Quantum memory and non-demolition measurement of single phonon state with nitrogen-vacancy centers ensemble

In diamond, the mechanical vibration induced strain can lead to interaction between the mechanical mode and the nitrogen-vecancy (NV) centers. In this work, we propose to utilize the strain induced coupling for the quantum non-demolition (QND) single phonon measurement and memory in diamond. The single phonon in a diamond mechanical resonator can be perfectly absorbed and emitted by the NV centers ensemble (NVE) with adiabatically tuning the microwave driving. An optical laser drives the NVE to the excited states, which have much larger coupling strength to the mechanical mode. By adiabatically eliminating the excited states under large detuning limit, the effective coupling between the mechanical mode and the NVE can be used for QND measurement of the single phonon state. Under realistic experimental conditions, we numerically simulate the scheme. It is found that the fidelity of the absorbing and emitting process can reach a much high value. The overlap between the input and the output phonon shapes can reach $98.57\%$.Comment: 7 pages, 3 figure

NAD tagSeq reveals that NAD+-capped RNAs are mostly produced from a large number of protein-coding genes in Arabidopsis.

The 5' end of a eukaryotic mRNA transcript generally has a 7-methylguanosine (m7G) cap that protects mRNA from degradation and mediates almost all other aspects of gene expression. Some RNAs in Escherichia coli, yeast, and mammals were recently found to contain an NAD+ cap. Here, we report the development of the method NAD tagSeq for transcriptome-wide identification and quantification of NAD+-capped RNAs (NAD-RNAs). The method uses an enzymatic reaction and then a click chemistry reaction to label NAD-RNAs with a synthetic RNA tag. The tagged RNA molecules can be enriched and directly sequenced using the Oxford Nanopore sequencing technology. NAD tagSeq can allow more accurate identification and quantification of NAD-RNAs, as well as reveal the sequences of whole NAD-RNA transcripts using single-molecule RNA sequencing. Using NAD tagSeq, we found that NAD-RNAs in Arabidopsis were produced by at least several thousand genes, most of which are protein-coding genes, with the majority of these transcripts coming from <200 genes. For some Arabidopsis genes, over 5% of their transcripts were NAD capped. Gene ontology terms overrepresented in the 2,000 genes that produced the highest numbers of NAD-RNAs are related to photosynthesis, protein synthesis, and responses to cytokinin and stresses. The NAD-RNAs in Arabidopsis generally have the same overall sequence structures as the canonical m7G-capped mRNAs, although most of them appear to have a shorter 5' untranslated region (5' UTR). The identification and quantification of NAD-RNAs and revelation of their sequence features can provide essential steps toward understanding the functions of NAD-RNAs

Dark Energy Perturbations Revisited

In this paper we study the evolution of cosmological perturbations in the presence of dynamical dark energy, and revisit the issue of dark energy perturbations. For a generally parameterized equation of state (EoS) such as w_D(z) = w_0+w_1\frac{z}{1+z}, (for a single fluid or a single scalar field ) the dark energy perturbation diverges when its EoS crosses the cosmological constant boundary w_D=-1. In this paper we present a method of treating the dark energy perturbations during the crossing of the $w_D=-1$ surface by imposing matching conditions which require the induced 3-metric on the hypersurface of w_D=-1 and its extrinsic curvature to be continuous. These matching conditions have been used widely in the literature to study perturbations in various models of early universe physics, such as Inflation, the Pre-Big-Bang and Ekpyrotic scenarios, and bouncing cosmologies. In all of these cases the EoS undergoes a sudden change. Through a detailed analysis of the matching conditions, we show that \delta_D and \theta_D are continuous on the matching hypersurface. This justifies the method used[1-4] in the numerical calculation and data fitting for the determination of cosmological parameters. We discuss the conditions under which our analysis is applicable.Comment: 10 pages and 1 figure

Private Estimation and Inference in High-Dimensional Regression with FDR Control

This paper presents novel methodologies for conducting practical differentially private (DP) estimation and inference in high-dimensional linear regression. We start by proposing a differentially private Bayesian Information Criterion (BIC) for selecting the unknown sparsity parameter in DP-Lasso, eliminating the need for prior knowledge of model sparsity, a requisite in the existing literature. Then we propose a differentially private debiased LASSO algorithm that enables privacy-preserving inference on regression parameters. Our proposed method enables accurate and private inference on the regression parameters by leveraging the inherent sparsity of high-dimensional linear regression models. Additionally, we address the issue of multiple testing in high-dimensional linear regression by introducing a differentially private multiple testing procedure that controls the false discovery rate (FDR). This allows for accurate and privacy-preserving identification of significant predictors in the regression model. Through extensive simulations and real data analysis, we demonstrate the efficacy of our proposed methods in conducting inference for high-dimensional linear models while safeguarding privacy and controlling the FDR