passive reflective markers realised four maximal 10 m sprints start on an indoor track an opto electronic motion analysis system consisting of 12 digital cameras 250 hz was used to collect the 3d marker trajectories during the pushing phase on the blocks the 3d angular velocity vector and its norm were calculated for each joint the kinetic energy of 16 segments of the lower and upper limbs and of the total body was calculated the 3d kinematic analysis of the whole body demonstrated that joints such as shoulders thoracic or hips did not reach their maximal angular velocity with a movement of flexion extension but with a combination of flexion extension abduction adduction and internal external rotation the maximal kinetic energy of the total body was reached before clearing block respectively 537 59 3 j vs 514 9 66 0 j p or 0 01 these results suggested that a better synchronization between the upper and lower limbs could increase the efficiency of pushing phase on the blocks besides to understand low interindividual variances in the sprint start performance in elite athletes a 3d complete body kinematic analysis shall be used

around a stationary phase theorem in large dimension in this article we want to present a stationary phase theorem appearing in a recent article by j sjostrand ann inst h poincare phys theor in press and explain the role it can play in the context of statistical mechanics this theorem is also technically connected to the semi classical determination of eigenvalues for a schrodinger operator in large dimension and also in the same spirit with small or large temperature expansions

completely analytical interactions constructive description an interactionu is called a completely analytical ca interaction if it satisfies one of 12 given conditions formulated in terms of analyticity properties of the partition functions zv u or correlation decay or truncated correlation bounds or asymptotic behavior of ln zv u v the 12 conditions are presented together with part of the proof of their equivalence the main result of the paper is that each condition is constructive in the following sense instead of checking it in all finite volumesv v it is enough to consider only a finite amount of volumes with restricted size in particular the partition functions z v u for the complex perturbationsu ofu do not vanish for all v v and all with provided this is true only forv with diam v c and but with

comparison of global and joint to joint methods for estimating the hip joint load and the muscle forces during walking a three dimensional musculoskeletal model of the lower limb was developed to study the influence of biarticular muscles on the muscle force distribution and joint loads during walking a complete walking cycle was recorded for 9 healthy subjects using the standard optoelectronic motion tracking system ground contact forces were also measured using a 6 axes force plate inverse dynamics was used to compute net joint reactions forces and torques in the lower limb a static optimization method was then used to estimate muscle forces two different approaches were used in the first one named global method the biarticular muscles exerted a torque on the two joints they spanned at the same time and in the second one called joint by joint method these biarticular muscles were divided into two mono articular muscles with geometrical insertion origin via points and physiological properties remained unchanged the hip joint load during the gait cycle was then calculated taking into account the effect of muscle contractions the two approaches resulted in different muscle force repartition the biarticular muscles were favoured over any set of single joint muscles with the same physiological function when using the global method while the two approaches yielded only little difference in the resultant hip load the examination of muscle power showed that biarticular muscles could produce positive work at one joint and negative work at the other transferring energy between body segments and thus decreasing the metabolic cost of movement

cortical spatiotemporal dimensionality reduction for visual grouping the visual systems of many mammals including humans are able to integrate the geometric information of visual stimuli and perform cognitive tasks at the first stages of the cortical processing this is thought to be the result of a combination of mechanisms which include feature extraction at the single cell level and geometric processing by means of cell connectivity we present a geometric model of such connectivities in the space of detected features associated with spatiotemporal visual stimuli and show how they can be used to obtain low level object segmentation the main idea is to define a spectral clustering procedure with anisotropic affinities over data sets consisting of embeddings of the visual stimuli into higher dimensional spaces neural plausibility of the proposed arguments will be discussed

