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We prove the Marchenko-Pastur law for the eigenvalues of $p \times p$ samplecovariance matrices in two new situations where the data does not haveindependent coordinates. In the first scenario - the block-independent model -the $p$ coordinates of the data are partitioned into blocks in such a way thatthe entries in different blocks are independent, but the entries from the sameblock may be dependent. In the second scenario - the random tensor model - thedata is the homogeneous random tensor of order $d$, i.e. the coordinates of thedata are all $\binom{n}{d}$ different products of $d$ variables chosen from aset of $n$ independent random variables. We show that Marchenko-Pastur lawholds for the block-independent model as long as the size of the largest blockis $o(p)$ and for the random tensor model as long as $d = o(n^{1/3})$. Our maintechnical tools are new concentration inequalities for quadratic forms inrandom variables with block-independent coordinates, and for random tensors.

Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining variational Bayesian inference and MCMC simulation in order to improve their overall accuracy and computational efficiency. This marriage of fast evaluation and flexible approximation provides a promising means of designing scalable Bayesian inference methods. In this paper, we explore the possibility of incorporating variational approximation into a state-of-the-art MCMC method, Hamiltonian Monte Carlo (HMC), to reduce the required expensive computation involved in the sampling procedure, which is the bottleneck for many applications of HMC in big data problems. To this end, we exploit the regularity in parameter space to construct a free-form approximation of the target distribution by a fast and flexible surrogate function using an optimized additive model of proper random basis, which can also be viewed as a single-hidden layer feedforward neural network. The surrogate function provides sufficiently accurate approximation while allowing for fast computation in the sampling procedure, resulting in an efficient approximate Bayesian inference algorithm. We demonstrate the advantages of our proposed method using both synthetic and real data problems.

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov chain Monte Carlo methods, namely, Hamiltonian Monte Carlo. The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the-art methods.

Markov Chain Monte Carlo (MCMC) algorithms play an important role in statistical inference problems dealing with intractable probability distributions. Recently, many MCMC algorithms such as Hamiltonian Monte Carlo (HMC) and Riemannian Manifold HMC have been proposed to provide distant proposals with high acceptance rate. These algorithms, however, tend to be computationally intensive which could limit their usefulness, especially for big data problems due to repetitive evaluations of functions and statistical quantities that depend on the data. This issue occurs in many statistic computing problems. In this paper, we propose a novel strategy that exploits smoothness (regularity) in parameter space to improve computational efficiency of MCMC algorithms. When evaluation of functions or statistical quantities are needed at a point in parameter space, interpolation from precomputed values or previous computed values is used. More specifically, we focus on HMC algorithms that use geometric information for faster exploration of probability distributions. Our proposed method is based on precomputing the required geometric information on a set of grids before running sampling algorithm and approximating the geometric information for the current location of the sampler using the precomputed information at nearby grids at each iteration of HMC. Sparse grid interpolation method is used for high dimensional problems. Tests on computational examples are shown to illustrate the advantages of our method.

The diel vertical variations of chlorophyll a (Chl-a) concentration are thought of primarily as an external manifestation of regulating phytoplankton's biomass, which is essential for dynamically estimating the biogeochemical cycle in inland waters. However, information on these variations is limited due to insufficient measurements. Undersampled observations lead to delayed responses in phytoplankton assessment, impacting accurate evaluations of carbon export and water quality in dynamic inland waters. Here, we report the first lidar-observed diel vertical variations of inland Chl-a concentration. Strong agreement with r2 of 0.83 and a root mean square relative difference (RMSRD) of 9.0% between the lidar-retrieved and in situ measured Chl-a concentration verified the feasibility of the Mie–fluorescence–Raman lidar (MFRL). An experiment conducted at a fixed observatory demonstrated the lidar-observed diel Chl-a concentration variations. The results showed that diel variations of Chl-a and the formation of subsurface phytoplankton layers were driven by light availability and variations in water temperature. Furthermore, the facilitation from solar radiation-regulated water temperature on the phytoplankton growth rate was revealed by the high correlation between water temperature and Chl-a concentration anomalies. Lidar technology is expected to provide new insights into continuous three-dimension observations and be of great importance in dynamic inland water ecosystems. [ABSTRACT FROM AUTHOR]

