Spatially continuous networks with heterogeneous connections are ubiquitous in biological systems, in particular neural systems. To understand the mutual effects of locally homogeneous and globally heterogeneous connectivity, we investigate the stability of the rest-state activity of a neural field as a function of its connectivity. The variation of the connectivity is operationalized through m...

Neuroimaging findings have proposed that some brain regions including the precuneus, posterior cingulate, and medial prefrontal cortex play an essential role of a structural core in the brain. Network organization endures rapid alterations in development with changes in axonal synaptic connectivity, white matter volume, and the thickness of corresponding cortical regions. Structural maturation ...

Let $G$ be a connected graph of order $n$ and minimum degree $delta(G)$.The edge-connectivity $lambda(G)$ of $G$ is the minimum numberof edges whose removal renders $G$ disconnected. It is well-known that$lambda(G) leq delta(G)$,and if $lambda(G)=delta(G)$, then$G$ is said to be maximally edge-connected. A classical resultby Chartrand gives the sufficient condition $delta(G) geq frac{n-1}{2}$fo...

Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...

mobile sensor networks rely heavily on inter-sensor connectivity for collection of data. nodes in these networks monitor different regions of an area of interest and collectively present a global overview of some monitored activities or phenomena. a failure of a sensor leads to loss of connectivity and may cause partitioning of the network into disjoint segments. a number of approaches have bee...

INTRODUCTION Functional MRI is widely used to study task-related changes in neuronal activity as well as resting-state functional connectivity. In this study, we explore task-related changes in functional connectivity networks using fMRI. Dynamic connectivity may represent a new measure of neural network robustness that would impact both clinical and research efforts. However, prior studies of ...

the tenacity of a graph g, t(g), is dened by t(g) = min{[|s|+τ(g-s)]/[ω(g-s)]}, where the minimum is taken over all vertex cutsets s of g. we dene τ(g - s) to be the number of the vertices in the largest component of the graph g - s, and ω(g - s) be the number of components of g - s.in this paper a lower bound for the tenacity t(g) of a graph with genus γ(g) is obtained using the graph's...

Precuneus responds to a wide range of cognitive processes. Here, we examined how the patterns of resting state connectivity may define functional subregions in the precuneus. Using a K-means algorithm to cluster the whole-brain "correlograms" of the precuneus in 225 adult individuals, we corroborated the dorsal-anterior, dorsal-posterior, and ventral subregions, each involved in spatially guide...