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Ensuring precise and accurate six-degree-of-freedom (6 DoF) positioning of industrial robots is crucial in large-scale automotive and aerospace assembly cells, where even slight positional errors can compromise product quality and production efficiency. Traditional laser tracker–based methods commonly require multiple trackers to acquire complete 6 DoF measurements, leading to high costs and constraints such as limited measurement range, line-of-sight restrictions, and declining accuracy in large workspaces. This study presents a low-cost approach that combines pre-characterized target tracking with photogrammetry to overcome these limitations. By mounting a specially designed target artifact on a robot’s end effector and capturing images from multiple high-resolution cameras, the proposed system performs camera calibration and multi-view triangulation to calculate the artifact’s three-dimensional (3D) position and orientation. Preliminary results validate the method’s efficacy, showing that the edges of spherical targets can be accurately fitted in three dimensions. In the next phase of research, the corrected pose data from the vision system will be transmitted back to the robot, enabling a closed-loop feedback control strategy. Comprehensive validation trials will further quantify the system’s accuracy and robustness, laying the groundwork for broader adoption in large-scale industrial assembly applications.

Phononic frequency combs have attracted increasing attention both as a qualitatively new type of nonlinear phenomena in vibrational systems and from the point of view of applications. It is commonly believed that at least two modes must be involved in generating a comb. We demonstrate that a comb can be generated by a single nanomechanical mode driven by a resonant monochromatic drive. The comb emerges where the drive is still weak, so the anharmonic part of the mode potential energy remains small. We relate the experimental observation to a negative nonlinear friction induced by the resonant drive, which makes the vibrations at the drive frequency unstable. We directly map the measured trajectories of the emerging oscillations in the rotating frame and show how these oscillations lead to the frequency comb in the laboratory frame. The results go beyond nanomechanics and suggest a qualitatively new approach to generating tunable frequency combs in single-mode vibrational systems. They demonstrate new sides of the interplay of conservative and dissipative nonlinearities in driven systems.

Individual-level longitudinal data on biological, behavioural, and social dimensions are becoming increasingly available. Typically, these data are analysed using mixed effects models, with the result summarised in terms of an average trajectory plus measures of the individual variations around this average. However, public health investigations would benefit from finer modelling of these individual variations which identify not just one average trajectory, but several typical trajectories. If evidence of heterogeneity in the development of these variables is found, the role played by temporally preceding (explanatory) variables as well as the potential impact of differential trajectories may have on later outcomes is often of interest. A wide choice of methods for uncovering typical trajectories and relating them to precursors and later outcomes exists. However, despite their increasing use, no practical overview of these methods targeted at epidemiological applications exists. Hence we provide: (a) a review of the three most commonly used methods for the identification of latent trajectories (growth mixture models, latent class growth analysis, and longitudinal latent class analysis); and (b) recommendations for the identification and interpretation of these trajectories and of their relationship with other variables. For illustration, we use longitudinal data on childhood body mass index and parental reports of fussy eating, collected in the Avon Longitudinal Study of Parents and Children.

We report on a stringent test of the nonclassicality of the motion of a massive quantum particle, which propagates on a discrete lattice. Measuring temporal correlations of the position of single atoms performing a quantum walk, we observe a 6σ violation of the Leggett-Garg inequality. Our results rigorously excludes (i.e., falsifies) any explanation of quantum transport based on classical, well-defined trajectories. We use so-called ideal negative measurements—an essential requisite for any genuine Leggett-Garg test—to acquire information about the atom’s position, yet avoiding any direct interaction with it. The interaction-free measurement is based on a novel atom transport system, which allows us to directly probe the absence rather than the presence of atoms at a chosen lattice site. Beyond the fundamental aspect of this test, we demonstrate the application of the Leggett-Garg correlation function as a witness of quantum superposition. Here, we employ the witness to discriminate different types of walks spanning from merely classical to wholly quantum dynamics.

With the development of GPS-enabled devices, wireless communication and storage technologies, trajectories representing the mobility of moving objects are accumulated at an unprecedented pace. They contain a large amount of temporal and spatial semantic information. A great deal of valuable information can be obtained by mining and analyzing the trajectory dataset. Trajectory clustering is one of the simplest and most powerful methods to obtain knowledge from trajectory data, which is based on the similarity measure between trajectories. The existing similarity measurement methods cannot fully utilize the specific features of trajectory itself when measuring the distance between trajectories. In this paper, an enhanced trajectory model is proposed and a new trajectory clustering algorithm is presented based on multi-feature trajectory similarity measure, which can maximize the similarity of trajectories in the same cluster, and can be used to better serve for applications including traffic monitoring and road congestion prediction. Both the intuitive visualization presentation and the experimental results on synthetic and real trajectory datasets show that, compared to existing methods, the proposed approach improves the accuracy and efficiency of trajectory clustering.

The dynamics of a quantum system, undergoing unitary evolution and continuous monitoring, can be described in term of quantum trajectories. Although the averaged state fully characterizes expectation values, the entire ensemble of stochastic trajectories goes beyond simple linear observables, keeping a more attentive description of the entire dynamics. Here we go beyond the Lindblad dynamics and study the probability distribution of the expectation value of a given observable over the possible quantum trajectories. The measurements are applied to the entire system, having the effect of projecting the system into a product state. We develop an analytical tool to evaluate this probability distribution at any time t . We illustrate our approach by analyzing two paradigmatic examples: a single qubit subjected to magnetization measurements, and a free hopping particle subjected to position measurements.

