Nerodia rhombifera

Number of Pages: 4Integrative BiologyGeological Science

Functoriality for Lagrangian correspondences in Floer theory

Using quilted Floer cohomology and relative quilt invariants, we define a composition functor for categories of Lagrangian correspondences in monotone and exact symplectic Floer theory. We show that this functor agrees with geometric composition in the case that the composition is smooth and embedded. As a consequence we obtain 'categorification commutes with composition' for Lagrangian correspondences.Comment: minor corrections and updated references; original 120 page preprint got split into 4 parts - this is one of the

A wall-crossing formula for Gromov-Witten invariants under variation of git quotient

We prove a quantum version of Kalkman's wall-crossing formula comparing Gromov-Witten invariants on geometric invariant theory (git) quotients related by a change in polarization. The wall-crossing terms are gauged Gromov-Witten invariants with smaller structure group. As an application, we show that the graph Gromov-Witten potentials of quotients related by wall-crossings of crepant type are equivalent up to a distribution in the quantum parameter that is almost everywhere zero. This is a version of the crepant transformation conjecture of Li-Ruan, Bryan-Graber, Coates-Ruan etc. in cases where the crepant transformation is obtained by variation of git.Comment: 64 pages, 1 figure. Expanded and clarified exposition in a number of places in response to referee comment

Linear Precoding in Cooperative MIMO Cellular Networks with Limited Coordination Clusters

In a cooperative multiple-antenna downlink cellular network, maximization of a concave function of user rates is considered. A new linear precoding technique called soft interference nulling (SIN) is proposed, which performs at least as well as zero-forcing (ZF) beamforming. All base stations share channel state information, but each user's message is only routed to those that participate in the user's coordination cluster. SIN precoding is particularly useful when clusters of limited sizes overlap in the network, in which case traditional techniques such as dirty paper coding or ZF do not directly apply. The SIN precoder is computed by solving a sequence of convex optimization problems. SIN under partial network coordination can outperform ZF under full network coordination at moderate SNRs. Under overlapping coordination clusters, SIN precoding achieves considerably higher throughput compared to myopic ZF, especially when the clusters are large.Comment: 13 pages, 5 figure