On the projective plane there is a unique cubic root of canonical bundle and this acyclic. fake planes such exists if are no 3-torsion divisors (and usually exists, but not unique, otherwise). Earlier we conjectured that any must be In present note give two short proofs statement show acyclicity some other line bundles on with at least $9$ automorphisms. Similarly to our earlier work employ sim...

We construct a derived enhancement of Hom spaces between rigid analytic spaces. It encodes the hidden deformation-theoretic information underlying classical moduli space. The main tool in our construction is representability theorem geometry, which has been established previous work. provides us with sufficient and necessary conditions for an functor to possess structure stack. In order verify ...

In this paper we propose a computationally efficient multiple hypothesis testing procedure for persistent homology. The computational efficiency of our is based on the observation that one can empirically simulate null distribution universal across many applications involving persistence Our suggests efficiently small number summaries collected data and use in same way p-value tables were used ...

We present a restriction of the solos calculus which is stable under reduction and expressive enough to contain an encoding of the pi-calculus. As a consequence, it is shown that equalizing names that are already equal is not required by the encoding of the pi-calculus. In particular, the induced solo diagrams bear an acyclicity property that induces a faithful encoding into differential intera...

We develop a new approach to cluster algebras based on the notion of an upper cluster algebra, defined as an intersection of Laurent polynomial rings. Strengthening the Laurent phenomenon established in [6], we show that, under an assumption of “acyclicity”, a cluster algebra coincides with its “upper” counterpart, and is finitely generated; in this case, we also describe its defining ideal, an...

We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic) computation is given via a syntactic restriction, using an encoding of words that derives from proof theory. We show that the acceptance of a word by an observatio...

A formalism for constructing database schemata from simple components is presented in which the components are coupled to one another via communicating views. The emphasis is upon identifying the conditions under which such components can be interconnected in a conflict-free fashion, and a characterization of such, based upon the acyclicity of an underlying hypergraph, is obtained. The work is ...