For a class of robustly transitive diffeomorphisms on ${\mathbb T}^4$ introduced by Shub [Topologically transitive diffeomorphisms of $T^4$. Proceedings of the Symposium on Differential Equations and Dynamical Systems (Lecture notes in Mathematics, 206). Ed. D. Chillingworth. Springer, Berlin, 1971, pp. 39–40], satisfying an additional bunching condition, we show that there exists a $C^2$ open and $C^r$ dense subset ${\mathcal U}^r$, $2\leq r\leq \infty $, such that any two hyperbolic points of $g\in {\mathcal U}^r$ with stable index $2$ are homoclinically related. As a consequence, every $g\in {\mathcal U}^r$ admits a unique homoclinic class associated to the hyperbolic periodic points with index $2$, and this homoclinic class coincides with the whole ambient manifold. Moreover, every $g\in {\mathcal U}^r$ admits at most one measure of maximal entropy, and every $g\in {\mathcal U}^{\infty }$ admits a unique measure of maximal entropy.

Recent studies have shown that superimposing rhythmic perturbations to oscillating tailbeats could simultaneously enhance both the thrust and efficiency (Lehn et al., Phys. Rev. Fluids, vol. 2, 2017, p. 023101; Chao et al., PNAS Nexus, vol. 3, 2024, p. 073). However, these investigations were conducted with a tethered flapping foil, overlooking the self-propulsion intrinsic to real swimming fish. Here, we investigate how the high-frequency, low-amplitude superimposed rhythmic perturbations impact the self-propelled pitching and heaving swimming of a rigid foil. The swimming-speed-based Reynolds number ranges from 1400 to 2700 in our study, depending on superimposed perturbations and swimming modes. Numerical results reveal that perturbations significantly increase swimming speeds in both pitching and heaving motions, while enhancing efficiency exclusively in the heaving motion. Further derived scaling laws elucidate the relationships of perturbations with speeds, power costs and efficiency, respectively. These findings not only hypothesise the potential advantages of perturbations in biological systems, but also inspire designs and controls in biomimetic propulsion and manoeuvring within aquatic environments.

Childhood maltreatment is an established risk factor for psychopathology. However, it remains unclear how childhood traumatic events relate to mental health problems and how the brain is involved. This study examined the serial mediation effect of brain morphological alterations and emotion-/reward-related functions on linking the relationship from maltreatment to depression. We recruited 156 healthy adolescents and young adults and an additional sample of 31 adolescents with major depressive disorder for assessment of childhood maltreatment, depressive symptoms, cognitive reappraisal and anticipatory/consummatory pleasure. Structural MRI data were acquired to identify maltreatment-related cortical and subcortical morphological differences. The mediation models suggested that emotional maltreatment of abuse and neglect, was respectively associated with increased gray matter volume in the ventral striatum and greater thickness in the middle cingulate cortex. These structural alterations were further related to reduced anticipatory pleasure and disrupted cognitive reappraisal, which contributed to more severe depressive symptoms among healthy individuals. The above mediating effects were not replicated in our clinical group partly due to the small sample size. Preventative interventions can target emotional and reward systems to foster resilience and reduce the likelihood of future psychiatric disorders among individuals with a history of maltreatment.

We use nearly two decades of helioseismic data obtained from the GONG (2002–2020) and HMI (2010–2020) ring-diagram pipelines to examine the temporal variations of the properties of individual equatorial Rossby modes with azimuthal orders in the range 6 ≤ m ≤ 10. We find that the mode parameters obtained from GONG and HMI are consistent during the data overlapping period of 2010–2020. The power and the frequency of each mode exhibit significant temporal variations over the full observing period. Using the GONG data during solar cycles 23 and 24, we find that the mode power averaged over 6 ≤ m ≤ 10 shows a positive correlation with the sunspot number (0.42), while the averaged frequency shift is anti-correlated (–0.91). The anti-correlation between the average mode power and frequency shift is –0.44.

The Sun’s global inertial modes are very sensitive to the solar differential rotation and to properties of the deep solar convection zone which are currently poorly constrained. These properties include the superadiabatic temperature gradient, the latitudinal entropy gradient, and the turbulent viscosity. The inertial modes also play a key role in controlling the Sun’s large-scale structure and dynamics, in particular the solar differential rotation. This paper summarizes recent observations and advances in the (linear and nonlinear) modeling of the solar inertial modes.

