4 papers
A continuum of Künneth theorems for persistence modules
Nikola MiliÄeviÄ
We develop new aspects of the homological algebra theory for persistence modules, in both the one-parameter and multi-parameter settings. For a poset and an order preserving ma…
Singular homology of roots of unity
Nikola MiliÄeviÄ
We extend some basic results from the singular homology theory of topological spaces to the setting of Äech's closure spaces. We prove analogues of the excision and Mayer-Vietoris…
The directed Vietoris-Rips complex and homotopy and singular homology groups of finite digraphs
Nikola MiliÄeviÄ, Nicholas A. Scoville
We prove analogues of classical results for higher homotopy groups and singular homology groups of pseudotopological spaces. Pseudotopological spaces are a generalization of (Äech…
The combinatorial code and the graph rules of Dale networks
Nikola MiliÄeviÄ, Vladimir Itskov
We describe the combinatorics of equilibria and steady states of neurons in threshold-linear networks that satisfy Dale's law. The combinatorial code of a Dale network is character…