Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies

In previous work, empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here that if the network of oscillators synchronizes for the static time-average of the topology, then the network will synchronize with the time-varying topology if the time-average is achieved sufficiently fast. Fast switching, fast on the time-scale of the coupled oscillators, overcomes the descychnronizing decoherence suggested by disconnected instantaneous networks. This result agrees in spirit with that of where empirical evidence suggested that a moving averaged graph Laplacian could be used in the master-stability function analysis. A new fast switching stability criterion here-in gives sufficiency of a fast-switching network leading to synchronization. Although this sufficient condition appears to be very conservative, it provides new insights about the requirements for synchronization when the network topology is time-varying. In particular, it can be shown that networks of oscillators can synchronize even if at every point in time the frozen-time network topology is insufficiently connected to achieve synchronization.Comment: Submitted to SIAD

Response of electrically coupled spiking neurons: a cellular automaton approach

Experimental data suggest that some classes of spiking neurons in the first layers of sensory systems are electrically coupled via gap junctions or ephaptic interactions. When the electrical coupling is removed, the response function (firing rate {\it vs.} stimulus intensity) of the uncoupled neurons typically shows a decrease in dynamic range and sensitivity. In order to assess the effect of electrical coupling in the sensory periphery, we calculate the response to a Poisson stimulus of a chain of excitable neurons modeled by $n$-state Greenberg-Hastings cellular automata in two approximation levels. The single-site mean field approximation is shown to give poor results, failing to predict the absorbing state of the lattice, while the results for the pair approximation are in good agreement with computer simulations in the whole stimulus range. In particular, the dynamic range is substantially enlarged due to the propagation of excitable waves, which suggests a functional role for lateral electrical coupling. For probabilistic spike propagation the Hill exponent of the response function is $\alpha=1$, while for deterministic spike propagation we obtain $\alpha=1/2$, which is close to the experimental values of the psychophysical Stevens exponents for odor and light intensities. Our calculations are in qualitative agreement with experimental response functions of ganglion cells in the mammalian retina.Comment: 11 pages, 8 figures, to appear in the Phys. Rev.

Controversies in epilepsy: Debates held during the Fourth International Workshop on Seizure Prediction

Debates on six controversial topics were held during the Fourth International Workshop on Seizure Prediction (IWSP4) convened in Kansas City, KS, USA, July 4–7, 2009. The topics were (1) Ictogenesis: Focus versus Network? (2) Spikes and Seizures: Step-relatives or Siblings? (3) Ictogenesis: A Result of Hyposynchrony? (4) Can Focal Seizures Be Caused by Excessive Inhibition? (5) Do High-Frequency Oscillations Provide Relevant Independent Information? (6) Phase Synchronization: Is It Worthwhile as Measured? This article, written by the IWSP4 organizing committee and the debaters, summarizes the arguments presented during the debates

Data Driven Classification Using fMRI Network Measures: Application to Schizophrenia

Using classification to identify biomarkers for various brain disorders has become a common practice among the functional MR imaging community. Typical classification pipeline includes taking the time series, extracting features from them, and using them to classify a set of patients and healthy controls. The most informative features are then presented as novel biomarkers. In this paper, we compared the results of single and double cross validation schemes on a cohort of 170 subjects with schizophrenia and healthy control subjects. We used graph theoretic measures as our features, comparing the use of functional and anatomical atlases to define nodes and the effect of prewhitening to remove autocorrelation trends. We found that double cross validation resulted in a 20% decrease in classification performance compared to single cross validation. The anatomical atlas resulted in higher classification results. Prewhitening resulted in a 10% boost in classification performance. Overall, a classification performance of 80% was obtained with a double-cross validation scheme using prewhitened time series and an anatomical brain atlas. However, reproducibility of classification within subjects across scans was surprisingly low and comparable to across subject classification rates, indicating that subject state during the short scan significantly influences the estimated features and classification performance

Blocking NMDAR Disrupts Spike Timing and Decouples Monkey Prefrontal Circuits: Implications for Activity-Dependent Disconnection in Schizophrenia

We employed multi-electrode array recording to evaluate the influence of NMDA receptors (NMDAR) on spike-timing dynamics in prefrontal networks of monkeys as they performed a cognitive control task measuring specific deficits in schizophrenia. Systemic, periodic administration of an NMDAR antagonist (phencyclidine) reduced the prevalence and strength of synchronous (0-lag) spike correlation in simultaneously recorded neuron pairs. We employed transfer entropy analysis to measure effective connectivity between prefrontal neurons at lags consistent with monosynaptic interactions and found that effective connectivity was persistently reduced following exposure to the NMDAR antagonist. These results suggest that a disruption of spike timing and effective connectivity might be interrelated factors in pathogenesis, supporting an activity-dependent disconnection theory of schizophrenia. In this theory, disruption of NMDAR synaptic function leads to dys-regulated timing of action potentials in prefrontal networks, accelerating synaptic disconnection through a spike-timing-dependent mechanism

Network inference - with confidence - from multivariate time series

Networks - collections of interacting elements or nodes - abound in the natural and manmade worlds. For many networks, complex spatiotemporal dynamics stem from patterns of physical interactions unknown to us. To infer these interactions, it is common to include edges between those nodes whose time series exhibit sufficient functional connectivity, typically defined as a measure of coupling exceeding a pre-determined threshold. However, when uncertainty exists in the original network measurements, uncertainty in the inferred network is likely, and hence a statistical propagation-of-error is needed. In this manuscript, we describe a principled and systematic procedure for the inference of functional connectivity networks from multivariate time series data. Our procedure yields as output both the inferred network and a quantification of uncertainty of the most fundamental interest: uncertainty in the number of edges. To illustrate this approach, we apply our procedure to simulated data and electrocorticogram data recorded from a human subject during an epileptic seizure. We demonstrate that the procedure is accurate and robust in both the determination of edges and the reporting of uncertainty associated with that determination.Comment: 12 pages, 7 figures (low resolution), submitte

Review of the methods of determination of directed connectivity from multichannel data

The methods applied for estimation of functional connectivity from multichannel data are described with special emphasis on the estimators of directedness such as directed transfer function (DTF) and partial directed coherence. These estimators based on multivariate autoregressive model are free of pitfalls connected with application of bivariate measures. The examples of applications illustrating the performance of the methods are given. Time-varying estimators of directedness: short-time DTF and adaptive methods are presented

The response of a classical Hodgkin–Huxley neuron to an inhibitory input pulse

A population of uncoupled neurons can often be brought close to synchrony by a single strong inhibitory input pulse affecting all neurons equally. This mechanism is thought to underlie some brain rhythms, in particular gamma frequency (30–80 Hz) oscillations in the hippocampus and neocortex. Here we show that synchronization by an inhibitory input pulse often fails for populations of classical Hodgkin–Huxley neurons. Our reasoning suggests that in general, synchronization by inhibitory input pulses can fail when the transition of the target neurons from rest to spiking involves a Hopf bifurcation, especially when inhibition is shunting, not hyperpolarizing. Surprisingly, synchronization is more likely to fail when the inhibitory pulse is stronger or longer-lasting. These findings have potential implications for the question which neurons participate in brain rhythms, in particular in gamma oscillations