Reducing the Tension Between the BICEP2 and the Planck Measurements: A Complete Exploration of the Parameter Space

A large inflationary tensor-to-scalar ratio $r_\mathrm{0.002} = 0.20^{+0.07}_{-0.05}$ is reported by the BICEP2 team based on their B-mode polarization detection, which is outside of the $95\%$ confidence level of the Planck best fit model. We explore several possible ways to reduce the tension between the two by considering a model in which $\alpha_\mathrm{s}$, $n_\mathrm{t}$, $n_\mathrm{s}$ and the neutrino parameters $N_\mathrm{eff}$ and $\Sigma m_\mathrm{\nu}$ are set as free parameters. Using the Markov Chain Monte Carlo (MCMC) technique to survey the complete parameter space with and without the BICEP2 data, we find that the resulting constraints on $r_\mathrm{0.002}$ are consistent with each other and the apparent tension seems to be relaxed. Further detailed investigations on those fittings suggest that $N_\mathrm{eff}$ probably plays the most important role in reducing the tension. We also find that the results obtained from fitting without adopting the consistency relation do not deviate much from the consistency relation. With available Planck, WMAP, BICEP2 and BAO datasets all together, we obtain $r_{0.002} = 0.14_{-0.11}^{+0.05}$, $n_\mathrm{t} = 0.35_{-0.47}^{+0.28}$, $n_\mathrm{s}=0.98_{-0.02}^{+0.02}$, and $\alpha_\mathrm{s}=-0.0086_{-0.0189}^{+0.0148}$; if the consistency relation is adopted, we get $r_{0.002} = 0.22_{-0.06}^{+0.05}$.Comment: 8 pages, 4 figures, submitted to PL

Making Batch Normalization Great in Federated Deep Learning

Batch Normalization (BN) is widely used in {centralized} deep learning to improve convergence and generalization. However, in {federated} learning (FL) with decentralized data, prior work has observed that training with BN could hinder performance and suggested replacing it with Group Normalization (GN). In this paper, we revisit this substitution by expanding the empirical study conducted in prior work. Surprisingly, we find that BN outperforms GN in many FL settings. The exceptions are high-frequency communication and extreme non-IID regimes. We reinvestigate factors that are believed to cause this problem, including the mismatch of BN statistics across clients and the deviation of gradients during local training. We empirically identify a simple practice that could reduce the impacts of these factors while maintaining the strength of BN. Our approach, which we named FIXBN, is fairly easy to implement, without any additional training or communication costs, and performs favorably across a wide range of FL settings. We hope that our study could serve as a valuable reference for future practical usage and theoretical analysis in FL.Comment: An extended version of the workshop paper in NeurIPS 2023 (https://federated-learning.org/fl@fm-neurips-2023/

Using an integrated fuzzy inference system and artificial neural network to forecast daily discharge

Given the nonlinearity and uncertainty in the rainfall-runoff process, estimating or predicting hydrologic data often encounters tremendous difficulty. This study applied fuzzy theory to create a daily flow forecasting modeL To improve the time-consuming definition process of membership function, which is usually concluded by a trial-and-error approach, this study designated the membership function by artificial neural network {ANN} with either a supervised or unsupervised learning procedure. The supervised learning was processed by the adaptive network based fuzzy inference system {ANFIS}, while the unsupervised learning was created by fuzzy and self-organizing map {SOMFIS}. The results indicate that the ANFIS method under increment flow data could provide more precise results for daily flow forecasting

Modelling and process analysis of hybrid hydration-absorption column for ethylene recovery from refinery dry gas

Effective recovery of ethylene from dry gas plays an increasingly important role to improve economic performance of refineries. Conventional approaches such as cryogenic separation and cold oil absorption are energy consuming. Hybrid hydration–absorption (HHA) process may be an effective way as hydrate formation takes place at temperature near the icing point. This paper aims to study the HHA column, which is the heart of the HHA process, through modelling and process analysis. A detailed steady state model was developed in gPROMS® for this vapour–liquid–water–hydrate (V–L–W–H) four phases system. A base case was analysed with real industry data as inputs. The composition distribution profiles inside the column were explored and the key parameters related with kinetics-controlled hydration process were investigated. Three case studies were carried out for different C₂H₄ concentrations in gas feed, L/G ratios and temperature profiles respectively. The results show (a) the separation performance of CH₄ and C₂H₄ in the HHA process remains significant for big range of C₂H₄ feed concentration; (b) L/G ratio has a great impact for hydrate formation and the separation performance of CH₄ and C₂H₄ improves when L/G ratio increases until reaching an optimal point; and (c) a cooling system is required to draw out the heat generated inside the HHA column so that the operating temperature of each plate can be at the temperature near the icing point to retain hydrate formation. This study indicates that the HHA process may be a more promising approach to recover ethylene from refinery dry gas in future industry application