Papers by Vagn Lundsgaard Hansen
WORLD SCIENTIFIC eBooks, Apr 1, 1998
Aktuel Naturvidenskab, 2017
Aktuel Naturvidenskab, 2012
Aktuel Naturvidenskab, 2014
Design and analysis of networks have many applications in the engineering sciences. This disserta... more Design and analysis of networks have many applications in the engineering sciences. This dissertation seeks to contribute to the methods used in the analysis of networks with a view towards assisting decision making processes. Networks are initially considered as objects in the category of graphs and later as objects in the category of hypergraphs. The connection with the category of simplicial pairs become apparent when the topology is analyzed using homological algebra. A topological ranking is developed that measures the ability of the network to stay path-connected. Combined with the analysis of cover ideals of hypergraphs, the topological ranking demonstrates the non-trivial decisions that needs to be considered in system design. All the methods developed here have an underlying common structure, namely that they all appear at solution sets for systems of polynomials. These solution sets are called algebraic varieties.
Quaestiones Mathematicae, Nov 8, 2017
Users may download and print one copy of any publication from the public portal for the purpose... more Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.
Math Horizons, Nov 1, 2009
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Papers by Vagn Lundsgaard Hansen