the structure of fluctuations in stochastic homogenization four quantities are fundamental in homogenization of elliptic systems in divergence form and in its applications the field and the flux of the solution operator applied to a general deterministic right hand side and the field and the flux of the corrector homogenization is the study of the large scale properties of these objects in case of random coefficients these quantities fluctuate and their fluctuations are a priori unrelated depending on the law of the coefficient field and in particular on the decay of its correlations on large scales these fluctuations may display different scalings and different limiting laws if any in this contribution we identify another crucial intrinsic quantity motivated by h convergence which we refer to as the homogenization commutator and is related to variational quantities first considered by armstrong and smart in the simplified setting of the random conductance model we show what we believe to be a general principle namely that the homogenization commutator drives at leading order the fluctuations of each of the four other quantities in a strong norm in probability which is expressed in form of a suitable two scale expansion and reveals the pathwise structure of fluctuations in stochastic homogenization in addition we show that the rescaled homogenization commutator converges in law to a gaussian white noise and we analyze to which precision the covariance tensor that characterizes the latter can be extracted from the representative volume element method this collection of results constitutes a new theory of fluctuations in stochastic homogenization that holds in any dimension and yields optimal rates extensions to the non symmetric continuum setting are also discussed the details of which are postponed to forthcoming works

on the spectrum of semi classical witten laplacians and schrodinger operators in large dimension we investigate the low lying spectrum of witten laplacians on forms of arbitrary degree in the semi classical limit and uniformly in the space dimension we show that under suitable assumptions implying that the phase function has a unique local minimum one obtains a number of clusters of discrete eigenvalues at the bottom of the spectrum moreover we are able to count the number of eigenvalues in each cluster we apply our results to certain sequences of schrodinger operators having strictly convex potentials and show that some well known results of semi classical analysis hold also uniformly in the dimension

witten laplacian method for the decay of correlations the aim of this paper is to apply direct methods to the study of integrals that appear naturally in statistical mechanics and euclidean field theory we provide weighted estimates leading to the exponential decay of the two point correlation functions for certain classical convex unbounded models the methods involve the study of the solutions of the witten laplacian equations associated with the hamiltonian of the system

correlation at low temperature i exponential decay abstract the present paper generalizes the analysis in ann h poincare 1 2000 59 math j ams 8 1997 123 of the correlations for a lattice system of real valued spins at low temperature the gibbs measure is assumed to be generated by a fairly general hamiltonian function with pair interaction the novelty as compared to 2 20 is that the single site self energies of the spins are not required to have only a single local minimum and no other extrema our derivation of exponential decay of correlations goes through the spectral analysis of a deformed laplacian closely related to the witten laplacian studied in 2 20 we prove that this laplacian has a spectral gap above zero and argue that this implies exponential decay of the correlations

grad o perturbations of massless gaussian fields we investigate weak perturbations of the continuum massless gaussian measure by a class of approximately local analytic functionals and use our general results to give a new proof that the pressure of the dilute dipole gas is analytic in the activity

semi classical analysis for the transfer operator formal wkb constructions in large dimension this paper is devoted to problems coming from statistical mechanics the transfer matrix or transfer operator approach consists in reducing the analysis of asymptotic properties of statistical systems to the analysis of the spectral properties of their transfer operator sometimes the new problem appears to have a semi classical nature although the problem is similar to the semiclassical study of kac s operator presented in our paper with m brunaud bruhe which was devoted to the study of for h small new features appear for the model our first results concern semi classical analysis of the ground state for this second operator we then analyze the two models in the large dimension situation one basic technique is sjostrand s formalism of the 0 standard functions as introduced in sj5 the one dimensional case was presented in he11

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

a new method for estimating joint parameters from motion data joint centers and axes of rotation joint parameters are central to all branches of movement analysis in gait analysis the standard protocol used to determine hip and knee joint parameters is prone to errors arising from palpation anthropometric regression equations and misplaced alignment devices several alternative methods have been proposed but to date none have been shown to be accurate and reliable enough for use in the clinical setting this article describes a new method for joint parameter estimation the new method can be summarized as follows i the motions of two adjacent segments spanning a single joint are tracked ii the axis of rotation between every pair of observed segment configurations is computed iii the most likely intersection of all axes effective joint center and most likely orientation of the axes effective joint axis is found initial validation of the method was conducted on a hinged mechanical analog and a single healthy adult subject for the analog the center was found to be within 3 8 mm of the geometric center and 2 0 degrees of the geometric axis standard deviation for the adult subject hip centers varied on the order of 1 3 mm knee centers by 3 9 mm and knee axes by 2 0 degrees the results suggest that the new method is an objective precise and practical alternative to the standard clinical approach

