We study the sets of points where a Lévy function and a translated Lévy function share a given couple of Hölder exponents, and we investigate how their Hausdorff dimensions depend on the translation parameter.

In this paper, we numerically investigate the orbit dynamics of three-dimensional symmetric Janus drops in shear flow using an improved ternary-fluids phase field method, focusing on how drop deformation and initial orientation affect the orbit drift of two configurations of Janus drops: dumbbell-shaped and near-spherical. We find that the motion of dumbbell-shaped drops eventually evolves into tumbling, while near-spherical drops attain stable spinning. We attribute this bifurcation in orbit drift to contrasting deformation dynamics and shape-dependent hydrodynamics of the two configurations. Specifically, the drift bifurcation is closely related to the aspect ratio of Janus drops at equilibrium, giving rise to two distinct mechanisms: (1) coupling between outer interface deformation and the surrounding flow field; and (2) interplay between inner interface deformation and vortices enclosed within the drop. In addition, we observe that for the dumbbell-shaped Janus drops with different aspect ratios, their tumbling dynamics resembles ellipsoids in shear flow. Moreover, the trajectories of the dumbbell-shaped Janus drops during orbit drift collapse onto a universal curve, independent of their initial orientations, and significant deformation and inertia accelerate the orbit transition. To quantitatively evaluate the effect of drop deformation on the orbit drift of the dumbbell-shaped Janus drops, we propose an effective aspect ratio model based on the drop shapes at equilibrium and at the maximum elongation. By incorporating the effective aspect ratio into Jeffery’s theory for solid particles, we accurately predict the rotation period and angular velocity of Janus drops in the tumbling regime and during the orbit drift, especially for drops with linear deformation. Moreover, the orbit parameter $C$ is found to vary exponentially with time for drops with linear deformation, while the time variation of $C$ transits from one exponential function to another for drops with nonlinear deformation.

Previous studies highlighted the health benefits of coffee and tea, but they only focused on the comparisons between different consumptions. Consequently, the association estimate lacked a clear interpretation, as the substitution of beverages and distribution of doses were not explicitly prescribed. We focused on the ‘relative association’ to ascertain the optimal consumption strategy (including total intake and optimal allocation strategy) for coffee, tea and plain water associated with decreased mortality. Self-reported coffee, tea and plain water intake were used from the UK Biobank. Within a compositional data analysis framework, a multivariate Cox model was used to assess the relative associations after adjusting for a range of potential confounders. The lower mortality risk was observed with at least approximately 7–8 drinks/d of total consumption. When the total intake > 4 drinks/d, substituting plain water with coffee or tea was linked to reduced mortality; nevertheless, the benefit was not seen for ≤ 4 drinks/d. Besides, a balanced consumption of coffee and tea (roughly a ratio of 2:3) associated with the lowest hazard ratios of 0·55 (95 % CI 0·47, 0·64) for all-cause mortality, 0·59 (95 % CI 0·48, 0·72) for cancer mortality, 0·69 (95 % CI 0·49, 0·99) for CVD mortality, 0·28 (95 % CI 0·15, 0·52) for respiratory disease mortality and 0·35 (95 % CI 0·15, 0·82) for digestive disease mortality than other combinations. These results highlight the importance of the rational combination of coffee, tea and plain water, with particular emphasis on ensuring adequate total intake, offering more comprehensive and explicit guidance for individuals.

As the global elderly population expands, the associated risks of longevity intensify, presenting significant challenges to traditional retirement security systems. We study actuarial fairness in tontines under the Volterra mortality framework, integrating long-range dependence mortality models rates with tontine structures. Initially, we establish an optimal tontine model for a homogeneous tontine under this framework. However, according only to individual actuarial fairness can neglect the collective nature of tontines. So we propose a hybrid optimization model that accounts for age and wealth discrepancies affecting payment amounts and the collective fairness. Specially, we first apply the f-value fairness measure in age-heterogeneous tontines for assessing fairness. Our results reveal that while the model ensures actuarial fairness at the group level, relative payments are lower for older age groups. By incorporating dynamic mortality modeling through the Volterra mortality framework, our work demonstrates that this comprehensive scheme significantly enhances the robustness and sustainability of retirement security systems. These findings provide valuable insights for the future integration of dynamic mortality models with innovative retirement income structures.

