statistical mechanics of a neurobiological dynamical system the spectrum of local entropies s α applied to cocaine perturbed behavior abstract the singularity spectrum of local entropies s computed from the microcanonical dynamical partition function is used to describe the sequential dynamical structure of rat locomotor paths under the influence of cocaine the approach used was analogous to the microcanonical ensemble of statistical mechanics and permitted the sensitive detection of phase transition like behavior the results suggest that the behavioral sequences exhibited by the rats are determined by two processes each with its own entropy i h the processes are changed simultaneously by cocaine suggesting that they coexist as local repellers with overlapping insets and undergo a change to first order phase transition

on the multifractal nature of fully developed turbulence and chaotic systems it is generally argued that the energy dissipation of three dimensional turbulent flow is concentrated on a set with non integer hausdorff dimension recently in order to explain experimental data it has been proposed that this set does not possess a global dilatation invariance it can be considered to be a multifractal set the authors review the concept of multifractal sets in both turbulent flows and dynamical systems using a generalisation of the beta model

the entropy function for characteristic exponents using a thermodynamic formalism we define an entropy function s a which measures large deviations of the liapunov characteristic exponents of certain hyperbolic dynamical systems the function s a is a legendre transform of a free energy or pressure associated with the dynamical system we show that s a is the noncompact topological entropy of the set of points a with characteristic exponent a that s a a is the hausdorff dimension of a and that a s a is the escape rate from a we explain how to use the formalism for cookie cutters to describe the distribution of scales in the universal period doubled attractor and critical golden circle mapping we relate s a to the renyi entropies prove a conjecture of kantz and grassberger relating the escape rate from hyperbolic repellors and saddles to the characteristic exponents and information dimension and study the fluctuations of escape rates we discuss the escape rate from f x 4 e x 1 x and the behaviour of the associated s a as e 0 finally we discuss how to apply these ideas to experimental time series and non hyperbolic attractors

an empirical analysis of scenario generation methods for stochastic optimization this work presents an empirical analysis of popular scenario generation methods for stochastic optimization including quasi monte carlo moment matching and methods based on probability metrics as well as a new method referred to as voronoi cell sampling solution quality is assessed by measuring the error that arises from using scenarios to solve a multi dimensional newsvendor problem for which analytical solutions are available in addition to the expected value the work also studies scenario quality when minimizing the expected shortfall using the conditional value at risk to quickly solve problems with millions of random parameters a reformulation of the risk averse newsvendor problem is proposed which can be solved via benders decomposition the empirical analysis identifies voronoi cell sampling as the method that provides the lowest errors with particularly good results for heavy tailed distributions a controversial finding concerns evidence for the ineffectiveness of widely used methods based on minimizing probability metrics under high dimensional randomness

multifractal decompositions of moran fractals we present a rigorous construction and generalization of the multifractal decomposition for moran fractals with infinite product measure the generalization is specified by a system of nonnegative weights in the partition sum all the usual smooth properties of the f theory are recovered for the case that the weights are equal to unity the generalized spectrum f w is invariant to a group of gauge transformations of the weights and in addition need no longer be concave in case the fractal is a cantor set generated by an iterated function system of similarities is the pointwise dimension of the measure we discuss properties of some examples

lumped parameter electromyogram driven musculoskeletal hand model a potential platform for real time prosthesis control simple lumped parameter musculoskeletal models may be more adaptable and practical for clinical real time control applications such as prosthesis control in this study we determined whether a lumped parameter emg driven musculoskeletal model with four muscles could predict wrist and metacarpophalangeal mcp joint flexion extension forearm emg signals and joint kinematics were collected simultaneously from 5 able bodied ab subjects for one subject with unilateral transradial amputation tra joint kinematics were collected from the sound arm during bilateral mirrored motion twenty two model parameters were optimized such that joint kinematics predicted by emg driven forward dynamic simulation closely matched measured kinematics cross validation was employed to evaluate the model kinematic predictions using pearson s correlation coefficient r model predictions of joint angles were highly to very highly positively correlated with measured values at the wrist ab mean r 0 94 tra r 0 92 and mcp ab mean r 0 88 tra r 0 93 joints during single joint wrist and mcp movements respectively in simultaneous multi joint movement the prediction accuracy for tra at the mcp joint decreased r 0 56 while r values derived from ab subjects and tra wrist motion were still above 0 75 though parameters were optimized to match experimental sub maximal kinematics passive and maximum isometric joint moments predicted by the model were comparable to reported experimental measures our results showed the promise of a lumped parameter musculoskeletal model for hand wrist kinematic estimation therefore the model might be useful for emg control of powered upper limb prostheses but more work is needed to demonstrate its online performance

