dynamic margins of stability during human walking in destabilizing environments understanding how humans maintain stability when walking particularly when exposed to perturbations is key to preventing falls here we quantified how imposing continuous pseudorandom anterior posterior ap and mediolateral ml oscillations affected the control of dynamic walking stability twelve subjects completed five 3 minute walking trials in the computer assisted rehabilitation environment caren system under each of 5 conditions no perturbation nop ap platform app or visual apv or ml platform mlp or visual mlv oscillations we computed ap and ml margins of stability mos for each trial mean mosml were consistently slightly larger during all perturbation conditions than during nop p 0 038 mean mosap for the app mlp and mlv oscillations were significantly smaller than during nop p 0 0005 variability of both mosap and mosml was significantly greater during the mlp and mlv oscillations than during nop p 0 0005 we also directly quantified how the mos on any given step affected the mos on the following step using first return plots there were significant changes in step to step mosml dynamics between experimental conditions p 0 0005 these changes suggested that subjects may have been trying to control foot placement and consequently stability during the perturbation conditions quantifying step to step changes in margins of dynamic stability may be more useful than mean mos in assessing how individuals control walking stability

aging regularity and variability in maximum isometric moments this study examined the variability and regularity of maximum isometric moment production of the plantar flexors in young and old subjects it was hypothesized that in the development of maximum isometric moments there would be greater regularity in the moment profiles for older subjects compared with young subjects due to the reduced number of motor units present in elderly muscle two groups of subjects produced three maximal isometric plantar flexions young n 11 mean age 23 8 2 8 years mean mass 81 2 10 4 kg mean height 1 78 0 05 m elderly n 13 mean age 74 0 3 3 years mean mass 78 5 3 4 kg mean height 1 73 0 05 m the plateau of the moment time curve was analyzed for each trial a repeat measures analysis of variance showed the young subjects produced statistically greater peak plantar flexion moments than the elderly subjects but similar coefficients of variation signal regularity was determined by computing the signal s approximate entropy which demonstrated that the older group had greater regularity in their generation of moment profiles the hypothesis was accepted with a potential explanation for this increased regularity in old age being the reduced number of motor units to coordinate

multiscaled randomness a possible source of 1 f noise in biology we evaluate the possibility that the 1 f fluctuations observed in many biological time series result simply from the fact that biological processes have many inputs with differing time scales we present a stochastic model whose output is the summation of multiple random inputs i e different regulatory mechanisms we derive the conditions under which the model reproduces the complex fluctuations and 1 f scaling observed in biological systems simulations demonstrate that if model parameters are unconstrained the likelihood of generating 1 f noise is quite small thus while the model can be used to generate 1 mathit f mathrm ensuremath beta noise with various scaling exponents it is unlikely that the 1 f behavior observed in many biological systems is due only to the fact that these systems are regulated by many different inputs acting on different time scales textcopyright 1996 the american physical society

multidimensional inverse problems and completeness of the products of solutions to pde a method is given for proving uniqueness theorems for some inverse problems the method is based on a result on completeness of the products of solutions to pde as an example the following uniqueness theorems are proved 1 the scattering amplitude a k known for all s2 and a fixed k 0 determines the compactly supported q x l2 d uniquely 2 the surface data u x y k known for all x y p x x3 0 and a fixed k 0 determine the compactly supported x l2 d d r 3 x x3 0 is arbitrarily small determine aj x j 1 2 uniquely here 2u k2u k2a1x a2 x u x y in r3 a1 l2 d a2 h2 d the same conclusion holds if the surface data are known at two distinct frequencies 4 the surface data u x y k known for all x y p and all k 0 determine v x and h k uniquely here 2 k2 k2 x u x y h k x l2 d h k is fourier transform of a wavelet of compact support 5 the conductivity x w2 2 d x c 0 is uniquely determined by the measurements of u and un on d here n is the outward normal to d d r3 is a bounded domain with a smooth boundary d x u 0 in d 6 necessary and sufficient conditions are given for a function a k s2 k 0 is fixed to be the scattering amplitude corresponding to a local potential from a certain class

