Stochastic modeling of neurobiological time series: power, coherence, Granger causality, and separation of evoked responses from ongoing activity.

In this article we consider the stochastic modeling of neurobiological time series from cognitive experiments. Our starting point is the variable-signal-plus-ongoing-activity model. From this model a differentially variable component analysis strategy is developed from a Bayesian perspective to estimate event-related signals on a single trial basis.

Differentially variable component analysis: Identifying multiple evoked components using trial-to-trial variability.

Electric potentials and magnetic fields generated by ensembles of synchronously active neurons, either spontaneously or in response to external stimuli, provide information essential to understanding the processes underlying cognitive and sensorimotor activity. Interpreting recordings of these potentials and fields is difficult because detectors record signals simultaneously generated by various regions throughout the brain. We introduce a novel approach to this problem, the differentially variable component analysis (dVCA) algorithm, which relies on trial-to-trial variability in response amplitude and latency to identify multiple components.

Analyzing stability of equilibrium points in neural networks: a general approach.

Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable under parameter variations. Here we present a general methodology to yield explicit constraints on the coupling strengths to ensure the stability of the equilibrium point.

Synchronized activity in prefrontal cortex during anticipation of visuomotor processing.

It is commonly presumed, though not well established, that the prefrontal cortex exerts top-down control of sensory processing. One aspect of this control is thought to be a facilitation of sensory pathways in anticipation of such processing. To investigate the possible involvement of prefrontal cortex in anticipatory top-down control, we studied the statistical relations between prefrontal activity, recorded while a macaque monkey waited for presentation of a visual stimulus, and subsequent sensory and motor events.

Trial-to-trial variability of cortical evoked responses: implications for the analysis of functional connectivity.

Objectives: The time series of single trial cortical evoked potentials typically have a random appearance, and their trial-to-trial variability is commonly explained by a model in which random ongoing background noise activity is linearly combined with a stereotyped evoked response. In this paper, we demonstrate that more realistic models, incorporating amplitude and latency variability of the evoked response itself, can explain statistical properties of cortical potentials that have often been attributed to stimulus-related changes in functional connectivity or other intrinsic neural parameters.

Methods: Implications of trial-to-trial evoked potential variability for variance, power spectrum, and interdependence measures like cross-correlation and spectral coherence, are first derived analytically.