iterated function system and ruelle operator abstract we consider a generalized iterated function system where the weights are variable functions by using the ruelle operator and a dynamical system consideration we prove that if the system is contractive and the weights are strictly positive functions and satisfy the dini condition then there exists a unique eigenmeasure corresponding to the ruelle operator on the attractor if in addition the maps are conformal and satisfy the open set condition then we prove that they satisfy the strong open set condition and by using this we can give a description of the l p scaling spectrum and the multifractal structure of the eigenmeasure the work extends some results of proc london math soc 73 1996 105 154 adv appl math 19 1997 486 513 j statist phys 86 1997 233 275 indiana univ math j 42 1993 367 411

on multifractality and time subordination for continuous functions let be a continuous function this paper relates to the existence of a decomposition of z as z g f where is a monofractal function with exponent 0 h 1 and f 0 1 0 1 is a time subordinator i e the integral of a positive borel measure supported by 0 1 an equivalent question consists of searching for a multifractal parametrization of z which transforms z into a monofractal function we establish that such a decomposition can be found for a large class of functions which includes the usual examples of multifractal functions we find an interesting relationship between self similar functions and self similar measures as an application of our results our theorems yield new insights in the understanding of the multifractal behaviour of functions giving a significant role to the regularity analysis of borel measures

on the design of an optimal quantizer the problem of designing an optimal quantizer with a fixed number of levels for a wide class of error weighting functions and an arbitrary distribution function is discussed the existence of an optimal quantizer is proved and a two stage algorithm for its design is suggested in this algorithm at the first stage lloyd s iterative method i is applied for reducing the region where at the second stage the search for an optimal quantizer is performed using a hybrid of the dynamic programming algorithm and the lloyd max algorithm which achieves the absolute optimality of dynamic programming with much less computational effort for a continuous distribution with log concave density and an increasing convex weighting function of the absolute quantization error a reliable method is presented to compute the parameters of the optimal quantizer with a known precision using a generalization either of lloyd s method i or of the lloyd max algorithm

sufficient conditions for uniqueness of a locally optimal quantizer for a class of convex error weighting functions sufficient conditions are presented for uniqueness of a locally optimal quantizer being a stationary point of the quantization distortion measure e f x eta the expected value of an error weighting function f x eta where x is a random variable to be quantized where the probability density function p x describing x is continuous and positive on some finite or infinite interval and zero outside it and where eta is the quantization error the function f x eta is assumed convex and symmetric in eta and zero only for eta 0 it is shown that in the cases of f x eta eta 2 and f x eta eta the simple condition of concavity of in p x is sufficient for uniqueness of a locally optimal quantizer

asymptotics of the geometric mean error in the quantization for product measures on moran sets abstract assuming a separation property for moran sets we give a sufficient condition for the s 0 dimensional upper and lower quantization coefficient for of order zero to be both positive and finite when the quantization dimension exists and equals s 0 for certain product measures associated with multiscale moran sets we determine the exact value s 0 of the quantization dimension of order zero and present a subclass of such measures for which the s 0 dimensional upper and lower quantization coefficient are both positive and finite several examples are constructed to illustrate the main results

a space quantization method for numerical integration abstract we propose a new method sqm for numerical integration of c functions 0 2 defined on a convex subset c of rd with respect to a continuous distribution it relies on a space quantization of c by a n tuplex x1 xn cn fd is approximated by a weighted sum of the f xi s the integration error bound depends on the distortion en x of the voronoi tessellation of x this notion comes from information theoretists its main properties existence of a minimizing n tuple in cn asymptotics of mincn en as n are presented for a wide class of measures a simple stochastic optimization procedure is proposed to compute in any dimension d x and the characteristics of its voronoi tessellation some new results on the competitive learning vector quantization algorithm when 2 are obtained as a by product some tests simulations and provisional remarks are proposed as a conclusion

sample size formulae for intervention studies with the cluster as unit of randomization this paper presents sample size formulae for both continuous and dichotomous endpoints obtained from intervention studies that use the cluster as the unit of randomization the formulae provide the required number of clusters or the required number of individuals per cluster when the other number is given the proposed formulae derive from student s t test with use of cluster summary measures and a variance that consists of within and between cluster components power contours are provided to help in the design of intervention studies that use cluster randomization sample size formulae for designs with and without stratification of clusters appear separately

