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The body mass index (BMI), defined as weight in kilograms divided by height in meters squared, has been widely used to assess thinness and obesity in all age groups, including children and adolescents. However, the validity and utility of BMI as a reliable measure of nutritional health have been questioned. This study discusses the mathematical conditions that support the validity of BMI based on population statistics. Here, we propose a condition defined as allometric uni-scaling to ensure the validity of BMI as an objective height-adjusted measure. Any given centile curve, including the median curve, in a weight-for-height distribution should be approximated using power-law functions with the same scaling exponent. In contrast, when the scaling exponent varies depending on the position of the centile curve, it is called allometric multi-scaling. By introducing a method for testing these scaling properties using quantile regression, we analyzed a large-scale Japanese database that included 7,863,520 children aged 5-17 years. We demonstrated the remarkable multi-scaling properties at ages 5-13 years for males and 5-11 years for females, and the convergence to uni-scaling with a scaling exponent close to 2 as they approached 17 years of age for both sexes. We confirmed that conventional BMI is appropriate as an objective height-adjusted mass measure at least 17 years of age, close to adulthood, for both males and females. However, the validity of BMI could not be confirmed in younger age groups. Our findings indicate that the growth of children's weight-for-height relation is much more complex than previously assumed. Therefore, a single BMI-type formula cannot be used to assess thinness and obesity in children and adolescents., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Ogata et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Dexterous postural control subtly complements movement variability with sensory correlations at many scales. The expressive poise of gymnasts exemplifies this lyrical punctuation of release with constraint, from coarse grain to fine scales. Dexterous postural control upon a 2D support surface might collapse the variation of center of pressure (CoP) to a relatively 1D orientation-a direction often oriented towards the focal point of a visual task. Sensory corrections in dexterous postural control might manifest in temporal correlations, specifically as fractional Brownian motions whose differences are more and less correlated with fractional Gaussian noises ( fGn s) with progressively larger and smaller Hurst exponent H . Traditional empirical work examines this arrangement of lower-dimensional compression of CoP along two orthogonal axes, anteroposterior (AP) and mediolateral (ML). Eyes-open and face-forward orientations cultivate greater variability along AP than ML axes, and the orthogonal distribution of spatial variability has so far gone hand in hand with an orthogonal distribution of H , for example, larger in AP and lower in ML. However, perturbing the orientation of task focus might destabilize the postural synergy away from its 1D distribution and homogenize the temporal correlations across the 2D support surface, resulting in narrower angles between the directions of the largest and smallest H . We used oriented fractal scaling component analysis (OFSCA) to investigate whether sensory corrections in postural control might thus become suborthogonal. OFSCA models raw 2D CoP trajectory by decomposing it in all directions along the 2D support surface and fits the directions with the largest and smallest H . We studied a sample of gymnasts in eyes-open and face-forward quiet posture, and results from OFSCA confirm that such posture exhibits the classic orthogonal distribution of temporal correlations. Head-turning resulted in a simultaneous decrease in this angle Δ θ , which promptly reversed once gymnasts reoriented their heads forward. However, when vision was absent, there was only a discernible negative trend in Δ θ , indicating a shift in the angle's direction but not a statistically significant one. Thus, the narrowing of Δ θ may signify an adaptive strategy in postural control. The swift recovery of Δ θ upon returning to a forward-facing posture suggests that the temporary reduction is specific to head-turning and does not impose a lasting burden on postural control. Turning the head reduced the angle between these two orientations, facilitating the release of postural degrees of freedom towards a more uniform spread of the CoP across both dimensions of the support surface. The innovative aspect of this work is that it shows how fractality might serve as a control parameter of adaptive mechanisms of dexterous postural control., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Mangalam, Seleznov, Kolosova, Popov, Kelty-Stephen and Kiyono.)