Lyle E. Muller

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The number of connected components and the size of the largest connected component are studied under node and edge removal in the connectivity graph of the C. elegans nervous system. By studying the two subgraphs – the directed graph of chemical synapses and the undirected graph of electrical junctions – we observe that adding a small number of undirected(More)
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks using graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the presence of serious uncertainties, such as major undersampling of the experimental data. In the specific case of neural(More)
We introduce an analytic model for directed Watts-Strogatz small-world graphs and deduce an algebraic expression of its defining adjacency matrix. The latter is then used to calculate the small-world digraph's asymmetry index and clustering coefficient in an analytically exact fashion, valid nonasymptotically for all graph sizes. The proposed approach is(More)
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the presence of serious uncertainties, such as major undersampling of the experimental data. In the specific case of neural(More)
Beta (β)- and gamma (γ)-oscillations are present in different cortical areas and are thought to be inhibition-driven, but it is not known if these properties also apply to γ-oscillations in humans. Here, we analyze such oscillations in high-density microelectrode array recordings in human and monkey during the wake-sleep cycle. In these recordings, units(More)
In recent years, small-world graphs have gained considerable interest as models of real-world systems, which often display features residing between regularity and randomness. The most notable of these models is the Watts-Strogatz graph [1], though alternatives have been proposed [2]. The unifying characteristics of these models are that any two nodes are(More)
The existence of propagating waves, either spontaneous or stimulus-evoked, in neocortex during the awake state has been a subject of recent interest [1,2]. Here, following work done previously in voltage-sensitive dye imaging of the primary visual cortex in the awake monkey [3], we apply an analysis method for non-parametric, automated detection of(More)
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