Persistence homology of entangled rings

Entangled Rings

Consider a ring of N qubits in a translationally invariant quantum state. We ask to what extent each pair of nearest neighbors can be entangled. Under certain assumptions about the form of the state, we find a formula for the maximum possible nearest-neighbor entanglement. We then compare this maximum with the entanglement achieved by the ground state of an antiferromagnetic ring consisting of ...

Floer homology and Novikov rings

We prove the Arnold conjecture for compact symplectic manifolds under the assumption that either the first Chern class of the tangent bundle vanishes over π2(M) or the minimal Chern number is at least half the dimension of the manifold. This includes the important class of CalabiYau manifolds. The key observation is that the Floer homology groups of the loop space form a module over Novikov’s r...

Operads and -homology of Commutative Rings

A NEW PROOF OF THE PERSISTENCE PROPERTY FOR IDEALS IN DEDEKIND RINGS AND PR¨UFER DOMAINS

In this paper, by using elementary tools of commutative algebra,we prove the persistence property for two especial classes of rings. In fact, thispaper has two main sections. In the first main section, we let R be a Dedekindring and I be a proper ideal of R. We prove that if I1, . . . , In are non-zeroproper ideals of R, then Ass1(Ik11 . . . Iknn ) = Ass1(Ik11 ) [ · · · [ Ass1(Iknn )for all k1,...

Comparing High Order Networks by Persistence Homology

This paper presents methods to compare high order networks using persistence homology. High order networks induce well-founded homological features and the difference between networks is measured by the difference between the homological features. This is a reasonable approximation to a valid metric in the space of high order networks modulo permutation isomorphisms. The approximations succeed ...