On the Bartnik extension problem for the static vacuum Einstein equations

We develop a framework for understanding the existence of asymptotically flat solutions to the static vacuum Einstein equations with prescribed boundary data consisting of the induced metric and mean curvature on a 2-sphere. A partial existence result is obtained, giving a partial resolution of a conjecture of Bartnik on such static vacuum extensions. The existence and uniqueness of such extensions is closely related to Bartnik's definition of quasi-local mass.Comment: 33 pages, 1 figure. Minor revision of v2. Final version, to appear in Class. Quantum Gravit

Zika Virus Attenuation by Codon Pair Deoptimization Induces Sterilizing Immunity in Mouse Models.

Zika virus (ZIKV) infection during the large epidemics in the Americas is related to congenital abnormities or fetal demise. To date, there is no vaccine, antiviral drug, or other modality available to prevent or treat Zika virus infection. Here we designed novel live attenuated ZIKV vaccine candidates using a codon pair deoptimization strategy. Three codon pair-deoptimized ZIKVs (Min E, Min NS1, and Min E+NS1) were de novo synthesized and recovered by reverse genetics and contained large amounts of underrepresented codon pairs in the E gene and/or NS1 gene. The amino acid sequence was 100% unchanged. The codon pair-deoptimized variants had decreased replication fitness in Vero cells (Min NS1 ≫ Min E > Min E+NS1), replicated more efficiently in insect cells than in mammalian cells, and demonstrated diminished virulence in a mouse model. In particular, Min E+NS1, the most restrictive variant, induced sterilizing immunity with a robust neutralizing antibody titer, and a single immunization achieved complete protection against lethal challenge and vertical ZIKV transmission during pregnancy. More importantly, due to the numerous synonymous substitutions in the codon pair-deoptimized strains, reversion to wild-type virulence through gradual nucleotide sequence mutations is unlikely. Our results collectively demonstrate that ZIKV can be effectively attenuated by codon pair deoptimization, highlighting the potential of Min E+NS1 as a safe vaccine candidate to prevent ZIKV infections.IMPORTANCE Due to unprecedented epidemics of Zika virus (ZIKV) across the Americas and the unexpected clinical symptoms, including Guillain-Barré syndrome, microcephaly, and other birth defects in humans, there is an urgent need for ZIKV vaccine development. Here we provided the first attenuated versions of ZIKV with two important genes (E and/or NS1) that were subjected to codon pair deoptimization. Compared to parental ZIKV, the codon pair-deoptimized ZIKVs were mammal attenuated and preferred insect to mammalian cells. Min E+NS1, the most restrictive variant, induced sterilizing immunity with a robust neutralizing antibody titer and achieved complete protection against lethal challenge and vertical virus transmission during pregnancy. More importantly, the massive synonymous mutational approach made it impossible for the variant to revert to wild-type virulence. Our results have proven the feasibility of codon pair deoptimization as a strategy to develop live attenuated vaccine candidates against flaviviruses such as ZIKV, Japanese encephalitis virus, and West Nile virus

In vivo imaging of Zika virus reveals dynamics of viral invasion in immune-sheltered tissues and vertical propagation during pregnancy

Rationale: Zika virus (ZIKV) is a pathogenic virus known to cause a wide range of congenital abnormalities, including microcephaly, Guillain-Barre syndrome, meningoencephalitis, and other neurological complications, in humans. This study investigated the noninvasive detection of ZIKV infection in vivo, which is necessary for elucidating the virus's mechanisms of viral replication and pathogenesis, as well as to accelerate the development of anti-ZIKV therapeutic strategies. Methods: In this study, a recombinant ZIKV harbouring Nluc gene (ZIKV-Nluc) was designed, recovered, and purified. The levels of bioluminescence were directly correlated with viral loads in vitro and in vivo. The dynamics of ZIKV infection in A129 (interferon (IFN)-α/β receptor deficient), AG6 (IFN-α/β and IFN-γ receptor deficient), and C57BL/6 mice were characterized. Pregnant dams were infected with ZIKV-Nluc at E10 via intra footpad injection. Then, the pooled immune sera (anti-ZIKV neutralizing antibodies) #22-1 in ZIKV-Nluc virus-infected mice were visualized. Results: ZIKV-Nluc showed a high genetic stability and replicated well in cells with similar properties to the wild-type ZIKV (ZIKVwt). Striking bioluminescence signals were consistently observed in animal organs, including spleen, intestine, testis, uterus/ovary, and kidney. The ileocecal junction was found to be the crucial visceral target. Infection of pregnant dams with ZIKV-Nluc showed that ZIKV was capable of crossing the maternal-fetal barrier to infect the fetuses via vertical transmission. Furthermore, it was visualized that treatment with the pooled immune sera was found to greatly restrict the spread of the ZIKV-Nluc virus in mice. Conclusions: This study is the first to report the real-time noninvasive tracking of the progression of ZIKV invading immune-sheltered tissues and propagating vertically during pregnancy. The results demonstrate that ZIKV-Nluc represents a powerful tool for the study of the replication, dissemination, pathogenesis, and treatment of ZIKV in vitro and in vivo

Bounds on the growth of high Sobolev norms of solutions to 2D Hartree Equations

In this paper, we consider Hartree-type equations on the two-dimensional torus and on the plane. We prove polynomial bounds on the growth of high Sobolev norms of solutions to these equations. The proofs of our results are based on the adaptation to two dimensions of the techniques we previously used to study analogous problems on $S^1$, and on $\mathbb{R}$.Comment: 38 page

Three dimensionality of band structure and a large residual quasiparticle population in Ba0.67_{0.67}K0.33_{0.33}Fe2_2As2_2 as revealed by the c-axis polarized optical measurement

We report on a c-axis polarized optical measurement on a Ba$_{0.67}$K$_{0.33}$Fe$_2$As$_2$ single crystal. We find that the c-axis optical response is significantly different from that of high-T$_c$ cuprates. The experiments reveal an anisotropic three-dimensional optical response with the absence of the Josephson plasma edge in R($\omega$) in the superconducting state. Furthermore, different from the ab-plane optical response, a large residual quasiparticle population down to $T\sim\frac{1}{5}T_c$ was observed in the c-axis polarized reflectance measurement. We elaborate that there exist nodes for the superconducting gap in regions of the 3D Fermi surface that contribute dominantly to the c-axis optical conductivity.Comment: 4 figure