Geometric phase predicts locomotion performance in undulating living systems across scales.

Self-propelling organisms locomote via generation of patterns of self-deformation. Despite the diversity of body plans, internal actuation schemes and environments in limbless vertebrates and invertebrates, such organisms often use similar traveling waves of axial body bending for movement. Delineating how self-deformation parameters lead to locomotor performance (e.g. speed, energy, turning capabilities) remains challenging. We show that a geometric framework, replacing laborious calculation with a diagrammatic scheme, is well-suited to discovery and comparison of effective patterns of wave dynamics in diverse living systems. We focus on a regime of undulatory locomotion, that of highly damped environments, which is applicable not only to small organisms in viscous fluids, but also larger animals in frictional fluids (sand) and on frictional ground. We find that the traveling wave dynamics used by mm-scale nematode worms and cm-scale desert dwelling snakes and lizards can be described by time series of weights associated with two principal modes. The approximately circular closed path trajectories of mode weights in a self-deformation space enclose near-maximal surface integral (geometric phase) for organisms spanning two decades in body length. We hypothesize that such trajectories are targets of control (which we refer to as "serpenoid templates"). Further, the geometric approach reveals how seemingly complex behaviors such as turning in worms and sidewinding snakes can be described as modulations of templates. Thus, the use of differential geometry in the locomotion of living systems generates a common description of locomotion across taxa and provides hypotheses for neuromechanical control schemes at lower levels of organization.

Using mindfulness-based intervention to promote executive function in young children: a multivariable and multiscale sample entropy study.

Early childhood marks a pivotal period in the maturation of executive function, the cognitive ability to consciously regulate actions and thoughts. Mindfulness-based interventions have shown promise in bolstering executive function in children. This study used the functional near-infrared spectroscopy technique to explore the impact of mindfulness-based training on young children. Brain imaging data were collected from 68 children (41 boys, aged 61.8 ± 10.7 months) who were randomly assigned to either an intervention group (N = 37, aged 60.03 ± 11.14 months) or a control group (N = 31, aged 59.99 ± 10.89 months). Multivariate and multiscale sample entropy analyses were used. The results showed that: (1) brain complexity was reduced in the intervention group after receiving the mindfulness-based intervention in all three executive function tasks (ps < 0.05), indicating a more efficient neural processing mechanism after the intervention; (2) difference comparisons between the intervention and control groups showed significant differences in relevant brain regions during cognitive shifting (left dorsolateral prefrontal cortex and medial prefrontal cortex) and working memory tasks (left dorsolateral prefrontal cortex), which corroborates with improved behavioral results in the intervention group (Z = -3.674, P < 0.001 for cognitive shifting; Z = 2.594, P < 0.01 for working memory). These findings improve our understanding of early brain development in young children and highlight the neural mechanisms by which mindfulness-based interventions affect executive function. Implications for early intervention to promote young children's brain development are also addressed.

Surprising simplicities and syntheses in limbless self-propulsion in sand.

Animals moving on and in fluids and solids move their bodies in diverse ways to generate propulsion and lift forces. In fluids, animals can wiggle, stroke, paddle or slap, whereas on hard frictional terrain, animals largely engage their appendages with the substrate to avoid slip. Granular substrates, such as desert sand, can display complex responses to animal interactions. This complexity has led to locomotor strategies that make use of fluid-like or solid-like features of this substrate, or combinations of the two. Here, we use examples from our work to demonstrate the diverse array of methods used and insights gained in the study of both surface and subsurface limbless locomotion in these habitats. Counterintuitively, these seemingly complex granular environments offer certain experimental, theoretical, robotic and computational advantages for studying terrestrial movement, with the potential for providing broad insights into morphology and locomotor control in fluids and solids, including neuromechanical control templates and morphological and behavioral evolution. In particular, granular media provide an excellent testbed for a locomotion framework called geometric mechanics, which was introduced by particle physicists and control engineers in the last century, and which allows quantitative analysis of alternative locomotor patterns and morphology to test for control templates, optimality and evolutionary alternatives. Thus, we posit that insights gained from movement in granular environments can be translated into principles that have broader applications across taxa, habitats and movement patterns, including those at microscopic scales.

Modulation of orthogonal body waves enables high maneuverability in sidewinding locomotion.

Many organisms move using traveling waves of body undulation, and most work has focused on single-plane undulations in fluids. Less attention has been paid to multiplane undulations, which are particularly important in terrestrial environments where vertical undulations can regulate substrate contact. A seemingly complex mode of snake locomotion, sidewinding, can be described by the superposition of two waves: horizontal and vertical body waves with a phase difference of ± 90°. We demonstrate that the high maneuverability displayed by sidewinder rattlesnakes (Crotalus cerastes) emerges from the animal's ability to independently modulate these waves. Sidewinder rattlesnakes used two distinct turning methods, which we term differential turning (26° change in orientation per wave cycle) and reversal turning (89°). Observations of the snakes suggested that during differential turning the animals imposed an amplitude modulation in the horizontal wave whereas in reversal turning they shifted the phase of the vertical wave by 180°. We tested these mechanisms using a multimodule snake robot as a physical model, successfully generating differential and reversal turning with performance comparable to that of the organisms. Further manipulations of the two-wave system revealed a third turning mode, frequency turning, not observed in biological snakes, which produced large (127°) in-place turns. The two-wave system thus functions as a template (a targeted motor pattern) that enables complex behaviors in a high-degree-of-freedom system to emerge from relatively simple modulations to a basic pattern. Our study reveals the utility of templates in understanding the control of biological movement as well as in developing control schemes for limbless robots.