Multiomic profiling can reveal population heterogeneity for both health and disease states. Obesity drives a myriad of metabolic perturbations and is a risk factor for multiple chronic diseases. Here we report an atlas of cross-sectional and longitudinal changes in 1,111 blood analytes associated with variation in body mass index (BMI), as well as multiomic associations with host polygenic risk scores and gut microbiome composition, from a cohort of 1,277 individuals enrolled in a wellness program (Arivale). Machine learning model predictions of BMI from blood multiomics captured heterogeneous phenotypic states of host metabolism and gut microbiome composition better than BMI, which was also validated in an external cohort (TwinsUK). Moreover, longitudinal analyses identified variable BMI trajectories for different omics measures in response to a healthy lifestyle intervention; metabolomics-inferred BMI decreased to a greater extent than actual BMI, whereas proteomics-inferred BMI exhibited greater resistance to change. Our analyses further identified blood analyte–analyte associations that were modified by metabolomics-inferred BMI and partially reversed in individuals with metabolic obesity during the intervention. Taken together, our findings provide a blood atlas of the molecular perturbations associated with changes in obesity status, serving as a resource to quantify metabolic health for predictive and preventive medicine. Integrated analyses reveal that multiomics captured the heterogeneity of metabolic states accompanying obesity and changes in metabolic health in response to lifestyle intervention that are not apparent in body mass index measurements.

A fundamental challenge regarding disordered solids is predicting macroscopic yield—the point at which elastic behaviour changes to plastic behaviour—from the microscopic arrangements of constituent particles. Yield is accompanied by a sudden and large increase in energy dissipation due to the onset of plastic rearrangements. This suggests that one path to understanding bulk rheology is to map particle configurations to their mode of deformation. Here, we subject two-dimensional dense colloidal systems to oscillatory shear, measure the particle trajectories and bulk rheology, and quantify particle microstructure using excess entropy. Our results reveal a direct relation between excess entropy and energy dissipation that is insensitive to the nature of interactions amongst particles. We use this relation to build a physically informed model that connects rheology to microstructure. Our findings suggest a framework for tailoring the rheological response of disordered materials by tuning microstructural properties. Whether and when a material deforms elastically or plastically depends on its microstructure. Experiments on two-dimensional colloidal systems show that in disordered materials, packing density, stress and a microstructure-related entropy govern deformations.

Living systems are complex dynamic entities that operate far from thermodynamic equilibrium. Their active, non-equilibrium behaviour requires energy to drive cellular organization and dynamics. Unfortunately, most statistical mechanics approaches are not valid in non-equilibrium situations, forcing researchers to use intricate and often invasive methods to study living processes. Here we experimentally demonstrate that an observable termed mean back relaxation quantifies the active mechanics of living cells from passively observed particle trajectories. The mean back relaxation represents the average trajectory of a particle after a recent motion and is calculated from three-point probabilities. We show that this parameter allows the detection of broken detailed balance in confined systems. We experimentally observe that it provides access to the non-equilibrium generating energy and viscoelastic properties of artificial bulk materials and living cells. These findings suggest that the mean back relaxation can function as a marker of non-equilibrium dynamics and is a non-invasive avenue to determine viscoelastic material properties from passive measurements. An approach based on the average trajectory of moving particles allows for the quantification of the mechanics of living systems, namely, the non-equilibrium energy and viscoelastic properties of cells, in a non-invasive manner.

Purpose The aim of this study is to measure the trajectory of healthy ageing among Chinese middle-aged and older population, and explore the disparity of the trajectory, as well as contributing factors, between urban and rural areas in China. Methods A total of 9402 respondents aged 45 years and older interviewed in four waves (2011, 2013, 2015 and 2018) were selected from the China Health and Retirement Longitudinal Study. Healthy ageing score was calculated through item response theory. A latent growth mixture model (LGMM) was applied to distinguish the trajectory of healthy aging. A multinomial logistics regression model (MLRM) was used to explore the relationship between urban-rural areas and healthy aging trajectories, and further to explore associated factors in rural and urban areas separately. Results The healthy ageing score was lower in rural areas than urban areas in each survey wave. Five classes (“continuing-low”, “continuing-middle”, “continuing-middle-to-high”, “significantly-declining”, “continuing-high”) were grouped through LGMM. The MLRM results showed that urban living was significantly associated with a higher likelihood of being healthy (for [continuing-low/continuing-high]: β = − 1.17, RRR = 0.31, P  < 0.001, 95% CI = 0.18–0.53; and for [continuing-middle/continuing-high]: β = − 0.53, RRR = 0.59, P  < 0.001, 95% CI = 0.49–0.71). Conclusion Healthy ageing is a prominent objective in the development of a country, and rural-urban disparities are an essential obstacle to overcome, with the rural population more likely to develop a low level of healthy ageing trajectory. Prevention and standardized management of chronic diseases should be enhanced, and social participation should be encouraged to promote healthy ageing. The policy inclination and resource investment should be enhanced to reduce disparity in healthy ageing between urban and rural areas in China.