The integrality of the numbers $A_{n,m}={(2n)!(2m)!}/{n!m!(n+m)!}$ was observed by Catalan as early as 1874 and Gessel named $A_{n,m}$ the super Catalan numbers. The positivity of the q-super Catalan numbers (q-analogue of the super Catalan numbers) was investigated by Warnaar and Zudilin [‘A q-rious positivity’, Aequationes Math. 81 (2011), 177–183]. We prove the divisibility of sums of q-super Catalan numbers, which establishes a q-analogue of Apagodu’s congruence involving super Catalan numbers.

We examined the trade-off between the cost of response redundancy and the gain in output quality on the popular crowdsourcing platform Mechanical Turk, as a partial replication of Kosinski et al. (2012) who demonstrated a significant improvement in performance by aggregating multiple responses through majority vote. We submitted single items from a validated intelligence test as Human Intelligence Tasks (HITs) and aggregated the responses from “virtual groups” consisting of 1 to 24 workers. While the original study relied on resampling from a relatively small number of responses across a range of experimental conditions, we randomly and independently sampled from a large number of HITs, focusing only on the main effect of group size. We found that – on average – a group of six MTurkers has a collective IQ one standard deviation above the mean for the general population, thus demonstrating a “wisdom of the crowd” effect. The relationship between group size and collective IQ was characterised by diminishing returns, suggesting moderately sized groups provide the best return on investment. We also analysed performance of a smaller subset of workers who had each completed all 60 test items, allowing for a direct comparison between a group’s collective IQ and the individual IQ of its members. This demonstrated that randomly selected groups collectively equalled the performance of the best-performing individual within the group. Our findings support the idea that substantial intellectual capacity can be gained through crowdsourcing, contingent on moderate redundancy built into the task request.

Late Palaeozoic igneous rock associations in response to subduction, accretion, and final closure of the eastern Palaeo-Asian Ocean play a significant role in understanding the geodynamic evolution of the southeastern Central Asian Orogenic Belt. Previous studies have identified a Permian arc magmatic belt associated with the southward-dipping subduction of the eastern Palaeo-Asian Ocean along the Solonker–Changchun suture zone. The genetic mechanism and associated geodynamic settings are of great importance in deciphering the evolution of the eastern Palaeo-Asian Ocean. This paper presents zircon U–Pb–Hf isotope and whole-rock geochemical analyses for a suite of magmatic rocks including the early Permian diorite porphyrites (ca. 281.0 Ma), andesites (ca. 276 Ma) and rhyolites (ca. 275 Ma) in the Kulun region. The diorite porphyrites and andesites have high SiO2 and total alkali contents, and low MgO contents and Mg no. values, with enrichments in large ion lithophile elements and depletions in high-field-strength elements. These geochemical characteristics, together with low-Sr and high-Yb contents, a weak concave-upward shape of middle rare earth elements and negative Eu anomalies, suggest that these intermediate igneous rocks were generated by partial melting of amphibolitic lower crust at a crustal depth of 30–40 km. The rhyolites have heterogeneous isotopic compositions, with ϵHf(t) values and TDM2 ages of –20.8 to +0.5 and 3578∼1494 Ma, implying that they were likely derived from partial melting of a mixed source dominated by recycled ancient crust with minor juvenile crustal materials. The rhyolites show potassic affinity with relatively high K2O and very low Na2O, which was attributed to liquid immiscibility of felsic magma and subsequent limited fractional crystallization of plagioclase. The regional igneous associations, metamorphic events, and coeval sedimentary rocks along the Solonker–Changchun suture zone indicate that the early Permian igneous rocks were formed in an active continental arc environment in response to southward subduction of the eastern Palaeo-Asian Ocean.

Low molecular weight glutenin subunits (LWM-GSs) play a crucial role in determining wheat flour processing quality. In this work, 35 novel LMW-GS genes (32 active and three pseudogenes) from three Aegilops umbellulata (2n = 2x = 14, UU) accessions were amplified by allelic-specific PCR. We found that all LMW-GS genes had the same primary structure shared by other known LMW-GSs. Thirty-two active genes encode 31 typical LMW-m-type subunits. The MZ424050 possessed nine cysteine residues with an extra cysteine residue located in the last amino acid residue of the conserved C-terminal III, which could benefit the formation of larger glutenin polymers, and therefore may have positive effects on dough properties. We have found extensive variations which were mainly resulted from single-nucleotide polymorphisms (SNPs) and insertions and deletions (InDels) among the LMW-GS genes in Ae. umbellulata. Our results demonstrated that Ae. umbellulata is an important source of LMW-GS variants and the potential value of the novel LMW-GS alleles for wheat quality improvement.

