Enumerative aspects of the Gross-Siebert program

We present enumerative aspects of the Gross-Siebert program in this introductory survey. After sketching the program's main themes and goals, we review the basic definitions and results of logarithmic and tropical geometry. We give examples and a proof for counting algebraic curves via tropical curves. To illustrate an application of tropical geometry and the Gross-Siebert program to mirror symmetry, we discuss the mirror symmetry of the projective plane.Comment: A version of these notes will appear as a chapter in an upcoming Fields Institute volume. 81 page

Inflammatory potential of dust from schools and building related symptoms

Methods: Ten schools with high prevalence of BRS and 10 schools with low prevalence were selected. Dust collected from floors, horizontal surfaces, and exhaust outlets was tested at five concentrations on the lung epithelial cell line A549. The potency of the dust (PF) to stimulate IL-8 secretion was calculated from the initial linear part of the dose-response curves. The organic fraction of the dust samples was determined by incineration. Results: The schools with low prevalence of symptoms had a BRS% of 4.4–11.0 and the schools with high prevalence a BRS% of 19.6–31.9. The PF of floor dust and surface dust correlated, and the PF was associated with the organic content of the dust. The schools with low prevalence of symptoms had a significantly lower PF than the schools with high prevalence. Using the cut point value of 4.5 ng IL-8/mg floor dust, significantly more high prevalence schools were found above the cut point than below. Conclusion: The PF of the floor dust samples correlated significantly with the prevalence of symptoms in the schools. The content of endotoxin and microorganisms did not seem to explain the inflammatory potential of the dust or BRS, and the substances in the dust causing the inflammatory potential are presently unknown