Purple nutsedge (Cyperus rotundus L.) is a globally distributed noxious weed that poses a significant challenge for control due to its fast and efficient propagation through the tuber, which is the primary reproductive organ. Gibberellic acid (GA3) has proven to be crucial for tuberization in tuberous plants. Therefore, understanding the relationship between GA3 and tuber development and propagation of C. rotundus will provide valuable information for controlling this weed. This study shows that the GA3 content decreases with tuber development, which corresponds to lower expression of bioactive GA3 synthesis genes (CrGA20ox, two CrGA3ox genes) and two upregulated GA3 catabolism genes (CrGA2ox genes), indicating that GA3 is involved in tuber development. Simultaneously, the expression of two CrDELLA genes and CrGID1 declines with tuber growth and decreased GA3, and yeast two-hybrid assays confirm that the GA3 signaling is DELLA-dependent. Furthermore, exogenous application of GA3 markedly reduces the number and the width of tubers and represses the growth of the tuber chain, further confirming the negative impact that GA3 has on tuber development and propagation. Taken together, these results demonstrate that GA3 is involved in tuber development and regulated by the DELLA-dependent pathway in C. rotundus and plays a negative role in tuber development and propagation.

The Viséan–Serpukhovian boundary is poorly defined in South China, hampering regional and global stratigraphical correlations. The foraminiferal and conodont distribution of the Baping Formation in the carbonate-slope Danlu section permits the recognition of an interval from the middle Viséan to the uppermost Serpukhovian in a continuous succession. The base of the Serpukhovian in Danlu is recognized by the first occurrences of Janischewskina delicata, Howchinia subplana and questionable ‘Millerella’ tortula. At a slightly younger level, the conodont Lochriea ziegleri is first recorded. A calibration on the first occurrence of L. ziegleri in different basins at a global scale has been revised compared to auxiliary markers within the ammonoids and foraminifers. The late occurrence of L. ziegleri in the Danlu section also supports a lack of synchronicity in the global first occurrence of this taxon. This study calls for the recognition of a new base for the Serpukhovian under a far better correlation between different zonal schemes and fossil groups.

Fat deposition and lipid metabolism are closely related to the morphology, structure and function of mitochondria. The morphology of mitochondria between fusion and fission processes is mainly regulated by protein posttranslational modification. Intermittent fasting (IF) promotes high expression of Sirtuin 3 (Sirt3) and induces mitochondrial fusion in high-fat diet (HFD)-fed mice. However, the mechanism by which Sirt3 participates in mitochondrial protein acetylation during IF to regulate mitochondrial fusion and fission dynamics remains unclear. This article demonstrates that IF promotes mitochondrial fusion and improves mitochondrial function in HFD mouse inguinal white adipose tissue. Proteomic sequencing revealed that IF increased protein deacetylation levels in HFD mice and significantly increased Sirt3 mRNA and protein expression. After transfecting with Sirt3 overexpression or interference vectors into adipocytes, we found that Sirt3 promoted adipocyte mitochondrial fusion and improved mitochondrial function. Furthermore, Sirt3 regulates the JNK-FIS1 pathway by deacetylating malate dehydrogenase 2 (MDH2) to promote mitochondrial fusion. In summary, our study indicates that IF promotes mitochondrial fusion and improves mitochondrial function by upregulating the high expression of Sirt3 in HFD mice, promoting deacetylation of MDH2 and inhibiting the JNK-FIS1 pathway. This research provides theoretical support for studies related to energy limitation and animal lipid metabolism.

This study aimed to explore the mediation effects of one-carbon metabolism (OCM) related nutrients on the association between MTHFR rs1801133 polymorphism and gestational diabetes mellitus (GDM). Folate, vitamin B12 and homocysteine (Hcy) were measured in the serum of 1254 pregnant women. Linear and logistic regressions were used to estimate the associations of OCM nutrients and MTHFR rs1801133 polymorphism with blood glucose levels and GDM risk. Mediation analysis was applied to test the mediation effects of folate, vitamin B12 and Hcy on the association of MTHFR rs1801133 polymorphism with blood glucose concentrations and GDM. Pregnant women with MTHFR rs1801133 CC genotype had higher serum folate (10·75 v. 8·90 and 9·40 ng/ml) and lower serum Hcy (4·84 v. 4·93 and 5·20 μmol/l) than those with CT and TT genotypes. Folate concentrations were positively associated with fasting plasma glucose (FPG), 1-h plasma glucose (1-h PG), 2-h plasma glucose (2-h PG) and GDM risk. Vitamin B12 levels were negatively correlated with FPG and GDM. Although no direct association was found between MTHFR rs1801133 genotypes and GDM, there were significant indirect effects of MTHFR rs1801133 CC genotype on FPG (β: 0·005; 95 % CI: 0·001, 0·013), 1-h PG (β: 0·006; 95 % CI: 0·001, 0·014), 2-h PG (β: 0·007; 95 % CI: 0·001, 0·015) and GDM (β: 0·006; 95 % CI: 0·001, 0·014) via folate. In conclusion, serum folate mediates the effect of MTHFR rs1801133 on blood glucose levels and GDM. Our findings potentially provide a feasible GDM prevention strategy via individualised folate supplementation according to the MTHFR genotypes.