the exact rate of convergence of the lq spectra of self similar measures for q 0 abstract the l q spectrum of a borel measure is one of the key objects in multifractal analysis and it is widely believed that l q spectrum associated with a fractal measure encode important information about the underlying dynamics and geometry the study of the l q spectrum therefore plays a fundamental role in the understanding of dynamical systems or fractal measures for q 0 olsen l olsen empirical multifractal moment measures and moment scaling functions of self similar multifractals math proc cambridge philos soc 133 2002 459 485 recently determined the exact rate of convergence of the l q spectra of a self similar measure satisfying the open set condition osc unfortunately nothing is known about the rate of convergence for q 0 indeed the problem of analysing l q spectra for q 0 is generally considered significantly more difficult since the l q spectra are extremely sensitive to small variations in the distribution of for q 0 the purpose of this paper is to overcome these obstacles and to investigate the more difficult problem of determining the exact rate of convergence of the multifractal l q spectra of a self similar measure satisfying the osc for q 0

global convergence and empirical consistency of the generalized lloyd algorithm the generalized lloyd algorithm for vector quantizer design is analyzed as a descent algorithm for nonlinear programming a broad class of convex distortion functions is considered and any input distribution that has no singular continuous part is allowed a well known convergence theorem is applied to show that iterative applications of the algorithm produce a sequence of quantizers that approaches the set of fixed point quantizers the methods of the theorem are extended to sequences of algorithms yielding results on the behavior of the algorithm when an unknown distribution is approximated by a training sequence of observations it is shown that as the length of the training sequence grows large that 1 fixed point quantizers for the training sequence approach the set of fixed point quantizers for the true distribution and 2 limiting quantizers produced by the algorithm with the training sequence distribution perform no worse than limiting quantizers produced by the algorithm with the true distribution

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

functional quantization of gaussian processes quantization consists in studying the lr error induced by the approximation of a random vector x by a vector quantized version taking a finite number n of values for rm valued random vectors the theory and practice is quite well established and in particular the asymptotics as n of the resulting minimal quantization error for nonsingular distributions is well known it behaves like c x r m n 1 m this paper is a transposition of this problem to random vectors in an infinite dimensional hilbert space and in particular to stochastic processes xt t 0 1 viewed as l2 0 1 dt valued random vectors for gaussian vectors and the l2 error we present detailed results for stationary and optimal quantizers we further establish a precise link between the rate problem and shannon kolmogorov s entropy of x this allows us to compute the exact rate of convergence to zero of the minimal l2 quantization error under rather general conditions on the eigenvalues of the covariance operator typical rates are o logn a a 0 they are obtained for instance for the fractional brownian motion and the fractional ornstein uhlenbeck process the exponent a is closely related with the l2 regularity of the process

multifractal analysis of bernoulli measures on a class of homogeneous cantor sets abstract we study multifractal properties of bernoulli measure p supported on homogeneous cantor set determined by 0 1 2 k 1 c k k 1 where 0 p 1 2 and c k is either d 1 or d 2 with 0 d 1 d 2 1 2 let and be the lower and upper limits of the occurrence frequency of d 1 in c k k 1 respectively it is proved by wu 2005 14 that if then the multifractal formalism holds after given some conditions on c k k 1 we get multifractal spectra for any 0 1 we show that if 0 and 1 the refined formalism does not hold while olsen s concave multifractal formalism holds in some cases this answers a question asked by olsen 1995 10 we also show that if 0 1 olsen s concave multifractal formalism does not hold

quantitative stability analysis for minimax distributionally robust risk optimization this paper considers distributionally robust formulations of a two stage stochastic programming problem with the objective of minimizing a distortion risk of the minimal cost incurred at the second stage we carry out a stability analysis by looking into variations of the ambiguity set under the wasserstein metric decision spaces at both stages and the support set of the random variables in the case when the risk measure is risk neutral the stability result is presented with the variation of the ambiguity set being measured by generic metrics of zeta structure which provides a unified framework for quantitative stability analysis under various metrics including total variation metric and kantorovich metric when the ambiguity set is structured by a zeta ball we find that the hausdorff distance between two zeta balls is bounded by the distance of their centers and difference of their radii the findings allow us to strengthen some recent convergence results on distributionally robust optimization where the center of the wasserstein ball is constructed by the empirical probability distribution