We successfully fabricated Ag@Cu2O core–shell decorated on reduced graphene oxide (rGO) nanocomposites (ACRN) with a simple and convenient in situ substitution method. The properties of these ACRNs with heterostructure layers were characterized by scanning and transmission electron microscopy and absorption spectroscopy. We used 4-nitrophenol (4-NP) as a probe molecule to determine the chemical catalytic activity of the ACRN. Upon introduction of rGO, a high electron transfer efficiency was achieved; thus, the catalytic activity was improved significantly. Therefore, the ACRN exhibited significantly improved catalytic activity for the reduction of 4-NP and showed high application value in the removal of toxic and harmful substances from water. The catalytic efficiency was improved by 1.7 times by using the ACRN compared to Ag–rGO. In addition, the fabricated ACRN was used for the reduction of an organic dye (methyl orange, MO), and explosive pollutant (trinitrophenol, TNP) to generate nontoxic products. Furthermore, the high charge redistribution and transfer among Ag, Cu2O, and rGO in the ACRN induced the high catalytic reduction of organic pollutants, indicating the excellent potential of these materials for applications in water pollution treatment. [ABSTRACT FROM AUTHOR]

Road traffic crashes are becoming thorny issues being faced worldwide. Traffic crashes are spatiotemporal events and the research on the spatiotemporal patterns and variation trends of traffic crashes has been carried out. However, the impact of built environment on traffic crash spatiotemporal trends has not received much attention. Moreover, the spatial non-stationarity between the variation trends of traffic crashes and their influencing factors is usually neglected. To make up for the lack of analysis of built environment factors influencing spatiotemporal hotspot trends in traffic crashes, this paper proposed a method of "ST-GWLR" for analyzing the influence of built environment factors on spatiotemporal hotspot trends of traffic crashes by combining the spatiotemporal hotspot trend analysis and Geographically Weighted Logistic Regression (GWLR) modeling methods. Firstly, the traffic crash spatiotemporal hotspot trends were explored using the space-time cube model, hotspot analysis, and Mann-Kendall trend test. Then, the GWLR was introduced to capture the spatial non-stationarity neglected by the classic Global Logistic Regression (GLR) model, to improve the accuracy of the model estimation. GWLR model is used for the first time to analyze the significant local correlation between the traffic crash spatiotemporal hotspot trends and the built environment factors, to accurately and effectively identify the built environment factors that have significant influences on the hotspot trends of traffic crashes. The performance of the GWLR models and GLR models was examined and compared sufficiently. The results showed that the proposed ST-GWLR, which captured spatial non-stationarity, performed better than the classic GLR combined with spatiotemporal analysis, and improved the prediction accuracy of the models by 14.9%, 13.9%, and 15.1%, respectively. There were significant local correlations between intensifying hotspots and persistent hotspots of traffic crashes and the built environment factors. The findings of this paper have positive implications for traffic safety management and urban built environment planning. [ABSTRACT FROM AUTHOR]

In the present contribution, an environmental-friendly and cost-effective adsorbent was reported for soil treatment and desertification control. A novel foam gel material was synthesized here by the physical foaming in the absence of catalyst. By adopting modified microcrystalline cellulose and chitosan as raw materials and sodium dodecyl sulfonate (SDS) as foaming agent, a microcrystalline cellulose/chitosan blend foam gel was synthesized. It is expected to replace polymers derived from petroleum for agricultural applications. In addition, a systematical study was conducted on the adsorbability, water holding capacity and re-expansion performance of foam gel in deionized water and brine under different SDS concentrations (2%–5%) as well as adsorption time. To be specific, the adsorption capacity of foam gel was up to 105g/g in distilled water and 54g/g in brine, indicating a high water absorption performance. As revealed from the results of Fourier transform infrared spectroscopy (FTIR) analysis, both the amino group of chitosan and the aldehyde group modified by cellulose were involved. According to the results of Scanning electron microscope (SEM) analysis, the foam gel was found to exhibit an interconnected pore network with uniform pore space. As suggested by Bet analysis, the macroporous structure was formed in the sample, and the pore size ranged from 0 to 170nm. The mentioned findings demonstrated that the foam gel material of this study refers to a potential environmental absorbent to improve soil and desert environments. It can act as a powerful alternative to conventional petroleum derived polymers.

