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Item: Title: Discussion and Conclusions Item: Title: Acknowledgements Item: Title: Figure 1 Topological aspect ratio (ARt) of the Pozzolane Rosse ignimbrite (Colli Albani, Italy see Table S1 in Suppl. Item: Title: Figure 2 Topological aspect ratio (ARt) of the Cerro Galan Ignimbrite (Argentina see Table S1 in Suppl. Item: Title: Figure 3 Topological aspect ratio (ARt) of the Peperino Albano (Colli Albani, Italy see Table S1 in Suppl. Item: Title: Figure 4 Model explaining ARt gradients of ignimbrites in terms of degree of forcing or inertia of the parent PDCs (see text for explanation). 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