The dynamics of quasi-static posture control
TL;DR: The FDT exists for human balance control and that postural sway can be modeled by an equilibrium stochastic process, and these findings suggest that the postural control system utilizes the same neuromuscular control mechanisms under quiet-standing and dynamic conditions.
About: This article is published in Human Movement Science.The article was published on 1999-10-01. It has received 27 citations till now. The article focuses on the topics: Balance (ability).
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TL;DR: Different from the standard continuous model, whose PSD function is similar to an over-damped second order system without a resonance, the intermittent control model is capable to exhibit the two power law scaling regimes that are typical of physiological sway movements in humans.
Abstract: The main purpose of this study is to compare two different feedback controllers for the stabilization of quiet standing in humans, taking into account that the intrinsic ankle stiffness is insufficient and that there is a large delay inducing instability in the feedback loop: 1) a standard linear, continuous-time PD controller and 2) an intermittent PD controller characterized by a switching function defined in the phase plane, with or without a dead zone around the nominal equilibrium state. The stability analysis of the first controller is carried out by using the standard tools of linear control systems, whereas the analysis of the intermittent controllers is based on the use of Poincare maps defined in the phase plane. When the PD-control is off, the dynamics of the system is characterized by a saddle-like equilibrium, with a stable and an unstable manifold. The switching function of the intermittent controller is implemented in such a way that PD-control is ‘off’ when the state vector is near the stable manifold of the saddle and is ‘on’ otherwise. A theoretical analysis and a related simulation study show that the intermittent control model is much more robust than the standard model because the size of the region in the parameter space of the feedback control gains (P vs. D) that characterizes stable behavior is much larger in the latter case than in the former one. Moreover, the intermittent controller can use feedback parameters that are much smaller than the standard model. Typical sway patterns generated by the intermittent controller are the result of an alternation between slow motion along the stable manifold of the saddle, when the PD-control is off, and spiral motion away from the upright equilibrium determined by the activation of the PD-control with low feedback gains. Remarkably, overall dynamic stability can be achieved by combining in a smart way two unstable regimes: a saddle and an unstable spiral. The intermittent controller exploits the stabilizing effect of one part of the saddle, letting the system evolve by alone when it slides on or near the stable manifold; when the state vector enters the strongly unstable part of the saddle it switches on a mild feedback which is not supposed to impose a strict stable regime but rather to mitigate the impending fall. The presence of a dead zone in the intermittent controller does not alter the stability properties but improves the similarity with biological sway patterns. The two types of controllers are also compared in the frequency domain by considering the power spectral density (PSD) of the sway sequences generated by the models with additive noise. Different from the standard continuous model, whose PSD function is similar to an over-damped second order system without a resonance, the intermittent control model is capable to exhibit the two power law scaling regimes that are typical of physiological sway movements in humans.
271 citations
Cites background from "The dynamics of quasi-static postur..."
...It is known indeed [8,9,10] that the PSD function of natural sway, if plotted in a loglog scale, can be well fitted by two linearly scaled regimes (or three if very low frequencies are included)....
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...5 depending on the value of the switching parameter a: this is close to the physiological scaling factor [8,9,10] and the PSD is more or less similar to Fig....
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TL;DR: The results indicate that a simple biomechanical model of walking can generate long-range correlations and thus perhaps these correlations are not a complex result of higher level neuronal control, as has been previously suggested.
Abstract: When humans walk, the time duration of each stride varies from one stride to the next. These temporal fluctuations exhibit long-range correlations. It has been suggested that these correlations stem from higher nervous system centers in the brain that control gait cycle timing. Existing proposed models of this phenomenon have focused on neurophysiological mechanisms that might give rise to these long-range correlations, and generally ignored potential alternative mechanical explanations. We hypothesized that a simple mechanical system could also generate similar long-range correlations in stride times. We modified a very simple passive dynamic model of bipedal walking to incorporate forward propulsion through an impulsive force applied to the trailing leg at each push-off. Push-off forces were varied from step to step by incorporating both “sensory” and “motor” noise terms that were regulated by a simple proportional feedback controller. We generated 400 simulations of walking, with different combinations of sensory noise, motor noise, and feedback gain. The stride time data from each simulation were analyzed using detrended fluctuation analysis to compute a scaling exponent, a. This exponent quantified how each stride interval was correlated with previous and subsequent stride intervals over different time scales. For different variations of the noise terms and feedback gain, we obtained short-range correlations (α 1.0). Our results indicate that a simple biomechanical model of walking can generate long-range correlations and thus perhaps these correlations are not a complex result of higher level neuronal control, as has been previously suggested.