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

on the distribution of long term time averages on symbolic space the pressure was studied in a rather abstract theory as an important notion of the thermodynamic formalism the present paper gives a more concrete account in the case of symbolic spaces including subshifts of finite type we relate the pressure of an interaction function to its long term time averages through the hausdorff and packing dimensions of the subsets on which has prescribed long term time average values functions with values in d are considered for those depending only on finitely many symbols we get complete results unifying and completing many partial results

a one parameter neural activation to muscle activation model estimating isometric joint moments from electromyograms nonlinearities have been observed in the isometric emg force relationship however these are generally not included when using emg driven hill type muscle models that account for muscle activation dynamics in this paper we present a formulation for a one parameter transformation model i e a model that accounts for the type of physiological nonlinearities observed at low levels of force the general shape for the curvilinear portion of the curve was based on phenomenological data reported by woods and bigland ritchie the one parameter a model is easy to implement and when used with an emg driven hill type model was shown to provide a better fit of the measured joint moment optimization methods were used to determine the appropriate curvature of the relationship for each muscle and thus introduced a degree of tuning to each subject

a multifractal analysis of equilibrium measures for conformal expanding maps and moran like geometric constructions in this paper we establish the complete multifractal formalism for equilibrium measures for holder continuous conformal expanding maps andexpanding markov moran like geometric constructions examples include markov maps of an interval beta transformations of an interval rational maps with hyperbolic julia sets and conformal toral endomorphisms we also construct a holder continuous homeomorphism of a compact metric space with an ergodic invariant measure of positive entropy for which the dimension spectrum is not convex and hence the multifractal formalism fails

iterated function systems and the global construction of fractals iterated function systems i f ss are introduced as a unified way of generating a broad class of fractals these fractals are often attractors for i f ss and occur as the supports of probability measures associated with functional equations the existence of certain p balanced measures for i f ss is established and these measures are uniquely characterized for hyperbolic i f ss the hausdorff besicovitch dimension for some attrac tors of hyperbolic i f ss is estimated with the aid of p balanced measures what appears to be the broadest framework for the exactly computable moment theory of p balanced measures that of linear i f ss and of probabilistic mixtures of iterated riemann surfaces is presented this extensively generalizes earlier work on orthogonal polynomials on julia sets an example is given of fractal reconstruction with the use of linear i f ss and moment theory

on multifractal formalism for self similar measures with overlaps let mu be a self similar measure generated by an ifs varphi phi i i 1 ell of similarities on mathbb r d d ge 1 when varphi is dimensional regular see definition 1 1 we give an explicit formula for the l q spectrum tau mu q of mu over 0 1 and show that tau mu is differentiable over 0 1 and the multifractal formalism holds for mu at any alpha in tau mu 1 tau mu 0 we also verify the validity of the multifractal formalism of mu over tau mu infty tau mu 0 for two new classes of overlapping algebraic ifss by showing that the asymptotically weak separation condition holds for one of them the proof appeals to the recent result of shmerkin ann math 2 189 2 319 391 2019 on the l q spectrum of self similar measures

a comparison of generalized linear mixed model procedures with estimating equations for variance and covariance parameter estimation in longitudinal studies and group randomized trials response data in longitudinal studies and group randomized trials are gathered on units that belong to clusters within which data are usually positively correlated therefore estimates and confidence intervals for intraclass correlation or variance components are helpful when designing a longitudinal study or group randomized trial data simulated from both study designs are used to investigate the estimation of variance and covariance parameters from the following procedures for continuous outcomes restricted maximum likelihood reml and estimating equations ee for binary outcomes restricted pseudo likelihood repl and estimating equations ee we evaluate these procedures to see which provide valid and precise estimates as well as correct standard errors for the intraclass correlation coefficient or variance components reml seems the better choice for estimating terms related to correlation for models with normal outcomes especially in group randomized trial situations results for reml and ee are mixed when outcomes are continuous and non normal with binary outcomes neither repl nor ee provides satisfactory estimation or inference in longitudinal study situations while repl is preferable for group randomized trials

estimation of the design effect in community intervention studies this paper considers the estimation of the variance of a mortality rate in community intervention studies with little or no replication of intervention regimens our approach in estimation of this cluster sampling variance is to determine the variance for simple random sampling and multiply it by a design effect which we calculate with use of information obtained from other sources when the county is the unit of randomization and the outcome is mortality we calculate the design effect as the ratio of the age adjusted mortality rates for single stage cluster sampling relative to simple random sampling we use information from all counties in a state in the calculations we apply this approach empirically for breast cancer mortality we found that these design effects were dependent on length of time for accumulation of deaths 1 1 for one year up to 3 5 for eight years and were quite consistent for the three states and nine years considered in the investigation we present a model that accounts for the time dependence of the design effect and we show it provides a good representation of the observed relationship

