Directed Flow of Information in Chimera States

We investigated interactions within chimera states in a phase oscillator network with two coupled subpopulations. To quantify interactions within and between these subpopulations, we estimated the corresponding (delayed) mutual information that -- in general -- quantifies the capacity or the maximum rate at which information can be transferred to recover a sender's information at the receiver with a vanishingly low error probability. After verifying their equivalence with estimates based on the continuous phase data, we determined the mutual information using the time points at which the individual phases passed through their respective Poincar\'{e} sections. This stroboscopic view on the dynamics may resemble, e.g., neural spike times, that are common observables in the study of neuronal information transfer. This discretization also increased processing speed significantly, rendering it particularly suitable for a fine-grained analysis of the effects of experimental and model parameters. In our model, the delayed mutual information within each subpopulation peaked at zero delay, whereas between the subpopulations it was always maximal at non-zero delay, irrespective of parameter choices. We observed that the delayed mutual information of the desynchronized subpopulation preceded the synchronized subpopulation. Put differently, the oscillators of the desynchronized subpopulation were 'driving' the ones in the synchronized subpopulation. These findings were also observed when estimating mutual information of the full phase trajectories. We can thus conclude that the delayed mutual information of discrete time points allows for inferring a functional directed flow of information between subpopulations of coupled phase oscillators

Multivariate Ornstein-Uhlenbeck processes with mean-field dependent coefficients: Application to postural sway

We study the transient and stationary behavior of many-particle systems in terms of multivariate OrnsteinUhlenbeck processes with friction and diffusion coefficients that depend nonlinearly on process mean fields. Mean-field approximations of this kind of system are derived in terms of Fokker-Planck equations. In such systems, multiple stationary solutions as well as bifurcations of stationary solutions may occur. In addition, strictly monotonically decreasing steady-state autocorrelation functions that decay faster than exponential functions are found, which are used to describe the erratic motion of the center of pressure during quiet standing

Effects of velocity and limb loading on the coordination between limb movements during walking.

The authors investigated the effects of velocity (increasing from 0.5 to 5.0 km/hr in steps of 0.5 km/hr) and limb loading on the coordination between arm and leg movements during treadmill walking in 7 participants. Both the consistency of the individual limb movements and the stability of their coordination increased with increasing velocity; the frequency coordination between arm and leg movements was 2:1 at the lower velocities and 1:1 at the higher velocities. The mass manipulation affected the individual limb movements but not their coordination, indicating that a stable walking pattern was preserved. The results differed qualitatively from those obtained in studies on bimanual interlimb coordination, implying that the dynamical principles identified therein are not readily applicable to locomotion

Multiple time scales and multiform dynamics in learning to juggle.

To study the acquisition of perceptual-motor skills as an instance of dynamic pattern formation, we examined the evolution of postural sway and eye and head movements in relation to changes in performance, while 13 novices practiced 3-ball cascade juggling for 9 weeks. Ball trajectories, postural sway, and eye and head movements were recorded repeatedly. Performance improved exponentially, both in terms of the number of consecutive throws and the degree of frequency and phase locking between the ball trajectories. These aspects of performance evolved at different time scales, indicating the presence of a temporal hierarchy in learning. Postural sway, and eye and head movements were often 3:2 and sometimes 3:1 frequency locked to the ball trajectories. As a rule, the amplitudes of these oscillatory processes decreased exponentially at rates similar to that of the increase in the degree of phase locking between the balls. In contrast, the coordination between these oscillatory processes evolved exponentially at different time scales, apart from some erratic evolutions. Collectively, these findings indicate that skill acquisition in the perceptual-motor domain involves multiple time scales and multiform dynamics, both in terms of the development of the goal behavior itself and the evolution of the processes subserving this goal behavior

Neural synchrony within the motor system: what have we learned so far?

Synchronization of neural activity is considered essential for information processing in the nervous system. Both local and inter-regional synchronization are omnipresent in different frequency regimes and relate to a variety of behavioral and cognitive functions. Over the years, many studies have sought to elucidate the question how alpha/mu, beta, and gamma synchronization contribute to motor control. Here, we review these studies with the purpose to delineate what they have added to our understanding of the neural control of movement. We highlight important findings regarding oscillations in primary motor cortex, synchronization between cortex and spinal cord, synchronization between cortical regions, as well as abnormal synchronization patterns in a selection of motor dysfunctions. The interpretation of synchronization patterns benefits from combining results of invasive and non-invasive recordings, different data analysis tools, and modeling work. Importantly, although synchronization is deemed to play a vital role, it is not the only mechanism for neural communication. Spike timing and rate coding act together during motor control and should therefore both be accounted for when interpreting movement-related activity

Dynamical coupling between locomotion and respiration.

In search of the formative principles underwriting locomotor-respiratory coupling, we reanalyzed and modeled the data collected by Siegmund and coworkers (1999) on the synchronization of respiration during rowing. Apart from the frequency doubling in respiration reported earlier, detailed time-resolved spectral analyses revealed decreasing stability of entrainment close to abrupt changes in frequency relations as well as switches in the relative phase between respiration and locomotion. A single physiological, albeit mechanically constrained, quantity sufficed to explain the observed frequency and phase locking phenomena: the effective value of oxygen volume in the lungs. The cyclic abdominal pressure modulates the self-sustaining rhythmic respiration, modifies the total lung pressure, and causes (local) maxima at frequency ratios between movement and respiration that are composed of small integers. Hence, optimizing the effective oxygen volume can be seen as the mechanism that drives respiration to synchronize with locomotion. © Springer-Verlag 2004