77 citations
TL;DR: In this paper, the authors studied the transient and stationary behavior of many-particle systems in terms of multivariate Ornstein-Uhlenbeck processes with friction and diffusion coefficients that depend nonlinearly on process mean fields.
Abstract: We study the transient and stationary behavior of many-particle systems in terms of multivariate Ornstein-Uhlenbeck processes with friction and diffusion coefficients that depend nonlinearly on process mean fields. Mean-field approximations of this kind of system are derived in terms of Fokker-Planck equations. In such systems, multiple stationary solutions as well as bifurcations of stationary solutions may occur. In addition, strictly monotonically decreasing steady-state autocorrelation functions that decay faster than exponential functions are found, which are used to describe the erratic motion of the center of pressure during quiet standing.
76 citations
TL;DR: The results show that the analysis of features computed from the displacement of the COP are of great importance in studies trying to understand the ageing process, and the LDA-value showed to be an adequate feature for assessment of changes in the postural control which can be related to functional changes that occur over the ageing.
Abstract: The human body adopts a number of strategies to maintain an upright position. The analysis of the human balance allows for the understanding and identification of such strategies. The displacement of the centre of pressure (COP) is a measure that has been successfully employed in studies regarding the postural control. Most of these investigations are related to the analysis of individuals suffering from neuromuscular disorders. Recent studies have shown that the elderly population is growing very fast in many countries all over the world, and therefore, researches that try to understand changes in this group are required. In this context, this study proposes the analysis of the postural control, measured by the displacement of the COP, in groups of young and elderly adults. In total 59 subjects participated of this study. They were divided into seven groups according to their age. The displacement of the COP was collected for each subject standing on a force plate. Two experimental conditions, of 30 seconds each, were investigated: opened eyes and closed eyes. Traditional and recent digital signal processing tools were employed for feature computation from the displacement of the COP. Statistical analyses were carried out in order to identify significant differences between the features computed from the distinct groups that could allow for their discrimination. Our results showed that Linear Discrimination Analysis (LDA), which is one of the most popular feature extraction and classifier design techniques, could be successfully employed as a linear transformation, based on the linear combination of standard features for COP analysis, capable of estimating a unique feature, so-called LDA-value, from which it was possible to discriminate the investigated groups and show a high correlation between this feature and age. These results show that the analysis of features computed from the displacement of the COP are of great importance in studies trying to understand the ageing process. In particular, the LDA-value showed to be an adequate feature for assessment of changes in the postural control which can be related to functional changes that occur over the ageing.
70 citations
Cites methods from "The dynamics of quasi-static postur..."
...As the displacement of the COP reflects the behavior of the corporal segments to maintain itself in balance, this signal has been widely used to study the postural control [1-26]....
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TL;DR: A new technique is proposed which describes with continuity the transition among different scaling regimes, and a linear classifier is designed which gave very high performance classifying, with the best set of features, provided by the two parameters of the new model.
66 citations
References
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19 Aug 2009
TL;DR: In this article, the mean and autocovariance functions of ARIMA models are estimated for multivariate time series and state-space models, and the spectral representation of the spectrum of a Stationary Process is inferred.
Abstract: 1 Stationary Time Series.- 2 Hilbert Spaces.- 3 Stationary ARMA Processes.- 4 The Spectral Representation of a Stationary Process.- 5 Prediction of Stationary Processes.- 6* Asymptotic Theory.- 7 Estimation of the Mean and the Autocovariance Function.- 8 Estimation for ARMA Models.- 9 Model Building and Forecasting with ARIMA Processes.- 10 Inference for the Spectrum of a Stationary Process.- 11 Multivariate Time Series.- 12 State-Space Models and the Kalman Recursions.- 13 Further Topics.- Appendix: Data Sets.
5,260 citations
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01 Jan 1987
TL;DR: In this paper, the authors provide a complete treatment of an important and frequently ignored topic, namely measurement error models, including regression models with errors in the variables, latent variable models, and factor models.
Abstract: The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.
"The effort of Professor Fuller is commendable . . . [the book] provides a complete treatment of an important and frequently ignored topic. Those who work with measurement error models will find it valuable. It is the fundamental book on the subject, and statisticians will benefit from adding this book to their collection or to university or departmental libraries."
