A conjectural generating function for numbers of curves on surfaces

I give a conjectural generating function for the numbers of $\delta$-nodal curves in a linear system of dimension $\delta$ on an algebraic surface. It reproduces the results of Vainsencher for the case $\delta\le 6$ and Kleiman-Piene for the case $\delta\le 8$. The numbers of curves are expressed in terms of five universal power series, three of which I give explicitly as quasimodular forms. This gives in particular the numbers of curves of arbitrary genus on a K3 surface and an abelian surface in terms of quasimodular forms, generalizing the formula of Yau-Zaslow for rational curves on K3 surfaces. The coefficients of the other two power series can be determined by comparing with the recursive formulas of Caporaso-Harris for the Severi degrees in $\P_2$. We verify the conjecture for genus 2 curves on an abelian surface. We also discuss a link of this problem with Hilbert schemes of points.Comment: amslatex 13 page

The Omega deformed B-model for rigid N=2 theories

We give an interpretation of the Omega deformed B-model that leads naturally to the generalized holomorphic anomaly equations. Direct integration of the latter calculates topological amplitudes of four dimensional rigid N=2 theories explicitly in general Omega-backgrounds in terms of modular forms. These amplitudes encode the refined BPS spectrum as well as new gravitational couplings in the effective action of N=2 supersymmetric theories. The rigid N=2 field theories we focus on are the conformal rank one N=2 Seiberg-Witten theories. The failure of holomorphicity is milder in the conformal cases, but fixing the holomorphic ambiguity is only possible upon mass deformation. Our formalism applies irrespectively of whether a Lagrangian formulation exists. In the class of rigid N=2 theories arising from compactifications on local Calabi-Yau manifolds, we consider the theory of local P2. We calculate motivic Donaldson-Thomas invariants for this geometry and make predictions for generalized Gromov-Witten invariants at the orbifold point.Comment: 73 pages, no figures, references added and typos correcte

Developing sustainability in a dental practice through an Action Research approach

Introduction: For dental practices to become more environmentally sustainable, the full cooperation of all practice staff can lead to greater engagement with proposed initiatives. Action Research is a participatory approach to change that involves participants in the decisions that affect them. Aim: The aim of this study was to collaboratively develop interventions to improve environmental sustainability at one dental practice. Methods: This was a mixed methods study following an Action Research process for intervention design. The study was set in a mixed NHS / private dental practice in England, UK. Results: Participants engaged in the process and were able to choose the measures they wished to implement. Feedback showed that whilst some measures had been discarded, others had led to changes both in professional and personal behaviour. Conclusion: Action Research offers an innovative and constructive method of engaging participants in developing their own sustainability strategies and can encourage positive change

Five-dimensional gauge theory and compactification on a torus

We study five-dimensional minimally supersymmetric gauge theory compactified on a torus down to three dimensions, and its embedding into string/M-theory using geometric engineering. The moduli space on the Coulomb branch is hyperkaehler equipped with a metric with modular transformation properties. We determine the one-loop corrections to the metric and show that they can be interpreted as worldsheet and D1-brane instantons in type IIB string theory. Furthermore, we analyze instanton corrections coming from the solitonic BPS magnetic string wrapped over the torus. In particular, we show how to compute the path-integral for the zero-modes from the partition function of the M5 brane, or, using a 2d/4d correspondence, from the partition function of N=4 SYM theory on a Hirzebruch surface.Comment: 30 pages, 2 figures; v2: typos corrected, added references, JHEP versio

Orbifold cohomology for global quotients

For an orbifold X which is the quotient of a manifold Y by a finite group G we construct a noncommutative ring with an action of G such that the orbifold cohomology of X as defined in math.AG/0004129 by Chen and Ruan is the G invariant part. In the case thar Y is S^n for a surface S with trivial canonical class we prove that (a small modification of) the orbifold cohomology of X is naturally isomorphic to the cohomology ring of the Hilbert scheme of n points on S computed in math.AG/0012166 by Lehn and Sorger

Controlled delivery of naltrexone by an intraoral device:In vivo study on human subjects

Naltrexone is widely used in the treatment of opiate addiction but its current peroral administration is characterized by low bioavailability with various side effects. The development of a long-acting trans- buccal delivery device(IntelliDrug) for NLX may be useful to improve patient compliance and the therapy effectiveness. The aims of the study are(a)to test basic safety and effectiveness of controlled transbuccal drug delivery on human subjects;(b)to compare NLX bioavailability following transbuccal delivery vs per os conventional delivery; and(c)to test the hypothesis that transbuccal delivery is more efficient than the conventional route. In this randomized cross-over pilot study,12 healthy subjects received in a different order 2 types of NLX administration,per os or transbuccal delivery, based on which grou they were randomized to. For per os administration 50mg NLX tablets were used, while for transbuccal administration, a NLX-loaded prototype of the IntelliDrug device was fixed on patients\u2019 dental arch. Serial blood samples were drawn and analysed for the NLX concentration. The IntelliDrug prototype functioned properly and it did not exert any adverse side-effect. The transbuccal route resulted in administration efficiency 4\u201317 times higher than conventional per os route. Transbuccal delivery of NLX appears to be a more efficient drug administration route compared to peroral one. It allows to reach a given therapeutic blood level using a small drug dose