Null Gravitational Redshift by a Reissner-Nordstr\"{o}m Black Hole in the Strong Field Limit

The gravitational shift of electromagnetic frequency in the strong field limit is usually investigated under the common scenario, where the light receiver is far away from the central body while the emitter is in the strong-field region of the lens. In this paper, the gravitational frequency shift of light caused by a Reissner-Nordstr\"{o}m (RN) black hole is studied numerically in the traditional strong-field scenario, as well as in the scenario where both the light emission and reception events happen in the strong-field region of the black hole. In order to obtain the numerical results of the gravitational redshift, we first derive the exact null equations of motion in the RN geometry in harmonic coordinates. For a given light observer, a new numerical technique is proposed in the integration of the geodesic equations to determine the spatial position of the emitter, considering the fact that their spatial positions are not always known simultaneously. Our work might be helpful to the related observations for probing strong gravity.Comment: 7 pages, 2 figure

Experimental preparation and verification of quantum money

A quantum money scheme enables a trusted bank to provide untrusted users with verifiable quantum banknotes that cannot be forged. In this work, we report an experimental demonstration of the preparation and verification of unforgeable quantum banknotes. We employ a security analysis that takes experimental imperfections fully into account. We measure a total of $3.6\times 10^6$ states in one verification round, limiting the forging probability to $10^{-7}$ based on the security analysis. Our results demonstrate the feasibility of preparing and verifying quantum banknotes using currently available experimental techniques.Comment: 12 pages, 4 figure

Clathrin and AP2 are required for PtdIns(4,5)P2-mediated formation of LRP6 signalosomes

Canonical Wnt signaling is initiated by the binding of Wnt proteins to their receptors, low-density lipoprotein-related protein 5 and 6 (LRP5/6) and frizzled proteins, leading to phosphatidylinositol (4,5)bisphosphate (PtdIns(4,5)P2) production, signalosome formation, and LRP phosphorylation. However, the mechanism by which PtdIns(4,5)P2 regulates the signalosome formation remains unclear. Here we show that clathrin and adaptor protein 2 (AP2) were part of the LRP6 signalosomes. The presence of clathrin and AP2 in the LRP6 signalosomes depended on PtdIns(4,5)P2, and both clathrin and AP2 were required for the formation of LRP6 signalosomes. In addition, WNT3A-induced LRP6 signalosomes were primarily localized at cell surfaces, and WNT3A did not induce marked LRP6 internalization. However, rapid PtdIns(4,5)P2 hydrolysis induced artificially after WNT3A stimulation could lead to marked LRP6 internalization. Moreover, we observed WNT3A-induced LRP6 and clathrin clustering at cell surfaces using super-resolution fluorescence microscopy. Therefore, we conclude that PtdIns(4,5)P2 promotes the assembly of LRP6 signalosomes via the recruitment of AP2 and clathrin and that LRP6 internalization may not be a prerequisite for Wnt signaling to β-catenin stabilization

Altered Functional Connectivity of Striatum Based on the Integrated Connectivity Model in First-Episode Schizophrenia

Background: The human striatum is a heterogeneous structure involved in diverse functional domains that related to distinct striatum subregions. Striatal dysfunction was thought to be a fundamental element in schizophrenia. However, the connectivity pattern of striatum solely based on functional or structural characteristics leads to inconsistent findings in healthy adult and also schizophrenia. This study aims to develop an integrated striatal model and reveal the altered functional connectivity pattern of the striatum in schizophrenia. Methods: Two data-driven approaches, task-dependent meta-analytic connectivity modeling (MACM) and task-independent resting-state functional connectivity (RSFC), were used for seven anatomical connectivity-based striatum subregions to provide an integrated striatal model. Then, RSFC analyses of seven striatal subregions were applied to 45 first-episode schizophrenia (FES) and 27 healthy controls to examine the difference, based on the integrated model, of functional connectivity pattern of striatal subregions. Results: MACM and RSFC results showed that striatum subregions were associated with discrete cortical regions and involved in distinct cognitive processes. Besides, RSFC results overlapped with MACM findings but showed broader distributions. Importantly, significantly reduced functional connectivity was identified between limbic subregion and thalamus, medial prefrontal cortex, anterior cingulate cortex, and insula and also between executive subregions and thalamus, supplementary motor area, and insula in FES. Conclusions: Combing functional and structural connectivity information, this study provides the integrated model of corticostriatal subcircuits and confirms the abnormal functional connectivity of limbic and executive striatum subregions with different networks and thalamus, supporting the important role of the corticostriatal-thalamic loop in the pathophysiology of schizophrenia