correlational analysis of acoustic cues for the discrimination of auditory motion the sound of a source moving in a straight path and passing directly in front of the listener on the azimuthal plane was synthesized over headphones to include three dynamic cues for motion doppler effect overall intensity and interaural time difference discriminability of a change in displacement velocity and acceleration of this source was measured using a standard two interval forced choice procedure in each case the relative reliance or weight given to the three acoustic cues was estimated from correlations of the listener s response with small independent perturbations imposed on cues from trial to trial group estimates of threshold agreed well with results from past studies while the obtained pattern of weights depended on the individual starting velocity and discrimination task for the discrimination of displacement at moderate velocity 10 m s responses were most highly correlated with intensity or interaural time difference for the discrimination of velocity and to a lesser extent acceleration responses were most highly correlated with doppler effect at higher velocity 50 m s responses in all discrimination tasks were most strongly correlated with doppler effect with few exceptions randomizing source spectrum or roving distance of the source from trial to trial did not significantly affect the pattern of results the results suggest that motion perception is mutable and not in all cases based on a single invariant acoustic cue

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

possible biomechanical origins of the long range correlations in stride intervals of walking 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 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

limb dominance changes in walking evolution explored by asymmetric correlations in gait dynamics abstract fluctuations in the stride interval time series of unconstrained walking are not random but seem to exhibit long range correlations that decay as a power law hausdorff et al 1995 35 here we examine whether asymmetries are present in the long range correlations of different gait parameters stride swing and stance intervals for the left and right limbs gait dynamics corresponding to 16 healthy subjects were obtained from the physionet database which contains stride stance and swing intervals for both left and right limbs detrended fluctuation analysis dfa revealed the presence of asymmetric long range correlations in all gait cycle variables investigated a rich variety of scaling exponent dynamics was found with the presence of synchronicity decreased correlations and dominant correlations the results are discussed in terms of the hypothesis that reduced strength of long range correlations reflect both enhanced stability and adaptability

formal solutions of inverse scattering problems iv error estimates the formal solutions of certain three dimensional inverse scattering problems presented in papers i iii in this series j math phys 10 1819 1969 17 1175 1976 21 2648 1980 are employed here to obtain quantitative estimates on the error resulting from the use of the born approximations in both direct and inverse potential scattering problems these estimates are uniformly valid at all energies and for all sufficiently weak potentials

a stochastic model of human gait dynamics abstract we present a stochastic model of gait rhythm dynamics based on transitions between different neural centers that reproduces distinctive statistical properties of normal human walking by tuning one model parameter the transition hopping range the model can describe alterations in gait dynamics from childhood to adulthood including a decrease in the correlation and volatility exponents with maturation the model also generates time series with multifractal spectra whose broadness depends only on this parameter moreover we find that the volatility exponent increases monotonically as a function of the width of the multifractal spectrum suggesting the possibility of a change in multifractality with maturation

formula for the radius of the support of the potential in terms of scattering data let q r r x be a real valued square integrable compactly supported function and be the smallest interval containing the support of q r let be the corresponding scattering amplitude at a fixed positive energy let be the phase shifts at k 1 it is proved that provided that q r does not change sign in some arbitrary small neighbourhood of a

evenly spacing in detrended fluctuation analysis abstract detrended fluctuation analysis is a widely used method which aims at assessing the level of self similarity in time series this method analyzes the diffusion properties of the signal by computing the linear regression slope in the diffusion plot representing in log log coordinates the relationship between the variability of the signal and the length of the intervals over which this variability is computed we compare in this paper the results obtained with logarithmically spaced and evenly spaced diffusion plots the study shows the substantial benefits of evenly spacing especially in the reduction of the variability of estimation

detection and discrimination of simulated motion of auditory targets in the horizontal plane three experiments investigated subjects ability to detect and discriminate the simulated horizontal motion of auditory targets in an anechoic environment moving stimuli were produced by dynamic application of stereophonic balancing algorithms to a two loudspeaker system with a 30 separation all stimuli were 500 hz tones in experiment 1 subjects had to discriminate a left to right moving stimulus from a stationary stimulus pulsed for the same duration 300 or 600 ms for both durations minimum audible movement angles mama s were on the order of 5 for stimuli presented at 0 azimuth straight ahead and increased to greater than 30 for stimuli presented at 90 azimuth experiment 2 further investigated mama s at 0 azimuth employing two different procedures to track threshold holding stimulus duration constant at 100 600 ms while varying velocity or holding the velocity constant at 22 360 s while varying duration results from the two procedures agreed with each other and

