In this paper, we generalize the concept of functional dependence (FD) from time series (see Wu [2005, Proceedings of the National Academy of Sciences 102, 14150–14154]) and stationary random fields (see El Machkouri, Volný, and Wu [2013, Stochastic Processes and Their Applications 123, 1–14]) to nonstationary spatial processes. Within conventional settings in spatial econometrics, we define the concept of spatial FD measure and establish a moment inequality, an exponential inequality, a Nagaev-type inequality, a law of large numbers, and a central limit theorem. We show that the dependent variables generated by some common spatial econometric models, including spatial autoregressive (SAR) models, threshold SAR models, and spatial panel data models, are functionally dependent under regular conditions. Furthermore, we investigate the properties of FD measures under various transformations, which are useful in applications. Moreover, we compare spatial FD with the spatial mixing and spatial near-epoch dependence proposed in Jenish and Prucha ([2009, Journal of Econometrics 150, 86–98], [2012, Journal of Econometrics 170, 178–190]), and we illustrate its advantages.

Power scaling in conventional broad-area (BA) lasers often leads to the operation of higher-order lateral modes, resulting in a multiple-lobe far-field profile with large divergence. Here, we report an advanced sawtooth waveguide (ASW) structure integrated onto a wide ridge waveguide. It strategically enhances the loss difference between higher-order modes and the fundamental mode, thereby facilitating high-power narrow-beam emission. Both optical simulations and experimental results illustrate the significant increase in additional scattering loss of the higher-order modes. The optimized ASW lasers achieve an impressive output power of 1.1 W at 4.6 A at room temperature, accompanied by a minimal full width at half maximum lateral divergence angle of 4.91°. Notably, the far-field divergence is reduced from 19.61° to 11.39° at the saturation current, showcasing a remarkable 42% improvement compared to conventional BA lasers. Moreover, the current dependence of divergence has been effectively improved by 38%, further confirming the consistent and effective lateral mode control capability offered by our design.

Zinc (Zn) is widely known as an essential trace element for fish and new ways to supply it to them are needed. Palygorskite (Pal) is a natural silicate clay mineral and the palygorskite structure contains nano-channels, which are filled with water and exchangeable ions. Zn-bearing palygorskites (Zn-Pal) prepared using ion exchange have attracted attention due to the durable antibacterial properties that limit pathogens and as a potential new Zn source for livestock. The present study was conducted to evaluate the effects of Zn-Pal supplementation on the growth performance, nutrient retention, meat quality, Zn accumulation, and intestinal Zn transporter protein gene expression in blunt snout bream Megalobrama amblycephala. The fish were fed a basal diet without an exogenous Zn source and the basal diet was supplemented with 125 mg/kg Zn as Zn sulfate (ZnSO4) or 35, 80, or 125 mg/kg Zn as Zn-Pal. Each diet was tested using three replicates for 7 weeks. The results showed that dietary Zn-Pal supplementation quadratically (P<0.05) increased growth performance, nutrient retention, total and Cu/Zn superoxide dismutase activity, Zn content in scales, and intestinal Zn transporter protein gene expression. The muscular cooking loss in blunt snout bream decreased with the optimum Zn-Pal Zn level of 35 mg/kg. Compared to the fish treated with ZnSO4, the fish supplemented with 35 mg/kg as Zn-Pal exhibited similar growth performance and nutrient retention (P>0.05), increased mRNA expression of the metal-response element-binding transcription factor-1 in the intestine (P<0.05), and decreased cooking loss of muscle (P<0.05).The results suggested that 35 mg/kg Zn supplementation as Zn-Pal could improve the growth performance and body composition, increase nutrient retention and tissue Zn concentrations, enhance the muscle water-holding capacity, and enhance antioxidant status in blunt snout bream. The Zn-Pal was more efficient and could be used as an alternative Zn source to ZnSO4 in the diet of blunt snout bream.

As the southernmost part of the central segment of the Central Asian Orogenic Belt, the northern Alxa area is characterized by abundant Permian magmatism and records key information on the geological evolution of the Palaeo-Asian Ocean. This study reports new zircon U–Pb and Lu–Hf isotopic and whole-rock geochemical data of the early Permian (285–286 Ma) Huisentala gabbro and Huodonghaer diorites from the Zhusileng–Hangwula Belt in the northern Alxa area. The gabbro is characterized by high Al, Ca, Mg# and light rare-earth elements, and low K, P and high field strength elements (e.g., Ti, Nb and Ta). Furthermore, the gabbro shows heterogeneous zircon ϵHf(t) value (−2.5 to +2.6). The Huodonghaer diorites show high MgO (3.46–6.32 wt%), Mg# (49–58), Sr (408–617 ppm) and Ba (223–419 ppm), and low FeOT/MgO (1.27–1.83) and TiO2 (0.48–0.90 wt%), with geochemical features similar to the high-Mg andesite/diorite. They show radiogenic zircon ϵHf(t) values of +1.2 to +4.9 and high Th/Nb ratios. These features suggest that the Huisentala gabbro and the Huodonghaer diorites were derived from the partial melting of mantle peridotite that was metasomatized by subduction-related fluids and by subducted sediment-derived melts, respectively.

Pie charts are often used to communicate risk, such as the risk of driving. In the foreground-background salience effect (FBSE), foreground (probability of bad event) has greater salience than background (no bad event) in such a chart. Experiment 1 confirmed that the displays format of pie charts showed a typical FBSE. Experiment 2 showed that the FBSE resulted from a difference in cognitive efforts in processing the messages and that a foreground-emphasizing display was easier to process. Experiment 3 manipulated subjects’ information processing mindset and explored the interaction between displays format and information processing mindset. In the default mindset, careless subjects displayed a typical FBSE, while those who were instructed to be careful reported similar risk-avoidant behavior preference reading both charts. Suggestions for improving risk communication are discussed.

