We investigate trace and observability inequalities for Laplace eigenfunctions on the d-dimensional torus $\mathbb {T}^d$, with respect to arbitrary Borel measures $\mu $. Specifically, we characterize the measures $\mu $ for which the inequalities

$$ \begin{align*} \int |u|^2 \mathop{}\!\mathrm{d}\mu \lesssim \int |u|^2 \mathop{}\!\mathrm{d} x \quad \text{(trace)}, \qquad \int |u|^2 \mathop{}\!\mathrm{d}\mu \gtrsim \int |u|^2 \mathop{}\!\mathrm{d} x \quad \text{(observability)} \end{align*} $$

hold uniformly for all eigenfunctions u of the Laplacian. Sufficient conditions are derived based on the integrability and regularity of $\mu $, while necessary conditions are formulated in terms of the dimension of the support of the measure. These results generalize classical theorems of Zygmund and Bourgain–Rudnick to higher dimensions. Applications include results in the spirit of Cantor–Lebesgue theorems, constraints on quantum limits, and control theory for the Schrödinger equation. Our approach combines several tools: the cluster structure of lattice points on spheres; decoupling estimates; and the construction of eigenfunctions exhibiting strong concentration or vanishing behavior, tailored respectively to the trace and observability inequalities.

The traditional design of laser drivers for inertial confinement fusion (ICF) is highly dependent on coherent laser light fields, which have significant advantages in achieving harmonic conversion and enhancing amplification efficiency. However, they also bring the core challenge of achieving uniform irradiation. This paper investigates the dynamic evolution process of uniform irradiation of multi-mode spatiotemporal light fields and analyzes the influence mechanism of spatiotemporal coherence on irradiation uniformity with different integration times. By balancing the relationship between the spatiotemporal coherence of the light field and uniform irradiation, we explore a possible scheme to alleviate the beam smoothing problem while satisfying the basic requirements of laser amplification and high-efficiency harmonic conversion. Based on this scheme, the overall architecture of the ICF laser driver is constructed.

Laser-driven plasma wakefield acceleration (LWFA) offers exceptionally high acceleration gradients and can produce high-brightness electron beams. However, the laser-to-electron energy conversion efficiency typically remains limited to a few percent. Theoretically, the self-mode transition from LWFA to beam-driven plasma wakefield acceleration (PWFA) provides a pathway for fully utilizing the laser energy. Here, we demonstrate the single-stage LPWFA (hybrid LWFA–PWFA) scheme, validated through comparative experiments using a 300 TW tightly focused laser interacting with sub-critical density nitrogen gas targets. The experiments produce an electron beam with charge of approximately 31 nC above 6 MeV and approximately 116 nC above 2 MeV. The laser-to-electron energy conversion efficiency is approximately 6.1% (>6 MeV) and 16.4% (>2 MeV), respectively. Particle-in-cell simulations confirm that the single-stage LPWFA mechanism depletes the laser energy and enables continual electron injection. This high-charge, multi-MeV electron beam has great value in the generation of high-brightness $\unicode{x3b3}$-rays and high-flux neutron sources.

Alfalfa is a widely cultivated forage crop with high nutritional value, and it relies heavily on pollinators for successful reproduction owing to its keel petal structure. Numerous studies have shown the differences in pollinator diversity at different landscapes and/or regions, subsequently impacting plant reproduction. However, there is still insufficient evidence on variation in pollinator diversity at different sites with different landscapes and its effects on alfalfa reproduction. In this study, we investigated the diversity and abundance of floral visitors, and their impacts on alfalfa seed yield, across three sites represented by different landscapes, i.e. urban (Gongzhuling), semi-natural grassland (Changling), and farmland (Harbin) in north-eastern China. Our results showed that the diversity and abundance of all visitors, including bees in Changling were significantly higher than those of the other two sites. Changes in visitor diversity and abundance of alfalfa were closely related to climate variables, with positive effects of air temperature, and complex effects of precipitation. Meanwhile, the differences in pollinators may also be attributed to landscape types due to different habitat heterogeneity. Alfalfa seed yield in Changling was also significantly higher than that in the other two sites. Among these factors, air temperature, and diversity of floral visitors, particularly bees were positively related to alfalfa seed yield, indicating that pollinators combined with climate have an important contribution to changes in alfalfa seed yield. The findings from this study emphasise the importance of conserving pollinators to sustain and even enhance alfalfa yields, especially in the context of climate change and alterations in landscape types.

