Topological modularity of supermoonshine

Simple Topological Features Reflect Dynamics and Modularity in Protein Interaction Networks

The availability of large-scale protein-protein interaction networks for numerous organisms provides an opportunity to comprehensively analyze whether simple properties of proteins are predictive of the roles they play in the functional organization of the cell. We begin by re-examining an influential but controversial characterization of the dynamic modularity of the S. cerevisiae interactome ...

Topological string theory on compact Calabi-Yau: modularity and boundary conditions

The topological string partition function Z(λ, t, t̄) = exp(λ2g−2Fg(t, t̄)) is calculated on a compact Calabi-Yau M . The Fg(t, t̄) fulfill the holomorphic anomaly equations, which imply that Ψ = Z transforms as a wave function on the symplectic space H3(M,Z). This defines it everywhere in the moduli space M(M) along with preferred local coordinates. Modular properties of the sections Fg as well a...

Subcategories of topological algebras

In addition to exploring constructions and properties of limits and colimits in categories of topological algebras, we study special subcategories of topological algebras and their properties. In particular, under certain conditions, reflective subcategories when paired with topological structures give rise to reflective subcategories and epireflective subcategories give rise to epireflective s...

The Business of Modularity and the Modularity of Business

REDUNDANCY OF MULTISET TOPOLOGICAL SPACES

In this paper, we show the redundancies of multiset topological spaces. It is proved that $(P^star(U),sqsubseteq)$ and $(Ds(varphi(U)),subseteq)$ are isomorphic. It follows that multiset topological spaces are superfluous and unnecessary in the theoretical view point.