a strong central limit theorem for a class of random surfaces this paper is concerned with d 2 dimensional lattice field models with action v nabla phi cdot where v mathbf r d rightarrow mathbf r is a uniformly convex function the fluctuations of the variable phi 0 phi x are studied for large x via the generating function given by g x mu ln langle e mu phi 0 phi x rangle a in two dimensions g x mu partial 2g x mu partial mu 2 is proportional to ln vert x vert the main result of this paper is a bound on g x mu partial 3 g x mu partial mu 3 which is uniform in vert x vert for a class of convex v the proof uses integration by parts following helffer sjostrand and witten and relies on estimates of singular integral operators on weighted hilbert spaces

toward isometric force capabilities evaluation by using a musculoskeletal model comparison with direct force measurement abstract developing formalisms to determine force capabilities of human limbs by using musculoskeletal models could be useful for biomechanical and ergonomic applications in this framework the purpose of this study was to compare measured maximal isometric force capabilities at the hand in a set of cartesian directions with forces computed from a musculoskeletal model of the upper limb the results were represented under the form of a measured force polytope mfp and a musculoskeletal force polytope msfp both of them were obtained from the convex hull of measured and simulated force vectors endpoints nine subjects participated to the experiment for one posture recorded with an optoelectronic system maximum isometric forces exerted at the hand were recorded in twenty six directions of the cartesian space with a triaxial force sensor results showed significant differences between the polytopes global shapes the msfp was more elongated than the mfp concerning the polytopes volumes no significant difference was found mean maximal isometric forces provided by mfp and msfp were 509 6 118 4 n and 627 9 73 3 n respectively moreover the angle between the main axes of the two polytopes was 5 5 2 3 on average finally rms error values between mfp and msfp were lower than 100 n in 88 of the considered directions the proposed msfp based on a musculoskeletal model gave interesting information on optimal force orientation parameters the possible applications in the frame of ergonomics rehabilitation and biomechanics are proposed and discussed

validation of a functional method for the estimation of hip joint centre location the present study assesses the accuracy with which the subject specific coordinates of the hip joint centre hjc in a pelvic anatomical frame can be estimated using different methods the functional method was applied by calculating the centre of the best sphere described by the trajectory of markers placed on the thigh during several trials of hip rotations different prediction methods proposed in the literature and in the present investigation which estimate the hjc of adult subjects using regression equations and anthropometric measurements were also assessed the accuracy of each of the above mentioned methods was investigated by comparing their predictions with measurements obtained on a sample of 11 male adult able bodied volunteers using roentgen stereophotogrammetric analysis rsa assumed to provide the true hjc locations prediction methods estimated the hjc location at an average rms distance of 25 30 mm the functional method performed significantly better and estimated hjcs within a rms distance of 13 mm on average this result may be confidently generalised if the photogrammetric experiment is carefully conducted and an optimal analytical approach used the method is therefore suggested for use in motion analysis when the subject s hip range of motion is not limited in addition the facts that it is not an invasive technique and that it has relatively small and un biased errors make it suitable for regression equations identification with no limit to sample size and population typology

large deviations and concentration properties for ϕ interface models we consider the massless field with zero boundary conditions outside d n d d n n d a suitable subset of d i e the continuous spin gibbs measure n on d n with hamiltonian given by h x y x y 1 v x y and x 0 for x d n c the interaction v is taken to be strictly convex and with bounded second derivative this is a standard effective model for a d 1 dimensional interface represents the height of the interface over the base d n due to the choice of scaling of the base we scale the height with the same factor by setting n n we study various concentration and relaxation properties of the family of random surfaces n and of the induced family of gradient fields n n as the discretization step 1 n tends to zero n in particular we prove a large deviation principle for n and show that the corresponding rate function is given by d u x dx where is the surface tension of the model this is a multidimensional version of the sample path large deviation principle we use this result to study the concentration properties of n under the volume constraint i e the constraint that 1 n d x dn n x stays in a neighborhood of a fixed volume v 0 and the hard wall constraint i e n x 0 for all x this is therefore a model for a droplet of volume v lying above a hard wall we prove that under these constraints the field n of rescaled heights concentrates around the solution of a variational problem involving the surface tension as it would be predicted by the phenomenological theory of phase boundaries our principal result however asserts local relaxation properties of the gradient field n n to the corresponding extremal gibbs states thus our approach has little in common with traditional large deviation techniques and is closer in spirit to hydrodynamic limit type of arguments the proofs have both probabilistic and analytic aspects essential analytic tools are p estimates for elliptic equations and the theory of young measures on the side of probability tools a central role is played by the helffer sjostrand 31 pde representation for continuous spin systems which we rewrite in terms of random walk in random environment and by recent results of t funaki and h spohn 25 on the structure of gradient fields