Self-organizing systems (SOS) are developed to perform complex tasks in unforeseen situations with adaptability. Predefining rules for self-organizing agents can be challenging, especially in tasks with high complexity and changing environments. Our previous work has introduced a multiagent reinforcement learning (RL) model as a design approach to solving the rule generation problem of SOS. A deep multiagent RL algorithm was devised to train agents to acquire the task and self-organizing knowledge. However, the simulation was based on one specific task environment. Sensitivity of SOS to reward functions and systematic evaluation of SOS designed with multiagent RL remain an issue. In this paper, we introduced a rotation reward function to regulate agent behaviors during training and tested different weights of such reward on SOS performance in two case studies: box-pushing and T-shape assembly. Additionally, we proposed three metrics to evaluate the SOS: learning stability, quality of learned knowledge, and scalability. Results show that depending on the type of tasks; designers may choose appropriate weights of rotation reward to obtain the full potential of agents’ learning capability. Good learning stability and quality of knowledge can be achieved with an optimal range of team sizes. Scaling up to larger team sizes has better performance than scaling downwards.

Existing studies have examined the demand elasticities for organic products only in select categories, and their results for consumers' sensitivity to price changes are inconsistent. Evidence regarding the effects of price promotions on the demand for organic foods vs non-organic foods is scarce. This study aims to (1) examine the own-price elasticities of organic foods vs non-organic counterparts both with and without a promotion in a variety of product categories, and (2) investigate how the distinctive promotion effects between organic and non-organic counterparts depend on food category features. Using purchase data for 36 food categories from the 2015 Nielsen Consumer Panel, we find differential own-price elasticities for organic and non-organic foods, regardless of whether the product is purchased with a promotion. When the products are purchased with a promotion, we find stronger price promotion effects of organic virtues than non-organic virtues and weaker price promotion effects of organic vices than conventional vices. Price promotions of organic foods are more likely to induce health-conscious consumers to switch from conventional purchases to organic purchases in virtues.

Late Mesozoic igneous rocks are important for deciphering the Mesozoic tectonic setting of NE China. In this paper, we present whole-rock geochemical data, zircon U–Pb ages and Lu–Hf isotope data for Early Cretaceous volcanic rocks from the Tulihe area of the northern Great Xing’an Range (GXR), with the aim of evaluating the petrogenesis and genetic relationships of these rocks, inferring crust–mantle interactions and better constraining extension-related geodynamic processes in the GXR. Zircon U–Pb ages indicate that the rhyolites and trachytic volcanic rocks formed during late Early Cretaceous time (c. 130–126 Ma). Geochemically, the highly fractionated I-type rhyolites exhibit high-K calc-alkaline, metaluminous to weakly peraluminous characteristics. They are enriched in light rare earth elements (LREEs) and large-ion lithophile elements (LILEs) but depleted in high-field-strength elements (HFSEs), with their magmatic zircons ϵHf(t) values ranging from +4.1 to +9.0. These features suggest that the rhyolites were derived from the partial melting of a dominantly juvenile, K-rich basaltic lower crust. The trachytic volcanic rocks are high-K calc-alkaline series and exhibit metaluminous characteristics. They have a wide range of zircon ϵHf(t) values (−17.8 to +12.9), indicating that these trachytic volcanic rocks originated from a dominantly lithospheric-mantle source with the involvement of asthenospheric mantle materials, and subsequently underwent extensive assimilation and fractional crystallization processes. Combining our results and the spatiotemporal migration of the late Early Cretaceous magmatic events, we propose that intense Early Cretaceous crust–mantle interaction took place within the northern GXR, and possibly the whole of NE China, and that it was related to the upwelling of asthenospheric mantle induced by rollback of the Palaeo-Pacific flat-subducting slab.