Intestinal health challenges – including dysbiosis, inflammatory disorders, and pathogen susceptibility – impose severe economic losses and welfare concerns in intensive livestock production. Functional lipids, defined as bioactive lipid molecules with physiological benefits beyond basic nutrition, offer promising solutions to these issues. This review establishes a comprehensive definition of functional lipids and elucidates their metabolic process. Using short- and medium-chain fatty acid glycerides as a prime example, we examine their significant roles in energy homeostasis, gut microbiota composition and diversity, immune modulation, and antibacterial and antiviral activities. Additionally, we critically evaluate their current applications and future industrial potential in livestock production, providing evidence-based recommendations for their optimal implementation in animal nutrition strategies.

The incorporation of trace metals into land snail shells may record the ambient environmental conditions, yet this potential remains largely unexplored. In this study, we analyzed modern snail shells (Cathaica sp.) collected from 16 sites across the Chinese Loess Plateau to investigate their trace metal compositions. Our results show that both the Sr/Ca and Ba/Ca ratios exhibit minimal intra-shell variability and small inter-shell variability at individual sites. A significant positive correlation is observed between the shell Sr/Ca and Ba/Ca ratios across the plateau, with higher values being recorded in the northwestern sites where less monsoonal rainfall is received. We propose that shell Sr/Ca and Ba/Ca ratios, which record the composition of soil solution, may be controlled by the Rayleigh distillation in response to prior calcite precipitation. Higher rainfall amounts may lead to a lower degree of Rayleigh distillation and thus lower shell Sr/Ca and Ba/Ca ratios. This is supported by the distinct negative correlation between summer precipitation and shell Sr/Ca and Ba/Ca ratios, enabling us to reconstruct summer precipitation amounts using the Sr/Ca and Ba/Ca ratios of Cathaica sp. shells. The potential application of these novel proxies may also be promising for other terrestrial mollusks living in the loess deposits globally.

Human milk oligosaccharides offer unique benefits for infant growth and development. Buffalo milk, characterized by a mild flavor and high nutritional value, has attracted considerable interest. To characterize the oligosaccharide profile and composition of buffalo milk, we conducted qualitative and quantitative analysis of milk oligosaccharides at the early- and late-lactation stages of crossbred (Nili-Ravi × Murrah × local) buffaloes from Guangxi, China. The results revealed a total of 97 oligosaccharides including 17 novel oligosaccharides, with concentrations of 416.6 ± 25.86 and 368.3 ± 10.29 mg/L in milk from early- and late-lactation stages, respectively. The most abundant oligosaccharides were 3’-sialyllactose (3’-SL), difucosyllactose (DFL), 6’-sialyllactose (6’-SL), and a newly discovered compound, 2142. The oligosaccharides in crossbred (Nili-Ravi × Murrah × local) buffaloes demonstrated greater diversity than those found in the milk of other dairy animals, highlighting its potential as a high-quality nutritional resource for adults and infants.

The high comorbidity of major depressive disorder (MDD), anxiety disorders (ANX), and post-traumatic stress disorder (PTSD) complicates the study of their structural neural correlates, particularly in white matter (WM) alterations. Using fractional anisotropy (FA), this meta-analysis aimed to identify both unique and shared WM characteristics for these disorders by comparing them with healthy controls (HC). The aggregated sample size across studies includes 3,661 individuals diagnosed with MDD, ANX, or PTSD and 3,140 HC participants. The whole-brain analysis revealed significant FA reductions in the corpus callosum (CC) across MDD, ANX, and PTSD, suggesting a common neurostructural alteration underlying these disorders. Further pairwise comparisons highlighted disorder-specific differences: MDD patients showed reduced FA in the middle cerebellar peduncles and bilateral superior longitudinal fasciculus II relative to ANX patients and decreased FA in the CC extending to the left anterior thalamic projections (ATPs) when compared with PTSD. In contrast, PTSD patients exhibited reduced FA in the right ATPs compared to HC. No significant FA differences were observed between ANX and PTSD or between ANX and HC. These findings provide evidence for both shared and unique WM alterations in MDD, ANX, and PTSD, reflecting the neural underpinnings of the clinical characteristics that distinguish these disorders.

