Performance Engineering for Real and Complex Tall & Skinny Matrix Multiplication Kernels on GPUs

General matrix-matrix multiplications with double-precision real and complex entries (DGEMM and ZGEMM) in vendor-supplied BLAS libraries are best optimized for square matrices but often show bad performance for tall & skinny matrices, which are much taller than wide. NVIDIA's current CUBLAS implementation delivers only a fraction of the potential performance as indicated by the roofline model in this case. We describe the challenges and key characteristics of an implementation that can achieve close to optimal performance. We further evaluate different strategies of parallelization and thread distribution, and devise a flexible, configurable mapping scheme. To ensure flexibility and allow for highly tailored implementations we use code generation combined with autotuning. For a large range of matrix sizes in the domain of interest we achieve at least 2/3 of the roofline performance and often substantially outperform state-of-the art CUBLAS results on an NVIDIA Volta GPGPU.Comment: 12 pages, 22 figures. Extended version of arXiv:1905.03136v1 for journal submissio

A Spectroscopic and Photometric Investigation of the Mercury-Manganese Star KIC 6128830

The advent of space-based photometry provides the opportunity for the first precise characterizations of variability in Mercury-Manganese (HgMn/CP3) stars, which might advance our understanding of their internal structure. We have carried out a spectroscopic and photometric investigation of the candidate CP3 star KIC 6128830. A detailed abundance analysis based on newly-acquired high-resolution spectra was performed, which confirms that the star's abundance pattern is fully consistent with its proposed classification. Photometric variability was investigated using four years of archival Kepler data. In agreement with results from the literature, we have identified a single significant and independent frequency $f_1$=0.2065424 d$^{-1}$ with a peak-to-peak amplitude of $\sim$3.4 mmag and harmonic frequencies up to $5f_1$. Drawing on the predictions of state-of-the-art pulsation models and information on evolutionary status, we discuss the origin of the observed light changes. Our calculations predict the occurrence of g-mode pulsations at the observed variability frequency. On the other hand, the strictly mono-periodic nature of the variability strongly suggests a rotational origin. While we prefer the rotational explanation, the present data leave some uncertainty.Comment: 13 pages, 13 figures, accepted for publication in MNRA

Plenary Agenda Report for Research Group B-II-1

Political authority over extensive territories is a well-known phenomenon of the ancient world, and one conceptualized already in antiquity through the image of the succession of empires. Each such politico-spatial order was based on the successful interrelationship of heterogeneous symbolic and concrete forms of governance in the context of contingent structural conditions. While each major empire must be regarded as a singular historical case, the question nonetheless presents itself of how an awareness of such structures of political administration were constituted in premodern states. In the framework of Area B »Mechanisms of Control and Social Spaces« large-scale phenomena of governance were examined particularly with regard to the forms of knowledge associated with the organizational implementation of these of hegemonic structures. This research group investigates the interdependency of spatial structures and the organization of authority with reference to four major empires. Brought to light through the analysis of contrasting interventions into these territories are continuities and discontinuities of practice within which the spectrum of forms of knowledge as well as the object of knowledge itself become discernible. The geographic region of investigation is the Near East. Three ancient Near Eastern case studies, namely the Hittite and Mittani Kingdoms and the Middle Assyrian Empire, illustrate the region of Anatolia-Upper Mesopotamia in a dense chronological stratification which traverses a period lasting circa 500 years. Emerging within this chronotope both geographically and chronologically are intersections through which commonalities and differences in the organization of governance are revealed, not least of all in their spatial conditionality. In contrast, the subproject in Ancient History dealing with the system of rule of the Imperium Romanum in the Ancient Near East focuses on the early period of the Principate, with a special focus on the Palestinian-Syrian realm. In terms of systematics and chronology, two detailed studies contrast the relatively homogeneous perspectives of the four above-named empires: the first examines »trade relations« in the Neo-Babylonian empire of the 1st millennium BCE, and the second »multiethnicity« in the formation of the ancient Near Eastern empires of the later 1st millennium BCE. The analysis proceeds via archaeological, philological, and historical methods and focuses on concrete forms of political authority as exercised in interdependency with the governed regions on various scales. Settlement structures, artifacts, and border formations have been investigated along with a multiplicity of textual genres, including historical documents such as treaties, but also epigraphic materials, legal, and commercial documents. Some of the sources are being made accessible and published for the first time in the framework of these investigations. A web- supported map project will permit links to be created between geographically defined discursive horizons and object data such as settlement patterns, areas of settlement, and texts

Thickness dependence of the anomalous Hall effect in thin films of the topological semimetal Co2_2MnGa

Topological magnetic semimetals promise large Berry curvature through the distribution of the topological Weyl nodes or nodal lines and further novel physics with exotic transport phenomena. We present a systematic study of the structural and magnetotransport properties of Co$_2$MnGa films from thin (20 nm) to bulk like behavior (80 nm), in order to understand the underlying mechanisms and the role on the topology. The magnetron sputtered Co$_2$MnGa films are $L$$2_{\mathrm {1}}$-ordered showing very good heteroepitaxy and a strain-induced tetragonal distortion. The anomalous Hall conductivity was found to be maximum at a value of 1138 S/cm, with a corresponding anomalous Hall angle of 13 %, which is comparatively larger than topologically trivial metals. There is a good agreement between the theoretical calculations and the Hall conductivity observed for the 80 nm film, which suggest that the effect is intrinsic. Thus, the Co$_2$MnGa compound manifests as a promising material towards topologically-driven spintronic applications.Comment: 7 pages, 5 figures, 1 tabl

A Diffusion Model Predicts 3D Shapes from 2D Microscopy Images

Diffusion models are a special type of generative model, capable of synthesising new data from a learnt distribution. We introduce DISPR, a diffusion-based model for solving the inverse problem of three-dimensional (3D) cell shape prediction from two-dimensional (2D) single cell microscopy images. Using the 2D microscopy image as a prior, DISPR is conditioned to predict realistic 3D shape reconstructions. To showcase the applicability of DISPR as a data augmentation tool in a feature-based single cell classification task, we extract morphological features from the red blood cells grouped into six highly imbalanced classes. Adding features from the DISPR predictions to the three minority classes improved the macro F1 score from $F1_\text{macro} = 55.2 \pm 4.6\%$ to $F1_\text{macro} = 72.2 \pm 4.9\%$. We thus demonstrate that diffusion models can be successfully applied to inverse biomedical problems, and that they learn to reconstruct 3D shapes with realistic morphological features from 2D microscopy images