Structured chaos shapes spike-response noise entropy in balanced neural networks

Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. A striking feature of these networks is that they are chaotic. How does this chaos manifest in the neural code? Specifically, how variable are the spike patterns that such a network produces in response to an input signal? To answer this, we derive a bound for the entropy of multi-cell spike pattern distributions in large recurrent networks of spiking neurons responding to fluctuating inputs. The analysis is based on results from random dynamical systems theory and is complimented by detailed numerical simulations. We find that the spike pattern entropy is an order of magnitude lower than what would be extrapolated from single cells. This holds despite the fact that network coupling becomes vanishingly sparse as network size grows -- a phenomenon that depends on ``extensive chaos," as previously discovered for balanced networks without stimulus drive. Moreover, we show how spike pattern entropy is controlled by temporal features of the inputs. Our findings provide insight into how neural networks may encode stimuli in the presence of inherently chaotic dynamics.Comment: 9 pages, 5 figure

Dynamic reconfiguration of human brain networks during learning

Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes -- flexibility and selection -- must operate over multiple temporal scales as performance of a skill changes from being slow and challenging to being fast and automatic. Such selective adaptability is naturally provided by modular structure, which plays a critical role in evolution, development, and optimal network function. Using functional connectivity measurements of brain activity acquired from initial training through mastery of a simple motor skill, we explore the role of modularity in human learning by identifying dynamic changes of modular organization spanning multiple temporal scales. Our results indicate that flexibility, which we measure by the allegiance of nodes to modules, in one experimental session predicts the relative amount of learning in a future session. We also develop a general statistical framework for the identification of modular architectures in evolving systems, which is broadly applicable to disciplines where network adaptability is crucial to the understanding of system performance.Comment: Main Text: 19 pages, 4 figures Supplementary Materials: 34 pages, 4 figures, 3 table

Evidence accumulation in a Laplace domain decision space

Evidence accumulation models of simple decision-making have long assumed that the brain estimates a scalar decision variable corresponding to the log-likelihood ratio of the two alternatives. Typical neural implementations of this algorithmic cognitive model assume that large numbers of neurons are each noisy exemplars of the scalar decision variable. Here we propose a neural implementation of the diffusion model in which many neurons construct and maintain the Laplace transform of the distance to each of the decision bounds. As in classic findings from brain regions including LIP, the firing rate of neurons coding for the Laplace transform of net accumulated evidence grows to a bound during random dot motion tasks. However, rather than noisy exemplars of a single mean value, this approach makes the novel prediction that firing rates grow to the bound exponentially, across neurons there should be a distribution of different rates. A second set of neurons records an approximate inversion of the Laplace transform, these neurons directly estimate net accumulated evidence. In analogy to time cells and place cells observed in the hippocampus and other brain regions, the neurons in this second set have receptive fields along a "decision axis." This finding is consistent with recent findings from rodent recordings. This theoretical approach places simple evidence accumulation models in the same mathematical language as recent proposals for representing time and space in cognitive models for memory.Comment: Revised for CB

Dynamic Construction of Stimulus Values in the Ventromedial Prefrontal Cortex

Signals representing the value assigned to stimuli at the time of choice have been repeatedly observed in ventromedial prefrontal cortex (vmPFC). Yet it remains unknown how these value representations are computed from sensory and memory representations in more posterior brain regions. We used electroencephalography (EEG) while subjects evaluated appetitive and aversive food items to study how event-related responses modulated by stimulus value evolve over time. We found that value-related activity shifted from posterior to anterior, and from parietal to central to frontal sensors, across three major time windows after stimulus onset: 150–250 ms, 400–550 ms, and 700–800 ms. Exploratory localization of the EEG signal revealed a shifting network of activity moving from sensory and memory structures to areas associated with value coding, with stimulus value activity localized to vmPFC only from 400 ms onwards. Consistent with these results, functional connectivity analyses also showed a causal flow of information from temporal cortex to vmPFC. Thus, although value signals are present as early as 150 ms after stimulus onset, the value signals in vmPFC appear relatively late in the choice process, and seem to reflect the integration of incoming information from sensory and memory related regions

Resting state MEG oscillations show long-range temporal correlations of phase synchrony that break down during finger movement

The capacity of the human brain to interpret and respond to multiple temporal scales in its surroundings suggests that its internal interactions must also be able to operate over a broad temporal range. In this paper, we utilize a recently introduced method for characterizing the rate of change of the phase difference between MEG signals and use it to study the temporal structure of the phase interactions between MEG recordings from the left and right motor cortices during rest and during a finger-tapping task. We use the Hilbert transform to estimate moment-to-moment fluctuations of the phase difference between signals. After confirming the presence of scale-invariance we estimate the Hurst exponent using detrended fluctuation analysis (DFA). An exponent of >0.5 is indicative of long-range temporal correlations (LRTCs) in the signal. We find that LRTCs are present in the α/μ and β frequency bands of resting state MEG data. We demonstrate that finger movement disrupts LRTCs correlations, producing a phase relationship with a structure similar to that of Gaussian white noise. The results are validated by applying the same analysis to data with Gaussian white noise phase difference, recordings from an empty scanner and phase-shuffled time series. We interpret the findings through comparison of the results with those we obtained from an earlier study during which we adopted this method to characterize phase relationships within a Kuramoto model of oscillators in its sub-critical, critical, and super-critical synchronization states. We find that the resting state MEG from left and right motor cortices shows moment-to-moment fluctuations of phase difference with a similar temporal structure to that of a system of Kuramoto oscillators just prior to its critical level of coupling, and that finger tapping moves the system away from this pre-critical state toward a more random state

Detecting event-related recurrences by symbolic analysis: Applications to human language processing

Quasistationarity is ubiquitous in complex dynamical systems. In brain dynamics there is ample evidence that event-related potentials reflect such quasistationary states. In order to detect them from time series, several segmentation techniques have been proposed. In this study we elaborate a recent approach for detecting quasistationary states as recurrence domains by means of recurrence analysis and subsequent symbolisation methods. As a result, recurrence domains are obtained as partition cells that can be further aligned and unified for different realisations. We address two pertinent problems of contemporary recurrence analysis and present possible solutions for them.Comment: 24 pages, 6 figures. Draft version to appear in Proc Royal Soc