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We give new algorithms based on Markov chains to sample and approximately count satisfying assignments to k-uniform CNF formulas where each variable appears at most d times. For any k and d satisfying kd < no (1) and k ≥ 20 log k + 20 log d + 60, the new sampling algorithm runs in close to linear time, and the counting algorithm runs in close to quadratic time. Our approach is inspired by Moitra (JACM, 2019), which remarkably utilizes the Lovász local lemma in approximate counting. Our main technical contribution is to use the local lemma to bypass the connectivity barrier in traditional Markov chain approaches, which makes the well-developed MCMC method applicable on disconnected state spaces such as SAT solutions. The benefit of our approach is to avoid the enumeration of local structures and obtain fixed polynomial running times, even if k = ω (1) or d = ω (1). [ABSTRACT FROM AUTHOR]

In the emerging aqueous zinc ion batteries (AZIBs), proton (H+) with the smallest molar mass and fast (de)coordination kinetics is considered as the most ideal charge carrier compared with Zn2+ counterpart, however, searching for new hosting materials for H+ storage is still at its infancy. Herein, redox‐active hydrogen‐bonded organic frameworks (HOFs) assembled from diaminotriazine moiety decorated hexaazatrinnphthalene (HOF‐HATN) are for the first time developed as the stable cathode hosting material for boosting H+ storage in AZIBs. The unique integration of hydrogen‐bonding networks and strong π‐π stacking endow it rapid Grotthuss proton conduction, stable supramolecular structure and inclined H+ storage. As a consequence, HOF‐HATN displays a high capacity (320 mAh g−1 at 0.05 A g−1) and robust cyclability of (>10000 cycles at 5 A g−1) based on three‐step cation coordination storage. These findings get insight into the proton transport and storage behavior in HOFs and provide the molecular engineering strategy for constructing well‐defined cathode hosting materials for rechargeable aqueous batteries. [ABSTRACT FROM AUTHOR]

Background: This study aimed to assess the association of baseline insulin resistance (IR) surrogates and their longitudinal trajectories with cardiovascular diseases (CVD) to provide a useful reference for preventing CVD. Methods: This study was a prospective cohort study conducted in the 51st Regiment of the Third Division of Xinjiang Corps. A total of 6362 participants were recruited in 2016 to conduct the baseline survey, and the follow-up surveys in 2019, 2020, 2021, and 2022. The Kaplan-Meier method was used to estimate the cumulative incidence of CVD according to the baseline IR surrogates of metabolic insulin resistance score (METS-IR) and triglycerideglucose (TyG) index. Cox regression models were used to assess the association between the baseline IR surrogates and CVD. The impact of the longitudinal trajectories of the IR surrogates on CVD was analyzed after excluding those with IR surrogate data measured ≤2 times. Based on the group-based trajectory model (GBTM), the trajectory patterns of IR surrogates were determined. The Kaplan-Meier method was used to estimate the cumulative incidence of CVD in each trajectory group of METS-IR and TyG index. Cox regression models were used to analyze the association between different trajectory groups of each index and CVD. In addition, the Framingham model was utilized to evaluate whether the addition of the baseline IR surrogates increased the predictive potential of the model. Results: Baseline data analysis included 4712 participants. During a median follow-up of 5.66 years, 572 CVD events were recorded (mean age, 39.42 ± 13.67 years; males, 42.9%). The cumulative CVD incidence increased with the ascending baseline METS-IR and TyG index quartiles (Q1-Q4). The hazard ratio and 95% confidence interval for CVD risk in Q4 of the METS-IR and TyG index were 1.79 (1.25, 2.58) and 1.66 (1.28, 2.17), respectively, when compared with Q1. 4343 participants were included in the trajectory analysis, based on the longitudinal change patterns of the METS-IR and TyG index, the following three trajectory groups were identified: low-increasing, moderate-stable, and elevated-increasing groups. Multivariate Cox regression revealed that the hazard ratio (95% confidence interval) for CVD risk in the elevatedincreasing trajectory group of the METS-IR and TyG index was 2.13 (1.48, 3.06) and 2.63 (1.68, 4.13), respectively, when compared with the low-rising group. The C-index, integrated discrimination improvement value, and net reclassification improvement value were enhanced after adding the baseline METS-IR and TyG index values to the Framingham model (P<0.05). Conclusions: Elevated baseline IR surrogates and their higher long-term trajectories were strongly associated with a high risk of CVD incidence in Xinjiang's rural areas. Regular METS-IR and TyG index monitoring can aid in the early detection of CVD-risk groups. [ABSTRACT FROM AUTHOR]

Gear transmission errors are influenced by temperature especially in the aerospace field. A model is proposed to investigate the influence of temperature on cylindrical gear transmission errors based on the thermal network (TETN). The gear temperature field distribution model is established based on the thermal network method, and gear thermal deformation can be calculated along the gear meshing line. Regarding the gear single-flank rolling process, the variation of gear transmission errors under temperature is determined. In numerical calculations in MATLAB, the variation of gear transmission errors at 100 ℃ compared to 20 ℃ is -4.20 μm, which decreases almost linearly while the thermal expansion coefficient of the gear material increases. The simulation of the gear transmission errors variation of temperatures using the finite element method (FEM) were carried out in Workbench software under Ansys and the average difference of the TETN model results between calculations and FEM for different temperatures was 0.24 μm. Experiments were carried out on the gear tester in temperatures ranging from 0℃ to 100℃, the TETN model results in calculations were compared with the results of the tester, and the average difference was -1.15 μm. The results show that the proposed TETN can be used as an algorithm to determine the variation of gear transmission errors under the influence of temperature. [ABSTRACT FROM AUTHOR]