the visual cortex is a contact bundle it is now generally accepted among neuroscientists that the sensory cortex of the brain is arranged in a structure that is simultaneously topographic a pointwise mapping layered and columnar the microcolumns in the columnar structure exhibit both a directional and an areal response in addition to the pointwise one it is shown that these directional areal response fields are contact elements upon the visual manifold that generate visual contours as the lifts of the form stimuli upon the retina into a contact bundle embodied in the visual cortex itself those invariances of form perception termed the psychological constancies shape size motion color constancies etc represent the action of the conformal group co 1 3 upon the visual manifold it follows that the connection for the cortical contact bundle is a lie group connection the paper closes with an axiomatic treatment of visual perception and expression of riegel s dialectical psychology in terms of the symmetric difference operation to provide an association between perceptual and cognitive function

equilibrium fluctuations for nabla_ varphi interface model we study the large scale space time fluctuations of an interface which is modeled by a massless scalar field with reversible langevin dynamics for a strictly convex interaction potential we prove that on a large space time scale these fluctuations are governed by an infinite dimensional ornstein uhlenbeck process its effective diffusion type covariance matrix is characterized through a variational formula

the additive structure of elliptic homogenization one of the principal difficulties in stochastic homogenization is transferring quantitative ergodic information from the coefficients to the solutions since the latter are nonlocal functions of the former in this paper we address this problem in a new way in the context of linear elliptic equations in divergence form by showing that certain quantities associated to the energy density of solutions are essentially additive as a result we are able to prove quantitative estimates on the weak convergence of the gradients fluxes and energy densities of the first order correctors under blow down which are optimal in both scaling and stochastic integrability the proof of the additivity is a bootstrap argument completing the program initiated in armstrong et al commun math phys 347 2 315 361 2016 using the regularity theory recently developed for stochastic homogenization we reduce the error in additivity as we pass to larger and larger length scales in the second part of the paper we use the additivity to derive central limit theorems for these quantities by a reduction to sums of independent random variables in particular we prove that the first order correctors converge in the large scale limit to a variant of the gaussian free field

a three dimensional kinematic and dynamic model of the lower limb a model describing the kinematics and dynamics of the lower limb is presented the lower limb is modeled as a sequence of four rigid links connected by three universal rotary joints representing the hip knee and ankle joints each joint is modeled as a sequence of three single axis rotational joints thus ascribing to the lower limb a total of 12 degrees of freedom a method is described to measure the gait variables so that all nine angles can be computed based on the positions of nine markers placed on the subject during a gait study the gait variables are then used in an iterative newton euler formulation to compute the moments exerted about the axes of each joint during gait

the glenohumeral joint rotation centre in vivo within the framework of the current call for standardization in upper extremity research three methods to determine the glenohumeral joint rotation centre in vivo were tested therefore subjects performed humeral movements while a 3d electromagnetic tracking device registered the motion of the humerus with respect to the scapula for the first method to estimate the glenohumeral joint rotation centre five scapular bony landmarks served as input to regression equations the second method fitted a sphere through the humeral position data and the third method calculated the rotation centre determining an optimal helical axis the experiment consisted of two parts at first one subject was measured 10 times subsequently one observer measured 10 subjects twice and another observer measured these subjects once the first part of the experiment demonstrated that all methods are capable to reproduce the rotation centre within 4mm but the location of the centre differed significantly between methods p 0 001 the second part showed that inter and intra observer reliability was sufficiently for the sphere fitting method and for the helical axes method the two observations of one observer differed significantly p 0 008 using the regression method the authors prefer the helical axes method it is a reliable and valid method which can be applied in movement registration of healthy subjects and patients with a shoulder endoprosthesis it can be applied in hinge joints to determine a rotation axis instead of a rotation centre which is desirable in standardized upper extremity research and calculation time is short

