For each $n\geq 1$, let $FT_n$ be the free tree monoid of rank n and $E_n$ the full extensive transformation monoid over the finite chain $\{1, 2, \ldots , n\}$. It is shown that the monoids $FT_n$ and $E_{n+1}$ satisfy the same identities. Therefore, $FT_n$ is finitely based if and only if $n\leq 3$.

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.

Cavitation bubble pulsation and liquid jet loads are the main causes of hydraulic machinery erosion. Methods to weaken the load influences have always been hot topics of related research. In this work, a method of attaching a viscous layer to a rigid wall is investigated in order to reduce cavitation pulsations and liquid jet loads, using both numerical simulations and experiments. A multiphase flow model incorporating viscous effects has been developed using the Eulerian finite element method (EFEM), and experimental methods of a laser-induced bubble near the viscous layer attached on a rigid wall have been carefully designed. The effects of the initial bubble–wall distance, the thickness of the viscous layer, and the viscosity on bubble pulsation, migration and wall pressure load are investigated. The results show that the bubble migration distance, the normalised thickness of the oil layer and the wall load generally decrease with the initial bubble–wall distance or the oil-layer parameters. Quantitative analysis reveals that when the initial bubble–wall distance remains unchanged, there exists a demarcation line for the comparison of the bubble period and the reference period (the bubble period without viscous layer under the same initial bubble–wall distance), and a logarithmic relationship is observed that $\delta \propto \log_{10} \mu ^*$, where $\delta =h/R_{max}$ is the thickness of the viscous layer h normalised by the maximum bubble radius $R_{max}$, $\mu ^* = \mu /({R_{max }}\sqrt {{\rho }{{\mathop {P}\nolimits } _{{atm}}}})$ is the dynamic viscosity $\mu$ normalised by water density $ \rho $ and atmospheric pressure $P_{atm}$. The results of this paper can provide technical support for related studies of hydraulic cavitation erosion.

An actively controllable cascaded proton acceleration driven by a separate 0.8 picosecond (ps) laser is demonstrated in proof-of-principle experiments. MeV protons, initially driven by a femtosecond laser, are further accelerated and focused into a dot structure by an electromagnetic pulse (EMP) on the solenoid, which can be tuned into a ring structure by increasing the ps laser energy. An electrodynamics model is carried out to explain the experimental results and show that the dot-structured proton beam is formed when the outer part of the incident proton beam is optimally focused by the EMP force on the solenoid; otherwise, it is overfocused into a ring structure by a larger EMP. Such a separately controlled mechanism allows precise tuning of the proton beam structures for various applications, such as edge-enhanced proton radiography, proton therapy and pre-injection in traditional accelerators.

Deformation occurs in a thin liquid film when it is subjected to a non-uniform electric field, which is referred to as the electrohydrodynamic patterning. Due to the development of a non-uniform electrical force along the surface, the film would evolve into microstructures/nanostructures. In this work, a linear and a nonlinear model are proposed to thoroughly investigate the steady state (i.e. equilibrium state) of the electrohydrodynamic deformation of thin liquid film. It is found that the deformation is closely dependent on the electric Bond number BoE. Interestingly, when BoE is larger than a critical value, the film would be deformed remarkably and get in contact with the top template. To model the ‘contact’ between the liquid film and the solid template, the disjoining pressure is incorporated into the numerical model. From the nonlinear numerical model, a hysteresis deformation is revealed, i.e. the film may have different equilibrium states depending on whether the voltage is increased or decreased. To analyse the stability of these multiple equilibrium states, the Lyapunov functional is employed to characterise the system’s free energy. According to the Lyapunov functional analysis, at most three equilibrium states can be formed. Among them, one is stable, another is metastable and the third one is unstable. Finally, the model is extended to study the three-dimensional deformation of the electrohydrodynamic patterning.

The robot manipulator is commonly employed in the space station experiment cabinet for the disinfection task. The challenge lies in devising a motion trajectory for the robot manipulator that satisfies both performance criteria and constraints within the confined space of an experimental cabinet. To address this issue, this paper proposes a trajectory planning method in joint space. This method constructs the optimal trajectory by transforming the original problem into a constrained multi-objective optimization problem. This is then solved and integrated with the seventh-degree B-spline curve. The optimization algorithm utilizes an indicator-based adaptive differential evolution algorithm, enhanced with improved Tent chaotic mapping and opposition-based learning for population initialization. The method employed the Fréchet distance to design a trajectory selection strategy based on the Pareto solutions to ensure that the planned trajectory complies with Cartesian space requirements. This allows the robot manipulator end-effector to approximate the desired path in Cartesian space closely. The findings indicate that the proposed method can effectively design the robot manipulator trajectory, considering both joint motion performance and end-effector motion constraints. This ensures that the robot manipulator operates efficiently and safely within the experimental cabinet.