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

muscle moment arm and normalized moment contributions as reference data for musculoskeletal elbow and wrist joint models abstract a geometric musculoskeletal model of the elbow and wrist joints was developed to calculate muscle moment arms throughout elbow flexion extension forearm pronation supination wrist flexion extension and radial ulnar deviation model moment arms were verified with data from cadaver specimen studies and geometric models available in the literature coefficients of polynomial equations were calculated for all moment arms as functions of joint angle with special consideration to coupled muscles as a function of two joint angles additionally a normalized potential moment npm contribution index for each muscle across the elbow and wrist joints in four degrees of freedom was determined using each muscle s normalized physiological cross sectional area pcsa and peak moment arm ma we hypothesize that a a geometric model of the elbow and wrist joints can represent the major attributes of ma versus joint angle from many literature sources of cadaver and model data and b an index can represent each muscle s normalized moment contribution to each degree of freedom at the elbow and wrist we believe these data serve as a simple yet comprehensive reference for how the primary 16 muscles across the elbow and wrist contribute to joint moment and overall joint performance

approximate kalman bucy filter for continuous time semi markov jump linear systems the aim of this paper is to propose a new numerical approximation of the kalman bucy filter for semi markov jump linear systems this approximation is based on the selection of typical trajectories of the driving semi markov chain of the process by using an optimal quantization technique the main advantage of this approach is that it makes pre computations possible we derive a lipschitz property for the solution of the riccati equation and a general result on the convergence of perturbed solutions of semi markov switching riccati equations when the perturbation comes from the driving semi markov chain based on these results we prove the convergence of our approximation scheme in a general infinite countable state space framework and derive an error bound in terms of the quantization error and time discretization step we employ the proposed filter in a magnetic levitation example with markovian failures and compare its performance with both the kalman bucy filter and the markovian linear minimum mean squares estimator

multifractal formalism for almost all self affine measures we conduct the multifractal analysis of self affine measures for almost all family of affine maps besides partially extending falconer s formula of lq spectrum outside the range 1 q 2 the multifractal formalism is also partially verified

quantization dimension for condensation systems ii the geometric mean error abstract let f i 1 n be a family of similitudes on r 1 satisfying the strong separation condition and the self similar measure associated with f i 1 n and a probability vector t 1 t n let be the attracting measure of a condensation system associated with f i 1 n and a probability vector p 0 p 1 p n we establish a relationship between the quantization dimension of and its mass distribution on cylinder sets

multifractal analysis of brownian zero set the multifractal structure of zerosz of brownian motion is considered for different measures onz we find typical characteristics the function and the multifractal spectrumf a dimensional interpretation off is also discussed

an evaluation of methods for the stratified analysis of clustered binary data in community intervention trials a simulation study is conducted in a community intervention setting several methods of stratified analysis of clustered binary data are compared in terms of empirical significance and empirical power levels they are the mantel haenszel test statistic chi 2 mh the adjusted mantel haenszel test statistic of donald donner chi 2 dd rao scott chi 2 rsn and chi 2 rsp and zhang boos chi 2 zbn and chi 2 zbp wald chi 2 w robust wald chi 2 rw score chi 2 s robust score chi 2 rs and the test statistic based on generalized linear mixed model glmm chi 2 glmm when rho not equal 0 chi 2 mh has inflated type i error and it should not be used when observations are correlated the results also warn of the use of chi 2 rsn and chi 2 rw due to their poor performance in terms of empirical significance level chi 2 zbp and chi 2 glmm have better empirical significance levels as compared to other statistics however chi 2 zbp tends to have lower empirical powers than other statistics when the number of clusters n is less than 24 chi 2 rsp provides the highest empirical powers when rho or 0 1 and n or 12 when rho or 0 01 we recommend the use of chi 2 rs and chi 2 glmm since they have better overall performance in terms of empirical significance levels and empirical power levels

anomalies in multifractal formalism for local time of brownian motion the renyi function for the logical time measure of brownian motion is found it is shown that this function the legendre transform of the multifractal spectrum of and the function derived by the reciprocal measure formalism are not identical more examples of having similar anomalies are discussed

