A domain-specific language and matrix-free stencil code for investigating electronic properties of Dirac and topological materials

We introduce PVSC-DTM (Parallel Vectorized Stencil Code for Dirac and Topological Materials), a library and code generator based on a domain-specific language tailored to implement the specific stencil-like algorithms that can describe Dirac and topological materials such as graphene and topological insulators in a matrix-free way. The generated hybrid-parallel (MPI+OpenMP) code is fully vectorized using Single Instruction Multiple Data (SIMD) extensions. It is significantly faster than matrix-based approaches on the node level and performs in accordance with the roofline model. We demonstrate the chip-level performance and distributed-memory scalability of basic building blocks such as sparse matrix-(multiple-) vector multiplication on modern multicore CPUs. As an application example, we use the PVSC-DTM scheme to (i) explore the scattering of a Dirac wave on an array of gate-defined quantum dots, to (ii) calculate a bunch of interior eigenvalues for strong topological insulators, and to (iii) discuss the photoemission spectra of a disordered Weyl semimetal.Comment: 16 pages, 2 tables, 11 figure

GHOST: Building blocks for high performance sparse linear algebra on heterogeneous systems

While many of the architectural details of future exascale-class high performance computer systems are still a matter of intense research, there appears to be a general consensus that they will be strongly heterogeneous, featuring "standard" as well as "accelerated" resources. Today, such resources are available as multicore processors, graphics processing units (GPUs), and other accelerators such as the Intel Xeon Phi. Any software infrastructure that claims usefulness for such environments must be able to meet their inherent challenges: massive multi-level parallelism, topology, asynchronicity, and abstraction. The "General, Hybrid, and Optimized Sparse Toolkit" (GHOST) is a collection of building blocks that targets algorithms dealing with sparse matrix representations on current and future large-scale systems. It implements the "MPI+X" paradigm, has a pure C interface, and provides hybrid-parallel numerical kernels, intelligent resource management, and truly heterogeneous parallelism for multicore CPUs, Nvidia GPUs, and the Intel Xeon Phi. We describe the details of its design with respect to the challenges posed by modern heterogeneous supercomputers and recent algorithmic developments. Implementation details which are indispensable for achieving high efficiency are pointed out and their necessity is justified by performance measurements or predictions based on performance models. The library code and several applications are available as open source. We also provide instructions on how to make use of GHOST in existing software packages, together with a case study which demonstrates the applicability and performance of GHOST as a component within a larger software stack.Comment: 32 pages, 11 figure

Changes in the prevalence, treatment and control of hypertension in Germany? : a clinical-epidemiological study of 50.000 primary care patients

INTRODUCTION: Medical societies have developed guidelines for the detection, treatment and control of hypertension (HTN). Our analysis assessed the extent to which such guidelines were implemented in Germany in 2003 and 2001. METHODS: Using standardized clinical diagnostic and treatment appraisal forms, blood pressure levels and patient questionnaires for 55,518 participants from the cross-sectional Targets and Essential Data for Commitment of Treatment (DETECT) study (2003) were analyzed. Physician's diagnosis of hypertension (HTN(doc)) was defined as coding hypertension in the clinical appraisal questionnaire. Alternative definitions used were physician's diagnosis or the patient's self-reported diagnosis of hypertension (HTN(doc,pat)), physician's or patient's self-reported diagnosis or a BP measurement with a systolic BP≥140 mmHg and/or a diastolic BP≥90 (HTN(doc,pat,bp)) and diagnosis according to the National Health and Nutrition Examination Survey (HTN(NHANES)). The results were compared with the similar German HYDRA study to examine whether changes had occurred in diagnosis, treatment and adequate blood pressure control (BP below 140/90 mmHg) since 2001. Factors associated with pharmacotherapy and control were determined. RESULTS: The overall prevalence rate for hypertension was 35.5% according to HTN(doc) and 56.0% according to NHANES criteria. Among those defined by NHANES criteria, treatment and control rates were 56.0% and 20.3% in 2003, and these rates had improved from 55.3% and 18.0% in 2001. Significant predictors of receiving antihypertensive medication were: increasing age, female sex, obesity, previous myocardial infarction and the prevalence of comorbid conditions such as coronary heart disease (CHD), hyperlipidemia and diabetes mellitus (DM). Significant positive predictors of adequate blood pressure control were CHD and antihypertensive medication. Inadequate control was associated with increasing age, male sex and obesity. CONCLUSIONS: Rates of treated and controlled hypertension according to NHANES criteria in DETECT remained low between 2001 and 2003, although there was some minor improvement

On the non-Transversality of the Hyperelliptic Locus and the Supersingular Locus for g=3g=3

This paper gives a criterion for a moduli point to be a point of non-transversal intersection of the hyperelliptic locus and the supersingular locus in the Siegel moduli stack $\mathfrak{A}_3 \times \mathbb{F}_p$. It is shown that for infinitely many primes $p$ there exists such a point.Comment: 26 page

Theta Nullvalues of Supersingular Abelian varieties

Let $\eta$ be a polarization with connected kernel on a superspecial abelian variety $E^g$. We give a sufficient criterion which allows the computation of the theta nullvalues of any quotient of $E^g$ by a maximal isotropic subgroup scheme of $\ker(\eta)$ effectively. This criterion is satisfied in many situations studied by Li and Oort. We used our method to implement an algorithm that constructs supersingular curves of genus 3.Comment: Source code available at https://github.com/Andreas-Pieper/SuperThet

Magnetic Structure and Interactions in the Quasi-1D Antiferromagnet CaV2_2O4_4

CaV$_2$O$_4$ is a spin-1 antiferromagnet, where the magnetic vanadium ions are arranged on quasi-one-dimensional (1D) zig-zag chains with potentially frustrated antiferromagnetic exchange interactions. High temperature susceptibility and single-crystal neutron diffraction measurements are used to deduce the non-collinear magnetic structure, dominant exchange interactions and orbital configurations. The results suggest that at high temperatures CaV$_2$O$_4$ behaves as a Haldane chain, but at low temperatures, orbital ordering lifts the frustration and it becomes a spin-1 ladder.Comment: 5 pages, 4 figure