Hypertension represents one of the most common pre-existing conditions and comorbidities in Coronavirus disease 2019 (COVID-19) patients. To explore whether hypertension serves as a risk factor for disease severity, a multi-centre, retrospective study was conducted in COVID-19 patients. A total of 498 consecutively hospitalised patients with lab-confirmed COVID-19 in China were enrolled in this cohort. Using logistic regression, we assessed the association between hypertension and the likelihood of severe illness with adjustment for confounders. We observed that more than 16% of the enrolled patients exhibited pre-existing hypertension on admission. More severe COVID-19 cases occurred in individuals with hypertension than those without hypertension (21% vs. 10%, P = 0.007). Hypertension associated with the increased risk of severe illness, which was not modified by other demographic factors, such as age, sex, hospital geological location and blood pressure levels on admission. More attention and treatment should be offered to patients with underlying hypertension, who usually are older, have more comorbidities and more susceptible to cardiac complications.

In the present study, we analysed the effects of SNP rs174547 (T/C) in the fatty acid desaturase 1 (FADS1) gene on long-chain PUFA levels. Four databases were searched to retrieve related literature with keywords such as fatty acid (FA), SNP, FADS1 and rs174547. A meta-analysis of the data was performed using Stata12.0 software, including summary statistics, test for heterogeneity, evaluation of publication bias, subgroup analysis and sensitivity analysis. The associations between rs174547 in FADS1 and seven types of FA, and Δ-5 (D5D) and Δ-6 fatty acid desaturase (D6D) activity were assessed based on the pooled results from eleven papers. A total of 3713 individuals (1529 TT and 2184 TC + CC) were included. The results demonstrated that minor C allele carriers of rs174547 had higher linoleic acid (LA; P < 0·001) and α-linolenic acid (P = 0·020) levels, lower γ-linolenic acid (GLA; P = 0·001) and arachidonic acid (P = 0·024) levels, and lower D5D (P = 0·005) and D6D (P = 0·004) activities than the TT genotype group. Stratification analysis showed that minor C allele carriers of rs174547 had higher LA and lower GLA levels and lower D6D activities in plasma (LA, P < 0·001; GLA, P < 0·001; D6D activity, P < 0·001) samples and in Asian populations (LA, P < 0·001; GLA, P = 0·001; D6D activity, P = 0·001) than the TT genotype group. In conclusion, minor C allele carriers of the SNP rs174547 were associated with decreased activity of D5D and D6D.

The edge surface warping defect seriously affect the surface quality of strips. In this paper, a technology for diagnosis of warping defects in hot-rolled strip based on data-driven methods is studied. Based on the mechanism analysis of the warping defects, the process parameters affecting the warping defects were sorted out and used as the original input parameters of the defect diagnosis model. Firstly, a diagnostic model that combines the deep belief network and contribution plots of each dimensionality reduction layer is proposed. The deep belief network that integrates each dimensionality reduction layer can predict product defects more accurately and stably than the traditional deep belief network. Meanwhile, on the basis of the pre-judgment model, the method of contribution plot is further introduced to trace the defects, and the comprehensive diagnosis function of model pre-judgment and traceability is realized. Finally, collected the production data from a hot rolling production line for a period of time. Tested the model and predicted a hit rate of 85%. The main influencing factors of edge surface warping defects were determined that the rate of defect decrease with the increase of furnace temperature. When the heating temperature of the second stage of the heating furnace is higher than 1160°C, the incidence of defects is significantly reduced. Defect rate is relatively low within 240min of total furnace time. With the first and third pass phosphorus removal equipment turned on, the incidence of defects was relatively low.

To explore whether different polyvinylpyrrolidone (PVP) concentrations affect the results of intracytoplasmic sperm injection (ICSI), a prospective study was conducted for 194 couples undergoing 210 ICSI therapy cycles. These cycles were divided into three groups (10, 7 and 5% groups) using the corresponding concentration of PVP for sperm immobilization. The main outcome measures were analyzed. Results indicated that, with a decrease in PVP concentrations, all of the main outcome measures increased. In particular, the high-quality cleavage embryo rate in the 7% group was significantly lower than in the 5% group (P < 0.01), and the cleavage, high-quality cleavage embryo, and high-quality blastocyst rates in the 5% group were significantly higher than those in the 10% group (all P < 0.001). For high-/intermediate-quality semen, all of the main outcome measures were significantly increased with 5% PVP. For the poor-quality semen, only the high-quality cleavage embryo and high-quality blastocyst rates were significantly higher in the 5% group. Therefore, lowering PVP concentrations greatly promoted the development of embryos in ICSI cycles, with an optimal concentration of 5% for ICSI.

