What is it about?
In network design the question arises whether some cycles should be included in the network graph. Of course this answer depends on the objective functional, so it is necessary to know about the derivative of this functional at zero with respect to a parameter that describes the size of the cycle.
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Why is it important?
The efficiency of network depends on the network topology, so it is important to know how to optimize the network topology to obtain the best performance. Is it useful to include a cycle to improve the network design?
Perspectives
In the applications often intertwined cycles occur in the networks. This gives rise to the question: How many nested cycles should be included in the network graphs? How can the optimal number be determined? This is highly relevant for many applications and requires a delicate asymptotic analysis.
Martin Gugat
Friedrich-Alexander-Universitat Erlangen-Nurnberg
Read the Original
This page is a summary of: Topological derivative method for control of wave equation on networks, August 2023, Institute of Electrical & Electronics Engineers (IEEE),
DOI: 10.1109/mmar58394.2023.10242484.
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