measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

overall concordance correlation coefficient for evaluating agreement among multiple observers accurate and precise measurement is an important component of any proper study design as elaborated by lin 1989 biometrics 45 255 268 the concordance correlation coefficient ccc is more appropriate than other indices for measuring agreement when the variable of interest is continuous however this agreement index is defined in the context of comparing two fixed observers in order to use multiple observers in a study involving large numbers of subjects there is a need to assess agreement among these multiple observers in this article we present an overall ccc occc in terms of the interobserver variability for assessing agreement among multiple fixed observers the occc turns out to be equivalent to the generalized ccc king and chinchilli 2001 statistics in medicine 20 2131 2147 lin 1989 lin 2000 biometrics 56 324 325 when the squared distance function is used we evaluated the occc through generalized estimating equations barnhart and williamson 2001 biometrics 57 931 940 and u statistics king and chinchilli 2001 for inference this article offers the following important points first it addresses the precision and accuracy indices as components of the occc second it clarifies that the occc is the weighted average of all pairwise cccs third it is intuitively defined in terms of interobserver variability fourth the inference approaches of gee and the u statistics are compared via simulations for small samples fifth we illustrate the use of the occc by two medical examples with the gee u statistics and bootstrap approaches

nonparametric estimation of the concordance correlation coefficient under univariate censoring assessing agreement is often of interest in clinical studies to evaluate the similarity of measurements produced by different raters or methods on the same subjects lin s 1989 biometrics 45 255 268 concordance correlation coefficient ccc has become a popular measure of agreement for correlated continuous outcomes however commonly used estimation methods for the ccc do not accommodate censored observations and are therefore not applicable for survival outcomes in this article we estimate the ccc nonparametrically through the bivariate survival function the proposed estimator of the ccc is proven to be strongly consistent and asymptotically normal with a consistent bootstrap variance estimator furthermore we propose a time dependent agreement coefficient as an extension of lin s 1989 ccc for measuring the agreement between survival times among subjects who survive beyond a specified time point a nonparametric estimator is developed for the time dependent agreement coefficient as well it has the same asymptotic properties as the estimator of the ccc simulation studies are conducted to evaluate the performance of the proposed estimators a real data example from a prostate cancer study is used to illustrate the method

measuring agreement in method comparison studies with heteroscedastic measurements we propose a methodology for evaluation of agreement between two methods of measuring a continuous variable whose variability changes with magnitude this problem routinely arises in method comparison studies that are common in health related disciplines assuming replicated measurements we first model the data using a heteroscedastic mixed effects model wherein a suitably defined true measurement serves as the variance covariate fitting this model poses some computational difficulties as the likelihood function is not available in a closed form we deal with this issue by suggesting four estimation methods to obtain approximate maximum likelihood estimates two of these methods are based on numerical approximation of the likelihood and the other two are based on approximation of the model next we extend the existing agreement evaluation methodology designed for homoscedastic data to work under the proposed heteroscedastic model this methodology can be used with any scalar measure of agreement simulations show that the suggested inference procedures generally work well for moderately large samples they are illustrated by analyzing a data set of cholesterol measurements copyright 2013 john wiley sons ltd

plurality and resemblance in fmri data analysis abstract we apply nine analytic methods employed currently in imaging neuroscience to simulated and actual bold fmri signals and compare their performances under each signal type starting with baseline time series generated by a resting subject during a null hypothesis study we compare method performance with embedded focal activity in these series of three different types whose magnitudes and time courses are simple convolved with spatially varying hemodynamic responses and highly spatially interactive we then apply these same nine methods to bold fmri time series from contralateral primary motor cortex and ipsilateral cerebellum collected during a sequential finger opposition study paired comparisons of results across methods include a voxel specific concordance correlation coefficient for reproducibility and a resemblance measure that accommodates spatial autocorrelation of differences in activity surfaces receiver operating characteristic curves show considerable model differences in ranges less than 10 significance level false positives and greater than 80 power true positives concordance and resemblance measures reveal significant differences between activity surfaces in both data sets these measures can assist researchers by identifying groups of models producing similar and dissimilar results and thereby help to validate consolidate and simplify reports of statistical findings a pluralistic strategy for fmri data analysis can uncover invariant and highly interactive relationships between local activity foci and serve as a basis for further discovery of organizational principles of the brain results also suggest that a pluralistic empirical strategy coupled formally with substantive prior knowledge can help to uncover new brain behavior relationships that may remain hidden if only a single method is employed

