The Topological Radon Theorem states that, for every continuous function from the boundary of a (d + 1)-dimensional simplex into Rn, there exist a pair of disjoint faces in the domain whose images intersect in Rn. The similarity between that result and the classical Borsuk-Ulam Theorem is unmistakeable, but a proof that the Topological Radon Theorem follows from Borsuk-Ulam is not immediate. In...

In this paper we explore the topological semantics for conditional logic that arises from the Alexandroff equivalence between preorders and topological spaces. This clarifies the relation between the standard order semantics and premise semantics for conditionals. As an application we provide a construction of relative similarity orders between possible worlds from topologies of relevant propos...

Conceptual neighborhood graphs capture the similarity among qualitative relations. This paper derives the graphs for the thirty-three topological relations between two crisp, undirected lines and for the seventy-seven topological relations between two lines with uncertain boundaries. The analysis of the graphs shows that the normalized node degrees increases, from the crisp to the broad-boundar...

Protein complexes are of great importance in understanding the principles of cellular organization and function. The increase in available protein-protein interaction data, gene ontology and other resources make it possible to develop computational methods for protein complex prediction. Most existing methods focus mainly on the topological structure of protein-protein interaction networks, and...

The structure of the core of the neuronal 'SNARE complex', involved in neurotransmitter release, has been determined recently. Its topological similarity to viral fusion proteins suggests how the SNARE complex might facilitate membrane fusion.