Light density and color distribution in the earth's shadow

Light density and color in earth shadow during lunar eclips

Quantum Bayesian implementation

Bayesian implementation concerns decision making problems when agents have incomplete information. This paper proposes that the traditional sufficient conditions for Bayesian implementation shall be amended by virtue of a quantum Bayesian mechanism. In addition, by using an algorithmic Bayesian mechanism, this amendment holds in the macro world.Comment: 14 pages, 3 figure

Special biconformal changes of K\"ahler surface metrics

The term "special biconformal change" refers, basically, to the situation where a given nontrivial real-holomorphic vector field on a complex manifold is a gradient relative to two K\"ahler metrics, and, simultaneously, an eigenvector of one of the metrics treated, with the aid of the other, as an endomorphism of the tangent bundle. A special biconformal change is called nontrivial if the two metrics are not each other's constant multiples. For instance, according to a 1995 result of LeBrun, a nontrivial special biconformal change exists for the conformally-Einstein K\"ahler metric on the two-point blow-up of the complex projective plane, recently discovered by Chen, LeBrun and Weber; the real-holomorphic vector field involved is the gradient of its scalar curvature. The present paper establishes the existence of nontrivial special biconformal changes for some canonical metrics on Del Pezzo surfaces, viz. K\"ahler-Einstein metrics (when a nontrivial holomorphic vector field exists), non-Einstein K\"ahler-Ricci solitons, and K\"ahler metrics admitting nonconstant Killing potentials with geodesic gradients.Comment: 16 page

On the irredundant part of the first Piola-Kirchhoff stress tensor

Let us assume a given medium moves and deforms in an ambient smooth and oriented Riemannian manifold N with metric (, ). This medium at hand is supposed to maintain the shape of a compact smooth orientable and connected manifold M with boundary. Clearly dim M ≤ dim N. By a configuration j of the medium we mean a smooth embedding of M into N. The configuration space is E(M, N), the collection of all smooth embeddings of M into N endowed with the C∞-topology. [...] The main purpose of this notes is to exhibit (in absence of exterior force densities) the irredundant part of a(j) that determines the force densities mentioned and the virtual work caused by any infinitesimal distortion at j.[...

Implementation of higher-order absorbing boundary conditions for the Einstein equations

We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer boundary, which is taken to be a coordinate sphere. We reformulate the boundary conditions as conditions on the gauge-invariant Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated by rewriting the boundary conditions as a system of ODEs for a set of auxiliary variables intrinsic to the boundary. From these we construct boundary data for a set of well-posed constraint-preserving boundary conditions for the Einstein equations in a first-order generalized harmonic formulation. This construction has direct applications to outer boundary conditions in simulations of isolated systems (e.g., binary black holes) as well as to the problem of Cauchy-perturbative matching. As a test problem for our numerical implementation, we consider linearized multipolar gravitational waves in TT gauge, with angular momentum numbers l=2 (Teukolsky waves), 3 and 4. We demonstrate that the perfectly absorbing boundary condition B_L of order L=l yields no spurious reflections to linear order in perturbation theory. This is in contrast to the lower-order absorbing boundary conditions B_L with L<l, which include the widely used freezing-Psi_0 boundary condition that imposes the vanishing of the Newman-Penrose scalar Psi_0.Comment: 25 pages, 9 figures. Minor clarifications. Final version to appear in Class. Quantum Grav

MerTK is required for apoptotic cell–induced T cell tolerance

Self-antigens expressed by apoptotic cells (ACs) may become targets for autoimmunity. Tolerance to these antigens is partly established by an ill-defined capacity of ACs to inhibit antigen-presenting cells such as dendritic cells (DCs). We present evidence that the receptor tyrosine kinase Mer (MerTK) has a key role in mediating AC-induced inhibition of DC activation/maturation. Pretreatment of DCs prepared from nonobese diabetic (NOD) mice with AC blocked secretion of proinflammatory cytokines, up-regulation of costimulatory molecule expression, and T cell activation. The effect of ACs on DCs was dependent on Gas6, which is a MerTK ligand. NOD DCs lacking MerTK expression (NOD.MerTKKD/KD) were resistant to AC-induced inhibition. Notably, autoimmune diabetes was exacerbated in NOD.MerTKKD/KD versus NOD mice expressing the transgenic BDC T cell receptor. In addition, β cell–specific CD4+ T cells adoptively transferred into NOD.MerTKKD/KD mice in which β cell apoptosis was induced with streptozotocin exhibited increased expansion and differentiation into type 1 T cell effectors. In both models, the lack of MerTK expression was associated with an increased frequency of activated pancreatic CD11c+CD8α+ DCs, which exhibited an enhanced T cell stimulatory capacity. These findings demonstrate that MerTK plays a critical role in regulating self-tolerance mediated between ACs, DCs, and T cells

On the spectrum of the Page and the Chen-LeBrun-Weber metrics

We give bounds on the first non-zero eigenvalue of the scalar Laplacian for both the Page and the Chen-LeBrun-Weber Einstein metrics. One notable feature is that these bounds are obtained without explicit knowledge of the metrics or numerical approximation to them. Our method also allows the calculation of the invariant part of the spectrum for both metrics. We go on to discuss an application of these bounds to the linear stability of the metrics. We also give numerical evidence to suggest that the bounds for both metrics are extremely close to the actual eigenvalue.Comment: 15 pages, v2 substantially rewritten, section on linear stability added; v3 updated to reflect referee's comments, v4 final version to appear in Ann. Glob. Anal. Geo

A cord blood monocyte–derived cell therapy product accelerates brain remyelination

Microglia and monocytes play important roles in regulating brain remyelination. We developed DUOC-01, a cell therapy product intended for treatment of demyelinating diseases, from banked human umbilical cord blood (CB) mononuclear cells. Immunodepletion and selection studies demonstrated that DUOC-01 cells are derived from CB CD14+ monocytes. We compared the ability of freshly isolated CB CD14+ monocytes and DUOC-01 cells to accelerate remyelination of the brains of NOD/SCID/IL2Rγ null mice following cuprizone feeding-mediated demyelination. The corpus callosum of mice intracranially injected with DUOC-01 showed enhanced myelination, a higher proportion of fully myelinated axons, decreased gliosis and cellular infiltration, and more proliferating oligodendrocyte lineage cells than those of mice receiving excipient. Uncultured CB CD14+ monocytes also accelerated remyelination, but to a significantly lesser extent than DUOC-01 cells. Microarray analysis, quantitative PCR studies, Western blotting, and flow cytometry demonstrated that expression of factors that promote remyelination including PDGF-AA, stem cell factor, IGF1, MMP9, MMP12, and triggering receptor expressed on myeloid cells 2 were upregulated in DUOC-01 compared to CB CD14+ monocytes. Collectively, our results show that DUOC-01 accelerates brain remyelination by multiple mechanisms and could be beneficial in treating demyelinating conditions