Using spike train distances to identify the most discriminative neuronal subpopulation

Background: Spike trains of multiple neurons can be analyzed following the summed population (SP) or the labeled line (LL) hypothesis. Responses to external stimuli are generated by a neuronal population as a whole or the individual neurons have encoding capacities of their own. The SPIKE-distance estimated either for a single, pooled spike train over a population or for each neuron separately can serve to quantify these responses. New Method: For the SP case we compare three algorithms that search for the most discriminative subpopulation over all stimulus pairs. For the LL case we introduce a new algorithm that combines neurons that individually separate different pairs of stimuli best. Results: The best approach for SP is a brute force search over all possible subpopulations. However, it is only feasible for small populations. For more realistic settings, simulated annealing clearly outperforms gradient algorithms with only a limited increase in computational load. Our novel LL approach can handle very involved coding scenarios despite its computational ease. Comparison with Existing Methods: Spike train distances have been extended to the analysis of neural populations interpolating between SP and LL coding. This includes parametrizing the importance of distinguishing spikes being fired in different neurons. Yet, these approaches only consider the population as a whole. The explicit focus on subpopulations render our algorithms complimentary. Conclusions: The spectrum of encoding possibilities in neural populations is broad. The SP and LL cases are two extremes for which our algorithms provide correct identification results.Comment: 14 pages, 9 Figure

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

Generalized time-frequency coherency for assessing neural interactions in electrophysiological recordings

Time-frequency coherence has been widely used to quantify statistical dependencies in bivariate data and has proven to be vital for the study of neural interactions in electrophysiological recordings. Conventional methods establish time-frequency coherence by smoothing the cross and power spectra using identical smoothing procedures. Smoothing entails a trade-off between time-frequency resolution and statistical consistency and is critical for detecting instantaneous coherence in single-trial data. Here, we propose a generalized method to estimate time-frequency coherency by using different smoothing procedures for the cross spectra versus power spectra. This novel method has an improved trade-off between time resolution and statistical consistency compared to conventional methods, as verified by two simulated data sets. The methods are then applied to single-trial surface encephalography recorded from human subjects for comparative purposes. Our approach extracted robust alpha- and gamma-band synchronization over the visual cortex that was not detected by conventional methods, demonstrating the efficacy of this method

Ott-Antonsen attractiveness for parameter-dependent oscillatory systems

The Ott-Antonsen (OA) ansatz [Ott and Antonsen, Chaos 18, 037113 (2008); Chaos 19, 023117 (2009)] has been widely used to describe large systems of coupled phase oscillators. If the coupling is sinusoidal and if the phase dynamics does not depend on the specific oscillator, then the macroscopic behavior of the systems can be fully described by a low-dimensional dynamics. Does the corresponding manifold remain attractive when introducing an intrinsic dependence between an oscillator's phase and its dynamics by additional, oscillator specific parameters? To answer this, we extended the OA ansatz and proved that parameter-dependent oscillatory systems converge to the OA manifold given certain conditions. Our proof confirms recent numerical findings that already hinted at this convergence. Furthermore, we offer a thorough mathematical underpinning for networks of so-called theta neurons, where the OA ansatz has just been applied. In a final step, we extend our proof by allowing for time-dependent and multi-dimensional parameters as well as for network topologies other than global coupling. This renders the OA ansatz an excellent starting point for the analysis of a broad class of realistic settings

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

Equivalence of coupled networks and networks with multimodal frequency distributions:Conditions for the bimodal and trimodal case

Populations of oscillators can display a variety of synchronization patterns depending on the oscillators' intrinsic coupling and the coupling between them. We consider two coupled symmetric (sub)populations with unimodal frequency distributions. If internal and external coupling strengths are identical, a change of variables transforms the system into a single population of oscillators whose natural frequencies are bimodally distributed. Otherwise an additional bifurcation parameter κ enters the dynamics. By using the Ott-Antonsen ansatz, we rigorously prove that κ does not lead to new bifurcations, but that a symmetric two-coupled-population network and a network with a symmetric bimodal frequency distribution are topologically equivalent. Seeking for generalizations, we further analyze a symmetric trimodal network vis-à-vis three coupled symmetric unimodal populations. Here, however, the equivalence with respect to stability, dynamics, and bifurcations of the two systems no longer holds