Moduli and periods of simply connected Enriques surfaces

We describe a period map for those simply connected Enriques surfaces in characteristic 2 whose canonical double cover is K3. The moduli stack for these surfaces has a Deligne-Mumford quotient that is an open substack of a $\mathbb P^1$-bundle over the period space. We also give some general results relating local and global moduli for algebraic varieties and describe the difference in their dimensions in terms of the failure of the automorphism group scheme to be reduced

Ultrafast control of inelastic tunneling in a double semiconductor quantum

In a semiconductor-based double quantum well (QW) coupled to a degree of freedom with an internal dynamics, we demonstrate that the electronic motion is controllable within femtoseconds by applying appropriately shaped electromagnetic pulses. In particular, we consider a pulse-driven AlxGa1-xAs based symmetric double QW coupled to uniformly distributed or localized vibrational modes and present analytical results for the lowest two levels. These predictions are assessed and generalized by full-fledged numerical simulations showing that localization and time-stabilization of the driven electron dynamics is indeed possible under the conditions identified here, even with a simultaneous excitations of vibrational modes.Comment: to be published in Appl.Phys.Let

Integral points on elliptic curves and explicit valuations of division polynomials

Assuming Lang's conjectured lower bound on the heights of non-torsion points on an elliptic curve, we show that there exists an absolute constant C such that for any elliptic curve E/Q and non-torsion point P in E(Q), there is at most one integral multiple [n]P such that n > C. The proof is a modification of a proof of Ingram giving an unconditional but not uniform bound. The new ingredient is a collection of explicit formulae for the sequence of valuations of the division polynomials. For P of non-singular reduction, such sequences are already well described in most cases, but for P of singular reduction, we are led to define a new class of sequences called elliptic troublemaker sequences, which measure the failure of the Neron local height to be quadratic. As a corollary in the spirit of a conjecture of Lang and Hall, we obtain a uniform upper bound on h(P)/h(E) for integer points having two large integral multiples.Comment: 41 pages; minor corrections and improvements to expositio

Holomorphic maps and the complete 1/N expansion of 2D SU(N) Yang-Mills

We give a description of the complete 1/N expansion of SU(N) 2D Yang Mills theory in terms of the moduli space of holomorphic maps from non-singular worldsheets. This is related to the Gross-Taylor coupled 1/N expansion through a map from Brauer algebras to symmetric groups. These results point to an equality between Euler characters of moduli spaces of holomorphic maps from non-singular worldsheets with a target Riemann surface equipped with markings on the one hand and Euler characters of another moduli space involving worldsheets with double points (nodes).Comment: 17 pages + 8 (Appendices) ; 4 figure

Quantum curves for Hitchin fibrations and the Eynard-Orantin theory

We generalize the topological recursion of Eynard-Orantin (2007) to the family of spectral curves of Hitchin fibrations. A spectral curve in the topological recursion, which is defined to be a complex plane curve, is replaced with a generic curve in the cotangent bundle $T^*C$ of an arbitrary smooth base curve $C$. We then prove that these spectral curves are quantizable, using the new formalism. More precisely, we construct the canonical generators of the formal $\hbar$-deformation family of $D$-modules over an arbitrary projective algebraic curve $C$ of genus greater than $1$, from the geometry of a prescribed family of smooth Hitchin spectral curves associated with the $SL(2,\mathbb{C})$-character variety of the fundamental group $\pi_1(C)$. We show that the semi-classical limit through the WKB approximation of these $\hbar$-deformed $D$-modules recovers the initial family of Hitchin spectral curves.Comment: 34 page

From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators

In this letter,we present our conjecture on the connection between the Kontsevich--Witten and the Hurwitz tau-functions. The conjectural formula connects these two tau-functions by means of the $GL(\infty)$ group element. An important feature of this group element is its simplicity: this is a group element of the Virasoro subalgebra of $gl(\infty)$. If proved, this conjecture would allow to derive the Virasoro constraints for the Hurwitz tau-function, which remain unknown in spite of existence of several matrix model representations, as well as to give an integrable operator description of the Kontsevich--Witten tau-function.Comment: 13 page

