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

Synthetic approaches towards alkaloids bearing α-tertiary amines

Alkaloids account for some of the most beautiful and biologically active natural products. Although they are usually classified along biosynthetic criteria, they can also be categorized according to certain structural motifs. Amongst these, the α-tertiary amine (ATA), i.e. a tetrasubstituted carbon atom surrounded by three carbons and one nitrogen, is particularly interesting. A limited number of methods have been described to access this functional group and fewer still are commonly used in synthesis. Herein, we review some approaches to asymmetrically access ATAs and provide an overview of alkaloid total syntheses where those have been employed

Synthetic approaches towards alkaloids bearing α-tertiary amines

Alkaloids account for some of the most beautiful and biologically active natural products. Although they are usually classified along biosynthetic criteria, they can also be categorized according to certain structural motifs. Amongst these, the α-tertiary amine (ATA), i.e. a tetrasubstituted carbon atom surrounded by three carbons and one nitrogen, is particularly interesting. A limited number of methods have been described to access this functional group and fewer still are commonly used in synthesis. Herein, we review some approaches to asymmetrically access ATAs and provide an overview of alkaloid total syntheses where those have been employed

Soft-collinear gravity with fermionic matter

We extend the effective field theory for soft and collinear gravitons to interactions with fermionic matter fields. The full theory features a local Lorentz symmetry in addition to the usual diffeomorphisms, which requires incorporating the former into the soft-collinear gravity framework. The local Lorentz symmetry gives rise to Wilson lines in the effective theory that strongly resemble those in SCET for non-abelian gauge interactions, whereas the diffeomorphisms can be treated in the same fashion as in the case of scalar matter. The basic structure of soft-collinear gravity, which features a homogeneous soft background field, giving rise to a covariant derivative and multipole-expanded covariant Riemann-tensor interactions, remains unaltered and generalises in a natural way to fermion fields.Comment: v2: 27 pages, matches published versio

From nucleosides to alkaloids and polyketides

This dissertation describes the synthetic work on several natural products including nucleosides, alkaloids, and polyketides. The first and main part of this thesis focuses on the total synthesis of the nucleoside antibiotics herbicidin C and its hydrolysis product aureonuclemycin. Due to their diverse biological activity, the herbicidins are considered as promising herbicides for agricultural application. In cooperation with Bayer CropScience AG, a flexible and efficient access to the herbicidins was developed and the challenges and successes of this synthesis are described in detail. More specifically, the route to the undecose moiety integrates a stereoselective C-glycosylation with several reagent-controlled stereoselective transformations. The nucleobase was introduced by a surprisingly facile and highly diastereoselective late-stage N-glycosylation. In addition to that, natural herbicidin A was transformed into promising derivatives and all compounds, including the intermediates of the total synthesis, were provided to Bayer CropScience AG for a structure activity relationship study (SAR). A list of all provided derivatives is given at the end of the thesis. The progress toward the synthesis of stephadiamine is described in the second chapter of this thesis. The natural product is the first example of a C-norhasubanan alkaloid natural product and despite its structural beauty, no total synthesis of stephadiamine has been reported to date. The proposed racemic retrosynthetic analysis of stephadiamine makes use of a Curtius rearrangement and a late lactonization. The propellane skeleton of this alkaloid was envisioned to be made by means of a homoconjugated addition/Mannich cascade of the key enamine in an extremely efficient manner. An alternative strategy is proposed for future work, which includes a Tsuji-Trost allylation arising the potential for an enantioselective synthesis of stephadiamine. In chapter III, the progress toward the divergolides C and D is presented. Attention was focused on the large scale preparation of the volatile side chain, and its unusual isolation method is pointed out in detail. In addition, the assembly of the three main building blocks is discussed. The preparation of Legionella autoinducer 1 (LAI-1) is described in chapter IV. The bacterial signaling molecule LAI-1 belongs to the class of alpha-hydroxyketones (AHKs). Given the effects of LAI-1 on virulence and motility of the bacteria L. pneumophila, this signaling molecule has the potential for clinical or technical applications. For a deeper understanding of the signaling circuit in L. pneumophila and in order to gain more insight in the mechanism of cell-cell communication, synthetic LAI-1 was prepared and provided to the research group of H. Hilbi, who investigates the gene regulation by AHK-mediated signaling. Chapter V includes the experimental procedures for the preparation of all compounds, backed up by full analytical characterization. In addition, 1H- and 13C-NMR spectra as well as crystallographic details are given

