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Dürer polyhedra: the dark side of melancholia

Patrick W. Fowler, Peter E. John (2002)

Discussiones Mathematicae Graph Theory

Dürer's engraving Melencolia I famously includes a perspective view of a solid polyhedral block of which the visible portion is an 8-circuit bounding a pentagon-triple+triangle patch. The polyhedron is usually taken to be a cube truncated on antipodal corners, but an infinity of others are compatible with the visible patch. Construction of all cubic polyhedra compatible with the visible portion (i.e., Dürer Polyhedra) is discussed, explicit graphs and symmetries are listed for small cases ( ≤ 18...

Dynamic cage survey.

Exoo, Geoffrey, Jajcay, Robert (2008)

The Electronic Journal of Combinatorics [electronic only]

Dynamic WWW structures in 3 D .

Brandes, Ulrik, Kääb, Vanessa, Löh, Andres, Wagner, Dorothea, Willhalm, Thomas (2000)

Journal of Graph Algorithms and Applications

Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory

R. E. Lee DeVille, C. S. Peskin, J. H. Spencer (2010)

Mathematical Modelling of Natural Phenomena

We analyze a stochastic neuronal network model which corresponds to an all-to-all network of discretized integrate-and-fire neurons where the synapses are failure-prone. This network exhibits different phases of behavior corresponding to synchrony and asynchrony, and we show that this is due to the limiting mean-field system possessing multiple attractors. We also show that this mean-field limit exhibits a first-order phase transition as a function...

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