exact solutions to the ideal magneto gas dynamics equations through lie group analysis and substitution principles in this paper we consider the equations governing an inviscid thermally non conducting fluid of infinite electrical conductivity in the presence of a magnetic field and subject to no extraneous force by using conveniently the lie point symmetries admitted we map the governing system into an equivalent autonomous form the transformed system can be directly inspected in order to find some simple solutions that written in terms of the original variables provide non trivial exact solutions of the system at hand use is made of some finite transformations known in the literature as substitution principles enabling us to build exact solutions containing some arbitrary functions the link between the substitution principle and the recently discovered bogoyavlenskij symmetries for equilibrium magnetohydrodynamics is also discussed some of the recovered solutions are considered to solve well known physically relevant boundary value problems and the linear stability analysis is performed thus generalizing well established results

a practical approach for evaluating population and individual bioequivalence pharmacokinetic measurements provided by subjects to each of two formulations of a drug have a joint distribution that can be characterized by parameters reflecting scale and correlation as well as location the bioavailability of the formulations can be expressed in terms of the means of the marginal distributions their means and variances or the marginal means and variances and the joint correlation these expressions correspond respectively to average population and individual bioequivalence when the joint distribution of the measurements is bivariate normal current proposals for assessing the degree of bioequivalence of two formulations are based on statistics that are composites of variance components and squares of expected mean differences from a mixed linear model there are technical and practical issues associated with these proposals particularly that they require more complicated designs than the familiar 2 x 2 cross over this paper describes an alternative approach that can be applied with standard 2 x 2 cross over designs and that provides evaluations of population and individual bioequivalence that should be adequate for all practical clinical purposes the approach is based on easily computed correlation and regression coefficients whose statistical properties under normality are well known and for which non parametric and robust alternatives exist when normality cannot be assumed the approach yields conclusions consistent with those obtained by the current proposals when applied to data sets supplied by the fda in the cases where the conclusions do not match the new approach appears to be more consistent with the data

equivalence groups for balance equations abstract we consider a system of balance equations and by using ovsiannikov s method construct the most general equivalence algebra moreover some special cases are presented

a critical discussion of intraclass correlation coefficients in general intraclass correlation coefficients icc s are designed to assess consistency or conformity between two or more quantitative measurements they are claimed to handle a wide range of problems including questions of reliability reproducibility and validity it is shown that care must be taken in choosing a suitable icc with respect to the underlying sampling theory for this purpose a decision tree is developed it may be used to choose a coefficient which is appropriate for a specific study setting we demonstrate that different icc s may result in quite different values for the same data set even under the same sampling theory other general limitations of icc s are also addressed potential alternatives are presented and discussed and some recommendations are given for the use of an appropriate method

nonlinear dynamics in a laser with a negative delayed feedback abstract asymptotic solutions of nonlinear differential difference equations describing the lasing dynamics with a negative feedback are obtained periodic lasing regimes with a complex relaxational structure are shown to be possible in such lasers the phenomenon of multistability i e the co existence of a great number of structurally different and structurally similar attractors is analytically described asymptotic characteristics of lasing regimes pulse shape and radiation pulsation frequency are found and the domains in the parameter space and the initial conditions for their realization are determined for all types of solution the chaotic dynamics following the sequence of period doubling bifurcations is also numerically determined

stability and bifurcations of equilibria in a multiple delayed differential equation the influence of multiple negative delayed feedback loops on the stability of a single action mechanism are considered a characteristic equation for the linearized stability of the equilibrium is completely analyzed as a function of two parameters describing a delay in one loop and a ratio of the gains in the two feedback loops the bifurcations occurring as the linear stability is lost are analyzed by the construction of a centre manifold in particular the nature of hopf and more degenerate higher codimension bifurcations are explicitly determined

delay induced instabilities in nonlinear feedback systems extending general methods developed in synergetics to construct order parameter equations we work out a systematic elimination procedure for the stable modes in nonlinear delay systems it will be shown that in the vicinity of an instability the dynamical behavior of the infinite dimensional delay system is approximately governed by a low dimensional set of order parameter equations which turn out to be of the form of ordinary differential equations i e they no longer contain memory terms the general formalism will then be compared with experimental data obtained from the nonlinear operation of a phase locked loop where the finite propagation time of the signal in the feedback loop is taken into account