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

multifractal measures and a weak separation condition abstract we define a new separation property on the family of contractive similitudes that allows certain overlappings this property is weaker than the open set condition of hutchinson it includes the well known class of infinite bernoulli convolutions associated with the p v numbers and the solutions of the two scale dilation equations our main purpose in this paper is to prove the multifractal formalism under such condition

divergence points of self similar measures satisfying the osc recently barreira and schmeling 2000 1 and chen and xiong 1999 2 have shown that for self similar measures satisfying the ssc the set of divergence points typically has the same hausdorff dimension as the support k it is natural to ask whether we obtain a similar result for self similar measures satisfying the osc however with only the osc satisfied we cannot do most of the work on a symbolic space and then transfer the results to the subsets of rd which makes things more difficult in this paper by the box counting principle we show that the set of divergence points has still the same hausdorff dimension as the support k for self similar measures satisfying the osc

variation of muscle moment arms with elbow and forearm position we hypothesized that the moment arms of muscles crossing the elbow vary substantially with forearm and elbow position and that these variations could be represented using a three dimensional computer model flexion extension and pronation supination moment arms of the brachioradialis biceps brachialis pronator teres and triceps were calculated from measurements of tendon displacement and joint angle in two anatomic specimens and were estimated using a computer model of the elbow joint the anatomical measurements revealed that the flexion extension moment arms varied by at least 30 over a 95 degrees range of motion the changes in flexion extension moment arm magnitudes with elbow flexion angle were represented well by the computer model the anatomical studies and the computer model demonstrate that the biceps flexion moment arm peaks in a more extended elbow position and has a larger peak when the forearm is supinated also the peak biceps supination moment arm decreases as the elbow is extended these results emphasize the need to account for the variation of muscle moment arms with elbow flexion and forearm position

asymptotics of optimal quantizers for some scalar distributions we obtain semi closed forms for the optimal quantizers of some families of one dimensional probability distributions they yield the first examples of non log concave distributions for which uniqueness holds we give two types of applications of these results one is a fast computation of numerical approximations of one dimensional optimal quantizers and their use in a multidimensional framework the other is some asymptotics of the standard empirical measures associated to the optimal quantizers in terms of distribution function laplace transform and characteristic function moreover we obtain the rate of convergence in the bucklew wise theorem and finally the asymptotic size of the voronoi tessels

van der corput sequences kakutani transforms and one dimensional numerical integration abstract it is shown that many functions can be empirically integrated with the van der corput sequences with an o ln n n or o 1 n rate according to their smoothness the first rate derives from a new koksma hlawka like inequality using the diaphony then we show that as for the discrepancy estimates these properties still hold when considering an extension of these sequences generated by ergodic transforms

some remarks on absolute continuity and quantization of probability measures we introduce a notion of monotonicity of dimensions of measures we show that the upper and lower quantization dimensions are not monotone we give sufficient conditions in terms of so called vanishing rates such that implies d r d r as an application we determine the quantization dimension of a class of measures which are absolutely continuous w r t some self similar measure with the corresponding radon nikodym derivative bounded or unbounded we study the set of quantization dimensions of measures which are absolutely continuous w r t a given probability measure we prove that the infimum on this set coincides with the lower packing dimension of furthermore this infimum can be attained provided that the upper and lower packing dimensions of are equal

asymptotic uniformity of the quantization error of self similar measures let be a self similar measure on mathbb r d associated with a family of contractive similitudes s1 sn and a probability vector p1 pn let alpha n n 1 infty be a sequence of n optimal sets for of order r for each n we denote by p a alpha n a in alpha n a voronoi partition of mathbb r d with respect to n under the strong separation condition for s1 sn we show that the nth quantization error of of order r in 1 infty satisfies the following asymptotic uniformity property int limits p a alpha n rm d x a rd mu x asymp frac 1 n v n r mu quad rm for all a in alpha n

combining multifractal additive and multiplicative chaos the purpose of this article is the study of the new class of multifrac tal measures which combines additive and multiplicative chaos defined by x j 1 b j j 2 x

the dimension spectrum of some dynamical systems we analyze the dimension spectrum previously introduced and measured experimentally by jensen kadanoff and libchaber using large deviation theory we prove for some invariant measures of expanding markov maps that the hausdorff dimensionf of the set on which the measure has a singularity is a well defined concave and regular function in particular we show that this is the case for the accumulation of period doubling and critical mappings of the circle with golden rotation number we also show in these particular cases that the functionf is universal

moment arms and lengths of human upper limb muscles as functions of joint angles abstract modeling of musculoskeletal structures requires accurate data on anatomical parameters such as muscle lengths mls moment arms mas and those describing the upper limb position using a geometrical model of planar arm movements with three degrees of freedom we present in an analytical form the available information on the relationship between mas and mls and joint angles for thirteen human upper limb muscles the degrees of freedom included are shoulder flexion extension elbow flexion extension and either wrist flexion extension the forearm in supination or radial ulnar deviation the forearm in mid pronation previously published ma angle curves were approximated by polynomials ml angle curves were obtained by combining the constant values of mls defined by the distance between the origin and insertion points for a specific upper limb position with a variable part obtained by multiplying the ma joint radius and the joint angle the mas of the prime wrist movers in radial ulnar deviation were linear functions of the joint angle r 2 0 9904 while quadratic polynomials accurately described their mas during wrist flexion extensions the relationship between mas and the elbow angle was described by 2nd 3rd or 5th order polynomials r 2 0 9904 with a lesser quality of fit for the anconeus r 2 0 9349 in the full range of angular displacements the length of wrist elbow and shoulder muscles can change by 8 5 55 and 200 respectively

