simplicial complex. An abstract simplicial complex is a set {1, ..., N} with a set K of subsets such that if Y ∈ K and X ⊂ Y then X ∈ K. In other words, every subset of a subset in K is also included in K. Every simplicial complex is an abstract simplicial complex, where the elements of the set {1, ..., N} correspond to labelled vertices, and the set of subsets K corresponds to simplices (toget...

Intranasal route, ensuring suitable bioavailability of medicines under circumvention of the gastrointestinal degradation and hepatic first-pass elimination, has been a popular choice for drug delivery. Among nasal dosage forms, mucoadhesive solid inserts have been shown to resist mucociliary clearance and provide a prolonged nasal residence time. Hence, the purpose of this study was the prepara...

In this paper, we introduce the “semi-topological K-homology” of complex varieties, a theory related to semi-topological K-theory much as connective topological K-homology is related to connective topological K-theory. Our main theorem is that the semi-topological K-homology of a smooth, quasiprojective complex variety Y coincides with the connective topological Khomology of the associated anal...

A k-dimensional hypertree X is a k-dimensional complex on n vertices with a full (k−1)-dimensional skeleton and ( n−1 k ) facets such that Hk(X;Q) = 0. Here we introduce the following family of simplicial complexes. Let n, k be integers with k+1 and n relatively prime, and let A be a (k + 1)-element subset of the cyclic group Zn. The sum complex XA is the pure k-dimensional complex on the verte...

A few membrane vesicle trafficking (SNARE) proteins in plants are associated with signaling and transmembrane ion transport, including control of plasma membrane ion channels. Vesicle traffic contributes to the population of ion channels at the plasma membrane. Nonetheless, it is unclear whether these SNAREs also interact directly to affect channel gating and, if so, what functional impact this...