Cusps of Hilbert modular varieties

Motivated by a question of Hirzebruch on the possible topological types of cusp cross-sections of Hilbert modular varieties, we give a necessary and sufficient condition for a manifold M to be diffeomorphic to a cusp cross-section of a Hilbert modular variety. Specialized to Hilbert modular surfaces, this proves that every Sol 3-manifold is diffeomorphic to a cusp cross-section of a (generalized) Hilbert modular surface. We also deduce an obstruction to geometric bounding in this setting. Consequently, there exist Sol 3-manifolds that cannot arise as a cusp cross-section of a 1-cusped nonsingular Hilbert modular surface.Comment: To appear in Mathematical Proceedings Cambridge Philosophical Societ

Large-scale groundwater modeling using global datasets: a test case for the Rhine-Meuse basin

The current generation of large-scale hydrological models does not include a groundwater flow component. Large-scale groundwater models, involving aquifers and basins of multiple countries, are still rare mainly due to a lack of hydro-geological data which are usually only available in developed countries. In this study, we propose a novel approach to construct large-scale groundwater models by using global datasets that are readily available. As the test-bed, we use the combined Rhine-Meuse basin that contains groundwater head data used to verify the model output. We start by building a distributed land surface model (30 arc-second resolution) to estimate groundwater recharge and river discharge. Subsequently, a MODFLOW transient groundwater model is built and forced by the recharge and surface water levels calculated by the land surface model. Results are promising despite the fact that we still use an offline procedure to couple the land surface and MODFLOW groundwater models (i.e. the simulations of both models are separately performed). The simulated river discharges compare well to the observations. Moreover, based on our sensitivity analysis, in which we run several groundwater model scenarios with various hydro-geological parameter settings, we observe that the model can reasonably well reproduce the observed groundwater head time series. However, we note that there are still some limitations in the current approach, specifically because the offline-coupling technique simplifies the dynamic feedbacks between surface water levels and groundwater heads, and between soil moisture states and groundwater heads. Also the current sensitivity analysis ignores the uncertainty of the land surface model output. Despite these limitations, we argue that the results of the current model show a promise for large-scale groundwater modeling practices, including for data-poor environments and at the global scale

Including Limited Partners in the Diversity Jurisdiction Analysis

This paper presents the results of the Dynamic Pricing Challenge, held on the occasion of the 17th INFORMS Revenue Management and Pricing Section Conference on June 29–30, 2017 in Amsterdam, The Netherlands. For this challenge, participants submitted algorithms for pricing and demand learning of which the numerical performance was analyzed in simulated market environments. This allows consideration of market dynamics that are not analytically tractable or can not be empirically analyzed due to practical complications. Our findings implicate that the relative performance of algorithms varies substantially across different market dynamics, which confirms the intrinsic complexity of pricing and learning in the presence of competition

The Blanco Cosmology Survey: Data Acquisition, Processing, Calibration, Quality Diagnostics and Data Release

The Blanco Cosmology Survey (BCS) is a 60 night imaging survey of $\sim$80 deg$^2$ of the southern sky located in two fields: ($\alpha$,$\delta$)= (5 hr, $-55^{\circ}$) and (23 hr, $-55^{\circ}$). The survey was carried out between 2005 and 2008 in $griz$ bands with the Mosaic2 imager on the Blanco 4m telescope. The primary aim of the BCS survey is to provide the data required to optically confirm and measure photometric redshifts for Sunyaev-Zel'dovich effect selected galaxy clusters from the South Pole Telescope and the Atacama Cosmology Telescope. We process and calibrate the BCS data, carrying out PSF corrected model fitting photometry for all detected objects. The median 10$\sigma$ galaxy (point source) depths over the survey in $griz$ are approximately 23.3 (23.9), 23.4 (24.0), 23.0 (23.6) and 21.3 (22.1), respectively. The astrometric accuracy relative to the USNO-B survey is $\sim45$ milli-arcsec. We calibrate our absolute photometry using the stellar locus in $grizJ$ bands, and thus our absolute photometric scale derives from 2MASS which has $\sim2$% accuracy. The scatter of stars about the stellar locus indicates a systematics floor in the relative stellar photometric scatter in $griz$ that is $\sim$1.9%, $\sim$2.2%, $\sim$2.7% and$\sim$2.7%, respectively. A simple cut in the AstrOmatic star-galaxy classifier {\tt spread\_model} produces a star sample with good spatial uniformity. We use the resulting photometric catalogs to calibrate photometric redshifts for the survey and demonstrate scatter $\delta z/(1+z)=0.054$ with an outlier fraction $\eta<5$% to $z\sim1$. We highlight some selected science results to date and provide a full description of the released data products.Comment: 23 pages, 23 figures . Response to referee comments. Paper accepted for publication. BCS catalogs and images available for download from http://www.usm.uni-muenchen.de/BC

Weak and strong fillability of higher dimensional contact manifolds

For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of weak fillings and prove that it is indeed weaker (at least in dimension five),while also being obstructed by all known manifestations of "overtwistedness". We also find the first examples of contact manifolds in all dimensions that are not symplectically fillable but also cannot be called overtwisted in any reasonable sense. These depend on a higher-dimensional analogue of Giroux torsion, which we define via the existence in all dimensions of exact symplectic manifolds with disconnected contact boundary.Comment: 68 pages, 5 figures. v2: Some attributions clarified, and other minor edits. v3: exposition improved using referee's comments. Published by Invent. Mat

Statistical M-Estimation and Consistency in Large Deformable Models for Image Warping

