A graph G has maximal local edge-connectivity k if the maximum number of edge-disjoint paths between every pair of distinct vertices x and y is at most k. We prove Brooks-type theorems for k-connected graphs with maximal local edge-connectivity k, and for any graph with maximal local edge-connectivity 3. We also consider several related graph classes defined by constraints on connectivity. In p...

Coastal ecosystems are often stressed by non-point source and cumulative effects that can lead to local-scale community homogenisation and a concomitant loss of large-scale ecological connectivity. Here we investigate the use of β-diversity as a measure of both community heterogeneity and ecological connectivity. To understand the consequences of different environmental scenarios on heterogenei...

Let U ⊂ Ĉ be a simply connected domain whose complement K = Ĉ \ U contains more than one point. We show that the impression of a prime end of U contains at most two points at which K is locally connected. This is achieved by establishing a characterization of local connectivity of K at a point z0 ∈ ∂U in terms of the prime ends of U whose impressions contain z0 and then invoking a result of Urs...

S. E. Joel, P. Srinivasan, S. Spinelli, S. H. Mostofsky, and J. J. Pekar Radiology, Johns Hopkins University, Baltimore, MD, United States, FM Kirby Research Center for Functional Brain Imaging, Kennedy Krieger Institute, Baltimore, MD, United States, Laboratory for Neurocognitive and Imaging Research, Kennedy Krieger Institute, Baltimore, MD, United States, Neurology, Johns Hopkins University,...

We discuss the relationship between the local-global map hypothesis of Vl and Spiral Harmonic Mosaic algebra, illustrated with a simple model of Vl. We describe long-range patchy connections by assuming they share a symmetry with the local connectivity. We also show that the elongated pattems of connectivity, implicated in the orientation response property, can be related to the patterns of con...

A local property reconstructor for a graph property is an algorithm which, given oracle access to the adjacency list of a graph that is “close” to having the property, provides oracle access to the adjacency matrix of a “correction” of the graph, i.e. a graph which has the property and is close to the given graph. For this model, we achieve local property reconstructors for the properties of co...

IMPORTANCE Neurobiological models of obsessive-compulsive disorder (OCD) predict hyperactivity in brain circuits involving the orbitofrontal cortex and the basal ganglia, but it is unclear whether these areas are also characterized by altered brain network properties. OBJECTIVES To determine regions of abnormal degree connectivity in patients with OCD and to investigate whether connectivity m...

Linking local communities to a metacommunity can positively affect diversity by enabling immigration of dispersal-limited species and maintenance of sink populations. However, connectivity can also negatively affect diversity by allowing the spread of strong competitors or predators. In a microcosm experiment with five ciliate species as prey and a copepod as an efficient generalist predator, w...