Frequentist Consistency of Variational Bayes

<p>A key challenge for modern Bayesian statistics is how to perform scalable inference of posterior distributions. To address this challenge, variational Bayes (VB) methods have emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) methods. VB methods tend to be faster while achieving comparable predictive performance. However, there are few theoretical results around VB. In this article, we establish frequentist consistency and asymptotic normality of VB methods. Specifically, we connect VB methods to point estimates based on variational approximations, called frequentist variational approximations, and we use the connection to prove a variational Bernstein–von Mises theorem. The theorem leverages the theoretical characterizations of frequentist variational approximations to understand asymptotic properties of VB. In summary, we prove that (1) the VB posterior converges to the Kullback–Leibler (KL) minimizer of a normal distribution, centered at the truth and (2) the corresponding variational expectation of the parameter is consistent and asymptotically normal. As applications of the theorem, we derive asymptotic properties of VB posteriors in Bayesian mixture models, Bayesian generalized linear mixed models, and Bayesian stochastic block models. We conduct a simulation study to illustrate these theoretical results. Supplementary materials for this article are available online.</p

Highly Site-Selective Metal-Free C–H Acyloxylation of Stable Enamines

A highly site-selective acyloxylation of stable enamines with PhI­(OAc)₂ under metal-free conditions to afford (<i>E</i>)-vinyl acetate derivatives in good to excellent yields is described. Depending on the judicious choice of the solvent system, either the α- or β-site-selective product could be obtained with high selectivity. For the α-site-selective product, the rearranged amide compound is obtained as the major product. This reaction proceeds under mild reaction conditions (room temperature, metal-free, and open-flask) and features a broad substrate scope

Sulfur-Containing Carbon Nanospheres as Lubricant Additives for Antiwear and Friction Reduction

Herein, organic–inorganic hybrid sulfur-containing carbon nanospheres (SCNs) were successfully prepared by one-pot chemical oxidation polymerization of a thiophene monomer and then rigorous carbonization. On account of the good structural strength and organic phase derived from the precursor polythiophene, the as-prepared SCNs manifested remarkable oil-dispersing and tribological properties as lubricant nanoadditives. Subsequently, the friction mechanism of SCNs was deduced; the as-prepared SCNs had the capacity to take the shape of a strong protective film on the surface of friction pairs by intricate physical deposition and tribochemical reaction. So, the SCNs exhibited excellent tribological performance, including a high extreme pressure (950 N), an ultralow friction coefficient of less than 0.06, and a significant reduction in abrasion by 90%

Comprehensive energy, economic and thermal comfort assessments for the passive energy retrofit of historical buildings - A case study of a late nineteenth-century Victorian house renovation in the UK

This paper aims to evaluate the energy-saving potential, affordability and thermal comfort performance of various passive building retrofit measures for a historical building (late nineteenthcentury Victorian house) renovation. Three types of interior passive retrofit measures (i.e. internal wall insulation, glazing upgrade and airtightness improvement), classified as traditional and advanced measures, are further grouped into 63 retrofit combinations. In order to evaluate the performance of these defined retrofit combinations, five assessment indicators are proposed, including energy reduction rate, specific initial cost, discounted payback period, space volume reduction rate, and indoor thermal comfort. Under three internal space reduction scenarios with a space reduction rate of 5.2%, 2.6% and 1.3%, these combinations are evaluated and compared, and the most favourable combinations are determined to achieve multiple objectives (maximum energy saving, most cost-effective and most energy-efficient). The influence of the most favourable retrofit combinations on the internal thermal comfort level improvement is also dynamically evaluated using the EnergyPlus simulation tool. The final recommended passive retrofit combination consists of vacuum insulation windows, gypsum air infiltration reduction, and 2cm thickness of Polyisocyanurate (PIR) panels, with 51.8% of primary energy reduction, a specific initial investment of £144.71/m2 and a discounted payback period of 18 years

Hybrid Carbon Nanospheres with Encapsulated (Bi)Metallic Nanocrystals as Lubricant Additives for Antiwear and Friction Reduction

Herein, the novel core–shell organo-inorganic hybrid carbon nanospheres with encapsulated ultrafine bimetal nanocrystals were successfully prepared by a one-pot domino drive synthesis combined with postcarbonization. The excellent properties of the metals such as high strength and thermal conductivity are retained, and the poor dispersion of the metal in the oil could be improved by encapsulating the metal in organic–inorganic hybrid carbon nanospheres. The vanadium and wolframium nanocrystals embedded in nitrogen-doped carbon nanospheres (V/W@NCNs) manifested remarkable oil dispersity on account of the lipophilic organic phase of the carbon shell. It is worth noting that the as-obtained V/W@NCNs display better tribological properties compared with the base oil, such as a higher extreme pressure of 1250 N, a lower friction coefficient of about 0.09, and a significant reduction in wear volume of 91.5%, which are attributed to the robust protective film that was formed on the surface of the friction pair through mechanical deposition and physical and tribochemical reaction during the friction process

Preparation of Hydrophilic Hyper-Cross-Linked Polystyrene Nanospheres with Antibacterial for Improved Water Lubrication Performance

The present study utilizes styrene as a raw material to prepare hyper-cross-linked polystyrene nanospheres (HPSs) through the Friedel–Crafts reaction, establishing stable covalent bond structures within the polymer chains. The hydrophilic polystyrene nanospheresTMA@SHPSs were successfully synthesized via sulfonation and ion exchange reactions, demonstrating exceptional properties in reducing friction and wear. Compared with pure water, the addition of 4.0 wt % TMA@SHPSs results in a 62.2% reduction in the friction coefficient, accompanied by a significant decrease to 1.17 × 105 μm3 in wear volume. The results demonstrate that TMA@SHPSs, as water-based lubrication additives, generate composite protective films (tribo-chemical protective films and physical protective films) during the friction process, which effectively prevents direct contact between the friction pairs and achieves remarkable antifriction and antiwear effects. The results of the antimicrobial activity test indicate that TMA@SHPSs demonstrate exceptional antibacterial efficacy due to the bacteriostatic effect induced by hydration and the bactericidal properties of quaternary ammonium cations

