We study correlation functions of single-cycle chiral operators in Sym T 4, the symmetric product orbifold of N supersymmetric four-tori. Correlators of twist operators are evaluated on covering surfaces, generally of different genera, where fields are single-valued. We compute some simple four-point functions and study how the sum over inequivalent branched covering maps splits under OPEs. We ...

A Schnyder wood is an orientation and coloring of the edges of a planar map satisfying a simple local property. We propose a generalization of Schnyder woods to graphs embedded on the torus with application to graph drawing. We prove several properties on this new object. Among all we prove that a graph embedded on the torus admits such a Schnyder wood if and only if it is an essentially 3conne...

In this survey I list some of my main results on the three topics (covering systems, restricted sumsets and zero-sum problems). 1. On Covering Systems Let M be an additive abelian group. A triple 〈λ, a, n〉 with λ ∈M, n ∈ Z = {1, 2, 3, · · · } and a ∈ R(n) = {0, 1, . . . , n− 1}, can be viewed as the residue class a(n) = a+ nZ = {a+ nx : x ∈ Z} (1.1) associated with weight λ. For systems A = {〈λ...

In this supplementary document, we present how we characterize diversity in solutions along with some oracle statistics (Section 1.1) , and show some example success and failure cases of our re-ranker (Section 2). 1. Analyzing Diverse Segmentations In this section, we characterize the diversity achieved in the multiple segmentations. Specifically, we investigate the sources of diversity, and at...

Vegetation biomass is a globally important climate-relevant terrestrial carbon pool and also drives local hydrological systems via evapotranspiration. of individual vegetation types has been successfully estimated from active passive remote sensing data. However, for many tasks, landscape-level maps across several are more suitable than types. For example, the validation ecohydrological models ...

polarity development. The resulting protein interaction map provides tantalizing insights and identifies dozens of potential mechanistic connections worth closer examination. The authors used 68 yeast proteins associated with the actin cytoskeleton, septins, the secretory apparatus, and Rhotype GTPases as baits in parallel two-hybrid screens covering 90% of the preConnections in yeast cell pola...

Let M be a closed hyperbolic three manifold. We construct closed surfaces that map by immersions into M so that for each, one the corresponding mapping on the universal covering spaces is an embedding, or, in other words, the corresponding induced mapping on fundamental groups is an injection.