a constrained extended kalman filter for the optimal estimate of kinematics and kinetics of a sagittal symmetric exercise this paper presents a method for real time estimation of the kinematics and kinetics of a human body performing a sagittal symmetric motor task which would minimize the impact of the stereophotogrammetric soft tissue artefacts sta the method is based on a bi dimensional mechanical model of the locomotor apparatus the state variables of which joint angles velocities and accelerations and the segments lengths and inertial parameters are estimated by a constrained extended kalman filter cekf that fuses input information made of both stereophotogrammetric and dynamometric measurement data filter gains are made to saturate in order to obtain plausible state variables and the measurement covariance matrix of the filter accounts for the expected sta maximal amplitudes we hypothesised that the ensemble of constraints and input redundant information would allow the method to attenuate the sta propagation to the end results the method was evaluated in ten human subjects performing a squat exercise the cekf estimated and measured skin marker trajectories exhibited a rms difference lower than 4mm thus in the range of stas the rms differences between the measured ground reaction force and moment and those estimated using the proposed method 9n and 10nm were much lower than obtained using a classical inverse dynamics approach 22n and 30nm from the latter results it may be inferred that the presented method allows for a significant improvement of the accuracy with which kinematic variables and relevant time derivatives model parameters and therefore intersegmental moments are estimated

the log sobolev inequality for unbounded spin systems abstract in this note we would like to give a proof of log sobolev inequality for un bounded spin systems with weaker assumptions on the potentials than previously obtained

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

mass center of mass and moment of inertia estimates for infant limb segments to quantify limb dynamics accurate estimates are needed of anthropometric inertia parameters mass center of mass location and moments of inertia these estimates however are not available for human infants therefore the movement dynamics of infants have not been studied extensively here regression equations for the masses center of mass locations and transverse moments of inertia of upper and lower limb segments upper arm forearm and hand thigh leg and foot of 0 04 to 1 50 yr old infants are provided a mathematical model of the human body was used to determine the anthropometric inertia parameters for upper limbs in 44 infants and for lower limbs in 70 infants stepwise linear regressions were used to fit the distributions of the anthropometric inertia parameters the regression equations accounted for significant amounts of the variance 64 98 and the r2 values compared favorably when our equations were cross validated consequently these regression equations can provide for infants of similar ages reasonable estimates of upper and lower limb anthropometric inertia parameters suitable for equations of motion in the analysis of limb dynamics in human infants

high temperature differentiability of lattice gibbs states by dobrushin uniqueness techniques we establish conditions for the differentiability to any order of the gibbs states of classical lattice systems with arbitrary compact single spin space and with interactions in the dobrushin uniqueness region the derivatives are expressed as series expansions and are shown to be continuous on the uniqueness region we also provide a procedure for estimating the size of the derivatives these results verify a conjecture of l gross and extend his results in absence of second order phase transitions in the dobrushin uniqueness region journal of statistical physics25 1 57 72 1981 the techniques of this paper are based on those employed by gross

correlation structure of the corrector in stochastic homogenization recently the quantification of errors in the stochastic homogenization of divergence form operators has witnessed important progress our aim now is to go beyond error bounds and give precise descriptions of the effect of the randomness in the large scale limit this paper is a first step in this direction our main result is to identify the correlation structure of the corrector in dimension 33 and higher this correlation structure is similar to but different from that of a gaussian free field

