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Optimal experimental design (OED) is of great significance in efficient Bayesian inversion. A popular choice of OED methods is based on maximizing the expected information gain (EIG), where expensive likelihood functions are typically involved. To reduce the computational cost, in this work, a novel double-loop Bayesian Monte Carlo (DLBMC) method is developed to efficiently compute the EIG, and a Bayesian optimization (BO) strategy is proposed to obtain its maximizer only using a small number of samples. For Bayesian Monte Carlo posed on uniform and normal distributions, our analysis provides explicit expressions for the mean estimates and the bounds of their variances. The accuracy and the efficiency of our DLBMC and BO based optimal design are validated and demonstrated with numerical experiments.

Tensor completion is a fundamental tool to estimate unknown information from observed data, which is widely used in many areas, including image and video recovery, traffic data completion and the multi-input multi-output problems in information theory. Based on Tucker decomposition, this paper proposes a new algorithm to complete tensors with missing data. In decomposition-based tensor completion methods, underestimation or overestimation of tensor ranks can lead to inaccurate results. To tackle this problem, we design an alternative iterating method that breaks the original problem into several matrix completion subproblems and adaptively adjusts the multilinear rank of the model during optimization procedures. Through numerical experiments on synthetic data and authentic images, we show that the proposed method can effectively estimate the tensor ranks and predict the missing entries.

Based on the history monitoring data of Air Quality Index (AQI) during 2015-2019, we conducted a contrastive analysis of the temporal and spatial variation characteristics of air quality in the Pearl River Delta. Results showed that the variation trends of AQI annual averages in the Pearl River Delta were basically the same. The AQI annual averages rose after decline and the variation curves were W-shaped. In the Pearl River Delta, Shenzhen and Huizhou enjoyed better air quality. In this region, AQI quarterly averages were high in autumn and winter but low in summer, and in a same year, the variation trends of the nine cities were basically the same. In autumn, the ozone concentration increased dramatically and therefore ozone became a major pollutant in ambient air. In winter, Guangzhou, Shenzhen and Dongguan saw a double-peak phenomenon in AQI hourly values, which rose at rush hours.

Satellite-based aerosol optical depth (AOD) data are widely used to estimate land surface PM2.5 concentrations in areas not covered by ground PM2.5 monitoring stations. However, AOD data obtained from satellites are typically at coarse spatial resolutions, limiting their applications on small or medium scales. In this paper, we propose a new two-step approach to estimate 1-km-resolution PM2.5 concentrations in Shanghai using high spatial resolution AOD retrievals from MODIS. In the first step, AOD data are refined to a 1×1km2 resolution via a Bayesian AOD retrieval method. In the second step, a hierarchical Gaussian process model is used to estimate PM2.5 concentrations. We evaluate our approach by model fitting and out-of-sample cross-validation. Our results show that the proposed approach enjoys accurate predictive performance in estimating PM2.5 concentrations.

(AB) is rising as a human pathogen of critical priority worldwide as it is the leading cause of opportunistic infections in healthcare settings and carbapenem-resistant AB is listed as a \"super bacterium\" or \"priority pathogen for drug resistance\" by the World Health Organization. Clinical isolates of were collected and tested for antimicrobial susceptibility. Among them, carbapenem-resistant and carbapenem-sensitive were subjected to prokaryotic transcriptome sequencing. The change of sRNA and mRNA expression was analyzed by bioinformatics and validated by quantitative reverse transcription-PCR. A total of 687 clinical isolates were collected, of which 336 strains of were resistant to carbapenem. Five hundred and six differentially expressed genes and nineteen differentially expressed sRNA candidates were discovered through transcriptomic profile analysis between carbapenem-resistant isolates and carbapenem-sensitive isolates. Possible binding sites were predicted through software for sRNA21 and , sRNA27 and , sRNA29 and , sRNA36 and , indicating a possible targeting relationship. A negative correlation was shown between sRNA21 and (r = -0.581, P = 0.007), sRNA27 and (r = -0.612, P = 0.004), sRNA29 and (r = -0.516, P = 0.020). This study preliminarily screened differentially expressed mRNA and sRNA in carbapenem-resistant , and explored possible targeting relationships, which will help further reveal the resistance mechanism and provide a theoretical basis for the development of drugs targeting sRNA for the prevention and treatment of carbapenem-resistant infection.

