Coupled oscillators and multivariate phase statistics

Dynamical system formulations of weakly coupled oscillators are interesting because they have proven effective at capturing the properties of real-world systems and are compelling models of neural systems. For example, oscillations have been measured in the LGN and are thought to subserve varied processing such as binding and communication. A better understanding of these neural processes requires statistical tools that are designed to model oscillatory signals. With this goal in mind, we have produced novel pairwise phase distributions and algorithms to estimate the parameters of these distributions from observed phase statistics. Interestingly, we have shown a relation between these probabilistic models and dynamic models of coupled oscillators.

Estimating functional connectivity in the brain

It is well accepted that the brain processes information using networks of coupled but distributed regions. Neural oscillations are hypothesized to mediate communication and processing within these networks and subserve a wide range of functions including representing sensory information, regulating the flow of information, learning and recalling of information, and binding of distributed information. Thus to understand neural function, neuroscientists must be able to detect the presence of oscillatory coupling and changes in networks of coupled oscillators.

We are applying the statistical tools of multivariate phase distributions to capture how the oscillating networks in the brain communicate. Through our collaborations in the Robert Knight Lab, we work with electrocorticographic activity (ECoG) recorded directly from the cortex of patients undergoing neurosurgical treatment. Using these statistical techniques we are investigating how task-dependent activation exhibits differences in low frequency coupling during cognitive tasks.

Modeling the relationship between spiking and mesoscale activity

Sensory neurophysiologists typically study how individual neurons respond to external stimuli. In contrast, a growing body of work indicates that the network activity in which a neuron is embedded is equally relevant to sensory coding. Local network activity is highly structured and influenced by sensory stimuli and behavioral states. It is also known to be responsible for a large fraction of the observed variance in single neuron responses. Therefore, understanding the dependencies between mesoscale and spiking activity can shed light on the functional interactions subserving neural encoding, computation, and communication. Additionally, these dependencies can account for some of the trial-to-trial variability of single neuron responses and can improve models for neural prediction. In collaboration with Tim Blanche, we study the dependencies between individual neurons and local network activity using large scale neural recordings.

In collaboration with the Jose Carmena Lab, we are investigating the relationship between single spikes and large-scale cortical dynamics. We model the dependencies between spikes of individual neurons and LFP activity captured by multivariate phase coupling. Using these models, we investigate how neural phase coupling correlates with behavior and how it can be used as a mechanism for the selective control of distributed functional cell assemblies.

Modeling phase structure in natural images

In recent years a number of models have emerged for describing higher-order structure in images (i.e., beyond sparse, Gabor-like decompositions). These models utilize distributed representations of covariance matrices to form a combinatorial mixture of Gaussians model of the data. These models have been shown to effectively capture the non-stationary variance structure of natural images. A variety of related models have focused on the local radial (in vectorized image space) structure of natural images. While these models represent a significant step forward in modeling higher-order natural image structure, they only implicitly model local phase alignments across space and scale. Such local phase alignments are implicated as being hallmarks of edges, contours, and other shape structure in natural images.

We are applying machine learning techniques to learn image representations that are adapted to the statistics of natural scenes. When images are modeled using spherically symmetric subspaces, local amplitude and phase variables naturally emerge as learned parameters. Whereas the amplitude variables indicate the presence of structure, the structural content is contained in the phase variables. Using multivariate phase distributions, we explicitly model the dependencies among local amplitude and phase.

Information multiplexing in spiking neural networks

According to the prevailing view, spiking neural networks (e.g. in cortex or retina) use spike rates rather than spike timing for computation, encoding, and communication of information. This conclusions is drawn from the fact that spike timings show high variability in response to identical stimuli, whereas spike rates are more robust. According to this view, response variability that is caused by intrinsic network activity does not carry information and has to be considered noise. We investigate how intrinsic network activity can be used for computation, encoding, and communication of information.

For example, we have shown that intrinsic oscillations in the retina might be used by the thalamus to transmit information downstream. In collaboration with Fritz Sommer and the Judith Hirsch Lab at USC, we have shown that spike trains of single thalamic relay cells in vivo can transmit two separate streams of information, one encoded by firing rate and the other in oscillation phase. In collaboration with the Marty Usrey Lab at UC Davis, we verified this phenomenology in single cell recordings of retinal ganglion cells in vivo. In an ongoing collaboration, we are investigating the role of phase coupling and spike correlations in the computation and encoding of visual features.