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

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

on estimating the derivatives of symmetric diffusions in stationary random environment with applications to ϕ interface model we consider diffusions on d or random walks on d in a random environment which is stationary in space and in time and with symmetric and uniformly elliptic coefficients we show existence and holder continuity of second space derivatives and time derivatives for the annealed kernels of such diffusions and give estimates for these derivatives in the case of random walks these estimates are applied to the ginzburg landau interface model

methods for investigating the sensitivity of joint resultants to body segment parameter variations two methods are presented for determining the sensitivity of joint resultants to variations in body segment parameters bsps when solving inverse dynamics problems the exact sampling method esm and the approximate variational method avm these methods are illustrated by applying them to a single segment in fixed axis rotation the results indicate that a the avm provides first order linear approximations to the total variations in joint resultants obtained when using the esm b the esm should be used when bsp variations become large and higher order terms in these variations can no longer be ignored as negligible in the bsp dependent expansions for the joint resultants c small percent variations in bsps can propagate into considerably larger percent variations in the joint resultants obtained when solving inverse dynamics problems and d if bsp variations are sufficiently small to allow nonlinear terms in these variations to be ignored as negligible the avm is much simpler and easier to use than the esm

universal estimate of the gap for the kac operator in the convex case the aim of this paper is to prove that ifv is a strictly convex potential with quadratic behavior at then the quotient 2 1 between the largest eigenvalue and the second eigenvalue of the kac operator defined on l2 m by exp v x 2 exp x exp v x 2 where x is the laplacian on m satisfies the condition mu 2 mathord left vphantom mu 2 mu 1 leqslant exp cosh 1 sigma 1 mathord left vphantom leqslant exp cosh 1 sigma 1 2 right kern nulldelimiterspace 2 right kern nulldelimiterspace mu 1 leqslant exp cosh 1 sigma 1 mathord left vphantom leqslant exp cosh 1 sigma 1 2 right kern nulldelimiterspace 2 where is such that hessv x 0

a tangent bundle theory for visual curve completion visual curve completion is a fundamental perceptual mechanism that completes the missing parts e g due to occlusion between observed contour fragments previous research into the shape of completed curves has generally followed an axiomatic approach where desired perceptual geometrical properties are first defined as axioms followed by mathematical investigation into curves that satisfy them however determining psychophysically such desired properties is difficult and researchers still debate what they should be in the first place instead here we exploit the observation that curve completion is an early visual process to formalize the problem in the unit tangent bundle r2 s1 which abstracts the primary visual cortex v1 and facilitates exploration of basic principles from which perceptual properties are later derived rather than imposed exploring here the elementary principle of least action in v1 we show how the problem becomes one of finding minimum length admissible curves in r2 s1 we formalize the problem in variational terms we analyze it theoretically and we formulate practical algorithms for the reconstruction of these completed curves we then explore their induced visual properties vis a vis popular perceptual axioms and show how our theory predicts many perceptual properties reported in the corresponding perceptual literature finally we demonstrate a variety of curve completions and report comparisons to psychophysical data and other completion models

segment interaction analysis of the stance limb in sprint running a high angular velocity of the thigh of the stance limb generated by hip extensor musculature is commonly thought to be a performance determining factor in sprint running however the thigh segment is a component of a linked system i e the lower limb therefore it is unlikely that the kinematics of the thigh will be due exclusively to the resultant joint moment rjm at the hip the purpose of this study was to quantify by means of segment interaction analysis the determinants of sagittal plane kinematics of the lower limb segments during the stance phase of sprint running video and ground reaction force data were collected from four male athletes performing maximal effort sprints the analysis revealed that during the first third of the stance phase a hip extension moment was the major determinant of the increasing angular velocity of the thigh however during the mid third of stance hip and knee extension moments and segment interaction effects all contributed to the thigh attaining its peak angular velocity extension moments at the ankle and to a lesser extent the knee were attributed with preventing the collapse of the shank under the effects of the interactive moment due to ground reaction force the angular acceleration of the foot was determined almost completely by the rjm at the ankle and the interactive moment due to ground reaction force further research is required to determine if similar results exit for a wide range of athletes and for other stages of a sprint race e g early acceleration maximal velocity and deceleration phases

decay of correlations and uniqueness of gibbs lattice systems with nonquadratic interaction the aim of this paper is to develop the classical lattice models with unbounded spin to the case of nonquadratic polynomial interaction we demonstrate that the distinct relation between the growths of potentials leads to the uniqueness and the fast decay of correlations for gibbs measure

