Background:Interpersonal coordination is an essential aspect of daily life,and crucial to performance in cooperative and competitive team sports.While empirical research has investigated interpersonal coordination usi...Background:Interpersonal coordination is an essential aspect of daily life,and crucial to performance in cooperative and competitive team sports.While empirical research has investigated interpersonal coordination using a wide variety of analytical tools and frameworks,to date very few studies have employed multifractal techniques to study the nature of interpersonal coordination across multiple spatiotemporal scales.In the present study we address this gap.Methods:We investigated the dynamics of a simple dyadic interpersonal coordination task where each participant manually controlled a virtual object in relation to that of his or her partner.We tested whether the resulting hand-movement time series exhibits multi-scale properties and whether those properties are associated with successful performance.Results:Using the formalism of multifractals,we show that the performance on the coordination task is strongly multi-scale,and that the multi-scale properties appear to arise from interaction-dominant dynamics.Further,we find that the measure of across-scale interactions,multifractal spectrum width,predicts successful performance at the level of the dyad.Conclusion:The results are discussed with respect to the implications of multifractals and interaction-dominance for understanding control in an interpersonal context.展开更多
Let Sdp be the p-multiple time set of the Brownian motion in d dimensions. In this paper , the Hausdorff measure function for S32 is proved to be , and the Hausdorff measuure problem for S2p is also discussed. As a re...Let Sdp be the p-multiple time set of the Brownian motion in d dimensions. In this paper , the Hausdorff measure function for S32 is proved to be , and the Hausdorff measuure problem for S2p is also discussed. As a result, a conjecture suggested by J. Rosen is partially proved.展开更多
文摘Background:Interpersonal coordination is an essential aspect of daily life,and crucial to performance in cooperative and competitive team sports.While empirical research has investigated interpersonal coordination using a wide variety of analytical tools and frameworks,to date very few studies have employed multifractal techniques to study the nature of interpersonal coordination across multiple spatiotemporal scales.In the present study we address this gap.Methods:We investigated the dynamics of a simple dyadic interpersonal coordination task where each participant manually controlled a virtual object in relation to that of his or her partner.We tested whether the resulting hand-movement time series exhibits multi-scale properties and whether those properties are associated with successful performance.Results:Using the formalism of multifractals,we show that the performance on the coordination task is strongly multi-scale,and that the multi-scale properties appear to arise from interaction-dominant dynamics.Further,we find that the measure of across-scale interactions,multifractal spectrum width,predicts successful performance at the level of the dyad.Conclusion:The results are discussed with respect to the implications of multifractals and interaction-dominance for understanding control in an interpersonal context.
文摘Let Sdp be the p-multiple time set of the Brownian motion in d dimensions. In this paper , the Hausdorff measure function for S32 is proved to be , and the Hausdorff measuure problem for S2p is also discussed. As a result, a conjecture suggested by J. Rosen is partially proved.