A review on locomotion robophysics: the study of movement at the intersection of robotics, soft matter and dynamical systems.

Discovery of fundamental principles which govern and limit effective locomotion (self-propulsion) is of intellectual interest and practical importance. Human technology has created robotic moving systems that excel in movement on and within environments of societal interest: paved roads, open air and water. However, such devices cannot yet robustly and efficiently navigate (as animals do) the enormous diversity of natural environments which might be of future interest for autonomous robots; examples include vertical surfaces like trees and cliffs, heterogeneous ground like desert rubble and brush, turbulent flows found near seashores, and deformable/flowable substrates like sand, mud and soil. In this review we argue for the creation of a physics of moving systems-a 'locomotion robophysics'-which we define as the pursuit of principles of self-generated motion. Robophysics can provide an important intellectual complement to the discipline of robotics, largely the domain of researchers from engineering and computer science. The essential idea is that we must complement the study of complex robots in complex situations with systematic study of simplified robotic devices in controlled laboratory settings and in simplified theoretical models. We must thus use the methods of physics to examine both locomotor successes and failures using parameter space exploration, systematic control, and techniques from dynamical systems. Using examples from our and others' research, we will discuss how such robophysical studies have begun to aid engineers in the creation of devices that have begun to achieve life-like locomotor abilities on and within complex environments, have inspired interesting physics questions in low dimensional dynamical systems, geometric mechanics and soft matter physics, and have been useful to develop models for biological locomotion in complex terrain. The rapidly decreasing cost of constructing robot models with easy access to significant computational power bodes well for scientists and engineers to engage in a discipline which can readily integrate experiment, theory and computation.

Enhancing Chinese preschoolers' executive function via mindfulness training: An fNIRS study.

Mindfulness training has been found to enable cognitive and emotional awareness and diminish emotional distraction and cognitive rigidity. However, the existing intervention studies have largely focused on school children, adolescents, and adults, leaving young children unexplored. This study examined the influence of mindfulness training on young children using the one-group pretest-posttest design. Altogether 31 Chinese preschoolers (M age = 67.03 months, SD = 4.25) enrolled in a 5-week, twice-per-week mindfulness training. Their cognitive shifting, inhibitory control, and working memory were examined using a battery of executive function tasks. And their brain activations in the region of interest during the tasks were measured using fNIRS before and after the intervention. Results showed that their cognitive shifting and working memory tasks performance significantly improved, and their activation in the DLPFC significantly changed. Implications for this study were also included.

An fNIRS Study of Applicability of the Unity-Diversity Model of Executive Functions in Preschoolers.

Executive function (EF) includes a set of higher-order abilities that control one's actions and thoughts consciously and has a protracted developmental trajectory that parallels the maturation of the frontal lobes, which develop speedily over the preschool period. To fully understand the development of EF in preschoolers, this study examined the relationship among the three domains of executive function (cognitive shifting, inhibitory control, and working memory) to test the applicability of the unity-diversity model in preschoolers using both behavioral and fNIRS approaches. Altogether, 58 Chinese preschoolers (34 boys, 24 girls, Mage = 5.86 years, SD = 0.53, age range = 4.83-6.67 years) were administered the Dimensional Card Change Sort (DCCS), go/no-go, and missing scan task. Their brain activations in the prefrontal cortex during the tasks were examined using fNIRS. First, the behavioral results indicated that the missing scan task scores (working memory) correlated with the DCCS (cognitive shifting) and go/no-go tasks (inhibitory control). However, the latter two did not correlate with each other. Second, the fNIRS results demonstrated that the prefrontal activations during the working memory task correlated with those in the same regions during the cognitive shifting and inhibitory control tasks. However, the latter two still did not correlate. The behavioral and neuroimaging evidence jointly indicates that the unity-diversity model of EF does apply to Chinese preschoolers.

Tail use improves performance on soft substrates in models of early vertebrate land locomotors.

In the evolutionary transition from an aquatic to a terrestrial environment, early tetrapods faced the challenges of terrestrial locomotion on flowable substrates, such as sand and mud of variable stiffness and incline. The morphology and range of motion of appendages can be revealed in fossils; however, biological and robophysical studies of modern taxa have shown that movement on such substrates can be sensitive to small changes in appendage use. Using a biological model (the mudskipper), a physical robot model, granular drag measurements, and theoretical tools from geometric mechanics, we demonstrate how tail use can improve robustness to variable limb use and substrate conditions. We hypothesize that properly coordinated tail movements could have provided a substantial benefit for the earliest vertebrates to move on land.

Sidewinding with minimal slip: snake and robot ascent of sandy slopes.

Limbless organisms such as snakes can navigate nearly all terrain. In particular, desert-dwelling sidewinder rattlesnakes (Crotalus cerastes) operate effectively on inclined granular media (such as sand dunes) that induce failure in field-tested limbless robots through slipping and pitching. Our laboratory experiments reveal that as granular incline angle increases, sidewinder rattlesnakes increase the length of their body in contact with the sand. Implementing this strategy in a physical robot model of the snake enables the device to ascend sandy slopes close to the angle of maximum slope stability. Plate drag experiments demonstrate that granular yield stresses decrease with increasing incline angle. Together, these three approaches demonstrate how sidewinding with contact-length control mitigates failure on granular media.