Symmetries and itineracy in nonlinear systems with many degrees of freedom

Tsuda examines the potential contribution of nonlinear dynamical systems, with many degrees of freedom, to understanding brain function. We offer suggestions concerning symmetry and transients to strengthen the physiological motivation and theoretical consistency of this novel research direction: Symmetry plays a fundamental role, theoretically and in relation to real brains. We also highlight a distinction between chaotic "transience" and "itineracy"

Hydrodynamics and sedimentary structures of antidunes in gravel and sand mixtures

This thesis firstly reviews the current literature available on antidune bedforms and their hydrodynamic environment, alongside recent studies of the turbulence environments associated with bedforms in unidirectional flow. Based on this understanding, three suites of experiments were designed and conducted to elucidate turbulent flow structure within the standing waves above antidunes and to record the sedimentary response of a loose mobile bed that constituted the antidunes. The first suite of experiments used Acoustic Doppler Velocimetry (ADV) to quantify and characterise the flow structure above fixed bedforms and this was supported by a second suite of experiments that used high-speed video to visualise flow structure. Finally, in the third suite of experiments a loose bed of sediment was allowed to deform into antidunes beneath standing waves and the resultant sedimentary structures were recorded and related to the growth and decay of both standing waves and antidune form. Taken together these data have been interpreted in order to identify and elucidate the bulk-flow, turbulent environment of the flow field above antidunes and the sedimentary structures that characterise the preserved antidune bedding.The ADV experiments have shown that a coherent and organised spatial pattern of turbulence exists above antidune bedforms. Initially, when antidune amplitude is small, turbulent stresses are relatively equally distributed along the entire bed boundary layer, however as antidune amplitude increases there is a progressive concentration of turbulent stresses. Turbulence becomes increasingly concentrated in the near-bed region within the trough between upstream and downstream contiguous antidunes and on the upstream flank of the antidune immediately downstream. Velocities in the trough region drop significantly below the mean velocity elsewhere over antidune bedforms. A clear distinction can be drawn between sand and gravel antidunes, with gravel antidunes having comparatively much lower velocities in the trough region, and turbulence stresses (ejections, sweeps, turbulence Intensity, TKE and Reynolds Stress) an order of magnitude higher than for sand bedforms. Further, experiments over a porous gravel bed indicate levels of near bed turbulence higher than over a gravel-surfaced concrete bedform without interstitial flow. High-speed photography and interpretation of streak images further supports this ADV data.It is proposed that antidunes break when turbulence reaches an ‘intensity’ that constitutes a threshold above which rapid erosion occurs in the trough causing a pronounced increase in turbulent ejections laden with sediment and consequent rapid deposition on the downstream antidune flank. Flow then stalls over the downstream antidune; the standing wave collapses and erodes much of the bed. In terms of distinctive sedimentary structure, three types of bedding were observed in sediment sections taken after mobile bed runs where antidunes had been active. Type I bedding is formed by the erosion of the bed and marks the lowest surface formed by antidune downcutting during active migration or collapse. Type II bedding is formed by turbulent sweeps during antidune growth and migration. However the contrasts in sediment size and type that mark bedding are dependent on the heterogeneity of bed sediment. A third type of downstream dipping, bipartite planar bedding was observed to form under an upstream migrating standing wave. The preservation of a suite of sedimentologic features produced by a period of antidune activity is however dependent on the degree of downcutting and erosion during standing wave collapse

Mechanisms of Zero-Lag Synchronization in Cortical Motifs

Zero-lag synchronization between distant cortical areas has been observed in a diversity of experimental data sets and between many different regions of the brain. Several computational mechanisms have been proposed to account for such isochronous synchronization in the presence of long conduction delays: Of these, the phenomenon of "dynamical relaying" - a mechanism that relies on a specific network motif - has proven to be the most robust with respect to parameter mismatch and system noise. Surprisingly, despite a contrary belief in the community, the common driving motif is an unreliable means of establishing zero-lag synchrony. Although dynamical relaying has been validated in empirical and computational studies, the deeper dynamical mechanisms and comparison to dynamics on other motifs is lacking. By systematically comparing synchronization on a variety of small motifs, we establish that the presence of a single reciprocally connected pair - a "resonance pair" - plays a crucial role in disambiguating those motifs that foster zero-lag synchrony in the presence of conduction delays (such as dynamical relaying) from those that do not (such as the common driving triad). Remarkably, minor structural changes to the common driving motif that incorporate a reciprocal pair recover robust zero-lag synchrony. The findings are observed in computational models of spiking neurons, populations of spiking neurons and neural mass models, and arise whether the oscillatory systems are periodic, chaotic, noise-free or driven by stochastic inputs. The influence of the resonance pair is also robust to parameter mismatch and asymmetrical time delays amongst the elements of the motif. We call this manner of facilitating zero-lag synchrony resonance-induced synchronization, outline the conditions for its occurrence, and propose that it may be a general mechanism to promote zero-lag synchrony in the brain.Comment: 41 pages, 12 figures, and 11 supplementary figure

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

Dwelling Quietly in the Rich Club: Brain Network Determinants of Slow Cortical Fluctuations

For more than a century, cerebral cartography has been driven by investigations of structural and morphological properties of the brain across spatial scales and the temporal/functional phenomena that emerge from these underlying features. The next era of brain mapping will be driven by studies that consider both of these components of brain organization simultaneously -- elucidating their interactions and dependencies. Using this guiding principle, we explored the origin of slowly fluctuating patterns of synchronization within the topological core of brain regions known as the rich club, implicated in the regulation of mood and introspection. We find that a constellation of densely interconnected regions that constitute the rich club (including the anterior insula, amygdala, and precuneus) play a central role in promoting a stable, dynamical core of spontaneous activity in the primate cortex. The slow time scales are well matched to the regulation of internal visceral states, corresponding to the somatic correlates of mood and anxiety. In contrast, the topology of the surrounding "feeder" cortical regions show unstable, rapidly fluctuating dynamics likely crucial for fast perceptual processes. We discuss these findings in relation to psychiatric disorders and the future of connectomics.Comment: 35 pages, 6 figure

A dendritic mechanism for decoding traveling waves: Principles and applications to motor cortex

Traveling waves of neuronal oscillations have been observed in many cortical regions, including the motor and sensory cortex. Such waves are often modulated in a task-dependent fashion although their precise functional role remains a matter of debate. Here we conjecture that the cortex can utilize the direction and wavelength of traveling waves to encode information. We present a novel neural mechanism by which such information may be decoded by the spatial arrangement of receptors within the dendritic receptor field. In particular, we show how the density distributions of excitatory and inhibitory receptors can combine to act as a spatial filter of wave patterns. The proposed dendritic mechanism ensures that the neuron selectively responds to specific wave patterns, thus constituting a neural basis of pattern decoding. We validate this proposal in the descending motor system, where we model the large receptor fields of the pyramidal tract neurons — the principle outputs of the motor cortex — decoding motor commands encoded in the direction of traveling wave patterns in motor cortex. We use an existing model of field oscillations in motor cortex to investigate how the topology of the pyramidal cell receptor field acts to tune the cells responses to specific oscillatory wave patterns, even when those patterns are highly degraded. The model replicates key findings of the descending motor system during simple motor tasks, including variable interspike intervals and weak corticospinal coherence. By additionally showing how the nature of the wave patterns can be controlled by modulating the topology of local intra-cortical connections, we hence propose a novel integrated neuronal model of encoding and decoding motor commands