Let C and W be two integer sets. If $C+W=\mathbb {Z}$, then we say that C is an additive complement to W. If no proper subset of C is an additive complement to W, then we say that C is a minimal additive complement to W. We study the existence of a minimal additive complement to $W=\{w_i\}_{i=1}^{\infty}$ when W is not eventually periodic and $w_{i+1}-w_{i}\in \{2,3\}$ for all i.

Significant differences in life-history traits between the southern population (S) and northern (N) population of the cabbage beetle Colaphellus bowringi make it an excellent model for studying inheritance in this insect. In the present study, we observed the life-history traits of pure strains, F1, reciprocal backcross and reciprocal F2 progeny under a photoperiod of L:D 15:9 h at 22 °C. The S population had shorter larval development time, longer pupal time, higher body weight, growth rate and weight loss compared with the N population. In the F1 testing, the larval development time and body weight in hybrid populations were intermediate between the parents, and the paternal parents played a greater role in determining the larval development time, while the maternal parents exhibited a greater role in determining the body weight. The pupal time of hybrid populations was significantly shorter than that of the parents. In the reciprocal backcross testing, both father and grandfather affected the larval development time, while both mother and grandmother affected the body weight. Consistently, in the reciprocal F2 cross testing, the grandfather was more influential in determining the larval development time, and grandmother was more important in determining the body weight. In all tested populations, females had greater body weight, higher growth rate and weight loss than males. Hybridization pattern did not affect sex dimorphism and sex ratio. Overall, these findings suggest that different pathways (maternal or paternal effects) were involved in the inheritance of various life-history traits in C. bowringi.

The reading the mind in the eyes test (RMET) – which assesses the theory of mind component of social cognition – is often used to compare social cognition between patients with schizophrenia and healthy controls. There is, however, no systematic review integrating the results of these studies. We identified 198 studies published before July 2020 that administered RMET to patients with schizophrenia or healthy controls from three English-language and two Chinese-language databases. These studies included 41 separate samples of patients with schizophrenia (total n = 1836) and 197 separate samples of healthy controls (total n = 23 675). The pooled RMET score was 19.76 (95% CI 18.91–20.60) in patients and 25.53 (95% CI 25.19–25.87) in controls (z = 12.41, p < 0.001). After excluding small-sample outlier studies, this difference in RMET performance was greater in studies using non-English v. English versions of RMET (Chi [Q] = 8.54, p < 0.001). Meta-regression analyses found a negative association of age with RMET score and a positive association of years of schooling with RMET score in both patients and controls. A secondary meta-analysis using a spline construction of 180 healthy control samples identified a non-monotonic relationship between age and RMET score – RMET scores increased with age before 31 and decreased with age after 31. These results indicate that patients with schizophrenia have substantial deficits in theory of mind compared with healthy controls, supporting the construct validity of RMET as a measure of social cognition. The different results for English versus non-English versions of RMET and the non-monotonic relationship between age and RMET score highlight the importance of the language of administration of RMET and the possibility that the relationship of aging with theory of mind is different from the relationship of aging with other types of cognitive functioning.

In the absence of the necessary valley topography, karst depressions are sometimes used to construct conventional impoundments in order to contain tailings. Leakage is a primary concern for such impoundments. The purpose of the current study was to determine the characteristics and barrier performance of laterite mantling karst depressions, using, as an example, the Wujiwatang (WJWT) tailings impoundment, located in the Gejiu mining area, southwestern China. The geotechnical-hydrogeological properties, geochemistry, mineral compositions, and particle shapes of the laterite were investigated by geotechnical techniques, chemical analysis, X-ray diffraction (XRD), and scanning electron microscopy (SEM). The results showed that the laterite contained poorly sorted particles that covered a wide spectrum of grain sizes (<5 mm to <50 nm), and was unexpectedly categorized as silty clay or silt with a high liquid limit. The continuous gradation and small D90 value helped the laterite achieve saturated hydraulic conductivities in the range of <10–6 cm/s required for impoundment liners. The laterite beneath the tailings impoundment was finer-grained and had a lower permeability than that of the laterite on the depression walls within the same depression. Geochemically and mineralogically, the laterite was classified as true laterite and its major mineralogical constituents were gibbsite and goethite with chlorite occurring in trace amounts. The laterite was dominated by subspherolitic–spherolitic cohesionless grains (concretions) made up of Al, Fe, Ti, and Mn oxides and hydroxides. The laterite did not have plasticity indices in the clay range. Fortunately, slopewash prior to tailings containment selectively transported the finer oxide concretions to the depression floor, creating a natural low-permeability barrier for the WJWT tailings impoundment. This is undoubtedly important for the planning and design of future karst depression-type tailings impoundments around the world.