Highly Ion Selective Proton Exchange Membrane Based on Sulfonated Polybenzimidazoles for Iron–Chromium Redox Flow Battery

The iron–chromium redox flow battery (ICRFB) has great potential for large-scale energy storage, due to its low capital cost of redox-active materials. However, the trade-off between conductivity and selectivity in the membranes limits its applications. Herein, a series of sulfonated polybenzimidazoles with exactly controlled sulfonation degree (SD) (S-PBI-x, x refers to SD) are designed and synthesized via direct copolymerization from the sulfonated monomer. Combined with the electrostatic repulsion of the formed imidazoliums, the S-PBIx membranes facilitate the proton transport and repel the redox-active ion crossover efficiently. Especially, when compared with Nafion 212 membrane, the S-PBI-100 membrane displays a comparable conductivity and more than an order of magnitude lower Fe3+ and Cr3+ permeabilities. Thus, a higher columbic efficiency (CE) of 98.2% and energy efficiency (EE) of 83.17% are achieved at 80 mA cm–2 for the corresponding ICRFB. Most importantly, no chemical degradation is observed for the S-PBI-100 membrane after in situ and ex situ stability tests

Molecular-Level Interfacial Chemistry Regulation of MXene Enables Energy Storage beyond Theoretical Limit

Ti3C2Tx MXene often suffers from poor lithium storage behaviors due to its electrochemically unfavorable OH terminations. Herein, we propose molecular-level interfacial chemistry regulation of Ti3C2Tx MXene with phytic acid (PA) to directly activate its OH terminations. Through constructing hydrogen bonds (H-bonds) between oxygen atoms of PA and OH terminations on Ti3C2Tx surface, interfacial charge distribution of Ti3C2Tx has been effectively regulated, thereby enabling sufficient ion-storage sites and expediting ion transport kinetics for high-performance energy storage. The results show that Li ions preferably bind to H-bond acceptors (oxygen atoms from PA), and the flexibility of H-bonds therefore renders their interactions with adsorbed Li ions chemically “tunable”, thus alleviating undesirable localized geometric changes of the OH terminations. Meanwhile the H-bond-induced microscopic dipoles can act as directional Li-ion pumps to expedite ion diffusion kinetics with lower energy barrier. As a result, the as-designed Ti3C2Tx/PA achieves a 2.4-fold capacity enhancement compared with pristine Ti3C2Tx (even beyond theoretical capacity), superior long-term cyclability (220.0 mAh g–1 after 2000 cycles at 2.0 A g–1), and broad temperature adaptability (−20 to 50 °C). This work offers a promising interface engineering strategy to regulate microenvironments of inherent terminations for breaking through the energy storage performance of MXenes

Pathway analysis of gene signatures predicting metastasis of node-negative primary breast cancer-2

<p><b>Copyright information:</b></p><p>Taken from "Pathway analysis of gene signatures predicting metastasis of node-negative primary breast cancer"</p><p>http://www.biomedcentral.com/1471-2407/7/182</p><p>BMC Cancer 2007;7():182-182.</p><p>Published online 25 Sep 2007</p><p>PMCID:PMC2077336.</p><p></p>int, with an increasing number of genes were conducted in the training set of ER-positive tumors or ER-negative tumors. For ER-positive tumors, in the "apoptosis" pathway, 24 genes (reaching an AUC of 0.784) were considered optimal (Table 3). For the "regulation of cell cycle pathway" in ER-positive tumors, 17 genes (AUC of 0.777) were considered optimal (Table 4). For ER-negative tumors, the optimal number of genes was 7 (AUC of 0.790) for the "regulation for cell growth" pathway (Table 5), and 5 (AUC of 0.788) for the "regulation of G-protein coupled receptor signaling" pathway (Table 6), respectively. The selected genes for the top 2 pathways for ER-positive and ER-negative tumors were subsequently used to construct prognostic gene signatures separately for the 2 ER-subgroups of tumors. The 152-patient test set [23] consisted of 125 ER-positive tumors and 27 ER-negative tumors based on the expression level of ER gene on the chip. () ROC (Left) and Kaplan-Meier (Right) analysis of the 38-gene signature for ER-positive tumors. Thirteen patients with less than 5-year follow-up were excluded from ROC analysis. () ROC (Left) and Kaplan-Meier (Right) analysis of the 12-gene signature for ER-negative tumors. One patient with less than 5-year follow-up was excluded from ROC analysis. () ROC (Left) and Kaplan-Meier (Right) analysis of a combined 50-gene signature for ER-positive and ER-negative tumors. Fourteen patients with less than 5-year follow-up were excluded from ROC analysis

sj-pdf-1-aje-10.1177_10982140211071017 - Supplemental material for Program Value-Added: A Feasible Method for Providing Evidence on the Effectiveness of Multiple Programs Implemented Simultaneously in Schools

Supplemental material, sj-pdf-1-aje-10.1177_10982140211071017 for Program Value-Added: A Feasible Method for Providing Evidence on the Effectiveness of Multiple Programs Implemented Simultaneously in Schools by Robert Shand, Stephen M. Leach, Fiona M. Hollands, Florence Chang, Yilin Pan, Bo Yan, Dena Dossett, Samreen Nayyer-Qureshi, Yixin Wang and Laura Head in American Journal of Evaluation</p