In this work, we modified nylon 6 with liquid rubber by in-situ polymerization. The infrared analysis suggested that HDI urea diketone is successfully blocked by caprolactam after grafting on hydroxyl of HTPB, and the rubber-modified nylon copolymer is generated by the anionic polymerization. The impact section analysis indicated the rubber-modified nylon 6 resin exhibited an alpha crystal form.With an increase in the rubber content, nylon 6 was more likely to generate stable α crystal. Avrami equation was a good description of the non-isothermal crystallization kinetics of nylon-6 and rubber-modified nylon-6 resin. Moreover, it is found that the initial crystallization temperature of nylon-6 chain segment decreased due to the flexible rubber chain segment. n value of rubber-modified nylon-6 indicated that its growth was the coexistence of two-dimensional discoid and three-dimensional spherulite growth. Finally, the addition of the rubber accelerated the crystallization rate of nylon 6.

In this paper, a new Navier-Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier-Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented.

A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design.

Silver nanowire (AgNW) networks hold great promises as next‐generation flexible transparent electrodes (FTEs) for high‐performance flexible optoelectronic devices. However, achieving large‐area flexible AgNW network electrodes with low sheet resistance, high optical transmittance, and a smooth surface remains a grand challenge. Here, we report a straightforward and cost‐effective roll‐to‐roll method that includes interface assembly/wetting‐induced climbing transfer, nanowelding, and washing processess to fabricate flexible ordered layered AgNW electrodes with high network uniformity. By manipulating the stacking number of the interfacially assembled AgNW monolayer, we can precisely tailor and balance the transparency and the conductivity of the electrodes, achieving an exceptional Figure of Merit (FoM) value of 862. Moreover, the ordered layered structure enhances surface smoothness, compared with randomly arranged structures. To highlight the potential of these ordered layered AgNW network electrodes in flexible optoelectronic devices, we successfully employ them as highly sensitive strain sensors, large‐area flexible touch screens, and flexible smart windows. Overall, this work represents a substantial advance toward high‐performance FTEs over large areas, opening up exciting opportunities for the development of advanced optoelectronic devices. [ABSTRACT FROM AUTHOR]

Parameterizing the bioluminescent source globally in Gaussians provides several advantages over voxel representation in bioluminescence tomography. It is mathematically unique to recover Gaussians [Med. Phys. 31(8), 2289 (2004)] and practically sufficient to approximate various shapes by Gaussians in diffusive medium. The computational burden is significantly reduced since much fewer unknowns are required. Besides, there are physiological evidences that the source can be modeled by Gaussians. The simulations show that the proposed model and algorithm significantly improves accuracy and stability in the presence of Gaussian or non- Gaussian sources, noisy data or the optical background mismatch. It is also validated through in vivo experimental data.

In this paper we study the regularization with both l1 and total-variation norm for bioluminescence tomography based on radiative transfer equation, compare l1 data fidelity with l2 data fidelity for different type of noise, and propose novel interior-point methods for solving related optimization problems. Simulations are performed to show that our approach is not only capable of preserving shapes, details and intensities of bioluminescent sources in the presence of sparse or non-sparse sources with angular-resolved or angular-averaged data, but also robust to noise, and thus is potential for efficient high-resolution imaging with only boundary data. (C) 2010 Optical Society of America