By combining the technique of energy selective surface and frequency selective rasorber, an energy selective rasorber is proposed, which performs selective energy protection in the low communication frequency band (0.8–2 GHz) and wave-absorbing property in the high-frequency band (6–18 GHz). The design consists of two layers, of which the bottom one contains a lumped diode structure for energy selection function in the transmission band, while together with the top layer, they perform a wideband wave absorbing function. The simulated and measured results agree well with each other, and both show good absorption in 6–18 GHz and energy-selective property around 1.86 GHz. That is, when the incident power changes from −30 to 14 dBm, the reflection coefficient changes from below −22 dB to above −2 dB, while the transmission coefficient changes from above −3 dB to below −17 dB.

Let $S=\{s_{1}, s_{2}, \ldots \}$ be an unbounded sequence of positive integers with $s_{n+1}/s_{n}$ approaching $\alpha $ as $n\rightarrow \infty $ and let $\beta>\max (\alpha , 2)$. We show that for all sufficiently large positive integers l, if $A\subset [0, l]$ with $l\in A$, $\gcd A=1$ and $|A|\geq (2-{k}/{\lambda \beta })l/(\lambda +1)$, where $\lambda =\lceil {k}/{\beta }\rceil $, then $kA\cap S\neq \emptyset $ for $2<\beta \leq 3$ and $k\geq {2\beta }/{(\beta -2)}$ or for $\beta>3$ and $k\geq 3$.

Given a Borel probability measure µ on $\mathbb{R}^n$ and a real matrix $R\in M_n(\mathbb{R})$. We call R a spectral eigenmatrix of the measure µ if there exists a countable set $\Lambda\subset \mathbb{R}^n$ such that the sets $E_\Lambda=\big\{{\rm e}^{2\pi i \langle\lambda,x\rangle}:\lambda\in \Lambda\big\}$ and $E_{R\Lambda}=\big\{{\rm e}^{2\pi i \langle R\lambda,x\rangle}:\lambda\in \Lambda\big\}$ are both orthonormal bases for the Hilbert space $L^2(\mu)$. In this paper, we study the structure of spectral eigenmatrix of the planar self-affine measure $\mu_{M,D}$ generated by an expanding integer matrix $M\in M_2(2\mathbb{Z})$ and the four-elements digit set $D = \{(0,0)^t,(1,0)^t,(0,1)^t,(-1,-1)^t\}$. Some sufficient and/or necessary conditions for R to be a spectral eigenmatrix of $\mu_{M,D}$ are given.

Shortawn foxtail (Alopecurus aequalis Sobol.) is an obligate wetland plant that is widely distributed throughout Europe, temperate Asia, and North America. In China, it is widespread in the middle and lower reaches of the Yangtze River as a noxious weed in winter cropping fields with a rice (Oryza sativa L.) rotation. The acetolactate synthase (ALS)-inhibiting herbicide mesosulfuron-methyl has been widely used to control annual grass and broadleaf weeds, including A. aequalis, in wheat (Triticum aestivum L.) fields, leading to the selection of herbicide-resistant weeds. In this study, an A. aequalis population, AHFT-4, that survived mesosulfuron-methyl at the field-recommended rate (9 g ai ha−1) was collected in Anhui Province. Single-dose testing confirmed that the suspected resistant AHFT-4 had evolved resistance to mesosulfuron-methyl. Target gene sequencing revealed a resistance mutation of Pro-197-Ala in ALS1 of the resistant plants, and a derived cleaved amplified polymorphic sequence marker was developed to specifically detect the mutation. A relative expression assay showed no significant difference in ALS expression between AHFT-4 and a susceptible population without or with mesosulfuron-methyl treatment. Whole-plant dose–response bioassays indicated that AHFT-4 had evolved broad-spectrum cross-resistance to ALS-inhibiting herbicides of all five chemical families tested, with GR50 resistance index (RI) values ranging from 21 to 206. However, it remained susceptible to the photosystem II inhibitor isoproturon. Pretreatment with the cytochrome P450 inhibitor malathion or the glutathione S-transferase inhibitor 4-chloro-7-nitrobenzoxadiazole had no significant effects on the resistance of AHFT-4 to mesosulfuron-methyl. To our knowledge, this study reports for the first time the ALS gene Pro-197-Ala substitution conferring broad-spectrum cross-resistance to ALS-inhibiting herbicides in A. aequalis.