Femoral neck bone mineral density (FNBMD) is a high risk factor for femoral head fractures, and coffee intake affects bone mineral density, but the effect on FNBMD remains to be explored. First, we conducted an observational study in the National Health and Nutrition Examination Survey and collected data on coffee intake, FNBMD, and sixteen covariates. Weight linear regression was used to explore the association of coffee intake with FNBMD. Then, Mendelian randomisation (MR) was used to explore the causal relationship between coffee intake and FNBMD, the exposure factor was coffee intake, and the outcome factor was FNBMD. The inverse variance weighting (IVW) method was used for the analysis, while heterogeneity tests, sensitivity, and pleiotropy analysis were performed. A total of 5 915 people were included in the cross-sectional study, including 3 178 men and 2 737 women. In the completely adjusted model, no coffee was used as a reference. The ORs for the overall population at ‘< 1’, ‘1–<2’, ‘2–<4’, and ‘4+’ (95% CI) were 0.02 (–0.01, 0.04), 0.00 (–0.01, 0.02), –0.01 (–0.02, 0.00), and 0.00 (–0.01, 0.02), respectively. The male and female population showed no statistically significant differences in both univariate and multivariate linear regressions. In the MR study, the IVW results showed an OR (95% CI) of 1.06 (0.88–1.27), a P-value of 0.55, and an overall F-value of 80.31. The heterogeneity, sensitivity analyses, and pleiotropy had no statistical significance. Our study used cross-sectional studies and MR to demonstrate that there is no correlation or causal relationship between coffee intake and FNBMD.

Active fluids encompass a wide range of non-equilibrium fluids, in which the self-propulsion or rotation of their units can give rise to large-scale spontaneous flows. Despite the diversity of active fluids, they are commonly viscoelastic. Therefore, we develop a hydrodynamic model of isotropic active liquids by accounting for their viscoelasticity. Specifically, we incorporate an active stress term into a general viscoelastic liquid model to study the spontaneous flow states and their transitions in two-dimensional channel, annulus and disk geometries. We have discovered rich spontaneous flow states in a channel as a function of activity and Weissenberg number, including unidirectional flow, travelling-wave and vortex-roll states. The Weissenberg number acts against activity by suppressing the spontaneous flow. In an annulus confinement, we find that a net flow can be generated only if the aspect ratio of the annulus is not too large nor too small, akin to some three-dimensional active-flow phenomena. In a disk geometry, we observe a periodic chirality switching of a single vortex flow, resembling the bacteria-based active fluid experiments. The two phenomena reproduced in our model differ in Weissenberg number and frictional coefficient. As such, our active viscoelastic model offers a unified framework to elucidate diverse active liquids, uncover their connections and highlight the universality of dynamic active-flow patterns.

Bombyx mori Tryptophanyl-tRNA synthetase (BmWARS) belongs to the family of Ic-like aminoacyl-tRNA synthetases (aaRSs), whose specific recognition of the substrate Trp, tRNA, maintains the fidelity of protein synthesis. In this study, BmWARS was cloned and characterized from the midgut of the silkworm, Bombyx mori, resulting in an open reading frame (ORF) with a full length of 1,149 bp, which can encode 382 Aa. BmWARS is localized in the cytoplasm, and is expressed in all tissues of the silkworm, with higher expression in the testis, ovary, silk gland and malpighian tubule. The expression of BmWARS was significantly up-regulated in the midgut and silk gland after infection with Bombyx mori nuclear polyhedrosis virus (BmNPV). In addition, overexpression of BmWARS inhibited BmNPV infection and replication extremely significantly, while interference with BmWARS expression promoted BmNPV infection and replication. Analysis of the immune pathways in which BmWARS may be involved revealed that the expression of the key genes of the PI3K-Akt pathway, BmPI3K, BmAkt, BmPDK1, BmeIF4E, BmS6, and p-Akt protein was significantly reduced, whereas the expression of BmPTEN, BmFoxO, and BmCaspase9 was significantly increased in the cells that overexpressed BmWARS and were infected with BmNPV. Meanwhile, the results of the study interfering with the expression of BmWARS were completely opposite to those of the study overexpressing BmWARS. This is the first report that BmWARS has antiviral effects in Bombyx mori. Moreover, BmWARS inhibits BmNPV infection and replication in Bombyx mori cells by promoting apoptosis and inhibiting cell proliferation.

The betatron radiation source features a micrometer-scale source size, a femtosecond-scale pulse duration, milliradian-level divergence angles and a broad spectrum exceeding tens of keV. It is conducive to the high-contrast imaging of minute structures and for investigating interdisciplinary ultrafast processes. In this study, we present a betatron X-ray source derived from a high-charge, high-energy electron beam through a laser wakefield accelerator driven by the 1 PW/0.1 Hz laser system at the Shanghai Superintense Ultrafast Laser Facility (SULF). The critical energy of the betatron X-ray source is 22 ± 5 keV. The maximum X-ray flux reaches up to 4 × 109 photons for each shot in the spectral range of 5–30 keV. Correspondingly, the experiment demonstrates a peak brightness of 1.0 × 1023 photons·s−1·mm−2·mrad−2·0.1%BW−1, comparable to those demonstrated by third-generation synchrotron light sources. In addition, the imaging capability of the betatron X-ray source is validated. This study lays the foundation for future imaging applications.