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Super edge-connectivity and matching preclusion of data center networks
Edge-connectivity is a classic measure for reliability of a network in the
presence of edge failures. -restricted edge-connectivity is one of the
refined indicators for fault tolerance of large networks. Matching preclusion
and conditional matching preclusion are two important measures for the
robustness of networks in edge fault scenario. In this paper, we show that the
DCell network is super- for and ,
super- for and , or and , and
super- for and . Moreover, as an application of
-restricted edge-connectivity, we study the matching preclusion number and
conditional matching preclusion number, and characterize the corresponding
optimal solutions of . In particular, we have shown that is
isomorphic to the -star graph for .Comment: 20 pages, 1 figur
Further topics in connectivity
Continuing the study of connectivity, initiated in §4.1 of the Handbook, we survey here some (sufficient) conditions under which a graph or digraph has a given connectivity or edge-connectivity. First, we describe results concerning maximal (vertex- or edge-) connectivity. Next, we deal with conditions for having (usually lower) bounds for the connectivity parameters. Finally, some other general connectivity measures, such as one instance of the so-called “conditional connectivity,” are considered.
For unexplained terminology concerning connectivity, see §4.1.Peer ReviewedPostprint (published version
Synthetic reverberating activity patterns embedded in networks of cortical neurons
Synthetic reverberating activity patterns are experimentally generated by
stimulation of a subset of neurons embedded in a spontaneously active network
of cortical cells in-vitro. The neurons are artificially connected by means of
conditional stimulation matrix, forming a synthetic local circuit with a
predefined programmable connectivity and time-delays. Possible uses of this
experimental design are demonstrated, analyzing the sensitivity of these
deterministic activity patterns to transmission delays and to the nature of
ongoing network dynamics.Comment: 8 pages, 5 figure
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