Reduced classes and curve counting on surfaces II: calculations

We calculate the stable pair theory of a projective surface $S$. For fixed curve class $\beta\in H^2(S)$ the results are entirely topological, depending on $\beta^2$, $\beta.c_1(S)$, $c_1(S)^2$, $c_2(S)$, $b_1(S)$ \emph{and} invariants of the ring structure on $H^*(S)$ such as the Pfaffian of $\beta$ considered as an element of $\Lambda^2 H^1(S)^*$. Amongst other things, this proves an extension of the G\"ottsche conjecture to non-ample linear systems. We also give conditions under which this calculates the full 3-fold reduced residue theory of $K_S$. This is related to the reduced residue Gromov-Witten theory of $S$ via the MNOP conjecture. When the surface has no holomorphic 2-forms this can be expressed as saying that certain Gromov-Witten invariants of $S$ are topological. Our method uses the results of \cite{KT1} to express the reduced virtual cycle in terms of Euler classes of bundles over a natural smooth ambient space.Comment: 19 pages. Minor correction

5′‐Iodination of Solid‐Phase‐Linked Oligodeoxyribonucleotides

5′‐Iodinated oligodeoxyribonucleotides readily react with 3′‐phosphorothioated DNA in the presence of a complementary template to yield a conjugate that is identical to natural DNA in every respect except that one oxygen atom in the phosphodiester backbone is replaced by a sulfur atom. The 5′‐iodo group is easily converted to a variety of other functional groups and will quickly react with thiol‐containing labels to yield stable thioether conjugates. This unit presents manual and automated procedures for converting the 5′‐hydroxyl of protected CPG–bound oligodeoxyribonucleotides to an iodo group and for releasing and purifying the products.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143744/1/cpnc0419.pd

A short proof of the G\"ottsche conjecture

We prove that for a sufficiently ample line bundle $L$ on a surface $S$, the number of $\delta$-nodal curves in a general $\delta$-dimensional linear system is given by a universal polynomial of degree $\delta$ in the four numbers $L^2,\,L.K_S,\,K_S^2$ and $c_2(S)$. The technique is a study of Hilbert schemes of points on curves on a surface, using the BPS calculus of [PT3] and the computation of tautological integrals on Hilbert schemes by Ellingsrud, G\"ottsche and Lehn. We are also able to weaken the ampleness required, from G\"ottsche's $(5\delta-1)$-very ample to $\delta$-very ample.Comment: 8 pages. Published versio

VLT + UVES Spectroscopy of the Low-Ionization Intrinsic Absorber in SDSS J001130.56+005550.7

We analyse high-resolution VLT+UVES spectra of the low-ionization intrinsic absorber observed in the BAL QSO SDSS J001130.56+005550.7. Two narrow absorption systems at velocities -600 km/s and -22000 km/s are detected. The low-velocity system is part of the broad absorption line (BAL), while the high-velocity one is well detached. While most narrow absorption components are only detected in the high-ionization species, the lowest velocity component is detected in both high- and low-ionization species, including in the excited SiII* and CII* lines. From the analysis of doublet lines, we find that the narrow absorption lines at the low-velocity end of the BAL trough are completely saturated but do not reach zero flux, their profiles being dominated by a velocity-dependent covering factor. The covering factor is significantly smaller for MgII than for SiIV and NV, which demonstrates the intrinsic nature of absorber. From the analysis of the excited SiII* and CII* lines in the lowest velocity component, we find an electron density ~ 1000 cm^{-3}. Assuming photoionization equilibrium, we derive a distance ~ 20 kpc between the low-ionization region and the quasar core. The correspondence in velocity of the high- and low-ionization features suggests that all these species must be closely associated, hence formed at the same distance of ~ 20 kpc, much higher than the distance usually assumed for BAL absorbers.Comment: Accepted for publication in A&

Distance to Multiple Kinematic Components of Quasar Outflows: VLT Observations of QSO 2359-1241 and SDSS J0318-0600

Using high resolution VLT spectra, we study the multi-component outflow systems of two quasars exhibiting intrinsic Fe II absorption (QSO 2359-1241 and SDSS J0318-0600). From the extracted ionic column densities and using photoionization modeling we determine the gas density, total column density, and ionization parameter for several of the components. For each object the largest column density component is also the densest, and all other components have densities of roughly 1/4 of that of the main component. We demonstrate that all the absorbers lie roughly at the same distance from the source. Further, we calculate the total kinetic luminosities and mass outflow rates of all components and show that these quantities are dominated by the main absorption component.Comment: 27 pages, 5 figure

The Quasar Outflow Contribution to AGN Feedback: VLT Measurements of SDSS J0318-0600

We present high spectral resolution VLT observations of the BAL quasar SDSS J0318-0600. This high quality data set allows us to extract accurate ionic column densities and determine an electron number density of n_e=10^3.3 +/- 0.2 cm^-3 for the main outflow absorption component. The heavily reddened spectrum of SDSS J0318-0600 requires purely silicate dust with a reddening curve characteristic of predominately large grains, from which we estimate the bolometric luminosity. We carry out photoionization modeling to determine the total column density, ionization parameter and distance of the gas and find that the photionization models suggest abundances greater than solar. Due to the uncertainty in the location of the dust extinction, we arrive at two viable distances for the main ouflow component from the central source, 6 and 18 kpc, where we consider the 6 kpc location as somewhat more physically plausable. Assuming the canonical global covering of 20% for the outflow and a distance of 6 kpc, our analysis yields a mass flux of 120 M_sun yr^-1 and a kinetic luminosity that is ~0.1% of the bolometric luminosity of the object. Should the dust be part of the outflow, then these values are ~4x larger. The large mass flux and kinetic luminosity make this outflow a significant contributor to AGN feedback processes.Comment: Accepted for publication in ApJ, 57 pages, 14 figure

Deep Policy Dynamic Programming for Vehicle Routing Problems

Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical dynamic programming (DP) algorithms guarantee optimal solutions, but scale badly with the problem size. We propose Deep Policy Dynamic Programming (DPDP), which aims to combine the strengths of learned neural heuristics with those of DP algorithms. DPDP prioritizes and restricts the DP state space using a policy derived from a deep neural network, which is trained to predict edges from example solutions. We evaluate our framework on the travelling salesman problem (TSP), the vehicle routing problem (VRP) and TSP with time windows (TSPTW) and show that the neural policy improves the performance of (restricted) DP algorithms, making them competitive to strong alternatives such as LKH, while also outperforming most other 'neural approaches' for solving TSPs, VRPs and TSPTWs with 100 nodes.Comment: 21 page

Finding White Dwarfs with Transit Searches

We make predictions for the rate of discovery of eclipsing white dwarf-main sequence (WD-MS) binaries in terrestrial-planet transit searches, taking the planned Kepler and Eddington missions as examples. We use a population synthesis model to characterize the Galactic WD-MS population, and we find that, despite increased noise due to stellar variability compared with the typical planetary case, discovery of >100 non-accreting, eclipsing WD-MS systems is likely using Kepler and Eddington, with periods of 2-20 days and transit amplitudes of |delta m|~0.0003-0.00003 magnitudes. Follow-up observations of these systems could accurately test the theoretical white dwarf mass-radius relation or theories of binary star evolution.Comment: 5 pages, 3 figures, one table, accepted for publication in ApJ. Minor changes to Galactic model and to discusion section; conclusions unchange