behavior of the solutions to exterior boundary value problems at low frequencies abstract a simple method is given to study the low frequency behavior of the solutions to exterior boundary value problems for elliptic equations of second order

uniqueness theorems for multidimensional inverse problems with unbounded coefficients abstract in a g ramm inverse problems 3 1987 l77 l82 a method to prove uniqueness theorems is given the method uses an estimate of the solution to a partial differential equation with l d coefficients here the estimate is established for l2 d coefficients and the resulting uniqueness theorems are formulated

correlation coefficients and correlation ratios as estimates of observer weights in multiple observation tasks advantages of correlational methods are described for estimating the relative reliance or weight observers give to different elements of a complex display when performing auditory or visual discriminations correlational methods differ from other such methods by providing a least squares estimate of weights rather than a maximum likelihood estimate based on a presumed model the main benefit is that these methods can be generally applied in cases where the statistical properties of elements are unknown where correlations exist between elements or where it is necessary to evaluate decision models that are inherently nonlinear

molecular analysis of the effect of relative tone level on multitone pattern discrimination molecular psychophysics attempts to model the observer s response to stimuli as they vary from trial to trial the approach has gained popularity in multitone pattern discrimination studies as a means of estimating the relative reliance or decision weight listeners give to different tones in the pattern various factors affecting decision weights have been examined but one largely ignored is the relative level of tones in the pattern in the present study listeners detected a level increment in a sequence of 5 100 ms 2 0 khz tone bursts alternating in level between 40 and 80db spl the level increment was made largest on the 40 db tones yet despite this all four highly practiced listeners gave near exclusive weight to the 80 db tones the effect was the same when the tones were replaced by bursts of broadband gaussian noise alternating in level it was reduced only when the level differences were made 10db and it was entirely reversed only when the low level tones alternated with louder bursts of ga

partial identification of the potential from phase shifts we consider the three dimensional inverse scattering with fixed energy in the spherically symmetrical case we give a characterization of the sequences of phase shifts for two potentials which can be different only in a ball of radius a in other words we study how the large distance interaction influences the asymptotical behavior of the phase shifts we also characterize the tail of the potential by the growth order of the scattering amplitude f t for large t

revisiting the stability of 2d passive biped walking local behavior models of biped walking have demonstrated that stable walking motions are possible without active control stability of these motions has typically been quantified by studying the stability of an associated poincare map orbital stability however additional insight may be obtained by examining how perturbations evolve over the short term local stability for example there may be regions where small perturbations actually diverge from the unperturbed trajectory even if over the entire cycle small but perhaps not large perturbations are dissipated we present techniques to calculate local stability and demonstrate the utility of these techniques by examining the local stability of the 2d compass biped these techniques are relevant to the design of controllers to maintain stability in robots and in understanding how the neuromuscular system maintains stability in humans

influence of simulated neuromuscular noise on movement variability and fall risk in a 3d dynamic walking model people at risk of falling exhibit increased gait variability which may predict future falls however the causal mechanisms underlying these correlations are not well known increased neuronal noise associated with aging likely leads to increased gait variability which could in turn lead to increased fall risk this paper presents a model of how changes in neuromuscular noise independently affect gait variability and probability of falling and aims to determine the extent to which changes in gait variability directly predict fall risk we used a dynamic walking model that incorporates a lateral step controller to maintain lateral stability noise was applied to this controller to approximate neuromuscular noise in humans noise amplitude was varied between low amplitudes that did not induce falls and high amplitudes for which the model always fell with increases in noise amplitude the model fell more often and after fewer steps gait variability increased with noise amplitude and predicted increased probability of falling importantly these relationships were not linear at either low gait variability or very high gait variability small increases in noise and variability affected probability of falling very little conversely at intermediate noise and or variability levels the same small increases resulted in large increases in probability of falling our results validate the idea that age related increases in neuromuscular noise likely play a direct contributing role in increasing fall risk however neuromuscular noise remains only one of many important factors that need to be considered these findings have important implications for fall prevention research and practice

symmetry properties of scattering amplitudes and applications to inverse problems abstract for the transformations of the potential q q l where l is one of the following transformations rotation scaling or translation the corresponding transformation of the scattering amplitude is given a necessary and sufficient condition on the scattering amplitude for the scatterer to be spherically symmetric is derived as an application of the above results