Novel NiMoO4-integrated electrode materials were successfully prepared by solvothermal method using Na2MoO4·2H2O and NiSO4·6H2O as main raw materials, water, and ethanol as solvents. The morphology, phase, and structure of the as-prepared materials were characterized by SEM, XRD, Raman, and FT-IR. The electrochemical properties of the materials in supercapacitors were investigated by cyclic voltammetry, constant current charge–discharge, and electrochemical impedance spectroscopy techniques. The effects of volume ratio of water to ethanol (W/E) in solvent on the properties of the product were studied. The results show that the pure phase monoclinic crystal NiMoO4 product can be obtained when the W/E is 2:1. The diameter and length are 0.1–0.3 µm and approximately 3 µm, respectively. As an active material for supercapacitor, the NiMoO4 nanorods material delivered a discharge specific capacitance of 672, 498, and 396 F/g at a current density of 4, 7, and 10 A/g, respectively. The discharge specific capacitance slightly decreased from 815 to 588 F/g with a retention of 72% after 1000 cycles at a current density of 1 A/g. With these superior capacitance properties, the novel NiMoO4 integrated electrode materials could be considered as promising material for supercapacitors.

Co-receptor tropism has been identified to correlate with HIV-1 transmission and the disease progression in patients. A molecular epidemiology investigation of co-receptor tropism is important for clinical practice and effective control of HIV-1. In this study, we investigated the co-receptor tropism on HIV-1 variants of 85 antiretroviral-naive patients with Geno2pheno algorithm at a false-positive rate of 10%. Our data showed that a majority of the subjects harboured the CCR5-tropic virus (81.2%, 69/85). No significant differences in gender, age, baseline CD4+ T-cell counts and transmission routes were observed between subjects infected with CXCR4-tropic or CCR5-tropic virus. The co-receptor tropism appeared to be associated with the virus genotype; a significantly more CXCR4-use was predicted in CRF01_AE infections whereas all CRF07_BC and CRF08_BC were predicted to use CCR5 co-receptor. Sequences analysis of V3 revealed a higher median net charge in the CXCR4 viruses over CCR5 viruses (4.0 vs. 3.0, P < 0.05). The predicted N-linked glycosylation site between amino acids 6 and 8 in the V3 region was conserved in CCR5 viruses, but not in CXCR4 viruses. Besides, variable crown motifs were observed in both CCR5 and CXCR4 viruses, of which the most prevalent motif GPGQ existed in both viral tropism and almost all genotypes identified in this study except subtype B. These findings may offer important implications for clinical practice and enhance our understanding of HIV-1 biology.

CrFeNiTix (x = 0.2, 0.3, 0.4, 0.5, and 0.6 molar ratio) compositionally complex alloys were fabricated by vacuum arc melting to investigate the microstructure, hardness, and compressive properties. The results revealed that CrFeNiTix alloys consisted of the principal face-centered cubic (FCC) phase and body-centered cubic (BCC) solid solution, with an amount of (Ni, Ti)-rich hexagonal close-packed phase. CrFeNiTix alloys exhibited the typical dendrite. Ti0.2 and Ti0.3 alloys were composed of FCC and BCC solid solutions in the dendrite, as well as ε (Ni3Ti) and R (Ni2.67Ti1.33) phases in the inter-dendrite, simultaneously. For Ti0.4, Ti0.5, and Ti0.6 alloys, (Fe, Cr)-rich solid solution separated out and ε phase transformed into R phase gradually. Meanwhile, TEM analysis indicated that Ti0.4 alloy matrix consisted of the principal FCC phase containing (Ni, Ti)-rich intragranular nanoprecipitates. The hardness values of CrFeNiTix alloys were increased with the addition of Ti content and the high compressive strength of CrFeNiTix alloys was maintained, which was attributed to the solid solution strengthening and precipitation hardening.

In this work, we proposed a possible mechanism for the formation S-type planet in close binaries (0.5 au < aB < 3 au). Numerical simulations showed that the maximum capture probability is ∼ 10%, which can be comparable to the tidal capture probability of hot Jupiters in single star systems. The capture probability is related to binary configurations. Furthermore, we find that S-type planets with retrograde orbits can be naturally produced via capture process. These planets on retrograde orbits can help us distinguish in situ formation and post-capture origin for S-type planet in close binaries. The forthcoming missions (PLATO or TESS) will provide the opportunity and feasibility to detect such planets.