strategies used to stabilize the elbow joint challenged by inverted pendulum loading abstract the stiffness of activated muscles may stabilize a loaded joint by preventing perturbations from causing large displacements and injuring the joint here the elbow muscle recruitment patterns were compared with the forearm loaded vertically a potentially unstable inverted pendulum configuration and with horizontal loading eighteen healthy subjects were studied with the forearm vertical and supinated and the elbow flexed approximately 90 in the first experiment emg electrodes recorded activity of biceps triceps and brachioradialis muscles for joint torques produced a by voluntarily exerting a horizontal force isometrically b by voluntarily flexing and extending the elbow while the forearm was loaded vertically with 135 n the relationship between the emg and the torque generated was quantified by the linear regression slope and zero torque intercept in a second experiment a vertical load increasing linearly with time up to 300 n was applied in experiment 1 the emg torque relationships for biceps and triceps had an intercept about 10 of maximum voluntary effort greater with the vertical compared to the horizontal force the inverse was found for brachioradialis but the emg torque slopes for both agonist and antagonistic muscles were not different in experiment 2 there were 29 trials with minimal elbow displacement and all the three muscles activated on the order of 11 of maximum activation to stabilize the elbow 19 trials had small elbow extension and 14 trials small flexion requiring altered muscle forces for equilibrium 7 trials ended in large unstable displacement or early termination of the test an analysis indicate that the observed levels of muscle activation would only provide stability if the muscles short range stiffness was at the high end of the published range hence the elbow was marginally stable the stability analysis also indicated that the small elbow extension increased stability and flexion decreased stability

some results on the behavior and estimation of the fractal dimensions of distributions on attractors the strong interest in recent years in analyzing chaotic dynamical systems according to their asymptotic behavior has led to various definitions of fractal dimension and corresponding methods of statistical estimation in this paper we first provide a rigorous mathematical framework for the study of dimension focusing on pointwise dimension x and the generalized renyi dimensionsd q and give a rigorous proof of inequalities first derived by grassberger and procaccia and hentschel and procaccia we then specialize to the problem of statistical estimation of the correlation dimension and information dimension it has been recognized for some time that the error estimates accompanying the usual procedures which generally involve least squares methods and nearest neighbor calculations grossly underestimate the true statistical error involved in least squares analyses of and we identify sources of error not previously discussed in the literature and address the problem of obtaining accurate error estimates we then develop an estimation procedure for which corrects for an important bias term the local measure density and provides confidence intervals for the general applicability of this method is illustrated with various numerical examples

muscular synergism i on criteria for load sharing between synergistic muscles the use of optimization techniques to predict individual muscle forces in redundant biomechanical systems implies the formulation of a criterion for load sharing between the muscles in part i of this paper the characteristics and performance of several linear and non linear criteria reported in the literature have been compared for static isometric knee flexion the results show that linear criteria inherently predict discrete muscle action orderly recruitment of muscles whereas non linear criteria can predict synergistic action all criteria predict that relatively more force is allocated to muscles with large moment arms when muscle stresses or ratios of muscle force to maximum muscle force are used as the decision variables in the objective function then relatively more force is allocated to muscles with large maximum possible force as well future formulations of the optimization should consider the differences in fiber type composition among the muscles such an approach is presented in part ii of the paper

multifractal decompositions of digraph recursive fractals we prove that the multifractal decomposition behaves as expected for a family of sets k known as digraph recursive fractals using measures of markov type for each value of a parameter between a minimum min and maximum max we define multifractal components k of k and show that they are fractals in the sense of taylor the dimension f of k is computed from the data of the problem the typical concave multifractal f dimension spectrum curve results

mixed generalized dimensions of self similar measures abstract classical multifractal analysis studies the local scaling behaviour of a single measure however recently mixed multifractal has generated interest mixed multifractal analysis studies the simultaneous scaling behaviour of finitely many measures and provides the basis for a significantly better understanding of the local geometry of fractal measures the purpose of this paper is twofold firstly we define and develop a general and unifying mixed multifractal theory of mixed renyi dimensions also sometimes called the generalized dimensions mixed l q dimensions and mixed coarse multifractal spectra for arbitrary doubling measures secondly as an application of the general theory developed in this paper we provide a complete description of the mixed multifractal theory of finitely many self similar measures

