The augmentation category map induced by exact Lagrangian cobordisms

Rational Symplectic Field Theory over Z2 for Exact Lagrangian Cobordisms

We construct a version of rational Symplectic Field Theory for pairs (X, L), where X is an exact symplectic manifold, where L ⊂ X is an exact Lagrangian submanifold with components subdivided into k subsets, and where both X and L have cylindrical ends. The theory associates to (X, L) a Z-graded chain complex of vector spaces over Z2, filtered with k filtration levels. The corresponding k-level...

On exact category of $(m, n)$-ary hypermodules

We introduce and study category of $(m, n)$-ary hypermodules as a generalization of the category of $(m, n)$-modules as well as the category of classical modules. Also, we study various kinds of morphisms. Especially, we characterize monomorphisms and epimorphisms in this category. We will proceed to study the fundamental relation on $(m, n)$-hypermodules, as an important tool in the study of a...

Exact category of hypermodules

The theory of hyperstructures has been introduced byMarty in 1934 during the 8th Congress of the Scandinavian Mathematicians [4]. Marty introduced the notion of a hypergroup and since then many researchers have worked on this new topic of modern algebra and developed it. The notion of a hyperfield and a hyperring was studied first by Krasner [2] and then some authors followed him, for example, ...

The effective Lagrangian induced by the anomalous

Exact MAP Inference by Avoiding Fractional Vertices

Given a graphical model, one essential problem is MAP inference, that is, finding the most likely configuration of states according to the model. Although this problem is NP-hard, large instances can be solved in practice and it is a major open question is to explain why this is true. We give a natural condition under which we can provably perform MAP inference in polynomial time—we require tha...