Contrafreeloading (CFL) refers to animals’ tendency to prefer obtaining food through effort rather than accessing food that is freely available. Researchers have proposed various hypotheses to explain this intriguing phenomenon, but few studies have provided a comprehensive analysis of the factors influencing this behaviour. In this study, we observed the choice of alternative food containers in budgerigars (Melopsittacus undulatus) to investigate their CFL tendencies and the effects of pre-training, food deprivation, and effort required on the CFL tasks. The results showed that budgerigars did not exhibit significant difference in their first choices or the time interacting with less challenging versus more challenging food containers. Moreover, when evaluating each budgerigar’s CFL level, only half of them were identified as strong contrafreeloaders. Thus, we suggest that budgerigars exhibit an intermediate CFL level that lies somewhere between a strong tendency and the absence of such behaviour. Furthermore, we also found that food-deprived budgerigars tended to select less challenging food containers, and pre-trained budgerigars were more likely to choose highly challenging food containers than moderately challenging food containers, which means that the requirement of only a reasonable effort (access to food from moderately challenging food containers in this study) and the experience of pre-training act to enhance their CFL levels, whereas the requirement of greater effort and the experience of food deprivation act to decrease their CFL levels. Studying animal CFL can help understand why animals choose to expend effort to obtain food rather than accessing it for free, and it also has implications for setting feeding environments to enhance the animal welfare of captive and domesticated animals.

An advanced deformable Kirkpatrick–Baez (K-B) mirror system was developed, equipped with high-speed piezoelectric actuators, and designed to induce beam decoherence and significantly enhance the quality of X-ray imaging by minimizing undesirable speckles in synchrotron radiation or free-electron laser facilities. Each individual mirror is engineered with 36 independent piezoelectric actuators that operate in a randomized manner, orchestrating the mirror surface to oscillate at a high frequency up to 100 kHz. Through in situ imaging single-slit diffraction measurement, it has been demonstrated that this high-frequency-vibration mirror system is pivotal in disrupting the coherent nature, thereby diminishing speckle formation. The impact of the K-B mirror system is profound, with the capability to reduce the image contrast to as low as 0.04, signifying a substantial reduction in speckle visibility. Moreover, the coherence of the X-ray beam is significantly lowered from an initial value exceeding 80% to 13%.

Coccidiosis is a parasitic disease caused by Eimeria spp., and the emergence of drug resistance has seriously affected the control of the disease. Using RNA-seq, we previously found that phosphoglycerate kinase of Eimeria tenella (EtPGK) was differentially downregulated in diclazuril-resistant (DZR) and maduramicin-resistant (MRR) strains compared with drug-sensitive (DS) strain. In this study, we further analysed the characteristics and functions of EtPGK to find the possible mechanism of drug resistance of E. tenella. Quantitative real-time PCR (qRT-PCR) and western blot found that EtPGK was highly expressed in sporulated oocysts, followed by sporozoites and second-generation merozoites of E. tenella. Indirect immunofluorescence localization showed that EtPGK was located mainly in the cytoplasm and on the surface of the parasites. Invasion inhibition assays showed that anti-rEtPGK antibody significantly inhibited the invasion of parasites. Further studies using qRT-PCR and western blot found that the transcription and translation levels of EtPGK were downregulated in both resistant (DZR and MRR) strains compared with the DS strain, and the transcription level correlated negatively with the drug concentration. The enzyme activity assay revealed that EtPGK enzyme activity was decreased in the DZR strain compared with the DS strain. qRT-PCR revealed that the mRNA transcription level of EtPGK was significantly downregulated in the field DZR strain and salinomycin-resistant strain compared with the DS strain. These results suggested that EtPGK has other important roles that are separate and distinct from its function in glycolysis, and it might be involved in the development of drug resistance of E. tenella.

Previous animal studies found beneficial effects of choline and betaine on maternal glucose metabolism during pregnancy, but few human studies explored the association between choline or betaine intake and incident gestational diabetes mellitus (GDM). We aimed to explore the correlation of dietary choline or betaine intake with GDM risk among Chinese pregnant women. A total of 168 pregnant women with GDM cases and 375 healthy controls were enrolled at the Seventh People’s Hospital in Shanghai during their GDM screening at 24–28 gestational weeks. A validated semi-quantitative FFQ was used to estimate choline and betaine consumption through face-to-face interviews. An unconditional logistic regression model was adopted to examine OR and 95 % CI. Compared with the controls, those women with GDM incidence were likely to have higher pre-pregnancy BMI, be older, have more parities and have higher plasma TAG and lower plasma HDL-cholesterol. No significant correlation was observed between the consumption of choline or betaine and incident GDM (adjusted OR (95 % CI), 0·77 (0·41, 1·43) for choline; 0·80 (0·42, 1·52) for betaine). However, there was a significant interaction between betaine intake and parity on the risk of GDM (Pfor interaction = 0·01). Among those women with no parity history, there was a significantly inverse correlation between betaine intake and GDM risk (adjusted OR (95 % CI), 0·25 (0·06, 0·81)). These findings indicated that higher dietary betaine intake during pregnancy might be considered a protective factor for GDM among Chinese women with no parity history.