We find that common ownership among acquirers enhances rather than hinders competition in the firm sale process. One common owner raises the likelihood that target firms are sold through auction (vs. negotiation with one buyer) by 21.5%. The effect is causal according to identifications based on mergers between financial institutions. Exploring economic channels, we observe selling firms respond to common ownership among acquirers by avoiding cross-owned acquirers, bargaining hard, and inviting more buyers when cross-owned acquirers initiate the deal but not by terminating the deal. Consistent with enhanced competition, common ownership among acquirers is positively associated with deal quality.

The oriental armyworm, Mythimna separata (Walker), is a highly migratory pest known for its sudden larval outbreaks, which result in severe crop losses. These unpredictable surges pose significant challenges for timely and accurate monitoring, as conventional methods are labour-intensive and prone to errors. To address these limitations, this study investigates the use of machine learning for automated and precise identification of M. separata larval instars. A total of 1577 larval images representing different instar were analysed for geometric, colour, and texture features. Additionally, larval weight was predicted using 13 regression models. Instar identification was conducted using Support Vector Classifier (SVC), Random Forest, and Multi-Layer Perceptron. Key feature contributing to classification accuracy were subsequently identified through permutation feature importance analysis. The results demonstrated the potential of machine learning for automating instar identification with high efficiency and accuracy. Predicted larval weight emerged as a key feature, significantly enhancing the performance of all identification models. Among the tested approaches, BaggingRegressor exhibited the best performance for larval weight prediction (R2 = 98.20%, RMSE = 0.2313), while SVC achieved the highest instar identification accuracy (94%). Overall, the integration of larval weight with other image-derived features proved to be a highly effective strategy. This study demonstrates the efficacy of machine learning in enhancing pest monitoring systems by providing a scalable and reliable framework for precise pest management. The proposed methodology significantly improves larval instar identification accuracy and efficiency, offering actionable insights for implementing targeted biological and chemical control strategies.

Compliant and safe human–robot interaction is an important requirement in lower limb exoskeleton design. Motivated by this need, this paper presents the design of a compatible lower limb exoskeleton with variable stiffness actuation and anthropomorphic joint mechanisms, for walking assistance and gait rehabilitation. A novel variable stiffness actuator (VSA) based on a guide-bar mechanism was designed, to provide force and impedance controllability. By changing the crank length of the mechanism, the stiffness of the actuator is adjusted in a wide range (from 0 to 1301 Nm/rad), at fast speed (about 2582 Nm/rad/s), and with low-energy cost. These features make it possible for online stiffness adjustment during one gait cycle, to change the human–robot coupling behavior and improve the performance of the exoskeleton. An anthropomorphic hip joint mechanism was designed based on a parallelogram linkage and a passive joint compensation approach, which absorbs misalignment and improves kinematic compatibility between the human and the exoskeleton joint. Furthermore, a torque control-based multimode control strategy, which consists of passive mode, active mode, and hybrid mode, was developed for different disease stages. Finally, the torque control performance of the actuator was verified by benchtop test, and experimental validations of the exoskeleton with a human subject were carried out, which demonstrate that compliant human–robot interaction was achieved, and stiffness variation benefits for control performance improvement when the control mode changes.

In this paper, we consider the defocusing nonlinear wave equation $-\partial _t^2u+\Delta u=|u|^{p-1}u$ in $\mathbb {R}\times \mathbb {R}^d$. Building on our companion work (Self-similar imploding solutions of the relativistic Euler equations, arXiv:2403.11471), we prove that for $d=4, p\geq 29$ and $d\geq 5, p\geq 17$, there exists a smooth complex-valued solution that blows up in finite time.