The problem of defining appropriate distances between shapes or images and modeling the variability of natural images by group transformations is at the heart of modern image analysis. A current trend is the study of probabilistic and statistical aspects of deformation models, and the development of consistent statistical procedure for the estimation of template images. In this paper, we consider a set of images randomly warped from a mean template which has to be recovered. For this, we define an appropriate statistical parametric model to generate random diffeomorphic deformations in two-dimensions. Then, we focus on the problem of estimating the mean pattern when the images are observed with noise. This problem is challenging both from a theoretical and a practical point of view. M-estimation theory enables us to build an estimator defined as a minimizer of a well-tailored empirical criterion. We prove the convergence of this estimator and propose a gradient descent algorithm to compute this M-estimator in practice. Simulations of template extraction and an application to image clustering and classification are also provided

Status of Muon Collider Research and Development and Future Plans

The status of the research on muon colliders is discussed and plans are outlined for future theoretical and experimental studies. Besides continued work on the parameters of a 3-4 and 0.5 TeV center-of-mass (CoM) energy collider, many studies are now concentrating on a machine near 0.1 TeV (CoM) that could be a factory for the s-channel production of Higgs particles. We discuss the research on the various components in such muon colliders, starting from the proton accelerator needed to generate pions from a heavy-Z target and proceeding through the phase rotation and decay ($\pi \to \mu \nu_{\mu}$) channel, muon cooling, acceleration, storage in a collider ring and the collider detector. We also present theoretical and experimental R & D plans for the next several years that should lead to a better understanding of the design and feasibility issues for all of the components. This report is an update of the progress on the R & D since the Feasibility Study of Muon Colliders presented at the Snowmass'96 Workshop [R. B. Palmer, A. Sessler and A. Tollestrup, Proceedings of the 1996 DPF/DPB Summer Study on High-Energy Physics (Stanford Linear Accelerator Center, Menlo Park, CA, 1997)].Comment: 95 pages, 75 figures. Submitted to Physical Review Special Topics, Accelerators and Beam

Global raster dataset on historical coastline positions and shelf sea extents since the Last Glacial Maximum

Motivation: Historical changes in sea level caused shifting coastlines that affected the distribution and evolution of marine and terrestrial biota. At the onset of the Last Glacial Maximum (LGM) 26 ka, sea levels were >130 m lower than at present, resulting in seaward-shifted coastlines and shallow shelf seas, with emerging land bridges leading to the isolation of marine biota and the connection of land-bridge islands to the continents. At the end of the last ice age, sea levels started to rise at unprecedented rates, leading to coastal retreat, drowning of land bridges and contraction of island areas. Although a growing number of studies take historical coastline dynamics into consideration, they are mostly based on past global sea-level stands and present-day water depths and neglect the influence of global geophysical changes on historical coastline positions. Here, we present a novel geophysically corrected global historical coastline position raster for the period from 26 ka to the present. This coastline raster allows, for the first time, calculation of global and regional coastline retreat rates and land loss rates. Additionally, we produced, per time step, 53 shelf sea rasters to present shelf sea positions and to calculate the shelf sea expansion rates. These metrics are essential to assess the role of isolation and connectivity in shaping marine and insular biodiversity patterns and evolutionary signatures within species and species assemblages. Main types of variables contained: The coastline age raster contains cells with ages in thousands of years before present (bp), representing the time since the coastline was positioned in the raster cells, for the period between 26 ka and the present. A total of 53 shelf sea rasters (sea levels <140 m) are presented, showing the extent of land (1), shelf sea (0) and deep sea (NULL) per time step of 0.5 kyr from 26 ka to the present. Spatial location and grain: The coastline age raster and shelf sea rasters have a global representation. The spatial resolution is scaled to 120 arcsec (0.333° × 0.333°), implying cells of c. 3,704 m around the equator, 3,207 m around the tropics (±30°) and 1,853 m in the temperate zone (±60°). Time period and temporal resolution: The coastline age raster shows the age of coastline positions since the onset of the LGM 26 ka, with time steps of 0.5 kyr. The 53 shelf sea rasters show, for each time step of 0.5 kyr, the position of the shelf seas (seas shallower than 140 m) and the extent of land. Level of measurement: Both the coastline age raster and the 53 shelf sea rasters are provided as TIFF files with spatial reference system WGS84 (SRID 4326). The values of the coastline age raster per grid cell correspond to the most recent coastline position (in steps of 0.5 kyr). Values range from 0 (0 ka, i.e., present day) to 260 (26 ka) in bins of 5 (0.5 kyr). A value of “no data” is ascribed to pixels that have remained below sea level since 26 ka. Software format: All data processing was done using the R programming language

Measurement of the ttˉproductioncrosssectionint\bar{t} production cross section in p\bar{p}collisionsat collisions at \sqrt{s}$ = 1.8 TeV

We update the measurement of the top production cross section using the CDF detector at the Fermilab Tevatron. This measurement uses $t\bar{t}$ decays to the final states $e+\nu$+jets and $\mu+\nu$+jets. We search for $b$ quarks from $t$ decays via secondary-vertex identification or the identification of semileptonic decays of the $b$ and cascade $c$ quarks. The background to the $t\bar{t}$ production is determined primarily through a Monte Carlo simulation. However, we calibrate the simulation and evaluate its uncertainty using several independent data samples. For a top mass of 175 $GeV/c^2$, we measure $\sigma_{t\bar{t}}=5.1 \pm 1.5$ pb and $\sigma_{t\bar{t}}=9.2 \pm 4.3$ pb using the secondary vertex and the lepton tagging algorithms, respectively. Finally, we combine these results with those from other $t\bar{t}$ decay channels and obtain $\sigma_{t\bar{t}} = 6.5^{+1.7}_{-1.4}$ pb.Comment: The manuscript consists of 130 pages, 35 figures and 42 tables in RevTex. The manuscript is submitted to Physical Review D. Fixed typo in author lis