Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds

We present a proof of the mirror conjecture of Aganagic-Vafa [arXiv:hep-th/0012041] and Aganagic-Klemm-Vafa [arXiv:hep-th/0105045] on disk enumeration in toric Calabi-Yau 3-folds for all smooth semi-projective toric Calabi-Yau 3-folds. We consider both inner and outer branes, at arbitrary framing. In particular, we recover previous results on the conjecture for (i) an inner brane at zero framing in the total space of the canonical line bundle of the projective plane (Graber-Zaslow [arXiv:hep-th/0109075]), (ii) an outer brane at arbitrary framing in the resolved conifold (Zhou [arXiv:1001.0447]), and (iii) an outer brane at zero framing in the total space of the canonical line bundle of the projective plane (Brini [arXiv:1102.0281, Section 5.3]).Comment: 39 pages, 11 figure

Transient thermal effects in solid noble gases as materials for the detection of Dark Matter

The transient phenomena produced in solid noble gases by the stopping of the recoils resulting from the elastic scattering processes of WIMPs from the galactic halo were modelled, as dependencies of the temperatures of lattice and electronic subsystems on the distance to the recoil's trajectory, and time from its passage. The peculiarities of these thermal transients produced in Ar, Kr and Xe were analysed for different initial temperatures and WIMP energies, and were correlated with the characteristics of the targets and with the energy loss of the recoils. The results were compared with the thermal spikes produced by the same WIMPs in Si and Ge. In the range of the energy of interest, up to tens of keV for the self-recoil, local phase transitions solid - liquid and even liquid - gas were found possible, and the threshold parameters were established.Comment: Minor corrections and updated references; accepted to JCA

Scalar ground-state observables in the random phase approximation

We calculate the ground-state expectation value of scalar observables in the matrix formulation of the random phase approximation (RPA). Our expression, derived using the quasiboson approximation, is a straightforward generalization of the RPA correlation energy. We test the reliability of our expression by comparing against full diagonalization in 0 h-bar omega shell-model spaces. In general the RPA values are an improvement over mean-field (Hartree-Fock) results, but are not always consistent with shell-model results. We also consider exact symmetries broken in the mean-field state and whether or not they are restored in RPA.Comment: 7 pages, 3 figure

Tests of the random phase approximation for transition strengths

We investigate the reliability of transition strengths computed in the random-phase approximation (RPA), comparing with exact results from diagonalization in full $0\hbar\omega$ shell-model spaces. The RPA and shell-model results are in reasonable agreement for most transitions; however some very low-lying collective transitions, such as isoscalar quadrupole, are in serious disagreement. We suggest the failure lies with incomplete restoration of broken symmetries in the RPA. Furthermore we prove, analytically and numerically, that standard statements regarding the energy-weighted sum rule in the RPA do not hold if an exact symmetry is broken.Comment: 11 pages, 7 figures; Appendix added with new proof regarding violation of energy-weighted sum rul

Ageing is associated with molecular signatures of inflammation and type 2 diabetes in rat pancreatic islets.

AIMS/HYPOTHESIS: Ageing is a major risk factor for development of metabolic diseases such as type 2 diabetes. Identification of the mechanisms underlying this association could help to elucidate the relationship between age-associated progressive loss of metabolic health and development of type 2 diabetes. We aimed to determine molecular signatures during ageing in the endocrine pancreas. METHODS: Global gene transcription was measured in pancreatic islets isolated from young and old rats by Ilumina BeadChip arrays. Promoter DNA methylation was measured by Sequenom MassArray in 46 genes that showed differential expression with age, and correlations with expression were established. Alterations in morphological and cellular processes with age were determined by immunohistochemical methods. RESULTS: Age-related changes in gene expression were found at 623 loci (>1.5-fold, false discovery rate [FDR] <5%), with a significant (FDR < 0.05) enrichment in genes previously implicated in islet-cell function (Enpp1, Abcc8), type 2 diabetes (Tspan8, Kcnq1), inflammatory processes (Cxcl9, Il33) and extracellular matrix organisation (Col3a1, Dpt). Age-associated transcriptional differences negatively correlated with promoter DNA methylation at several loci related to inflammation, glucose homeostasis, cell proliferation and cell-matrix interactions (Il33, Cxcl9, Gpr119, Fbp2, Col3a1, Dpt, Spp1). CONCLUSIONS/INTERPRETATION: Our findings suggest that a significant proportion of pancreatic islets develop a low-grade 'chronic' inflammatory status with ageing and this may trigger altered functional plasticity. Furthermore, we identified changes in expression of genes previously linked to type 2 diabetes and associated changes in DNA methylation that could explain their age-associated dysregulation. These findings provide new insights into key (epi)genetic signatures of the ageing process in islets.Biotechnology and Biological Sciences Research Council (Grant ID: BB/H003312/1), British Heart Foundation, FP6 Epigenome Network of Excellence programme, GlaxoSmithKline, Nuffield Foundation, Royal Society, Medical Research Council (Grant ID: MRC_MC_UU_12012/4)This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s00125-015-3837-