multivariate regression analysis of distance matrices for testing associations between gene expression patterns and related variables a fundamental step in the analysis of gene expression and other high dimensional genomic data is the calculation of the similarity or distance between pairs of individual samples in a study if one has collected n total samples and assayed the expression level of g genes on those samples then an n n similarity matrix can be formed that reflects the correlation or similarity of the samples with respect to the expression values over the g genes this matrix can then be examined for patterns via standard data reduction and cluster analysis techniques we consider an alternative to conventional data reduction and cluster analyses of similarity matrices that is rooted in traditional linear models this analysis method allows predictor variables collected on the samples to be related to variation in the pairwise similarity distance values reflected in the matrix the proposed multivariate method avoids the need for reducing the dimensions of a similarity matrix can be used to assess relationships between the genes used to construct the matrix and additional information collected on the samples under study and can be used to analyze individual genes or groups of genes identified in different ways the technique can be used with any high dimensional assay or data type and is ideally suited for testing subsets of genes defined by their participation in a biochemical pathway or other a priori grouping we showcase the methodology using three published gene expression data sets

delay periodic solutions and their stability using averaging in delay differential equations with applications abstract using the method of averaging we analyze periodic solutions to delay differential equations where the period is near to the value of the delay time or a fraction thereof the difference between the period and the delay time defines the small parameter used in the perturbation method this allows us to consider problems with arbitrarily sized delay times or of the delay term itself we present a general theory and then apply the method to a specific model that has application in disease dynamics and lasers

when nonlinear differential equations are equivalent to linear differential equations a necessary and sufficient condition is established for the existence of a 1 1 transformation of a system of nonlinear differential equations to a system of linear equations the obtained theorems enable one to construct such transformations from the invariance groups of differential equations the hodograph transformation the legendre transformation and lie s transformation of the monge ampsre equation are shown to be special cases noninvertible transformations are also considered examples include burgers equation a nonlinear diffusion equation and the liouville equation introduction in this work we study transformations mapping nonlinear differen tial equations to linear differential equations in a 1 1 manner based upon the group analysis of differential equations we obtain necessary and sufficient conditions for the existence of such transformations the established theorems not only allow us to determine the existence of the transformations but also enable us to actually construct these transformations from invariance groups of the nonlinear equations in the following analysis two types of transformations are considered 1 the invariance groups of differential equations and 2 the mappings which transform nonlinear differential equations to linear differential equations theorems will be proved based upon the following observations clearly if there exists a 1 1 mapping between any two differential equations it must inject properties of one equation into the other including their invariance properties for this reason the often ignored fact that any linear differential equation admits an invariance group related to the superpo sition principle becomes very significant the generator of this particular group depends upon an arbitrary solution of the linear equation it follows then that any nonlinear equation transformable to a linear equation by a 1 1 mappingmust admit an invariance group whose generator depends upon an arbitrary solution of some linear differential equation the idea of comparing invariance groups of differential equations in the search of mappings connecting the equations was first used by bluman in his study of burgers equation 1 and it was applied to the study of the mappings of one dimensional linear parabolic equations to the heat equation 2 in the first section of this paper some basic properties of various transformations are summarized the theorems are presented in the second section the examples in the third section include the hodograph transformation the legendre transformation lie s transformation of themonge ampre equation and the equation ux uxx uyy 0 in the last section we examine properties of noninvertible mappings of burgers equation the diffusion equation u 2ux uy 0 and the liouville equation u y e u respectively into linear equations

reduction of nonhomogeneous quasilinear 2 2 systems to homogeneous and autonomous form by using the invariance with respect to suitable lie groups of point transformations necessary and sufficient conditions are determined allowing one to map through an invertible point transformation nonhomogeneous and nonautonomous quasilinear 2 2 systems to homogeneous and autonomous form the procedure is constructive and the new independent and dependent variables are obtained by determining the canonical variables associated with the lie groups of point symmetries admitted by the source system various examples of physical interest arising from different contexts are considered

preliminary group classification of equations vtt f x vx vxx g x vx a classification is given of equations vtt f v vx vxx g x vx admitting an extension by one of the principal lie algebra of the equation under consideration the paper is one of few applications of a new algebraic approach to the problem of group classification the method of preliminary group classification the result of the work is a wide class of equations summarized in table ii