dynamic coordinate data for describing muscle tendon paths a mathematical approach when modelling the musculoskeletal system over a range of joint angles the use of fixed points to describe muscle tendon paths has inherent limitations these result in fewer deflection points and the use of effective insertions to accommodate both relative marker movement and avoid muscle paths contacting bony structures model performance is dependent on the joint angle relative to the anatomical position where the muscle tendon paths were defined the present study proposes a scheme for the implementation of dynamic coordinates for describing muscle tendon paths for each muscle tendon element a plane is defined in which the muscle tendon complex acts when crossing a given joint the muscle tendon plane is dependent on 3d segment orientations and describes one degree of freedom while the remaining two degrees of freedom are described by polar coordinates and locate the dynamic point in the muscle tendon plane the dynamic approach is implemented on four muscles of the lower limb in modelled and simulated joint movements and offers a significant improvement on previous approaches based on fixed deflection points the scheme accommodates compound 3d rotations about joint axes is not computationally difficult or require large data sets and does not impose limitations on the number of points that may be defined along a muscle tendon path

convergence of markovian stochastic approximation with discontinuous dynamics this paper is devoted to the convergence analysis of stochastic approximation algorithms of the form theta n 1 theta n gamma n 1 h theta n x n 1 where left theta n n in mathbb n right is an mathbb r d valued sequence left gamma n n in mathbb n right is a deterministic stepsize sequence and left x n n in mathbb n right is a controlled markov chain we study the convergence under weak assumptions on smoothness in theta of the function theta mapsto h theta x it is usually assumed that this function is continuous for any x in this work we relax this condition our results are illustrated by considering stochastic approximation algorithms for adaptive quantile estimation and a penalized version of the vector quantization

numerical solution of the poisson equation over hypercubes using reduced chebyshev polynomial bases we describe how to use new reduced size polynomial approximations for the numerical solution of the poisson equation over hypercubes our method is based on a non standard galerkin method which allows test functions which do not verify the boundary conditions numerical examples are given in dimensions up to 8 on solutions with different smoothness using the same approximation basis for both situations a special attention is paid on conditioning problems

asymptotic quantization error of continuous signals and the quantization dimension extensions of the limiting qnanfizafion error formula of bennet are proved these are of the form d s k n f n beta b where n is the number of output levels d s k n f is the s th moment of the metric distance between quantizer input and output beta b 0 k s beta is the signal space dimension and f is the signal distribution if a suitably well behaved k dimensional signal density f x exists b b s k int f rho x dx 1 rho rho k s k and b s k does not depend on f for k 1 s 2 this reduces to bennett s formula if f is the cantor distribution on 0 1 0 and this k equals the fractal dimension of the cantor set 12 13 random quantization optimal quantization in the presence of an output information constraint and quantization noise in high dimensional spaces are also investigated

analysis of data arising from a stratified design with the cluster as unit of randomization this paper discusses statistical techniques for the analysis of dichotomous data arising from a design in which the investigator randomly assigns each of two clusters of possibly varying size to interventions within strata the problem addressed is that of assessing the statistical significance of the intervention effect over all strata we propose a weighted paired t test based on the empirical logistic transform for designs that randomize large aggregate clusters in each of several strata

on the existence of optimal quantizers corresp the existence of optimal n level quantizers is demonstrated for several classes of quantizers including block quantizers memoryless quantizers and uniform step size quantizers no assumptions whatsoever are made regarding the input probability distribution the distortion measure considered generalizes many of the commonly used error based distortion measures including mean squared error distortion and r th law distortion

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

problem based optimal scenario generation and reduction in stochastic programming scenarios are indispensable ingredients for the numerical solution of stochastic programs earlier approaches to optimal scenario generation and reduction are based on stability arguments involving distances of probability measures in this paper we review those ideas and suggest to make use of stability estimates based only on problem specific data for linear two stage stochastic programs we show that the problem based approach to optimal scenario generation can be reformulated as best approximation problem for the expected recourse function which in turn can be rewritten as a generalized semi infinite program we show that the latter is convex if either right hand sides or costs are random and can be transformed into a semi infinite program in a number of cases we also consider problem based optimal scenario reduction for two stage models and optimal scenario generation for chance constrained programs finally we discuss problem based scenario generation for the classical newsvendor problem