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

New electron source concept for single-shot sub-100 fs electron diffraction in the 100 keV range

We present a method for producing sub-100 fs electron bunches that are suitable for single-shot ultrafast electron diffraction experiments in the 100 keV energy range. A combination of analytical results and state-of-the-art numerical simulations show that it is possible to create 100 keV, 0.1 pC, 20 fs electron bunches with a spotsize smaller than 500 micron and a transverse coherence length of 3 nm, using established technologies in a table-top set-up. The system operates in the space-charge dominated regime to produce energy-correlated bunches that are recompressed by established radio-frequency techniques. With this approach we overcome the Coulomb expansion of the bunch, providing an entirely new ultrafast electron diffraction source concept

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

Design considerations for table-top, laser-based VUV and X-ray free electron lasers

A recent breakthrough in laser-plasma accelerators, based upon ultrashort high-intensity lasers, demonstrated the generation of quasi-monoenergetic GeV-electrons. With future Petawatt lasers ultra-high beam currents of ~100 kA in ~10 fs can be expected, allowing for drastic reduction in the undulator length of free-electron-lasers (FELs). We present a discussion of the key aspects of a table-top FEL design, including energy loss and chirps induced by space-charge and wakefields. These effects become important for an optimized table-top FEL operation. A first proof-of-principle VUV case is considered as well as a table-top X-ray-FEL which may open a brilliant light source also for new ways in clinical diagnostics.Comment: 6 pages, 4 figures; accepted for publication in Appl. Phys.

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