Synchronization from Second Order Network Connectivity Statistics

We investigate how network structure can influence the tendency for a neuronal network to synchronize, or its synchronizability, independent of the dynamical model for each neuron. The synchrony analysis takes advantage of the framework of second order networks, which defines four second order connectivity statistics based on the relative frequency of two-connection network motifs. The analysis identifies two of these statistics, convergent connections, and chain connections, as highly influencing the synchrony. Simulations verify that synchrony decreases with the frequency of convergent connections and increases with the frequency of chain connections. These trends persist with simulations of multiple models for the neuron dynamics and for different types of networks. Surprisingly, divergent connections, which determine the fraction of shared inputs, do not strongly influence the synchrony. The critical role of chains, rather than divergent connections, in influencing synchrony can be explained by their increasing the effective coupling strength. The decrease of synchrony with convergent connections is primarily due to the resulting heterogeneity in firing rates

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

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