Based on the historical data of air ozone monitoring of Pearl River Delta from 2016 to 2020, the temporal and spatial variation characteristics of ozone in the Pearl River Delta were analyzed. The results showed that the mean change curves of Q 3 in the seven cities in the Pearl River Delta region from 2016 to 2020 were M-shaped, and the change trend was basically the same, except Huizhou and Zhuhai. The over standard rate of daily mean value of Q 3 in Jiangmen City from 2016 to 2020 was more than 10%, and the over standard situation of daily mean value of Q 3 was serious. In the Pearl River Delta region, the change trend of the monthly mean value of Q 3 in the same year was basically the same. On the whole, the mean value from August to November was higher, and the mean value in June was lower. The peak of Q 3 concentration appeared between 12:00 and 16:00 in the daytime, and it was generally low at night.

Solving high-dimensional Bayesian inverse problems (BIPs) with the variational inference (VI) method is promising but still challenging. The main difficulties arise from two aspects. First, VI methods approximate the posterior distribution using a simple and analytic variational distribution, which makes it difficult to estimate complex spatially-varying parameters in practice. Second, VI methods typically rely on gradient-based optimization, which can be computationally expensive or intractable when applied to BIPs involving partial differential equations (PDEs). To address these challenges, we propose a novel approximation method for estimating the high-dimensional posterior distribution. This approach leverages a deep generative model to learn a prior model capable of generating spatially-varying parameters. This enables posterior approximation over the latent variable instead of the complex parameters, thus improving estimation accuracy. Moreover, to accelerate gradient computation, we employ a differentiable physics-constrained surrogate model to replace the adjoint method. The proposed method can be fully implemented in an automatic differentiation manner. Numerical examples demonstrate two types of log-permeability estimation for flow in heterogeneous media. The results show the validity, accuracy, and high efficiency of the proposed method.

It is known that standard stochastic Galerkin methods encounter challenges when solving partial differential equations with high-dimensional random inputs, which are typically caused by the large number of stochastic basis functions required. It becomes crucial to properly choose effective basis functions, such that the dimension of the stochastic approximation space can be reduced. In this work, we focus on the stochastic Galerkin approximation associated with generalized polynomial chaos (gPC), and explore the gPC expansion based on the analysis of variance (ANOVA) decomposition. A concise form of the gPC expansion is presented for each component function of the ANOVA expansion, and an adaptive ANOVA procedure is proposed to construct the overall stochastic Galerkin system. Numerical results demonstrate the efficiency of our proposed adaptive ANOVA stochastic Galerkin method for both diffusion and Helmholtz problems.

This work proposes a Tensor Train Random Projection (TTRP) method for dimension reduction, where pairwise distances can be approximately preserved. Our TTRP is systematically constructed through a Tensor Train (TT) representation with TT-ranks equal to one. Based on the tensor train format, this random projection method can speed up the dimension reduction procedure for high-dimensional datasets and requires fewer storage costs with little loss in accuracy, compared with existing methods. We provide a theoretical analysis of the bias and the variance of TTRP, which shows that this approach is an expected isometric projection with bounded variance, and we show that the scaling Rademacher variable is an optimal choice for generating the corresponding TT-cores. Detailed numerical experiments with synthetic datasets and the MNIST dataset are conducted to demonstrate the efficiency of TTRP.

As efficient separation of variables plays a central role in model reduction for nonlinear and nonaffine parameterized systems, we propose a stochastic discrete empirical interpolation method (SDEIM) for this purpose. In our SDEIM, candidate basis functions are generated through a random sampling procedure, and the dimension of the approximation space is systematically determined by a probability threshold. This random sampling procedure avoids large candidate sample sets for high-dimensional parameters, and the probability based stopping criterion can efficiently control the dimension of the approximation space. Numerical experiments are conducted to demonstrate the computational efficiency of SDEIM, which include separation of variables for general nonlinear functions, e.g., exponential functions of the Karhu nen–Loève (KL) expansion, and constructing reduced order models for FitzHugh–Nagumo equations, where symmetry among limit cycles is well captured by SDEIM.