high dimensional chaotic behavior in systems with time delayed feedback abstract the nature of high dimensional chaos exhibited by a class of delay differential equation is investigated by various methods this delay differential equation models systems with time delayed feedback such as nonlinear optical resonators we first describe briefly the bifurcation phenomena exhibited by the system with an increase in a control parameter representing the energy flow rate periodic states bi multi furcate themselves successively forming a hierarchy of multistable periodic states with increasing complexities finally each branch of multistable periodic states makes transition to chaos the possibility of applying such a multistability as a memory device for complicated information is discussed in the chaotic regime each of the bifurcated states in turn merge successively into fewer sets of states with larger attractor dimensions and finally a single developed chaos with a very large attractor dimension is formed lyapunov analysis is introduced to study the high dimensional chaotic states the lyapunov vectors as well as lyapunov spectrum are shown to be very useful to understand the underlying mechanism of the successive merging process mentioned above characteristics of developed chaos are investigated by high pass filtered time series hfts the intermittency characteristics of the hfts changes markedly at a certain frequency the lyapunov analysis reveals that this frequency corresponds to a characteristic lyapunov mode number this characteristic number can be looked upon as the dimension of subspace in which active chaotic information is generated and is different from the attractor dimension in the customary sense

comparison of new approaches to estimate mechanical output of individual joints in vertical jumps conventional calculation of joint power is not effective in order to assess translational motions of human body two new approaches were developed in this study to estimate translational mechanical outputs from individual joints they were applied to the analysis of vertical jump motions of six male subjects in both cases body of subjects were modeled with a four mass points system model and joints were regarded as motion generators in one approach increase of vertical component of ground reaction force grf was decomposed into push off force of three joints ankle knee and hip joints this procedure gave an estimation of impulse exerted per leg as 83 92 n s 95 confidential interval for squat jump which was similar to half of the impulse provided to mass center of the body calculated from grf 82 88 n s in the other approach amount of the power exerted by each joint vertically was estimated by calculating the scalar product of joint reaction force and relative velocity vectors of adjacent segments this approach gave estimation of vertical work provision per leg as 201 226 and 141 181 j for squat and counter movement jumps which were not so different from half of the work provided to mass center of the body calculated from grf 209 227 and 137 175 j respectively as these approaches make it possible to calculate translational mechanical outputs specifically they are useful and consistent concerning the analysis of translational motion of human body

chaotic attractors of an infinite dimensional dynamical system abstract we study the chaotic attractors of a delay differential equation the dimension of several attractors computed directly from the definition agrees to experimental resolution with the dimension computed from the spectrum of lyapunov exponents according to a conjecture of kaplan and yorke assuming this conjecture to be valid as the delay parameter is varied from computations of the spectrum of lyapunov exponents we observe a roughly linear increase from two to twenty in the dimension while the metric entropy remains roughly constant these results are compared to a linear analysis and the asymptotic behavior of the lyapunov exponents is derived

distinguishability and agreement with continuous data the analysis of concordance among repeated measures has received a huge amount of attention in the statistical literature leading to a range of different approaches however because all the approaches are able to assess the closeness among the readings taken on the same subject the conclusions about the degree of concordance should be similar regardless the approach applied here two indices to assess the concordance among continuous repeated measures the intraclass correlation coefficient and the total deviation index are applied and compared in two case examples the first example concerns the repeatability of individual nutrient allocation strategy assessed by stable isotope analysis the second example dealt with the assessment of the concordance of functional magnetic resonance imaging data that shows spatial correlation the results differ depending upon the approach applied leading to contradictory conclusions about the degree of concordance the reason behind these results is discussed reaching the conclusion that the total deviation index is just assessing agreement among repeated measurements whereas the intraclass correlation coefficient assesses the concept of distinguishability among subjects that involves agreement among repeated measurements and spread of subjects at once therefore the best way to select the right approach is to understand the right question behind the research hypothesis copyright 2013 john wiley sons ltd

spatiotemporal structures in a model with delay and diffusion pattern formation described by differential difference equations with diffusion is investigated it is shown that an arbitrarily small diffusion induces space time turbulence just at the instability threshold of the homogeneous stationary solution we prove this property by deriving a complex ginzburg landau equation on the basis of normal form analysis well above threshold such turbulent structures give way to synchronized states ordered by spirals and targets this secondary instability can be understood with an asymptotic method representing the system as a cellular automaton network

