Stokes matrices for the quantum differential equations of some Fano varieties

The classical Stokes matrices for the quantum differential equation of projective n-space are computed, using multisummation and the so-called monodromy identity. Thus, we recover the results of D. Guzzetti that confirm Dubrovin's conjecture for projective spaces. The same method yields explicit formulas for the Stokes matrices of the quantum differential equations of smooth Fano hypersurfaces in projective n-space and for weighted projective spaces.Comment: 20 pages. Introduction has been changed. Small corrections in the tex

Mirage in Temporal Correlation functions for Baryon-Baryon Interactions in Lattice QCD

Single state saturation of the temporal correlation function is a key condition to extract physical observables such as energies and matrix elements of hadrons from lattice QCD simulations. A method commonly employed to check the saturation is to seek for a plateau of the observables for large Euclidean time. Identifying the plateau in the cases having nearby states, however, is non-trivial and one may even be misled by a fake plateau. Such a situation takes place typically for the system with two or more baryons. In this study, we demonstrate explicitly the danger from a possible fake plateau in the temporal correlation functions mainly for two baryons ($\Xi\Xi$ and $NN$), and three and four baryons ($^3{\rm He}$ and $^4{\rm He})$ as well, employing (2+1)-flavor lattice QCD at $m_{\pi}=0.51$ GeV on four lattice volumes with $L=$ 2.9, 3.6, 4.3 and 5.8 fm. Caution is given for drawing conclusion on the bound $NN$, $3N$ and $4N$ systems only based on the temporal correlation functions.Comment: 32 pages, 13 figures, minor corrections, published version, typos correcte

A terahertz vibrational molecular clock with systematic uncertainty at the 10−1410^{-14} level

Neutral quantum absorbers in optical lattices have emerged as a leading platform for achieving clocks with exquisite spectroscopic resolution. However, the studies of these clocks and their systematic shifts have so far been limited to atoms. Here, we extend this architecture to an ensemble of diatomic molecules and experimentally realize an accurate lattice clock based on pure molecular vibration. We evaluate the leading systematics, including the characterization of nonlinear trap-induced light shifts, achieving a total systematic uncertainty of $4.6\times10^{-14}$. The absolute frequency of the vibrational splitting is measured to be 31 825 183 207 592.8(5.1) Hz, enabling the dissociation energy of our molecule to be determined with record accuracy. Our results represent an important milestone in molecular spectroscopy and THz-frequency standards, and may be generalized to other neutral molecular species with applications for fundamental physics, including tests of molecular quantum electrodynamics and the search for new interactions.Comment: 17 pages, 8 figure

'I thought if I marry the prophet I would not die': The significance of religious affiliation on marriage, HIV testing, and reproductive health practices among young married women in Zimbabwe

Published ArticleThis study examines the association between religious affiliation and reasons for marriage, perceived church attitudes, and reproductive health-seeking behaviors, including HIV testing, among young women in eastern rural Zimbabwe. The sample comprised women (N ¼ 35) who had married by 2012 while participating in a larger randomized controlled trial (RCT) to test the effects of school support on HIV-related risk. The RCT sample was identified in 2007 as all female sixth graders in 25 rural eastern Zimbabwe primary schools whose parents, one or both, had died (N ¼ 328). In our previous RCT analyses, we found that participants who affiliated with an Apostolic church were more than four times more likely to marry than those from non- Apostolic churches and that control group participants were twice as likely to marry as those in the intervention group. Other studies had found that marriage greatly increased the odds of HIV infection among adolescent women. Given the link between Apostolic affiliation and marriage, we conducted semi-structured interviews to explore type of marriage, reasons for marrying, church affiliation and attitudes, family planning, HIV testing, schooling, and family life. We were interested in differences, as perceived by our sample of young married women congregants, among Apostolic sects and other denominations in their attitudes about marriage and health-seeking behaviors. We were also interested in the influence of church affiliation on intervention participants’ decision to marry, since they had comprehensive school support and education is highly valued in Zimbabwe, but costly and often out of financial reach. Interviews were conducted from October 2012 through November 2013; data were analyzed using a general inductive approach. We found that pressure or perceived deception for coitus or marriage was reported only by intervention participants affiliated with Apostolic denominations. Other reasons for marriage were similar between Apostolic and non-Apostolic adherents, as well as intervention and control conditions. All participants believed HIV testing was important, but while all non-Apostolic denominations encouraged HIV testing and clinic/hospital care, there was considerable heterogeneity in attitudes among Apostolics, with ultraconservative denominations most likely to proscribe nonreligious health care. We conclude that some, but not all, Apostolic-affiliated women are afforded discretion in their healthseeking behaviors. Since HIV screening and treatment depend on access to clinic/hospital care, continued public health efforts to engage Apostolic leaders is needed, along with monitoring of progress in access and outcomes

Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds

We investigate the relationship between the Lagrangian Floer superpotentials for a toric orbifold and its toric crepant resolutions. More specifically, we study an open string version of the crepant resolution conjecture (CRC) which states that the Lagrangian Floer superpotential of a Gorenstein toric orbifold $\mathcal{X}$ and that of its toric crepant resolution $Y$ coincide after analytic continuation of quantum parameters and a change of variables. Relating this conjecture with the closed CRC, we find that the change of variable formula which appears in closed CRC can be explained by relations between open (orbifold) Gromov-Witten invariants. We also discover a geometric explanation (in terms of virtual counting of stable orbi-discs) for the specialization of quantum parameters to roots of unity which appears in Y. Ruan's original CRC ["The cohomology ring of crepant resolutions of orbifolds", Gromov-Witten theory of spin curves and orbifolds, 117-126, Contemp. Math., 403, Amer. Math. Soc., Providence, RI, 2006]. We prove the open CRC for the weighted projective spaces $\mathcal{X}=\mathbb{P}(1,\ldots,1,n)$ using an equality between open and closed orbifold Gromov-Witten invariants. Along the way, we also prove an open mirror theorem for these toric orbifolds.Comment: 48 pages, 1 figure; v2: references added and updated, final version, to appear in CM

Mirror Map as Generating Function of Intersection Numbers: Toric Manifolds with Two K\"ahler Forms

In this paper, we extend our geometrical derivation of expansion coefficients of mirror maps by localization computation to the case of toric manifolds with two K\"ahler forms. Especially, we take Hirzebruch surfaces F_{0}, F_{3} and Calabi-Yau hypersurface in weighted projective space P(1,1,2,2,2) as examples. We expect that our results can be easily generalized to arbitrary toric manifold.Comment: 45 pages, 2 figures, minor errors are corrected, English is refined. Section 1 and Section 2 are enlarged. Especially in Section 2, confusion between the notion of resolution and the notion of compactification is resolved. Computation under non-zero equivariant parameters are added in Section

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

Unified ethical principles and an animal research ‘Helsinki’ declaration as foundations for international collaboration

Ethical frameworks are the foundation for any research with humans or nonhuman animals. Human research is guided by overarching international ethical principles, such as those defined in the Helsinki Declaration by the World Medical Association. However, for nonhuman animal research, because there are several sets of ethical principles and national frameworks, it is commonly thought that there is substantial variability in animal research approaches internationally and a lack of an animal research ‘Helsinki Declaration’, or the basis for one. We first overview several prominent sets of ethical principles, including the 3Rs, 3Ss, 3Vs, 4Fs and 6Ps. Then using the 3Rs principles, originally proposed by Russell & Burch, we critically assess them, asking if they can be Replaced, Reduced or Refined. We find that the 3Rs principles have survived several replacement challenges, and the different sets of principles (3Ss, 3Vs, 4Fs and 6Ps) are complementary, a natural refinement of the 3Rs and are ripe for integration into a unified set of principles, as proposed here. We also overview international frameworks and documents, many of which incorporate the 3Rs, including the Basel Declaration on animal research. Finally, we propose that the available animal research guidance documents across countries can be consolidated, to provide a similar structure as seen in the Helsinki Declaration, potentially as part of an amended Basel Declaration on animal research. In summary, we observe substantially greater agreement on and the possibility for unification of the sets of ethical principles and documents that can guide animal research internationally

Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence

We show that the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, in genus zero and after an analytic continuation, the quantum singularity theory (FJRW theory) recently introduced by Fan, Jarvis and Ruan following ideas of Witten. Moreover, on both sides, we highlight two remarkable integral local systems arising from the common formalism of Gamma-integral structures applied to the derived category of the hypersurface {W=0} and to the category of graded matrix factorizations of W. In this setup, we prove that the analytic continuation matches Orlov equivalence between the two above categories.Comment: 72pages, v2: Appendix B and references added. Typos corrected, v3: several mistakes corrected, final versio