Phase response curves and the role of coordinates.

The "infinitesimal phase response curve" (PRC) is a common tool used to analyze phase resetting in the natural sciences in general and neuroscience in particular. We make the observation that the PRC with respect to a coordinate v actually depends on the choice of other coordinates. As a consequence, a complete delay embedding reconstruction of the dynamics using v which would allow phase to be computed still does not allow the v PRC to be computed.

Challenges in dynamic mode decomposition.

Dynamic mode decomposition (DMD) is a powerful tool for extracting spatial and temporal patterns from multi-dimensional time series, and it has been used successfully in a wide range of fields, including fluid mechanics, robotics and neuroscience. Two of the main challenges remaining in DMD research are noise sensitivity and issues related to Krylov space closure when modelling nonlinear systems. Here, we investigate the combination of noise and nonlinearity in a controlled setting, by studying a class of systems with linear latent dynamics which are observed via multinomial observables.

Data-driven geometric system identification for shape-underactuated dissipative systems.

Modeling system dynamics becomes challenging when the properties of individual system components cannot be directly measured, and often requires identification of properties from observed motion. In this paper, we show that systems whose movement is highly dissipative have features which provide an opportunity to more easily identify models and more quickly optimize motions than would be possible with general techniques. Geometric mechanics provides means for reduction of the dynamics by environmental homogeneity, while the dissipative nature minimizes the role of second order (inertial) features in the dynamics.

Multi-legged steering and slipping with low DoF hexapod robots.

Thanks to their sprawled posture and multi-legged support, stability is not as hard to achieve for hexapedal robots as it is for bipeds and quadrupeds. A key engineering challenge with hexapods has been to produce insect-like agility and maneuverability, of which steering is an essential part. However, the mechanisms of multi-legged steering are not always clear, especially for robots with underactuated legs.

Morphology and the gradient of a symmetric potential predict gait transitions of dogs.

Gaits and gait transitions play a central role in the movement of animals. Symmetry is thought to govern the structure of the nervous system, and constrain the limb motions of quadrupeds. We quantify the symmetry of dog gaits with respect to combinations of bilateral, fore-aft, and spatio-temporal symmetry groups.

Longitudinal quasi-static stability predicts changes in dog gait on rough terrain.

Legged animals utilize gait selection to move effectively and must recover from environmental perturbations. We show that on rough terrain, domestic dogs, , spend more time in longitudinal quasi-statically stable patterns of movement. Here, longitudinal refers to the rostro-caudal axis.

Thermal adaptation and phosphorus shape thermal performance in an assemblage of rainforest ants.

We studied the Thermal Performance Curves (TPCs) of 87 species of rainforest ants and found support for both the Thermal Adaptation and Phosphorus-Tolerance hypotheses. TPCs relate a fitness proxy (here, worker speed) to environmental temperature. Thermal Adaptation posits that thermal generalists (ants with flatter, broader TPCs) are favored in the hotter, more variable tropical canopy compared to the cooler, less variable litter below.

Constructing predictive models of human running.

Running is an essential mode of human locomotion, during which ballistic aerial phases alternate with phases when a single foot contacts the ground. The spring-loaded inverted pendulum (SLIP) provides a starting point for modelling running, and generates ground reaction forces that resemble those of the centre of mass (CoM) of a human runner. Here, we show that while SLIP reproduces within-step kinematics of the CoM in three dimensions, it fails to reproduce stability and predict future motions.

Instantaneous kinematic phase reflects neuromechanical response to lateral perturbations of running cockroaches.

Instantaneous kinematic phase calculation allows the development of reduced-order oscillator models useful in generating hypotheses of neuromechanical control. When perturbed, changes in instantaneous kinematic phase and frequency of rhythmic movements can provide details of movement and evidence for neural feedback to a system-level neural oscillator with a time resolution not possible with traditional approaches. We elicited an escape response in cockroaches (Blaberus discoidalis) that ran onto a movable cart accelerated laterally with respect to the animals' motion causing a perturbation.

Finding the dimension of slow dynamics in a rhythmic system.

Dynamical systems with asymptotically stable periodic orbits are generic models for rhythmic processes in dissipative physical systems. This paper presents a method for reconstructing the dynamics near a periodic orbit from multivariate time-series data. It is used to test theories about the control of legged locomotion, a context in which time series are short when compared with previous work in nonlinear time-series analysis.

Insects running on elastic surfaces.

In nature, cockroaches run rapidly over complex terrain such as leaf litter. These substrates are rarely rigid, and are frequently very compliant. Whether and how compliant surfaces change the dynamics of rapid insect locomotion has not been investigated to date largely due to experimental limitations.

Estimating the phase of synchronized oscillators.

The state of a collection of phase-locked oscillators is determined by a single phase variable or cyclic coordinate. This paper presents a computational method, Phaser, for estimating the phase of phase-locked oscillators from limited amounts of multivariate data in the presence of noise and measurement errors. Measurements are assumed to be a collection of multidimensional time series.

Active tails enhance arboreal acrobatics in geckos.

Geckos are nature's elite climbers. Their remarkable climbing feats have been attributed to specialized feet with hairy toes that uncurl and peel in milliseconds. Here, we report that the secret to the gecko's arboreal acrobatics includes an active tail.