Gut microbiota promote hematopoiesis to control bacterial infection

The commensal microbiota impacts specific immune cell populations and their functions at peripheral sites, such as gut mucosal tissues. However, it remains unknown whether gut microbiota control immunity through regulation of hematopoiesis at primary immune sites. We reveal that germ-free mice display reduced proportions and differentiation potential of specific myeloid cell progenitors of both yolk sac and bone marrow origin. Homeostatic innate immune defects may lead to impaired early responses to pathogens. Indeed, following systemic infection with Listeria monocytogenes, germ-free and oral antibiotic-treated mice display increased pathogen burden and acute death. Recolonization of germ-free mice with a complex microbiota restores defects in myelopoiesis and resistance to Listeria. These findings reveal that gut bacteria direct innate immune cell development via promoting hematopoiesis, contributing to our appreciation of the deep evolutionary connection between mammals and their microbiota.

A variational framework for spectral discretization of the density matrix in Kohn Sham density functional theory

Kohn-Sham density functional theory (KSDFT) is currently the main work-horse of quantum mechanical calculations in physics, chemistry, and materials science. From a mechanical engineering perspective, we are interested in studying the role of defects in the mechanical properties in materials. In real materials, defects are typically found at very small concentrations e.g., vacancies occur at parts per million, dislocation density in metals ranges from $10^{10} m^{-2}$ to $10^{15} m^{-2}$, and grain sizes vary from nanometers to micrometers in polycrystalline materials, etc. In order to model materials at realistic defect concentrations using DFT, we would need to work with system sizes beyond millions of atoms. Due to the cubic-scaling computational cost with respect to the number of atoms in conventional DFT implementations, such system sizes are unreachable. Since the early 1990s, there has been a huge interest in developing DFT implementations that have linear-scaling computational cost. A promising approach to achieving linear-scaling cost is to approximate the density matrix in KSDFT. The focus of this thesis is to provide a firm mathematical framework to study the convergence of these approximations. We reformulate the Kohn-Sham density functional theory as a nested variational problem in the density matrix, the electrostatic potential, and a field dual to the electron density. The corresponding functional is linear in the density matrix and thus amenable to spectral representation. Based on this reformulation, we introduce a new approximation scheme, called spectral binning, which does not require smoothing of the occupancy function and thus applies at arbitrarily low temperatures. We proof convergence of the approximate solutions with respect to spectral binning and with respect to an additional spatial discretization of the domain. For a standard one-dimensional benchmark problem, we present numerical experiments for which spectral binning exhibits excellent convergence characteristics and outperforms other linear-scaling methods.