Calibrated Sub-Bundles in Non-Compact Manifolds of Special Holonomy

This paper is a continuation of math.DG/0408005. We first construct special Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on the cotangent bundle of S^n by looking at the conormal bundle of appropriate submanifolds of S^n. We find that the condition for the conormal bundle to be special Lagrangian is the same as that discovered by Harvey-Lawson for submanifolds in R^n in their pioneering paper. We also construct calibrated submanifolds in complete metrics with special holonomy G_2 and Spin(7) discovered by Bryant and Salamon on the total spaces of appropriate bundles over self-dual Einstein four manifolds. The submanifolds are constructed as certain subbundles over immersed surfaces. We show that this construction requires the surface to be minimal in the associative and Cayley cases, and to be (properly oriented) real isotropic in the coassociative case. We also make some remarks about using these constructions as a possible local model for the intersection of compact calibrated submanifolds in a compact manifold with special holonomy.Comment: 20 pages; for Revised Version: Minor cosmetic changes, some paragraphs rewritten for improved clarit

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

Insulin-like Growth Factor II: An Essential Adult Stem Cell Niche Constituent in Brain and Intestine.

Tissue-specific stem cells have unique properties and growth requirements, but a small set of juxtacrine and paracrine signals have been identified that are required across multiple niches. Whereas insulin-like growth factor II (IGF-II) is necessary for prenatal growth, its role in adult stem cell physiology is largely unknown. We show that loss of Igf2 in adult mice resulted in a ∼50% reduction in slowly dividing, label-retaining cells in the two regions of the brain that harbor neural stem cells. Concordantly, induced Igf2 deletion increased newly generated neurons in the olfactory bulb accompanied by hyposmia, and caused impairments in learning and memory and increased anxiety. Induced Igf2 deletion also resulted in rapid loss of stem and progenitor cells in the crypts of Lieberkühn, leading to body-weight loss and lethality and the inability to produce organoids in vitro. These data demonstrate that IGF-II is critical for multiple adult stem cell niches

Homological Mirror Symmetry for Calabi-Yau hypersurfaces in projective space

We prove Homological Mirror Symmetry for a smooth d-dimensional Calabi-Yau hypersurface in projective space, for any d > 2 (for example, d = 3 is the quintic three-fold). The main techniques involved in the proof are: the construction of an immersed Lagrangian sphere in the `d-dimensional pair of pants'; the introduction of the `relative Fukaya category', and an understanding of its grading structure; a description of the behaviour of this category with respect to branched covers (via an `orbifold' Fukaya category); a Morse-Bott model for the relative Fukaya category that allows one to make explicit computations; and the introduction of certain graded categories of matrix factorizations mirror to the relative Fukaya category.Comment: 133 pages, 17 figures. Changes to the argument ruling out sphere bubbling in the relative Fukaya category, and dealing with the behaviour of the symplectic form under branched covers. Other minor changes suggested by the referee. List of notation include

Mesenchyme-derived IGF2 is a major paracrine regulator of pancreatic growth and function

The genetic mechanisms that determine the size of the adult pancreas are poorly understood. Imprinted genes, which are expressed in a parent-of-origin-specific manner, are known to have important roles in development, growth and metabolism. However, our knowledge regarding their roles in the control of pancreatic growth and function remains limited. Here we show that many imprinted genes are highly expressed in pancreatic mesenchyme-derived cells and explore the role of the paternally-expressed insulin-like growth factor 2 (Igf2) gene in mesenchymal and epithelial pancreatic lineages using a newly developed conditional Igf2 mouse model. Mesenchyme-specific Igf2 deletion results in acinar and beta-cell hypoplasia, postnatal whole-body growth restriction and maternal glucose intolerance during pregnancy, suggesting that the mesenchyme is a developmental reservoir of IGF2 used for paracrine signalling. The unique actions of mesenchymal IGF2 are demonstrated by the absence of any discernible growth or functional phenotypes upon Igf2 deletion in the developing pancreatic epithelium. Additionally, increased IGF2 levels specifically in the mesenchyme, through conditional Igf2 loss-of-imprinting or Igf2r deletion, leads to pancreatic acinar overgrowth. Furthermore, ex-vivo exposure of primary acinar cells to exogenous IGF2 activates AKT, a key signalling node, and increases their number and amylase production. Based on these findings, we propose that mesenchymal Igf2, and perhaps other imprinted genes, are key developmental regulators of adult pancreas size and function