The sulphur microbial diet (SMD), a dietary pattern associated with forty-three sulphur-metabolising bacteria, may influence gut microbiota composition and contribute to ageing process through gut-produced hydrogen sulfide (H2S). We aimed to explore the association between SMD and biological age (BA) acceleration, using the cross-sectional study that included 71 579 individuals from the UK Biobank. The SMD score was calculated by multiplying β-coefficients by corresponding serving sizes and summing them, based on dietary data collected using the Oxford WebQ, a 24-hour dietary assessment tool. BA was assessed using Klemerae–Doubal (KDM) and PhenoAge methods. The difference between BA and chronological age refers to the age acceleration (AgeAccel), termed ‘KDMAccel’ and ‘PhenoAgeAccel’. Generalised linear regression was performed. Mediation analyses were used to investigate underlying mediators including BMI and serum aspartate aminotransferase/alanine aminotransferase (AST/ALT) ratio. Following adjustment for multiple variables, a positive association was observed between consuming a dietary pattern with a higher SMD score and both KDMAccel (βQ4 v. Q1 = 0·35, 95 % CI = 0·27, 0·44, P < 0·001) and PhenoAgeAccel (βQ4 v. Q1 = 0·32, 95 % CI = 0·23, 0·41, P < 0·001). Each 1-SD increase in SMD score was positively associated with the acceleration of BA by 7·90 % for KDMAccel (P < 0·001) and 7·80 % for PhenoAgeAccel (P < 0·001). BMI and AST/ALT mediated the association. The stratified analysis revealed stronger accelerated ageing impacts in males and smokers. Our study indicated a higher SMD score is associated with elevated markers of biological ageing, supporting the potential utility of gut microbiota-targeted dietary interventions in attenuating the ageing process.

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.

This paper provides an overview of the current status of ultrafast and ultra-intense lasers with peak powers exceeding 100 TW and examines the research activities in high-energy-density physics within China. Currently, 10 high-intensity lasers with powers over 100 TW are operational, and about 10 additional lasers are being constructed at various institutes and universities. These facilities operate either independently or are combined with one another, thereby offering substantial support for both Chinese and international research and development efforts in high-energy-density physics.

Machine learning has already shown promising potential in tiled-aperture coherent beam combining (CBC) to achieve versatile advanced applications. By sampling the spatially separated laser array before the combiner and detuning the optical path delays, deep learning techniques are incorporated into filled-aperture CBC to achieve single-step phase control. The neural network is trained with far-field diffractive patterns at the defocus plane to establish one-to-one phase-intensity mapping, and the phase prediction accuracy is significantly enhanced thanks to the strategies of sin-cos loss function and two-layer output of the phase vector that are adopted to resolve the phase discontinuity issue. The results indicate that the trained network can predict phases with improved accuracy, and phase-locking of nine-channel filled-aperture CBC has been numerically demonstrated in a single step with a residual phase of λ/70. To the best of our knowledge, this is the first time that machine learning has been made feasible in filled-aperture CBC laser systems.

Previous observational studies have suggested an association between natural hair color and the risk of endometriosis; however, the causal relationship remains unclear. Here, we conducted a two-sample Mendelian randomization (MR) study to evaluate the potential causal link between natural hair color and endometriosis using 428 single nucleotide polymorphisms (SNPs) as genetic instruments derived from a genomewide meta-analysis comprising over 4511 cases and 227,260 controls of European ancestry. Our findings indicate that dark brown hair is associated with a decreased risk of developing endometriosis (dark brown IVW OR: 0.844, 95% CI [0.725, 0.984], p < .05). Conversely, dark hair color and lighter hair colors (red, blonde, and light brown) did not demonstrate a significant association with endometriosis risk (dark IVW OR: 0.568, 95% CI [0.280, 1.15], p = .117; red IVW OR: 1.058, 95% CI [0.719, 1.558], p = .77; blonde IVW OR: 1.158, 95% CI [0.886, 1.514], p = .28; light brown IVW OR: 1.306, 95% CI [0.978, 1.743], p = .07). These results provide compelling MR evidence supporting a causal association between natural hair color and endometriosis risk. Our findings underscore the need for larger scale studies and randomized controlled trials to delineate the biological mechanisms driving the association between hair color and endometriosis.

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.

The effect of the polarizations of two counter-propagating relativistic laser pulses interacting with subwavelength thin solid-density foil is investigated. Three-dimensional particle-in-cell simulations and analytical modelling show that the interaction and resulting transverse instability depend strongly on the polarization directions as well as the intensity distribution of the resultant light field in the foil. The left- and right-handed circularly polarized laser pair with the same phase at the common focal spot in the ultrathin foil leads to the strongest distortion of the foil. The fastest growing mode and maximum growth rate depend mainly on the laser intensity. For all polarization and phase-difference combinations, the instability is weakest when the two laser pulses are exactly out of phase at the common focusing point in the foil.