Stability of Minkowski spacetime in exterior regions

In 1993, the global stability of Minkowski spacetime has been proven in the celebrated work of Christodoulou and Klainerman \cite{Ch-Kl} in a maximal foliation. In 2003, Klainerman and Nic\`olo \cite{Kl-Ni} gave a second proof of the stability of Minkowski in the case of the exterior of an outgoing null cone. In this paper, we give a new proof of \cite{Kl-Ni}. Compared to \cite{Kl-Ni}, we reduce the number of derivatives needed in the proof, simplify the treatment of the last slice, and provide a unified treatment of the decay of initial data. Also, concerning the treatment of curvature estimates, we replace the vectorfield method used in \cite{Kl-Ni} by the $r^p$--weighted estimates of Dafermos and Rodnianski \cite{Da-Ro}.Comment: 80 pages, 3 figure

N-recollements and Virtually Gorenstein Algebras

The relation between the $n$-recollements of stable categories of Gorenstein projective modules and the virtual Gorensteinness of algebras are investigated. Let $A,B$, and $C$ be finite dimensional algebras. We prove that if the stable category of Gorenstein projective $A$-modules admits a $n$-recollement relative to that of $B$ and $C$ with $n\geq 2$, then $A$ is virtually Gorenstein if and only if so are $B$ and $C$

An index theorem on asymptotically static spacetimes with compact Cauchy surface

We consider the Dirac operator on asymptotically static Lorentzian manifolds with an odd-dimensional compact Cauchy surface. We prove that if Atiyah-Patodi-Singer boundary conditions are imposed at infinite times then the Dirac operator is Fredholm. This generalizes a theorem due to B\"ar-Strohmaier in the case of finite times, and we also show that the corresponding index formula extends to the infinite setting. Furthermore, we demonstrate the existence of a Fredholm inverse which is at the same time a Feynman parametrix in the sense of Duistermaat-H\"ormander. The proof combines methods from time-dependent scattering theory with a variant of Egorov's theorem for pseudo-differential hyperbolic systems.Comment: 40 page

Study on the Transit Network Evaluation Method Based on the Transit Ridership Model

AbstractTraditional four-step travel forecasting models are usually used to predict changes in car travel patterns and to evaluate the road transportation system. The application is unsatisfactory when they are used to evaluate the transit transportation system. Based on the transit origin-destination (OD) adjustment, this paper proposes a framework on future transit network evaluations, where the transit ridership model and OD difference method are simultaneously used. The proposed method formulates the relationship between transit ridership and zonal population, employment, transit service level, and so on. In addition, the difference between transit counts and estimates for base year are considered in the development of the transit OD for future year. It is expected to perform better than conventional models in terms of transit network evolutions. The validation of the proposed method is tested in Fuzhou City Transit Development Project

Inactivation of presenilins causes pre-synaptic impairment prior to post-synaptic dysfunction

Synaptic dysfunction is widely thought to be a pathogenic precursor to neurodegeneration in Alzheimer’s disease (AD), and the extent of synaptic loss provides the best correlate for the severity of dementia in AD patients. Presenilins 1 and 2 are the major causative genes of early‐onset familial AD. Conditional inactivation of presenilins in the adult cerebral cortex results in synaptic dysfunction and memory impairment, followed by age‐dependent neurodegeneration. To characterize further the consequence of presenilin inactivation in the synapse, we evaluated the temporal development of pre‐synaptic and post‐synaptic deficits in the Schaeffer‐collateral pathway of presenilin conditional double knockout (PS cDKO) mice prior to onset of neurodegeneration. Following presenilin inactivation at 4 weeks, synaptic facilitation and probability of neurotransmitter release are impaired in PS cDKO mice at 5 weeks of age, whereas post‐synaptic NMDA receptor (NMDAR)‐mediated responses are normal at 5 weeks but impaired at 6 weeks of age. Long‐term potentiation induced by theta burst stimulation is also reduced in PS cDKO mice at 6 weeks of age. These results show that loss of presenilins results in pre‐synaptic deficits in short‐term plasticity and probability of neurotransmitter release prior to post‐synaptic NMDAR dysfunction, raising the possibility that presenilins may regulate post‐synaptic NMDAR function in part via a trans‐synaptic mechanism.This work was supported by the National Institute of Health NS041783 (to J.S.). We would like to thank Xiaoyan Zou and Huailong Zhao for technical assistance. (NS041783 - National Institute of Health)Published versio

In Situ Engineering and Characterization of Correlated Materials with Integrated OMBE–ARPES

Oxide molecular beam epitaxy has emerged as an effective technique to fabricate complex oxide thin films and novel superlattices with atomic‐level precision. In this chapter, we first briefly introduce the oxide molecular beam epitaxy technique and then show how to use this technique to achieve high‐quality thin films with good stoichiometry. Moreover, we exhibit that the combination of oxide molecular beam epitaxy and in situ angle‐resolved photoemission spectroscopy is indeed a versatile toolkit to tailor and characterize properties of novel quantum materials