Angiostrongylus cantonensis causes a form of parasitic meningitis in humans. Albendazole (ABZ) kills nematode larvae in the brain. However, dead larvae can trigger a severe inflammatory response, resulting in brain damage. Accumulating evidence suggests that calycosin represents a potential anti-inflammatory therapeutic candidate. In this study, we investigated the combined effects of ABZ and calycosin in angiostrongyliasis caused by A. cantonensis in BALB/c mice. Inflammatory mediators (such as phospho-nuclear factor-κB, cyclooxygenase-2, matrix metalloproteinase-9, tumour necrosis factor-α and interleukin-1β) are associated with the development of meningitis and immune inflammatory reactions. We found that A. cantonensis significantly induces inflammatory mediator production and increases the blood–brain barrier (BBB) permeability. However, co-administration of both ABZ and calycosin markedly suppressed meningitis and inflammatory mediator production and decreased the BBB permeability compared to treatment with a single drug. Furthermore, calycosin and ABZ plus calycosin treatment facilitated production of the antioxidant haem oxygenase-1 (HO-1). Moreover, co-therapy with ABZ and calycosin failed to mitigate angiostrongyliasis in the presence of tin-protoporphyrin IX, an HO-1-specific inhibitor. This finding suggests that the beneficial effects of ABZ plus calycosin treatment on the regulation of inflammation are mediated by the modulation of HO-1 activation. The present results provide new insights into the treatment of human angiostrongyliasis using co-therapy with ABZ and calycosin.

Let $h \geq 2$ be a positive integer. We introduce the concept of minimal restricted asymptotic bases and obtain some examples of minimal restricted asymptotic bases of order h.

Previous studies have reported inconsistent associations between low-carbohydrate diets (LCD) and plasma lipid profile. Also, there is little evidence on the role of the quality and food sources of macronutrients in LCD in cardiometabolic health. We investigated the cross-sectional associations between LCD and plasma cardiometabolic risk markers in a nationwide representative sample of the US population. Diet was measured through two 24-h recalls. Overall, healthy (emphasising unsaturated fat, plant protein and less low-quality carbohydrates) and unhealthy (emphasising saturated fat, animal protein and less high-quality carbohydrate) LCD scores were developed according to the percentage of energy as total and subtypes of carbohydrate, protein and fat. Linear regression was used to estimate the percentage difference of plasma marker concentrations by LCD scores. A total of 34 785 participants aged 18–85 years were included. After adjusting for covariates including BMI, healthy LCD was associated with lower levels of insulin, homoeostatic model assessment for insulin resistance (HOMA-IR), C-reactive protein (CRP) and TAG, and higher levels of HDL-cholesterol, with the percentage differences (comparing extreme quartile of LCD score) of −5·91, −6·16, −9·13, −9·71 and 7·60 (all Ptrend < 0·001), respectively. Conversely, unhealthy LCD was associated with higher levels of insulin, HOMA-IR, CRP and LDL-cholesterol (all Ptrend < 0·001). Our results suggest that healthy LCD may have positive, whereas unhealthy LCD may have negative impacts on CRP and metabolic and lipid profiles. These findings underscore the need to carefully consider the quality and subtypes of macronutrients in future LCD studies.