The assessment of seed quality and physiological potential is essential in seed production and crop breeding. In the process of rapid detection of seed viability using tetrazolium (TZ) staining, it is necessary to spend a lot of labour and material resources to explore the pretreatment and staining methods of hard and solid seeds with physical barriers. This study explores the TZ staining methods of six hard seeds (Tilia miqueliana, Tilia henryana, Sassafras tzumu, Prunus subhirtella, Prunus sibirica, and Juglans mandshurica) and summarizes the TZ staining conditions required for hard seeds by combining the difference in fat content between seeds and the kinship between species, thus providing a rapid viability test method for the protection of germplasm resources of endangered plants and the optimization of seed bank construction. The TZ staining of six species of hard seeds requires a staining temperature above 35 °C and a TZ solution concentration higher than 1%. Endospermic seeds require shorter staining times than exalbuminous seeds. The higher the fat content of the seeds, the lower the required incubation temperature and TZ concentration for staining, and the longer the staining time. And the closer the relationship between the two species, the more similar their staining conditions become. The TZ staining method of similar species can be predicted according to the genetic distance between the phylogenetic trees, and the viability of new species can be detected quickly.

Spermatogenesis is a developmental process driven by interactions between germ cells and Sertoli cells. This process depends on appropriate gene expression, which might be regulated by transcription factors. This study focused on Rreb1, a zinc finger transcription factor, and explored its function and molecular mechanisms in spermatogenesis in a mouse model. Our results showed that RREB1 was predominantly expressed in the Sertoli cells of the testis. The decreased expression of RREB1 following injection of siRNA caused impaired Sertoli cell development, which was characterized using a defective blood–testis barrier structure and decreased expression of Sertoli cell functional maturity markers; its essential trigger might be SMAD3 destabilization. The decreased expression of RREB1 in mature Sertoli cells influenced the cell structure and function, which resulted in abnormal spermatogenesis, manifested as oligoasthenoteratozoospermia, and we believe RREB1 plays this role by regulating the transcription of Fshr and Wt1. RREB1 has been reported to activate Fshr transcription, and we demonstrated that the knockdown of Rreb1 caused a reduction in follicle-stimulating hormone receptor (FSHR) in the testis, which could be the cause of the increased sperm malformation. Furthermore, we confirmed that RREB1 directly activates Wt1 promoter activity, and RREB1 downregulation induced the decreased expression of Wt1 and its downstream polarity-associated genes Par6b and E-cadherin, which caused increased germ-cell death and reduced sperm number and motility. In conclusion, RREB1 is a key transcription factor essential for Sertoli cell development and function and is required for normal spermatogenesis.

Essential oils (including carvacrol, CAR) have been used in the medicinal and health field because of their broad-spectrum antibacterial activities. However, the volatility and pungent odor are still the greatest obstacles to wider application. The purpose of the present study was to address those problems by encapsulating the antibacterial CAR in palygorskite (Plg) by integrating it into Pickering emulsions with complex coacervation. The CAR in Pickering emulsion was formed firstly by stabilization with the CAR-modified Plg; then, the emulsion droplets were embedded and fixed in the microcapsule through the subsequent complex coacervation process, which occurred between the quaternary ammonium salt of chitooligosaccharides (HACC) and sodium alginate (SA) via calcium ions. The microcapsules obtained were characterized by Fourier-transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), and thermogravimetric analysis (TGA). The results demonstrated that the microcapsules presented a nearly sphere-like shape with a mean diameter of 3.5 mm but had a porous interior structure. The Plg plays multiple roles in the preparation process, including increasing the emulsion stability, improving the encapsulation efficiency of CAR, and the thermostability of microcapsules. The microcapsules showed remarkable antibacterial properties against Escherichia coli (E. coli) and Staphylococcus aureus (S. aureus), and inhibition rates toward E. coli and S. aureus reached 100% when the microcapsules were encapsulated with 15 or 20% of CAR, respectively. The microcapsules obtained could be used as antibacterial agents in food preservatives, animal feed, and other health-related consumer products.