Open Manifolds with Monotone Union Property

Action-Maslov Homomorphism for Monotone Symplectic Manifolds

Action-Maslov Homomorphism for Monotone Symplectic Manifolds

Monotone invariants and embeddings of statistical manifolds

In this note we prove certain necessary and sufficient conditions for the existence of an embedding of statistical manifolds. In particular, we prove that any smooth (C resp.) statistical manifold can be embedded into the space of probability measures on a finite set. As a result, we get positive answers to the Lauritzen question on a realization of smooth (C resp.) statistical manifolds as sta...

Markov Property of Monotone Lévy Processes

Monotone Lévy processes with additive increments are defined and studied. It is shown that these processes have natural Markov structure and their Markov transition semigroups are characterized using the monotone Lévy-Khintchine formula. 17 Monotone Lévy processes turn out to be related to classical Lévy processes via Attal's " remarkable transformation. " A monotone analogue of the family of e...

Every Monotone 3-Graph Property is Testable

Let k ≥ 2 be a fixed integer and P be a property of k-uniform hypergraphs. In other words, P is a (typically infinite) family of k-uniform hypergraphs and we say a given hypergraph H satisfies P if H ∈ P . For a given constant η > 0 a k-uniform hypergraph H on n vertices is η-far from P if no hypergraph obtained from H by changing (adding or deleting) at most ηn edges in H satisfies P . More pr...

The Union Problem on Complex Manifolds