The impact of Strouhal number St (= 0.1–1.0), Reynolds number Re (= 50–2000) and dimensionless wavelength λ (= 0.5–2.0) on the hydrodynamic performance of a travelling wavy foil of a constant length is extensively investigated. The relationship of time-mean thrust with St, Re and λ is presented, suggesting that the propulsive force increases with increasing St, Re and λ. As such, the drag–thrust boundary advances as these parameters increase. A shorter λ makes the thrust steadier while a longer λ enhances the maximum instantaneous thrust. The latter is beneficial for prey to escape from a predator. The fluid added mass caused by the foil oscillation increases with St and λ but declines with Re (<500). Seven types of wake structures produced by the foil are identified, discussed and connected to thrust generation, showing how St, Re and λ affect the fluid dynamics, wake transition, vortex strength, wake jet, velocity, added mass, added damping, power input, efficiency and pressure profiles. The outcome of this work renders a physical basis for understanding the swimming of aquatic animals.

Blood oxygen is an essential component for numerous biological processes of mammalian animals. Milk production of ruminants largely relies on the supply of nutrients, such as glucose, amino acids and fatty acids. To define the regulatory role of blood oxygen availability in regard to milk production, seventy-five healthy Guanzhong dairy goats with similar body weight, days in milk and parities were selected. For each animal, milk yield was recorded and milk sample was collected to determine compositions. Milk vein blood was collected to determine parameters including blood gas, physio-biochemistry and haematology. Another blood sample was prepared for transcriptome and RT-qPCR. Results showed that both pressure of oxygen (pO2) in the milk vein (positively) and numbers of neutrophils in mammary vein (negatively) were associated with milk yield of the animals. To learn the role of pO2 in blood cell functionality, twelve animals (six with higher yield (H-group) and six with lower yield (L-group)) from seventy-five goats were selected. Compared with animals in L-group, goats in H-group were higher in pO2 but lower in pCO2, lactate, lactate dehydrogenase activity and neutrophil abundance in milk vein, compared with L-group. The blood transcriptome analysis suggested that compared with L-group, animals in H-group were depressed in functionality including neutrophil activation and metabolic pathways including glycolysis, NF-κB and HIF-1. Our result revealed that lower milk production could be associated with neutrophil activation responding to low pO2 in the mammary vein. In the meantime, we highlighted the potential importance of blood oxygen as a milk yield regulator.

The sedimentary characteristics and preservation potential of lacustrine carbonates provide fundamental information on climate change. The lacustrine carbonate deposition in the Eocene Dongying Depression was investigated using a combination of mineralogical, petrological and geochemical analyses. Micritic calcite/dolomite, granular calcite, columnar calcite, calcareous shell fragments and reworked detrital calcite were identified. Varying patterns of carbonates (VPC) including lithofacies, geochemical indicators and carbonate distribution were revealed in the Dongying Depression: (i) carbonates hardly precipitate in the nearshore area (average 12 wt %); (ii) carbonate content is high (average 53 wt %) in the shallow lake and (iii) gradually decreases to reach a minimum (average 24 wt %) in the deeper part of the lake. Comparison of VPC in four Holocene lakes (the Qinghai Lake and Barkol Lake in China, Oro Lake in Canada and Montcortès Lake in Spain) with the Dongying Depression suggests that four distinct lake stages were developed, namely the terrigenous clastic/gypsum-rich, carbonate-rich, carbonate-decreasing and carbonate-poor stages. A depositional model of lacustrine carbonates influenced by detrital influx, climate, palaeoproductivity and salinity is developed. This study contributes to the understanding of the genetic mechanisms of lacustrine carbonate deposition to reconstruct environmental changes.