In one-dimensional Diophantine approximation, the Diophantine properties of a real number are characterized by its partial quotients, especially the growth of its large partial quotients. Notably, Kleinbock and Wadleigh [Proc. Amer. Math. Soc. 146(5) (2018), 1833–1844] made a seminal contribution by linking the improvability of Dirichlet’s theorem to the growth of the product of consecutive partial quotients. In this paper, we extend the concept of Dirichlet non-improvable sets within the framework of shrinking target problems. Specifically, consider the dynamical system $([0,1), T)$ of continued fractions. Let $\{z_n\}_{n \ge 1}$ be a sequence of real numbers in $[0,1]$ and let $B> 1$. We determine the Hausdorff dimension of the following set: $ \{x\in [0,1):|T^nx-z_n||T^{n+1}x-Tz_n|<B^{-n}\text { infinitely often}\}. $

Previous studies have revealed an association between dietary factors and atopic dermatitis (AD). To explore whether there was a causal relationship between diet and AD, we performed Mendelian randomisation (MR) analysis. The dataset of twenty-one dietary factors was obtained from UK Biobank. The dataset for AD was obtained from the publicly available FinnGen consortium. The main research method was the inverse-variance weighting method, which was supplemented by MR‒Egger, weighted median and weighted mode. In addition, sensitivity analysis was performed to ensure the accuracy of the results. The study revealed that beef intake (OR = 0·351; 95 % CI 0·145, 0·847; P = 0·020) and white bread intake (OR = 0·141; 95 % CI 0·030, 0·656; P = 0·012) may be protective factors against AD. There were no causal relationships between AD and any other dietary intake factors. Sensitivity analysis showed that our results were reliable, and no heterogeneity or pleiotropy was found. Therefore, we believe that beef intake may be associated with a reduced risk of AD. Although white bread was significant in the IVW analysis, there was large uncertainty in the results given the wide 95 % CI. Other factors were not associated with AD in this study.

Our previous studies have suggested that spastin, which aggregates on spindle microtubules in oocytes, may promote the assembly of mouse oocyte spindles by cutting microtubules. This action may be related to CRMP5, as knocking down CRMP5 results in reduced spindle microtubule density and maturation defects in oocytes. In this study, we found that, after knocking down CRMP5 in oocytes, spastin distribution shifted from the spindle to the spindle poles and errors in microtubule–kinetochore attachment appeared in oocyte spindles. However, CRMP5 did not interact with the other two microtubule-severing proteins, katanin-like-1 (KATNAL1) and fidgetin-like-1 (FIGNL1), which aggregate at the spindle poles. We speculate that, in oocytes, due to the reduction of spastin distribution on chromosomes after knocking down CRMP5, microtubule–kinetochore errors cannot be corrected through severing, resulting in meiotic division abnormalities and maturation defects in oocytes. This finding provides new insights into the regulatory mechanisms of spastin in oocytes and important opportunities for the study of meiotic division mechanisms.

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results by Deike et al. (J. Fluid Mech., vol. 829, 2017, pp. 364–391) and Pizzo et al. (J. Phys. Oceanogr., vol. 49, no. 4, 2019, pp. 983–992) have indicated transport by deep-water breaking waves is enhanced compared with non-breaking waves. To model particle transport in irregular waves, some of which break, we develop a stochastic differential equation describing both mean particle transport and its uncertainty. The equation combines a Brownian motion, which captures non-breaking drift-diffusion effects, and a compound Poisson process, which captures jumps in particle positions due to breaking. From the corresponding Fokker–Planck equation for the evolution of the probability density function for particle position, we obtain closed-form expressions for its first three moments. We corroborate these predictions with new experiments, in which we track large numbers of particles in irregular breaking waves. For breaking and non-breaking wave fields, our experiments confirm that the variance of the particle position grows linearly with time, in accordance with Taylor's single-particle dispersion theory. For wave fields that include breaking, the compound Poisson process increases the linear growth rate of the mean and variance and introduces a finite skewness of the particle position distribution.

Continuous risky decisions refer to decisions that involve trade-offs among options with persistent risks. People can use the probability of occurrence per unit time (e.g., ‘the probability of occurrence is 1% per month’) or the average time of risk occurrence (e.g., ‘the average occurrence time is 100 months’) to represent continuous risky options. In this study, we examined the effect of the presentation format (i.e., the probability of occurrence per unit time vs. the average time of risk occurrence) on continuous risky decisions in the gain domain and further explored the underlying mechanism. In Study 1 (N = 122), we demonstrated the effect of presentation format on continuous risky decisions and the moderating effect of the magnitude of probabilities. Specifically, when the probabilities were relatively low, compared with the probability of occurrence per unit time, using the average time of risk occurrence to present the continuous risky options led to more risk-averse decisions. However, when the probabilities were relatively high, compared with the probability of occurrence per unit time, the presentation format of the average time occurrence led to more risk-seeking decisions. In Study 2 (N = 136), we found that the moderating effect of the option probabilities on continuous risky decisions was mediated by the subjective attribute-wise difference judgment. In Study 3 (N = 221), we replicated the effect of presentation format on continuous risky decisions in more natural scenarios. The study offered a deep understanding of the mechanism of continuous risky decision-making, and the results were conducive to further developing theories in relevant fields.