The meta-surface is introduced into the design of band-notched monopole antennas with single/dual/triple notched bands around 3.6/5.5/7.2 GHz for ultra-wideband (UWB) communication. We show that strong coupling effects between the meta-surface and the antenna would be created through tuning the orientations of the meta-cells according to the field distributions on the antenna surface, and eventually, filter the unwanted radiations of the antenna. Especially, by simply attaching different meta-surfaces on the back of the antenna, the band-notched properties are shown to be changeable without hurting the original structure of the antenna. Both simulation and measurement results demonstrate the monopole with replaceable meta-surfaces has achieved an UWB operating band ranging from 3 to 9 GHz for voltage standing wave ratio (VSWR) ≤ 2 with single/dual/triple notched bands covering frequencies around 3.6/5.5/7.2 GHz. Such a design would obtain significant notched performances for the desired bands and maintain the good radiations in the operating frequency, which make it a suitable candidate for UWB applications.

To assess the role of dietary creatine on myofibre characteristics and protein synthesis in muscle, we fed grass carp (Ctenopharyngodon idellus, initial body weight: 88·47 ± 1·44 g) creatine-supplemented diets (1·84, 5·91, 8·48 and 15·44 g/kg diet) for 8 weeks. Creatine supplementation did not affect growth performance, but significantly increased creatine contents in muscle and liver. At 8·48 g/kg, creatine decreased the activities of alanine transaminase and aspartate aminotransferase in serum and improved hardness and chewiness of muscle due to shorter myofibre mean diameter, higher myofibre density and the frequencies of the diameters of classes I and III and collagen content, longer sarcomere length and upregulated mRNA levels of slow myosin heavy chains. Creatine supplementation upregulated the mRNA expressions of myogenic regulatory factors. The 8·48 g/kg creatine-supplemented diet significantly increased the contents of protein, total amino acids (AA), essential AA and free flavour AAs in muscle, the protein levels of insulin-like growth factor I, myogenic differentiation antigen and PPAR-γ coactlvator-1α in muscle and stimulated the phosphorylation of target of rapamycin (TOR) pathway in muscle. In summary, 8·48 mg/kg creatine improved fish health and skeletal muscle growth and increased hardness and protein synthesis in muscle of grass carp by affecting myofibre characteristics and the TOR signalling pathway. A second-order regression model revealed that the optimal dietary creatine supplementation of grass carp ranges between 8·48 and 12·04 g/kg.

There is limited evidence on fruit and vegetable intake in relation to cognitive function. This study aimed to evaluate the associations of quantity and variety in fruit and vegetable intake in midlife with cognitive impairment in late life. We used data from 16 737 participants of the Singapore Chinese Health Study, a population-based cohort study. The participants provided dietary data at recruitment at median age of 52·5 (range: 45–74) years and also participated in the third follow-up interview 20 years later at median age of 72·2 (range: 61–96) years. Quantity and variety of fruits and vegetables consumed at baseline were measured using a validated FFQ. Cognitive impairment at the third follow-up was defined using a Singapore-modified version of Mini-Mental State Examination. About 14·3 % participants had cognitive impairment. In multivariable logistic regression models, comparing extreme quartiles for intake of fruits and vegetables combined, the OR (95 % CI) associated with cognitive impairment was 0·83 (95 % CI: 0·73, 0·95; P-trend = 0·006) for quantity and 0·76 (95 % CI: 0·67, 0·87; P-trend< 0·001) for variety scores. Independently, those with increased variety of fruit intake or higher quantity of vegetable intake also had significantly 22 % and 15 % reduced odds of cognitive impairment, respectively. Finally, compared with those with low intake for both quantity and variety, those with both high quantity and variety for fruits and vegetables had 23 % reduction in odds of cognitive impairment. In conclusion, increase in quantity and variety of fruits and vegetables in midlife may reduce the risk of cognitive impairment in late life.

The aim of our study was to determine the distribution of hepatitis B virus (HBV) genotypes and subgenotypes in ethnic minorities in Yunnan province to provide evidence supporting the theoretical basis for hepatitis B prevention and control. We obtained serum samples and demographic data from 765 individuals reported by Yunnan province who had either acute or chronic HBV infection and were from one of 20 ethnic minority populations: Achang, Bai, Brown, Tibetan, Dai, Deang, Dulong, Hani, Hui, Jingpo, Lahu, Yi, Lisu Miao, Naxi, Nu, Pumi, Wa, Yao, or Zhuang people. We sequenced the HBV DNA and determined the genotypes and subgenotypes of the isolated HBVs. We mapped the genotype and subgenotype distribution by ethnic minority population and conducted descriptive analyses. There were four genotypes among the 20 ethnic groups: genotype B (21.3% of samples), C (76.6%), D (1.8%) and I (0.3%). The most common subgenotype was C1. There were no genotype differences by gender (P = 0.954) or age (P = 0.274), but there were differences by region (P < 0.001). There were differences in genotype distribution (P < 0.001) and subgenotype distribution (P = 0.011) by ethnic group. Genotype D was most prominent in Tibet and most HBV isolates were C/D recombinant viruses. The only two genotype I virus isolates were in Zhuang people. Susceptibility and geographic patterns may influence HBV prevalence in different ethnic populations, but additional research is needed for such a determination.