Inter-kingdom Signaling by the Legionella Quorum Sensing Molecule LAI-1 Modulates Cell Migration through an IQGAP1-Cdc42-ARHGEF9-Dependent Pathway

Small molecule signaling promotes the communication between bacteria as well as between bacteria and eukaryotes. The opportunistic pathogenic bacterium Legionella pneumophila employs LAI-1 (3-hydroxypentadecane-4-one) for bacterial cell-cell communication. LAI-1 is produced and detected by the Lqs (Legionella quorum sensing) system, which regulates a variety of processes including natural competence for DNA uptake and pathogen-host cell interactions. In this study, we analyze the role of LAI-1 in inter-kingdom signaling. L. pneumophila lacking the autoinducer synthase LqsA no longer impeded the migration of infected cells, and the defect was complemented by plasmid-borne lqsA. Synthetic LAI-1 dose-dependently inhibited cell migration, without affecting bacterial uptake or cytotoxicity. The forward migration index but not the velocity of LAI-1-treated cells was reduced, and the cell cytoskeleton appeared destabilized. LAI-1-dependent inhibition of cell migration involved the scaffold protein IQGAP1, the small GTPase Cdc42 as well as the Cdc42-specific guanine nucleotide exchange factor ARHGEF9, but not other modulators of Cdc42, or RhoA, Rac1 or Ran GTPase. Upon treatment with LAI-1, Cdc42 was inactivated and IQGAP1 redistributed to the cell cortex regardless of whether Cdc42 was present or not. Furthermore, LAI-1 reversed the inhibition of cell migration by L. pneumophila, suggesting that the compound and the bacteria antagonistically target host signaling pathway(s). Collectively, the results indicate that the L. pneumophila quorum sensing compound LAI-1 modulates migration of eukaryotic cells through a signaling pathway involving IQGAP1, Cdc42 and ARHGEF9

Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects

We first briefly report on the status and recent achievements of the ELPA-AEO (Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highly parallel methods for the solution of eigenvalue problems. Then we focus on a topic addressed in both projects, the use of mixed precision computations to enhance efficiency. We give a more detailed description of our approaches for benefiting from either lower or higher precision in three selected contexts and of the results thus obtained

Performance Engineering for a Tall & Skinny Matrix Multiplication Kernel on GPUs

General matrix-matrix multiplications (GEMM) 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 given by the roofline model) in this case. We describe the challenges and key properties of an implementation that can achieve perfect performance. We further evaluate different approaches of parallelization and thread distribution, and devise a flexible, configurable mapping scheme. A code generation approach enables a simultaneously flexible and specialized implementation with autotuning. This results in perfect performance for a large range of matrix sizes in the domain of interest, and at least 2/3 of maximum performance for the rest on an Nvidia Volta GPGPU

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

Activation of C–H Bonds via the Merger of Photoredox and Organocatalysis: A Coupling of Benzylic Ethers with Schiff Bases

The photoredox-mediated coupling of benzylic ethers with Schiff bases has been accomplished. Direct benzylic C–H activation by a combination of a thiol catalyst with an iridium photocatalyst and subsequent radical–radical coupling with secondary aldimines affords a variety of β-amino ether products in good to excellent yields. Mechanistic studies suggest that a reductive quenching pathway of the photocatalyst is operable