Asymptotic analysis of Einstein-\AE ther theory and its memory effects: the linearized case

This work analyzes the asymptotic behaviors of the asymptotically flat solutions of Einstein-\ae ther theory in the linear case. The vacuum solutions for the tensor, vector, and scalar modes are first obtained, written as sums of various multipolar moments. The suitable coordinate transformations are then determined, and the so-called pseudo-Newman-Unti coordinate systems are constructed for all radiative modes. In this coordinates, it is easy to identify the asymptotic symmetries. It turns out that all three kinds of modes possess the familiar Bondi-Metzner-Sachs symmetries or the extensions as in general relativity. Moreover, there also exist the \emph{subleading} asymptotic symmetries parameterized by a time-dependent vector field on a unit 2-sphere. Because of the spontaneously symmetry breaking by the nontrivial vacuum expectation value of the \ae ther field, one may choose a gauge similar to the unitary gauge such that the superboost symmetry is forbidden. The memory effects are also identified. The tensorial gravitational wave also excites similar displacement, spin, and center-of-mass memories to those in general relativity. New memory effects due to the vector and scalar modes exist. The subleading asymptotic symmetry is related to the (leading) vector displacement memory effect, while the scalar memory effect seems to have nothing to do with the asymptotic symmetries at least in the linearized theory.Comment: 36 pages. Comments are welcom

The Prognostic and Clinical Value of CD44 in Colorectal Cancer: A Meta-Analysis

Background: CD44 is widely used as a putative cancer stem cells (CSCs) marker for colorectal cancer (CRC). However, the prognostic role of CD44 in CRC remains controversial.Methods: We performed a systematic review and meta-analysis to evaluate the association of various CD44 isoforms and overall survival (OS) and clinicopathological features of CRC patients.Results: A total of 48 studies were included in the meta-analysis. Total CD44 isoforms overexpression was significantly correlated with worse OS of patients with CRC (HR = 1.32, 95% CI = 1.08–1.61, P = 0.007). In a stratified analysis, a higher level of either CD44v6 or CD44v2 had an unfavorable impact on OS (HRCD44v6 = 1.50, 95% CI = 1.10–2.14, P = 0.010; HRCD44v2 = 2.93, 95% CI = 1.49–5.77, P = 0.002). Additionally, CD44 was shown to be associated with some clinicopathological features, such as lymph node metastasis (ORCD44 = 1.56, 95% CI = 1.01–2.41, P = 0.044; ORCD44v6 = 1.97, 95% CI = 1.19–3.26, P = 0.008; ORTotal CD44 isoforms = 1.57, 95% CI = 1.15–2.14, P = 0.004), distant metastasis (ORCD44 = 2.90, 95% CI = 1.08–7.83, P = 0.035; ORTotal CD44 isoforms = 1.89, 95% CI = 1.02–3.53, P = 0.044). Moreover, a high level of CD44 showed a possible correlation with poor differentiation (ORTotal CD44 isoforms = 1.44, 95% CI = 1.00–2.08, P = 0.051), elevated level of CD44v6 tend to be correlated with tumor size (OR = 1.71, 95% CI = 0.99–2.96, P = 0.056).Conclusions: This meta-analysis demonstrated that CD44 overexpression might be an unfavorable prognostic factor for CRC patients and could be used to predict poor differentiation, lymph node metastasis and distant metastasis