a mathematical analysis to address the 6 degree of freedom segmental power imbalance abstract segmental power is used in human movement analyses to indicate the source and net rate of energy transfer between the rigid bodies of biomechanical models segmental power calculations are performed using segment endpoint dynamics kinetic method a theoretically equivalent method is to measure the rate of change in a segment s mechanical energy state kinematic method however these two methods have not produced experimentally equivalent results for segments proximal to the foot with the difference in methods deemed the power imbalance in a 6 degree of freedom model segments move independently resulting in relative segment endpoint displacement and non equivalent segment endpoint velocities at a joint in the kinetic method a segment s distal end translational velocity may be defined either at the anatomical end of the segment or at the location of the joint center defined here as the proximal end of the adjacent distal segment our mathematical derivations revealed the power imbalance between the kinetic method using the anatomical definition and the kinematic method can be explained by power due to relative segment endpoint displacement in this study we tested this analytical prediction through experimental gait data from nine healthy subjects walking at a typical speed the average absolute segmental power imbalance was reduced from 0 023 to 0 046 w kg using the anatomical definition to 0 001 w kg using the joint center definition in the kinetic method 95 56 98 39 reduction power due to relative segment endpoint displacement in segmental power analyses is substantial and should be considered in analyzing energetic flow into and between segments

analytical and numerical investigations of the phase locked loop with time delay we derive the normal form for the delay induced hopf bifurcation in the first order phase locked loop with time delay by the multiple scaling method the resulting periodic orbit is confirmed by numerical simulations further detailed numerical investigations demonstrate exemplarily that this system reveals a rich dynamical behavior with phase portraits fourier analysis and lyapunov spectra it is possible to analyze the scaling properties of the control parameter in the period doubling scenario both qualitatively and quantitatively within the numerical accuracy there is evidence that the scaling constant of the time delayed phase locked loop coincides with the feigenbaum constant delta approximately 4 669 in one dimensional discrete systems

a concordance correlation coefficient to evaluate reproducibility a new reproducibility index is developed and studied this index is the correlation between the two readings that fall on the 45 degree line through the origin it is simple to use and possesses desirable properties the statistical properties of this estimate can be satisfactorily evaluated using an inverse hyperbolic tangent transformation a monte carlo experiment with 5 000 runs was performed to confirm the estimate s validity an application using actual data is given

reduction of balance laws to conservation laws by means of equivalence transformations a class of partial differential equations a conservation law and two balance laws with three independent variables and involving six arbitrary continuously differentiable functions is considered in the framework of equivalence transformations these are point transformations of differential equations involving arbitrary elements and live in an augmented space of independent dependent and additional variables representing values taken by the arbitrary elements projecting the admitted symmetries into the space of independent and dependent variables we determine some finite transformations mapping the system of balance laws to an equivalent one with the same differential structure but involving different arbitrary elements in particular we are interested in finding an equivalent autonomous system of conservation laws it is shown how the results apply to some physical problems

summarizing the goodness of fit of generalized linear models for longitudinal data this paper extends four goodness of fit measures of a generalized linear model glm to random effects and marginal models for longitudinal data the four measures are the proportional reduction in entropy measure the proportional reduction in deviance measure the concordance correlation coefficient and the concordance index the extended measures satisfy the basic requirements for measures of association two examples illustrate their use in model selection

improved agreement of foot segmental power and rate of energy change during gait inclusion of distal power terms and use of three dimensional models abstract traditional models used to calculate foot segmental power have yielded poor agreement between foot power and the rate of energy change during the stance phase of gait and limited the applicability of foot segmental power analyses to swing phase only the purpose of this study was to improve the agreement of foot segemental power and rate of energy change by using more inclusive models to calculate foot segmental power and energy the gait of 15 adult subjects was studied and models were used to calculate foot segmental power that included either the proximal terms only model p the most common method in the literature or both proximal and distal terms model pd a mathematically complete model power and energy terms were computed in to ways from sagittal plane vector components only two dimensional condition and from complete three dimensional components three dimensional condition results revealed that the more inclusive the model the higher the agreement of foot power and rate of energy change during stance phase model p produced poor agreement rc 0 108 for both two dimensional and three dimensional conditions model pd 2d yielded higher agreement rc 0 645 and model pd 3d exhibited nearly perfect agreement rc 0 956 the advantages of a segmental power analysis include the ability to identify the mechanisms of energy transfer into and out of the foot during movement the results of this study suggest that foot power analyses are valid when using model pd 3d to describe foot function during locomotion

linearization procedure of nonlinear first order system of partial differential equations by means of canonical variables related to lie groups of point transformations an algorithm is given to linearize nonlinear first order systems of partial differential equations admitting an infinite parameter lie group of point trasformations the associated infinitesimal operator must be a linear combination of commuting operators which individually are not necessarily admitted by the basic system whereas the cofficents of the combination are given by arbitrary solutions of suitable linear system the procedure is based on the introduction of the canonical variables corresponding to the commuting operators within such a framework we reformulate a theorem already proved by kumei and bluman siam j appl math 42 1982 the paper concludes with some illustrative examples of the proposed algorithm