inertial characteristics of adolescent male body segments in response to the presently limited information on body segment inertial characteristics of children and adolescents this investigation estimated the mass centre of mass and principal moments of inertia of adolescent male body segments significant prediction equations based on anthropometric measurements were then sought thirteen subjects were measured at 6 monthly intervals for 2 5 yr to provide inertial characteristics for the leg thigh lower trunk and upper trunk segments these characteristics were derived using an elliptical zone modelling technique following a correlation analysis significant prediction equations of segment inertial parameters were derived from five or fewer anthropometric measurements for all cases more than 84 of the variance in the dependent variable was accounted for with a maximum r2 value of 94 being recorded for the prediction of thigh segment mass the use of these prediction equations offered accurate and convenient estimates of body segment inertial characteristics within the limitations applicable to all modelling approaches in contrast to recent studies these equations accommodated the current morphological status of the subject

tangent bundle curve completion with locally connected parallel networks we propose a theory for cortical representation and computation of visually completed curves that are generated by the visual system to fill in missing visual information e g due to occlusions recent computational theories and physiological evidence suggest that although such curves do not correspond to explicit image evidence along their length their construction emerges from corresponding activation patterns of orientation selective cells in the primary visual cortex previous theoretical work modeled these patterns as least energetic 3d curves in the mathematical continuous space which abstracts the mammalian striate cortex here we discuss the biological plausibility of this theory and present a neural architecture that implements it with locally connected parallel networks part of this contribution is also a first attempt to bridge the physiological literature on curve completion with the shape problem and a shape theory we present completion simulations of our model in natural and synthetic scenes and discuss various observations and predictions that emerge from this theory in the context of curve completion

the measurement of body segment inertial parameters using dual energy x ray absorptiometry abstract accurate body segment parameter bsp information is required for dynamic analyses of motion and the current methods available for obtaining these bsps have been criticized the purpose of this study was to determine whether dual energy x ray absorptiometry dxa could accurately measure the bsps of scanned objects and thus be used as a tool for measuring the bsps of human subjects whole body mass wbm of 11 males was measured from a dxa scan and the values were compared to criterion scale measured values by calculating the mean percent error two objects plastic cylinder human cadaver leg were also scanned and dxa measurements of mass length centre of mass location cm and moment of inertia about the centre of mass i cm were made using custom software criterion bsp measurements were then made and compared to dxa bsp values by calculating the percent error criterion i cm measurements of the two objects were made using a pendulum technique and a second criterion i cm calculation was made for the cylinder using a geometric formula a mean percent error of 1 05 1 32 was found for wbm measurements of the human subjects errors for the cylinder and cadaver leg were under 3 2 for all bsps except for i cm when dxa was compared to the pendulum method 14 3 and 8 2 for cylinder and leg respectively the errors between dxa and the pendulum method were attributed to uncertainty in the pendulum technique j biomech 2002 in review i cm error of the cylinder when dxa was compared to the geometric calculation was 2 63 this error combined with the low errors for all other bsps indicated that dxa can be used as a simple and accurate means of obtaining direct bsp information on living humans

witten laplacian method for generalized models of kac type we first study the exponential decay of correlations for classical models of kac type using recent results j jon on spectral properties of witten laplacians their range of projections and brascamp lieb inequality integral equ oper theory 36 3 288 324 2000 10 1007 bf01213926 about the witten laplacians we improve the bounds obtained a lo witten laplacian methods for the decay of correlations j stat phys 132 2 355 396 2008 10 1007 s10955 008 9547 6 to justify the conjecture that the critical point in the d 1 dimensional kac model is given by c 1 4d we also provide a new approach for proving the exponential decay of the usual truncated correlations which is more direct than the existing ones in the sense that it does not use any cluster type expansions

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

towards a nonperturbative renormalization group analysis we prove that a certain class of convex gradient models in high dimensional spaces without the presence of a small parameter renormalizes to a free field as a consequence we establish a certain asymptotic formula for the partition function in some ways this is a realization of gawedzki and kupiainen s idea to use correlation inequalities to augment the rigorous renormalization group methods we use the more particular suggestion of spencer to use certain inequalities of brascamp and lieb and also the formulation of the correlation functions in terms of the solutions to some partial differential equations given by helffer and sjostrand