The occurrence of chalkiness has decreased in new hybrid rice cultivars in China. As both chalkiness occurrence and starch granule size are associated with the biosynthesis of starch, we hypothesized that there may be a correlation between chalkiness occurrence and starch granule size, and this may partially explain the decreased chalkiness occurrence in the new hybrid rice cultivars. To test this hypothesis, a field experiment was conducted over eight environments (two years × four sowing dates) with two hybrid rice cultivars: one recently developed with low chalkiness occurrence, Jingliangyou 1468 (JLY1468) and a relatively older cultivar with high chalkiness occurrence, Liangyoupeijiu (LYPJ). Results showed that JLY1468 had a higher cumulative distribution of large-diameter (7.51–19.50 μm) starch granules and a lower grain weight of milled rice compared to LYPJ. As a consequence, mean and relative starch granule diameters were 6% and 21% higher in JLY1468 than in LYPJ, respectively. Although both the chalky grain rate and chalkiness degree were negatively correlated with mean and relative starch granule diameter, they were more closely correlated with the relative granule diameter. These results support our hypothesis regarding the relationship between chalkiness occurrence and starch granule size and suggest that the relative starch granule diameter is a relevant parameter in understanding the occurrence of chalkiness in hybrid rice.

This paper investigates the monolithic edge-cladding process for the elliptical disk of N31-type Nd-doped phosphate laser glass, which will be utilized under liquid cooling conditions for high-power laser systems. The thermal stress, interface bubbles and residual reflectivity, which are due to high-temperature casting and bonding during the monolithic edge-cladding process, are simulated and determined. The applied mould is optimized to a rectangular cavity mould, and the casting temperature is optimized to 1000°C. The resulting lower bubble density makes the mean residual reflectivity as low as 6.75 × 10−5, which is enough to suppress the amplified spontaneous emission generated in the Nd-glass disk, and the resulting maximum optical retardation is converged to 10.2–13.3 nm/cm, which is a favourable base for fine annealing to achieve the stress specification of less than or equal to 5 nm/cm. After fine annealing at the optimized 520°C, the maximum optical retardation is as low as 4.8 nm/cm, and the minimum transmitted wavefront peak-to-valley value is 0.222 wavelength (632.8 nm). An N31 elliptical disk with the size of 194 mm × 102 mm × 40 mm can be successfully cladded by the optimized monolithic edge-cladding process, whose edge-cladded disk with the size of 200 mm × 108 mm × 40 mm can achieve laser gain one-third higher than that of an N21-type disk of the same size.

For a set A of positive integers and any positive integer n, let $R_{1}(A, n)$, $R_{2}(A,n)$ and $R_{3}(A,n)$ denote the number of solutions of $a+a^{\prime }=n$ with $a, a^{\prime }\in A$ and the additional restriction that $a<a^{\prime }$ for $R_{2}$ and $a\leq a^{\prime }$ for $R_{3}$. We consider Problem 6 of Erdős et al. [‘On additive properties of general sequences’, Discrete Math. 136 (1994), 75–99] about locally small and locally large values of $R_{1}, R_{2}$ and $R_{3}$.

We examined whether physical activity (PA) explains the association between dietary inflammatory potential and osteoarthritis (OA) in the elderly. A total of 1249 elderly people (≥65 years) were eligible for this study from the National Health and Nutrition Examination Survey (NHANES) from 2011 to 2016. The semi-quantitative Food Frequency Questionnaire (FFQ) and Global PA Questionnaire (GPAQ) were used to evaluate the diet and PA of the elderly, respectively. The multivariable logistic regression model estimated the odds ratio (OR) and 95% confidence interval (CI) between Energy-adjusted Dietary Inflammatory Index (E-DII) and OA. The interaction of E-DII and PA on depressive events was tested, and the mediation analysis of PA was performed. The average E-DII in this study was +0.68 (SE 0.08), and the score ranges from -5.32 (most anti-inflammatory) to +4.26 (most pro-inflammatory). In comparison with the first quartile, the elderly from the second quartile (OR: 1.16 [95% CI: 1.06, 1.68]) to the fourth quartile (OR: 1.64 [95% CI: 1.13, 2.37]) had a higher risk of OA before adjustment for PA. An interaction was observed between E-DII and PA in terms of the risk of OA (PInteraction < 0.001). The whole related part was mediated by PA (20.08%). Our findings indicated that the higher pro-inflammatory potential of diet was associated with a higher risk of OA, and low PA was an important part of the mediating factor in the relationship between systemic low-grade dietary inflammation and the risk of OA.