Redroot pigweed (Amaranthus retroflexus L.) is a dominant weed in soybean [Glycine max (L.) Merr.] fields in Heilongjiang Province, China. High selective pressure caused by the extensive application of the protoporphyrinogen oxidase (PPO)-inhibiting herbicide fomesafen has caused A. retroflexus to evolve resistance to this herbicide. Two susceptible and two resistant populations (S1, S2, R1, and R2) were selected in this study to illustrate the target-site resistance mechanism in resistant A. retroflexus. Whole-plant bioassays indicated that R1 and R2 had evolved high-level resistance to fomesafen, with resistance factors of 27.0 to 27.9. Sequence alignment of the PPO gene showed an Arg-128-Gly substitution in PPX2. The basal expression differences of PPX1 and PPX2 between the S1 and R1 plants were essentially nonsignificant, whereas the basal expression of PPX2 in R2 plants was slightly lower than in S1 plants. Compared with the PPX1 gene, the PPX2 gene maintained higher expression in the resistant plants after treatment with fomesafen. An enzyme-linked immunosorbent assay showed a similar basal PPO content between the susceptible and resistant plants without treatment. After fomesafen treatment, the PPO content decreased sharply in the susceptible plants compared with the resistant plants. Furthermore, after 24 h of treatment, the resistant plants showed increased PPO content, whereas the susceptible plants had died. The PPO2 mutation resulted in high extractable PPO activity and low sensitivity to fomesafen along with changes in PPO enzyme kinetics. Although the mutant PPO2 exhibited increased Km values in the resistant plants, the Vmax values in these plants were also increased. Changes in the properties of the PPO enzyme due to an Arg-128-Gly substitution in PPX2, including changes in enzyme sensitivity and enzyme kinetics, are the target-site mechanism of resistance in A. retroflexus.

We present a 2 μm Tm:YAG disk laser multi-pass pumped by a 1 μm laser. The transitions in competition of up conversion (UC) and excited state absorption (ESA) are analyzed in detail based on a numerical model that considers stimulated emission, fluorescence, non-radiative decay, UC, andESA, showing good agreement with experiments. The proportions and fractional thermal loads of all transitions are derived quantitatively. The results show that UC and ESA are critical in Tm:YAG disk lasers, resulting in a decrease in the absorbed pump power and temperature after lasing for two different disk thicknesses. In addition, although the absorbed pump power of the 0.5 mm disk is lower than in the 1 mm case, its relatively weak UC and ESA and low total fractional thermal load can improve laser performance. A 0.5 mm Tm:YAG disk laser thus delivered the maximum output power of1.05 W with beam quality of Mx2 = 2.02 and My2 = 2.03.

A multicenter study of sharps injuries (SIs) and other blood or body fluid (OBBF) exposures was conducted among 33,156 healthcare workers (HCWs) from 175 hospitals in Anhui, China. In total, 12,178 HCWs (36.7%) had experienced at least 1 SI in the previous 12 months and 8,116 HCWs (24.5%) had experienced at least 1 OBBF exposure during the previous 12 months.

A suite of Jurassic–Cretaceous migmatites was newly identified in the Liaodong Peninsula of the eastern North China Craton (NCC). Anatexis is commonly associated with crustal thickening. However, the newly identified migmatites were formed during strong lithospheric thinning accompanied by voluminous magmatism and intense deformation. Field investigations show that the migmatites are spatially associated with low-angle detachment faults. Numerous leucosomes occur either as isolated lenses or thin layers (dykes), parallel to or cross-cutting the foliation. Peritectic minerals such as titanite and sillimanite are distributed mainly along the boundaries of reactant minerals or are accumulated along the foliation. Most zircons show distinct core–rim structures, and the rims have low Th/U ratios (0.01–0.24). Zircon U–Pb dating results indicate that the protoliths of the migmatites were either the Late Triassic (224–221 Ma) diorites or metasedimentary rocks deposited sometime after c. 1857 Ma. The zircon overgrowth rims record crystallization ages of 173–161 Ma and 125 Ma, which represent the formation time of leucosomes. These ages are consistent with those reported magmatic events in the Liaodong Peninsula and surrounding areas. The leucosomes indicate a strong anatectic event during the Jurassic–Cretaceous period. Partial melting occurred through the breakdown of muscovite and biotite with the presence of water-rich fluid under a thermal anomaly regime. The possible mechanism that caused the 173–161 Ma and 125 Ma anatectic events was intimately related to the regional crustal extension during the lithospheric thinning of the NCC. Meanwhile, the newly generated melts further weakened the rigidity of the crust and enhanced the extension.

