RESUMEN
Terrestrial locomotion is a complex phenomenon that is often linked to the survival of an individual and of an animal species. Mathematical models seek to express in quantitative terms how animals move, but this is challenging because the ways in which the nervous and musculoskeletal systems interact to produce body movement is not completely understood. Models with many variables tend to lack biological interpretability and describe the motion of an animal with too many independent degrees of freedom. Instead, reductionist models aim to describe the essential features of a gait with the smallest number of variables, often concentrating on the center of mass dynamics. In particular, spring-mass models have been successful in extracting and describing important characteristics of running. In this paper, we consider the spring loaded inverted pendulum model under the regime of constant angular velocity, small compression, and small angle swept during stance. We provide conditions for the asymptotic stability of periodic trajectories for the full range of parameters. The hypothesis of linear angular dynamics during stance is successfully tested on publicly available human data of individuals running on a treadmill at different velocities. Our analysis highlights a novel bifurcation phenomenon for varying Froude number: there are periodic trajectories of the spring loaded inverted pendulum model that are stable only in a restricted range of Froude numbers, while they become unstable for smaller or larger Froude numbers.
RESUMEN
Typically, animal locomotion studies involve consecutive strides, which are frequently assumed to be independent with parameters that do not vary across strides. This assumption is often not tested. However, failing in particular to account for dependence across strides may cause an incorrect estimate of the uncertainty of the measurements and thereby lead to either missing (overestimating variance) or over-evaluating (underestimating variance) biological signals. In turn, this impacts replicability of the results because variability is accounted for differently across experiments. In this paper, we analyse the changes of a couple of measures of human leg stiffness across strides during running experiments, using a publicly available dataset. A major finding of this analysis is that the time series of these measurements of stiffness show autocorrelation even at large lags and so there is dependence between individual strides, even when separated by many intervening strides. Our results question the practice in biomechanics research of using each stride as an independent observation or of sub-selecting strides at small lags. Following the outcome of our analysis, we strongly recommend caution in doing so without first confirming the independence of the measurements across strides and without confirming that sub-selection does not produce spurious results.
RESUMEN
The spring-mass model is a model of locomotion aimed at giving the essential mathematical laws of the trajectory of the center of mass of an animal during bouncing gaits, such as hopping (one-dimensional) and running (two-dimensional). This reductionist mechanical system has been extensively investigated for locomotion over horizontal surfaces, whereas it has been largely neglected on other ecologically relevant surfaces, including inclines. For example, how the degree of inclination impacts the dynamics of the center of mass of the spring-mass model has not been investigated thoroughly. In this work, we derive a mathematical model which extends the spring-mass model to inclined surfaces. Among our results, we derive an approximate solution of the system, assuming a small angular sweep of the limb and a small spring compression during stance, and show that this approximation is very accurate, especially for small inclinations of the ground. Furthermore, we derive theoretical bounds on the difference between the Lagrangian and Lagrange equations of the true and approximate system, and discuss locomotor stability questions of the approximate solutions. We test our models through a sensitivity analysis using parameters relevant to the locomotion of bipedal animals (quail, pheasant, guinea fowl, turkey, ostrich, and humans) and compare our approximate solution to the numerically derived solution of the exact system. We compare the two-dimensional spring-mass model on inclines with the one-dimensional spring-mass model to which it reduces under the limit of no horizontal velocity; we compare the two-dimensional spring-mass model on inclines with the inverted-pendulum model on inclines towards which it converges in the case of high stiffness-to-mass ratio. We include comparisons with historically prevalent no-gravity approximations of these models, as well. The insights we have gleaned through all these comparisons and the ability of our approximation to replicate some of the kinematic changes observed in animals moving on different inclines (e.g. reduction in vertical oscillation of the center of mass and decreased stride length) underlines the valuable and reasonable contributions that very simple, reductionist models, like the spring-mass model, can provide.
RESUMEN
Arboreal animals must learn to modulate their movements to overcome the challenges posed by the complexity of their heterogeneous environment, reduce performance failure, and survive. Anolis lizards are remarkable in the apparent ease with which they conquer this heterogeneity, demonstrating an impressive ability to modulate their locomotor behavior to maintain stable locomotion on widely disparate surfaces. Significant progress has been made towards understanding the impact of substrate structure on the behavioral plasticity of arboreal species, but it is unclear whether the same strategies employed to shift between substrates in one context can be employed to shift between those same substrates in a new context. Is the kinematic shift between broad and narrow perches achieved in a similar way on different inclines? Do all species within an ecomorph make similar adjustments? Here, we analyze the limb movements of two trunk-crown Anolis ecomorphs, A. carolinensis and A. evermanni, running on 6 different surfaces (3 inclinations × 2 perch diameters), from the perspective of Transfer Learning. Transfer learning is that field of machine learning which aims at exploiting the knowledge gained from one task to improve generalization about another, related task. In our setting, we use transfer learning to show that the strategies employed to improve locomotor stability on narrow perches are transferred across environments with different inclines. Further, behaviors used on vertical inclines are shared, and thus transfer well, across perch diameters whereas the relationship between horizontal and intermediate inclines change on different perch diameters, leading to lower transfer learning of shallow inclines across perch diameters. Interestingly, the best incline for transfer of behavior differs between limbs: forelimb models learn best from the vertical incline and hind limb models learn best from horizontal and intermediate inclines. Finally, our results suggest both that subtle differences exist in how A. carolinensis and A. evermanni adjust their behaviors in typical trunk-crown environments and that they may have converged on similar strategies for modulating forelimb behavior on vertical surfaces and hind limb behavior on shallow surfaces. The transfer of behavior is analogous to phenotypic plasticity, which likely plays a key role in the rapid adaptive evolution characteristic of Anolis lizards. This work is an example of how modern statistical methodology can provide an interesting perspective on new biological questions, such as on the role and nuances of behavioral plasticity and the key behaviors that help shape the versatility and rapid evolution of Anolis lizards.
RESUMEN
This study investigates the relationship between socio-economic determinants pre-dating the pandemic and the reported number of cases, deaths, and the ratio of deaths/cases in 199 countries/regions during the first months of the COVID-19 pandemic. The analysis is performed by means of machine learning methods. It involves a portfolio/ensemble of 32 interpretable models and considers the case in which the outcome variables (number of cases, deaths, and their ratio) are independent and the case in which their dependence is weighted based on geographical proximity. We build two measures of variable importance, the Absolute Importance Index (AII) and the Signed Importance Index (SII) whose roles are to identify the most contributing socio-economic factors to the variability of the COVID-19 pandemic. Our results suggest that, together with the established influence on cases and deaths of the level of mobility, the specific features of the health care system (smart/poor allocation of resources), the economy of a country (equity/non-equity), and the society (religious/not religious or community-based vs not) might contribute to the number of COVID-19 cases and deaths heterogeneously across countries.