The class of the locus of intermediate Jacobians of cubic threefolds

We study the locus of intermediate Jacobians of cubic threefolds within the moduli space of complex principally polarized abelian fivefolds, and its generalization to arbitrary genus - the locus of abelian varieties with a singular odd two-torsion point on the theta divisor. Assuming that this locus has expected codimension (which we show to be true for genus up to 5), we compute the class of this locus, and of is closure in the perfect cone toroidal compactification, in the Chow, homology, and the tautological ring. We work out the cases of genus up to 5 in detail, obtaining explicit expressions for the classes of the closures of the locus of products of an elliptic curve and a hyperelliptic genus 3 curve, in moduli of principally polarized abelian fourfolds, and of the locus of intermediate Jacobians in genus 5. In the course of our computation we also deal with various intersections of boundary divisors of a level toroidal compactification, which is of independent interest in understanding the cohomology and Chow rings of the moduli spaces.Comment: v2: new section 9 on the geometry of the boundary of the locus of intermediate Jacobians of cubic threefolds. Final version to appear in Invent. Mat

Disease acceptance and adherence to imatinib in Taiwanese chronic myeloid leukaemia outpatients

Background The launch of imatinib has turned chronic myeloid leukaemia (CML) into a chronic illness due to the dramatic improvement in survival. Several recent studies have demonstrated that poor adherence to imatinib may hamper the therapeutic outcomes and result in increased medical expenditures, whilst research on exploring the reasons for non-adherence to imatinib is still limited. Objective This study aimed to explore the experience of patients as they journey through their CML treatments and associated imatinib utilisation in order to understand the perceptions, attitudes and concerns that may influence adherence to imatinib treatment. Setting This study was conducted at oncology outpatient clinics in a medical centre in southern Taiwan. Methods CML patients who regularly attended the oncology outpatient clinics to receive imatinib treatment from October 2011 to March 2012 were invited to participate in the study. Semi-structured face-to-face interviews were used to explore patients’ experiences and views of their treatment, their current CML status and CML-related health conditions, their concerns about imatinib treatment and imatinib-taking behaviours. Patient interviews were recorded, transcribed verbatim and thematically analysed using the constant comparison approach. Main outcome measure Themes related to patients’ views of the disease and health conditions, worries and concerns influencing imatinib utilisation behaviours are reported. Results Forty-two CML patients participated in the interviews. The emerging themes included: acceptance of current disease and health status, misconceptions about disease progression, factors associated with adherence to imatinib, concerns and management of adverse drug effects. Participants regarded CML as a chronic disease but had misconceptions about disease progression, therapeutic monitoring, resistance to imatinib and symptoms of side effects. Participants were generally adherent to imatinib and favoured long-term prescriptions to avoid regular outpatient visits for medication refills. Experiencing adverse effect was the main reason influencing adherence and led to polypharmacy. Most participants altered medicine-taking behaviours to maintain long-term use of imatinib. Conclusion Taiwanese CML patients are adherent to imatinib but report changing their medication-taking behaviour due to adverse drug effects and associated polypharmacy. Patients’ misconceptions of the disease and medication suggests that it is necessary to improve communication between patients and healthcare professionals. Routinely providing updated information as part of the patient counselling process should be considered as a means of improving this communication

Can differences in medical drug compliance between European countries be explained by social factors: analyses based on data from the European Social Survey, round 2

<p>Abstract</p> <p>Background</p> <p>Non-compliance with medication is a major health problem. Cultural differences may explain different compliance patterns. The size of the compliance burden and the impact of socio-demographic and socio-economic status within and across countries in Europe have, however, never been analysed in one survey. The aim of this study was to analyse 1) medical drug compliance in different European countries with respect to socio-demographic and socio-economic factors, and to examine 2) whether cross-national differences could be explained by these factors.</p> <p>Methods</p> <p>A multi-country interview survey <it>European Social Survey, Round 2 </it>was conducted in 2004/05 comprising questions about compliance with last prescribed drug. Non-compliance was classified as primary and secondary, depending whether the drug was purchased or not. Statistical weighting allowed for adjustment for national differences in sample mechanisms. A multiple imputation strategy was used to compensate for missing values. The analytical approach included multivariate and multilevel analyses.</p> <p>Results</p> <p>The survey comprised 45,678 participants. Response rate was 62.5% (range 43.6–79.1%). Reported compliance was generally high (82%) but the pattern of non-compliance showed large variation between countries. Some 3.2% did not purchase the most recently prescribed medicine, and 13.6% did not take the medicine as prescribed. Multiple regression analyses showed that each variable had very different and in some cases opposite impact on compliance within countries. The multilevel analysis showed that the variation between countries did not change significantly when adjusted for increasing numbers of covariates.</p> <p>Conclusion</p> <p>Reported compliance was generally high but showed wide variation between countries. Cross-national differences could, however, not be explained by the socio-demographic and socio-economic variables measured.</p