The gut microbiota is directly influenced by dietary components, and it plays critical roles in chronic diseases. Excessive consumption of trans-fatty acids (TFA) is associated with obesity induced by alterations in gut microbiota, but the links between obesity and gut microbiota remain unclear. Therefore, studies examining the impact of TFA on intestinal microflora are essential. In our study, we performed 16S ribosomal RNA gene sequencing on faecal samples from Sprague–Dawley rats fed a basal diet (control (CON) group), high-fat (HF) diet (diet-induced obesity (DIO) group) or TFA diets (1 % TFA group and 8 % TFA group) for 8 weeks to investigate the effects of TFA/HF diets on obesity and gut microbiota composition. We found that the TFA/HF diets significantly induced obesity and changes in blood and brain physiological parameters of the rats. The relative abundance of the phyla Firmicutes and Bacteroidetes was inversely altered in the three test groups compared with the CON group. Proteobacteria increased slightly in the DIO, 1 % TFA and 8 % TFA groups. The genus Bacteroides increased in the DIO and 1 % TFA groups, but Muribaculaceae decreased in all experimental groups compared with the CON group. Moreover, significant differences were observed among clusters of orthologous group functional categories of the four dietary groups. Our observations suggested that the TFA/HF diets induced obesity and dysfunction of gut microbiota. Gut dysbiosis might mediate the obesity effects of TFA/HF diets.

Clay often has severe detrimental impacts on cement-based materials. Therefore, it is necessary to investigate the mechanism causing the deterioration to improve the service life of cement-based materials. Based on accurate dimensional analysis, a mechanism that influences clay is proposed: the intercalation of the side chains of superplasticizer molecules in the interlayer space of the clay. To lessen this harmful effect, a new clay-resistant admixture (CRA) possessing cationic groups of small molecular size was synthesized through a novel dimensional design. The length and width of the side chains of this superplasticizer molecule were 9.50–17.50 and 0.25–0.40 nm, respectively, with a radius of ~3.74 nm in solvent, which is larger than the interlayer spacing of montmorillonite (i.e. 1.09–2.14 nm). The longitudinal and latitudinal lengths of the CRA molecule were 0.468 and 9.456 nm, respectively, ensuring intercalation in the interlayer of montmorillonite. The increase in interlayer spacing of the clay was 0.364 nm following addition of polycarboxylate superplasticizer (PCE) plus CRA and 0.632 nm following addition of PCE, which suggests that the CRA plays the role of a ‘sacrificial agent’ that is preferentially intercalated into the interlayer space of clay to further prevent the side chains of the superplasticizer molecules from entering the interlayer. The aim of this study was to propose a suitable means of synthesizing a new CRA to address the impact of clay through dimensional design and mechanism analysis, which contributes to the theoretical study and technological improvement of cement-based materials.

Meditation is a type of mental training commonly applied in clinical settings and also practiced for general well-being. Brain functional connectivity (FC) patterns associated with meditation have revealed its brain mechanisms. However, the variety of FC methods applied has made it difficult to identify brain communication patterns associated with meditation. Here we carried out a coordinate-based meta-analysis to get preliminary evidence of meditation effects on changing brain network interactions. Fourteen seed-based, voxel-wise FC studies reported in 13 publications were reviewed; 10 studies with seeds in the default mode network (DMN) were meta-analyzed. Seed coordinates and the effect sizes in statistically significant regions were extracted, based on 170 subjects in meditation groups and 163 subjects in control groups. Seed-based d-mapping was used to analyze meditation versus control FC differences with DMN seeds. Meditation was associated with increased connectivity within DMN and between DMN and somatomotor network and with decreased connectivity between DMN and frontoparietal network (FPN) as well as ventral attention network (VAN). The pattern of decreased within-DMN FC and increased between-network FC (FPN and DAN with DMN) was more robust in highly experienced meditators compared to less experienced individuals. The identified neural network interactions may also promote meditation’s effectiveness in clinical interventions for treating physical and mental disorders.

The aim of this retrospective study was to investigate the prognostic significance of pre-treatment immunological and nutritional statuses in patients with locally advanced gastric cancer (GC), and to use the risk factors to develop a predictive score. A total of 731 patients who underwent gastrectomy for stage II/III GC from November 2010 to December 2015 were recruited into this retrospective study. On the basis of univariate and further multivariate Cox regression analyses, decreased pretreatment lymphocyte count (<1·5×109/litre) and prealbumin concentrations (<180 mg/l) were identified to be independently associated with poorer overall survival (OS) and disease-free survival (DFS). Low albumin concentrations (<33 g/l) were identified as an independent risk factor only for OS, but not for DFS. Thereafter, patients who had a decreased prealbumin concentration and lymphocyte count were given a combination of serum prealbumin concentration and lymphocyte count (Co-PaL) score of 2. Patients with only one or neither of these concentrations were given a Co-PaL score of 1 or 0, respectively. Both the OS and the DFS time were inversely related to the Co-PaL scores, and the differences among the three groups were all significant. In contrast, the prognosis did not differ significantly between patients with good nutrition and those with mild to moderate malnutrition according to the prognostic nutritional index. This study indicated that the simple scoring system could accurately predict the prognosis of patients who underwent gastrectomy for stage II/III GC. The score might be helpful in terms of clinical preoperative decision-making.