A medial cuneiform exhibiting complete bipartition was discovered at the Early Pleistocene site of Dmanisi, Georgia. The specimen is the oldest known instance of this anatomical variant in the hominin fossil record. Here we compare developmental variation of the medial cuneiform in fossil hominins, extant humans and great apes, and discuss potential implications of bipartition for hominin foot ...

A balanced bipartition of a graph G is a bipartition V1 and V2 of V (G) such that −1 ≤ |V1| − |V2| ≤ 1. Bollobás and Scott conjectured that if G is a graph with m edges and minimum degree at least 2 then G admits a balanced bipartition V1, V2 such that max{e(V1), e(V2)} ≤ m/3, where e(Vi) denotes the number of edges of G with both ends in Vi. In this note, we prove this conjecture for graphs wi...

We consider a cooperative game with a bipartition that indicates which players are participating. This paper provides an analytical solution for the Shapley value when the worth of a coalition only depends on the number of participating coalition players. The computational complexity grows linearly in the number of players, which contrasts with the usual exponential increase. Our result remains...

We consider the following problem: from a given set of gene families trees on a set of genomes, find a first speciation, that splits these genomes into two subsets, that minimizes the number of gene duplications that happened before this speciation. We call this problem the Minimum Duplication Bipartition Problem. Using a generalization of the Minimum Edge-Cut Problem, known as Submodular Funct...

A bipartition of the vertex set of a graph is called balanced if the sizes of the sets in the bipartition differ by at most one. Bollobás and Scott [3] conjectured that if G is a graph with minimum degree at least 2 then V (G) admits a balanced bipartition V1, V2 such that for each i, G has at most |E(G)|/3 edges with both ends in Vi. The minimum degree condition is necessary, and a result of B...

We prove, for any state in a conformal field theory defined on a set of boundary manifolds with corresponding classical holographic bulk geometry, that for any bipartition of the boundary into two non-clopen sets, the density matrix cannot be a tensor product of the reduced density matrices on each region of the bipartition. In particular, there must be entanglement across the bipartition surfa...