Code generation for AMReX with applications to numerical relativity

We present a new python/SymPy based code generator for producing executable numerical expressions for partial differential equations in AMReX-based applications. We demonstrate the code generator capabilities for the case of $3+1$ ADM formulations of numerical relativity for the constraint damped, conformal Z4 formulations (Z4c and CCZ4). The generated spacetime solvers are examined for stability and accuracy using a selection of checks from the standard Apples with Apples testbeds for numerical relativity applications. We also explore physically interesting vacuum spacetimes including head-on and inspiraling black hole binary collisions, and investigate the simulated gravitational waveforms from such events with the Newman-Penrose formulation of waveform extraction.Comment: 26 pages, 15 figure

The Structure of the Atypical Killer Cell Immunoglobulin-like Receptor, KIR2DL4

The engagement of Natural Killer (NK) cell Immunoglobulin-Like Receptors (KIRs) with their target ligands, Human Leukocyte Antigen (HLA) molecules, is a critical component of innate immunity. Structurally, KIRs typically have either two (D1-D2) or three (D0-D1-D2) extracellular immunoglobulin domains, with the D1 and D2 domain recognizing the α1 and α2 helices of HLA respectively, while the D0 domain of the KIR3DLs binds a loop region flanking the α1 helix of the HLA molecule. KIR2DL4 is distinct from other KIRs (except KIR2DL5) in that it does not contain a D1 domain and instead has a D0-D2 arrangement. Functionally, KIR2DL4 is also atypical in that, unlike all other KIRs, KIR2DL4 has both activating and inhibitory signaling domains. Here, we determined the 2.8 Å crystal structure of the extracellular domains of KIR2DL4. Structurally, KIR2DL4 is reminiscent of other KIR2DL receptors, with the D0 and D2 adopting the C2-type immunoglobulin fold arranged with an acute elbow angle. However, KIR2DL4 self-associated via the D0 domain in a concentration-dependent manner and was observed as a tetramer in the crystal lattice, by size-exclusion chromatography, dynamic light scattering, analytical ultra-centrifugation and small-angle X-ray scattering experiments. The assignment of residues in the D0 domain to forming the KIR2DL4 tetramer precludes an interaction with HLA akin to that observed for KIR3DL1. Accordingly, no interaction was observed to HLA by direct binding studies. Our data suggest that the unique functional properties of KIR2DL4 may be mediated by self-association of the receptor