-Biometrics
"Given the large and diverse literature on measurement error/errors-in-variables problems, Fuller's book is most welcome. Anyone with an interest in the subject should certainly have this book."
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"The author is to be commended for providing a complete presentation of a very important topic. Statisticians working with measurement error problems will benefit from adding this book to their collection."
-Technometrics
" . . . this book is a remarkable achievement and the product of impressive top-grade scholarly work."
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Measurement Error Models offers coverage of estimation for situations where the model variables are observed subject to measurement error. Regression models are included with errors in the variables, latent variable models, and factor models. Results from several areas of application are discussed, including recent results for nonlinear models and for models with unequal variances. The estimation of true values for the fixed model, prediction of true values under the random model, model checks, and the analysis of residuals are addressed, and in addition, procedures are illustrated with data drawn from nearly twenty real data sets.
2,801 citations
TL;DR: In this article, a relation between the generalized resistance and the generalized forces in linear dissipative systems is obtained, which forms the extension of the Nyquist relation for the voltage fluctuations in electrical impedances.
Abstract: A relation is obtained between the generalized resistance and the fluctuations of the generalized forces in linear dissipative systems. This relation forms the extension of the Nyquist relation for the voltage fluctuations in electrical impedances. The general formalism is illustrated by applications to several particular types of systems, including Brownian motion, electric field fluctuations in the vacuum, and pressure fluctuations in a gas.
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Book•
01 Dec 19921,818 citations
Book•
14 May 1975
TL;DR: The structure of this book is based on a few guiding ideas as mentioned in this paper, including the lack of a rigid separation between classical and quantum statistical mechanics, which is the major defect in most books existing on the market.
Abstract: PREFACEIn recent years many new and excellent books on statistical mechanicsnhave appeared Yet it was my impression for a long time that a certainntype of book was still lacking on the present market Being in this mood, Inwas enormously pleased -- and honored -- when Professor S Ricensuggested that I should write a book on this subject I accepted hisnproposition gratefully and enthusiastically and started immediately on thenproject The present book is the result of four years' work In these fournyears the manuscript underwent numerous and serious transformationsnthat reflected the changes in my own mental attitudes toward the subjectnThese transformations will remain, however, in a private domain Onlynmy close friends, co-workers, and students were exposed to them: Inremain very grateful for their moral support and encouragement in allnthese yearsThe decision to draw a final full stop at the end of a manuscript isnalways a very difficult one Just as in research one never feels fullynsatisfied with one's own work, one feels tempted to continue thenrefinement process ad infinitum But other factors work in the oppositendirection An active field like statistical mechanics is very far from beingnin a steady state While one works on refining, and possibly contractingnsome chapter, new and often important results are flowing in fromnanother side, and these in turn bring along the compelling need of anrevision of some other chapter It was my repeated experience that thenresult of such phenomena is an ever-expanding volume of the manuscript,nthe contractions being always overcompensated by unavoidable additionsnFor this reason, a compromise is necessary, and a pretty arbitraryndecision is needed to terminate the manuscriptnThe structure of this book is based on a few guiding ideas It appears tonme that in a faithful representation of present-day statistical mechanicsnthe equilibrium theory and the nonequilibrium theory must be given equalnweight The lack of balance between these two aspects is, in my opinion,nthe major defect in most books existing on the market Perhaps the onlynbooks in which this equilibrium is achieved are Gibbs' and Tolman's classics As, however, these books were published in 1902 and in 1938,nrespectively, an updating was quite necessary In the present book,nequilibrium theory and nonequilibrium theory occupy roughly comparablenspace In the presentation I have attempted to stress, as much asnpossible, the features that are similar in the two fields, in order to underlinenthe structural unity of statistical mechanicsA second general feature of this book is the lack of a rigid separationnbetween classical and quantum statistical mechanics This again proceedsnfrom my search for a unified presentation On purpose, in some chapters Ingo back and forth from the quantum to the classical language, while innother chapters I use a general symbolism that can be translated at will intonone or the other My view on this point is that statistical mechanics isnsomething like a qtransfer mechanicsq whose role is to transmit informationnfrom the microscopic to the macroscopic level As such, it hasndeveloped a formalism of its own, which is well adapted to this functionnand which, basically, does not depend on the type of description of thenunderlying molecular levelOne of the most difficult decisions with which I was faced in writing thisnbook was connected with the selection of the material It is of coursenimpossible, within a reasonable volume, to discuss or even list all thenmatters in a field of science whose size is quickly approaching the qthermodynamic limitq n n n n
1,557 citations