Tootfinder

Comprehensive indicators and fine granularity refine density scaling laws in rural-urban systems
Jack Sutton, Quentin S. Hanley, Gerri Mortimore, Ovidiu Bagdasar, Haroldo V. Ribeiro, Thomas Peron, Golnaz Shahtahmassebi, Peter Scriven
https://arxiv.org/abs/2509.14258

Comprehensive indicators and fine granularity refine density scaling laws in rural-urban systems
Density scaling laws complement traditional population scaling laws by enabling the analysis of the full range of human settlements and revealing rural-to-urban transitions with breakpoints at consistent population densities. However, previous studies have been constrained by the granularity of rural and urban units, as well as limitations in the quantity and diversity of indicators. This study addresses these gaps by examining Middle Layer Super Output Areas (MSOAs) in England and Wales, incor…

Flow polytopes for extensions of bipartite graphs
Benjamin Braun, Kaitlin Bruegge, Robert Davis, Derek Hanely
https://arxiv.org/abs/2509.26445 https://arxi…

Flow polytopes for extensions of bipartite graphs
The space of unit flows on a finite acyclic directed graph is a lattice polytope called the flow polytope of the graph. Given a bipartite graph $G$ with minimum degree at least two, we construct two associated acyclic directed graphs: the extension of $G$ and the almost-degree-whiskered graph of $G$. We prove that the normalized volume of the flow polytope for the extension of $G$ is equal to the number of matchings in the almost-degree-whiskered graph of $G$. Further, we refine this result by …

Crosslisted article(s) found for stat.AP. https://arxiv.org/list/stat.AP/new
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- Comprehensive indicators and fine granularity refine density scaling laws in rural-urban systems
Sutton, Hanley, Mortimore, Bagdasar, Ribeiro, Peron, Shahtahmassebi, Scriven