Large-Scale Spectroscopic Mapping of the ρ\rho Ophiuchi Molecular Cloud Complex I. The C2_{2}H to N2_2H+^+ Ratio as a Signpost of Cloud Characteristics

We present 2.5-square-degree C$_{2}$H N=1-0 and N$_2$H$^+$ J=1-0 maps of the $\rho$ Ophiuchi molecular cloud complex. These are the first large-scale maps of the $\rho$ Ophiuchi molecular cloud complex with these two tracers. The C$_{2}$H emission is spatially more extended than the N$_2$H$^+$ emission. One faint N$_2$H$^+$ clump Oph-M and one C$_{2}$H ring Oph-RingSW are identified for the first time. The observed C$_{2}$H to N$_{2}$H$^{+}$ abundance ratio ([C$_{2}$H]/[N$_{2}$H$^{+}$]) varies between 5 and 110. We modeled the C$_{2}$H and N$_2$H$^+$ abundances with 1-D chemical models which show a clear decline of [C$_2$H]/[N$_2$H$^+$] with chemical age. Such an evolutionary trend is little affected by temperatures when they are below 40 K. At high density (n$_H$ $>$ 10$^5$ cm$^{-3}$), however, the time it takes for the abundance ratio to drop at least one order of magnitude becomes less than the dynamical time (e.g., turbulence crossing time $\rm \sim$10$^5$ years). The observed [C$_2$H]/[N$_2$H$^+$] difference between L1688 and L1689 can be explained by L1688 having chemically younger gas in relatively less dense regions. The observed [C$_{2}$H]/[N$_{2}$H$^{+}$] values are the results of time evolution, accelerated at higher densities. For the relative low density regions in L1688 where only C$_2$H emission was detected, the gas should be chemically younger.Comment: Accepted by ApJ, 45 pages, 10 figure

Physical properties of CO-dark molecular gas traced by C+^+

Neither HI nor CO emission can reveal a significant quantity of so-called dark gas in the interstellar medium (ISM). It is considered that CO-dark molecular gas (DMG), the molecular gas with no or weak CO emission, dominates dark gas. We identified 36 DMG clouds with C$^+$ emission (data from Galactic Observations of Terahertz C+ (GOT C+) project) and HINSA features. Based on uncertainty analysis, optical depth of HI $\tau\rm_{HI}$ of 1 is a reasonable value for most clouds. With the assumption of $\tau\rm_{HI}=1$, these clouds were characterized by excitation temperatures in a range of 20 K to 92 K with a median value of 55 K and volume densities in the range of $6.2\times10^1$ cm$^{-3}$ to $1.2\times 10^3$ cm$^{-3}$ with a median value of $2.3\times 10^2$ cm$^{-3}$. The fraction of DMG column density in the cloud ($f\rm_{DMG}$) decreases with increasing excitation temperature following an empirical relation $f\rm_{DMG}=-2.1\times 10^{-3}T_(ex,\tau_{HI}=1)$+1.0. The relation between $f\rm_{DMG}$ and total hydrogen column density $N_H$ is given by $f\rm_{DMG}$=$1.0-3.7\times 10^{20}/N_H$. The values of $f\rm_{DMG}$ in the clouds of low extinction group ($A\rm_V \le 2.7$ mag) are consistent with the results of the time-dependent, chemical evolutionary model at the age of ~ 10 Myr. Our empirical relation cannot be explained by the chemical evolutionary model for clouds in the high extinction group ($A\rm_V > 2.7$ mag). Compared to clouds in the low extinction group ($A\rm_V \le 2.7$ mag), clouds in the high extinction group ($A\rm_V > 2.7$ mag) have comparable volume densities but excitation temperatures that are 1.5 times lower. Moreover, CO abundances in clouds of the high extinction group ($A\rm_V > 2.7$ mag) are $6.6\times 10^2$ times smaller than the canonical value in the Milky Way. #[Full version of abstract is shown in the text.]#Comment: Accepted for publishing in Astronomy & Astrophysics. 13 pages, 8 figure

Balancing Privacy Protection and Interpretability in Federated Learning

Federated learning (FL) aims to collaboratively train the global model in a distributed manner by sharing the model parameters from local clients to a central server, thereby potentially protecting users' private information. Nevertheless, recent studies have illustrated that FL still suffers from information leakage as adversaries try to recover the training data by analyzing shared parameters from local clients. To deal with this issue, differential privacy (DP) is adopted to add noise to the gradients of local models before aggregation. It, however, results in the poor performance of gradient-based interpretability methods, since some weights capturing the salient region in feature map will be perturbed. To overcome this problem, we propose a simple yet effective adaptive differential privacy (ADP) mechanism that selectively adds noisy perturbations to the gradients of client models in FL. We also theoretically analyze the impact of gradient perturbation on the model interpretability. Finally, extensive experiments on both IID and Non-IID data demonstrate that the proposed ADP can achieve a good trade-off between privacy and interpretability in FL