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PURPOSE We tested the ability of the 'Weight, IGF-1, Neonatal Retinopathy of Prematurity (WINROP)' clinical algorithm to detect preterm infants at risk of severe Retinopathy of Prematurity (ROP) in a birth cohort in the South East of Scotland. In particular, we asked the question: 'are weekly weight measurements essential when using the WINROP algorithm?'… (More)
Medical education reform can make an important contribution to the future health care of populations. Social accountability in medical education was defined by the World Health Organization in 1995, and an international movement for change is gathering momentum. While change can be enabled with policy levers, such as funding tied to achieving equity… (More)
This paper establishes an isomorphism between the Bar-Natan skein module of the solid torus with a particular boundary curve system and the homology of the (n, n) Springer variety. The results build on Khovanov's work with crossingless matchings and the cohomology of the (n, n) Springer variety. We also give a formula for comultiplication in the Bar-Natan… (More)
The sl 3 spider is a diagrammatic category used to study the representation theory of the quantum group Uq(sl 3). The morphisms in this category are generated by a basis of non-elliptic webs. Khovanov-Kuperberg observed that non-elliptic webs are indexed by semistandard Young tableaux. They establish this bijection via a recursive growth algorithm.… (More)
Consider the following question. Given a suitable linear series L on a smooth surface S, how many curves in L have a given analytic or topological type of singularity? By " suitable " linear series with respect to a type of singularity, we mean that there are finitely many curves with the singularity in the linear series and their codimension is maximal.… (More)
We develop a dimer model for the Alexander polynomial of a knot. This recovers Kauffman's state sum model for the Alexander polynomial using the language of dimers. By providing some additional structure we are able to extend this model to give a state sum formula for the twisted Alexander polynomial of a knot depending on a representation of the knot group.
Springer varieties are studied because their cohomology carries a natural action of the symmetric group S n and their top-dimensional cohomology is irreducible. In his work on tangle invariants, Khovanov constructed a family of Springer varieties X n as subvarieties of the product of spheres (S 2) n. We show that if X n is embedded antipodally in (S 2) n… (More)
We identify the ring of odd symmetric functions introduced by Ellis and Khovanov as the space of skew polynomials fixed by a natural action of the Hecke algebra at q = −1. This allows us to define graded modules over the Hecke algebra at q = −1 that are 'odd' analogs of the cohomology of type A Springer varieties. The graded module associated to the full… (More)
Given a graph G, its k-coloring graph is the graph whose vertex set is the proper k-colorings of the vertices of G with two k−colorings adjacent if they differ at exactly one vertex. In this paper, we consider the question: Which graphs can be coloring graphs? In other words, given a graph H, do there exist G and k such that H is the k-coloring graph of G?… (More)
Every link in R 3 can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.