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      Rhythmicity, Recurrence, and Recovery of Flagellar Beating

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      Physical review letters

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          Abstract

          The eukaryotic flagellum beats with apparently unfailing periodicity, yet responds rapidly to stimuli. Like the human heartbeat, flagellar oscillations are now known to be noisy. Using the alga C. reinhardtii, we explore three aspects of nonuniform flagellar beating. We report the existence of rhythmicity, waveform noise peaking at transitions between power and recovery strokes, and fluctuations of interbeat intervals that are correlated and even recurrent, with memory extending to hundreds of beats. These features are altered qualitatively by physiological perturbations. Further, we quantify the recovery of periodic breaststroke beating from transient hydrodynamic forcing. These results will help constrain microscopic theories on the origins and regulation of flagellar beating.

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          On the shape of a set of points in the plane

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            Assessing the stability of human locomotion: a review of current measures.

            Falling poses a major threat to the steadily growing population of the elderly in modern-day society. A major challenge in the prevention of falls is the identification of individuals who are at risk of falling owing to an unstable gait. At present, several methods are available for estimating gait stability, each with its own advantages and disadvantages. In this paper, we review the currently available measures: the maximum Lyapunov exponent (λS and λL), the maximum Floquet multiplier, variability measures, long-range correlations, extrapolated centre of mass, stabilizing and destabilizing forces, foot placement estimator, gait sensitivity norm and maximum allowable perturbation. We explain what these measures represent and how they are calculated, and we assess their validity, divided up into construct validity, predictive validity in simple models, convergent validity in experimental studies, and predictive validity in observational studies. We conclude that (i) the validity of variability measures and λS is best supported across all levels, (ii) the maximum Floquet multiplier and λL have good construct validity, but negative predictive validity in models, negative convergent validity and (for λL) negative predictive validity in observational studies, (iii) long-range correlations lack construct validity and predictive validity in models and have negative convergent validity, and (iv) measures derived from perturbation experiments have good construct validity, but data are lacking on convergent validity in experimental studies and predictive validity in observational studies. In closing, directions for future research on dynamic gait stability are discussed.
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              Scaling behaviour of heartbeat intervals obtained by wavelet-based time-series analysis.

              Biological time-series analysis is used to identify hidden dynamical patterns which could yield important insights into underlying physiological mechanisms. Such analysis is complicated by the fact that biological signals are typically both highly irregular and non-stationary, that is, their statistical character changes slowly or intermittently as a result of variations in background influences. Previous statistical analyses of heartbeat dynamics have identified long-range correlations and power-law scaling in the normal heartbeat, but not the phase interactions between the different frequency components of the signal. Here we introduce a new approach, based on the wavelet transform and an analytic signal approach, which can characterize non-stationary behaviour and elucidate such phase interactions. We find that, when suitably rescaled, the distributions of the variations in the beat-to-beat intervals for all healthy subjects are described by a single function stable over a wide range of timescales. However, a similar scaling function does not exist for a group with cardiopulmonary instability caused by sleep apnoea. We attribute the functional form of the scaling observed in the healthy subjects to underlying nonlinear dynamics, which seem to be essential to normal heart function. The approach introduced here should be useful in the analysis of other nonstationary biological signals.
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                Author and article information

                Journal
                0401141
                Phys Rev Lett
                Phys Rev Lett
                Physical review letters
                0031-9007
                1079-7114
                05 December 2014
                02 December 2014
                31 May 2024
                10 June 2024
                : 113
                : 23
                : 238103
                Affiliations
                Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
                Article
                EMS196589
                10.1103/PhysRevLett.113.238103
                7616081
                25526162
                0f2338ca-9ecc-47e8-995f-33c83346abcf

                Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License.

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