In this paper we study an l1-regularized multilevel approach for bioluminescence tomography based on radiative transfer equation with the emphasis on improving imaging resolution and reducing computational time. Simulations are performed to validate that our algorithms are potential for efficient high-resolution imaging. Besides, we study and compare reconstructions with boundary angular-averaged data, boundary angular-resolved data and internal angular-averaged data respectively. (C) 2010 Optical Society of America

In this paper, we study how to image both the location and the shape of extended targets using the response matrix obtained from inter-element response of an active array of transducers. In particular, the time reversal technique is used for efficient initial localization of the target and the level set method is used for shape reconstruction. We then show how to couple the location estimation and shape reconstruction in a complementary way to improve accuracy for range estimation. Resolution analysis for active arrays in remote sensing regime is also presented. We illustrate with numerical experiments which show that the method is capable of imaging objects with complicated shapes and that the method is robust with respect to noisy data. (C) 2004 Elsevier Inc. All rights reserved.

The article regards “The Belt and Road” initiative as a quasi-natural experiment. Based on the county panel data from 1999 to 2017, difference-in-differences model (DID) is used to examine the impact of the “The Belt and Road” initiative on regional economic growth and economic innovation. The study found that the “The Belt and Road” initiative can significantly increase the economic growth and innovation of the region. Through the placebo test and the robustness test, it shows good policy uniqueness characteristics. The article further analyzes the heterogeneity of the initiative. The study found that the initiative has more obvious economic growth and innovation in the central region.

He-Xe gas-cooled micro-molten salt reactor (HX-micro-MSR) is a novel reactor concept that integrates the technologies of molten salt reactor and closed Brayton cycle (CBC), which has a more compact structure compared with the other types of micro-MSRs. The reactor system probed in this paper has a thermal power of 2.5 MWth and consists of the core, fission gas collecting container, and CBC system. The He-Xe gas flows through the coolant channels in the core to transfer the nuclear heat to the CBC for electricity production. To withstand the large pressure difference between the He-Xe gas coolant (7 MPa) and molten salt (nearly atmospheric pressure), the sizes and wall thickness of coolant channels are analyzed and optimized to be 8 mm and 0.5 mm, respectively. In total, 1050 coolant channels are regularly arranged in the core to effectively remove the nuclear heat. The enrichment of U-235 in the fuel UF4 is determined to be 61% to meet the burnup goal of 5 years. To minimize the neutron leakage, the thickness of reflector is selected to be 23 cm. Six control drums with the diameter in 10.5 cm and neutron absorber layer thickness in 1 cm are symmetrically placed in the reflector to realize reactivity control under both normal and accident conditions. Radiation shield is designed and analyzed by varying the thickness of multiple shielding layers, and it is found that a combination of W layer in 14 cm and Mg(BH4)2 layer in 56 cm can satisfy the criterion of radiation dose (<1 mSv/h). The total weight of HX-micro-MSR is estimated to be 35 tonnes and falls into the acceptable range. [ABSTRACT FROM AUTHOR]

Initiating event analysis is an essential prerequisite of conducting probabilistic safety assessment for nuclear reactors, which plays an important role in improving the core design, identifying fault, and guiding operation. In order to determine the initiating event list of SIMONS (Small Innovative helium-xenon cooled Mobile Nuclear power System), preliminary researches on the initial event of SIMONS were carried out using the MLD (Main Logic Diagram) analysis method and referring to the initial event list and initial event analysis theory of other nuclear reactors such as HTGR (High Temperature Gas-cooled Reactor), MSR (Molten Salt Reactor), and PWR (Pressurized water reactor). With employing these methods, a total of 31 initial events are identified for SIMONS based on its latest conceptual design. These initial events are then divided into six groups according to the accident types, which are core heat removal increase, core heat removal decrease, abnormal reactivity and power distribution, pipeline crevasse and equipment leakage, anticipated transients without scram, and disasters (internal and external). The obtained results can provide a theoretical basis for the further safety analysis of SIMONS. [ABSTRACT FROM AUTHOR]