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A standard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞ . In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion. We demonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent. We also compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing single-trajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.

Background Maternal gestational diabetes (GDM) is an established risk factor for large size at birth, but its influence on intrauterine fetal growth in different ethnic populations is less well understood. Here, we examine the joint associations of GDM and ethnicity with longitudinal fetal growth in South Asian and White European origin women. Methods This study included 10,705 singletons (4747 White European and 5958 South Asian) from a prospective cohort of women attending an antenatal clinic in Bradford, in the North of England. All women completed a 75-g oral glucose tolerance test at 26–28 weeks’ gestation. Ultrasound measurements of fetal head circumference (HC), femur length (FL) abdominal circumference (AC), and estimated fetal weight (EFW), and corresponding anthropometric measurements at birth were used to derive fetal growth trajectories. Associations of GDM and ethnicity with these trajectories were assessed using multilevel fractional polynomial models. Results Eight hundred thirty-two pregnancies (7.8%) were affected by GDM: 10.4% of South Asians and 4.4% of White Europeans. GDM was associated with a smaller fetal size in early pregnancy [differences (95% CI) in mean HC at 12 weeks and mean AC and EFW at 16 weeks comparing fetuses exposed to GDM to fetuses unexposed (reference) = − 1.8 mm (− 2.6; − 1.0), − 1.7 mm (− 2.5; − 0.9), and − 6 g (− 10; − 2)] and a greater fetal size from 24 weeks’ gestation through to term [differences (95% CI) in mean HC, AC, and EFW comparing fetuses exposed to GDM to those unexposed = 0.9 mm (0.3; 1.4), 0.9 mm (0.2; 1.7), and 7 g (0; 13) at 24 weeks]. Associations of GDM with fetal growth were of similar magnitude in both ethnic groups. Growth trajectories, however, differed by ethnicity with South Asians being smaller than White Europeans irrespective of GDM status. Consequently, South Asian fetuses exposed to GDM were smaller across gestation than fetuses of White Europeans without GDM. Conclusions In both ethnic groups, GDM is associated with early fetal size deviations prior to GDM diagnosis, highlighting the need for novel strategies to diagnose pregnancy hyperglycemia earlier than current methods. Our findings also suggest that ethnic-specific fetal growth criteria are important in identifying hyperglycemia-associated pathological effects.

Rapid urbanization is profoundly impacting the ecological environment and landscape patterns, leading to a decline in ecosystem services (ES) and posing threats to both ecological security and human well-being. This study aimed to identify the spatial and temporal patterns of ecosystem service bundles (ESB) in the Beibu Gulf urban agglomeration from 2000 to 2030, analyze the trajectory of ESB evolution, and elucidate the drivers behind ESB formation and evolution. We utilized the Patch-generating Land Use Simulation (PLUS) model to establish baseline (BLS), carbon sequestration priority (CPS), and urbanization priority (UPS) scenarios for simulating land use patterns in 2030. Following the assessment of ecosystem service values (ESV) through the equivalent factor method, we identified the spatiotemporal distribution patterns of ESB using the K-means clustering algorithm. By employing stability mapping and landscape indices, we identified and analyzed various types of ESB evolutionary trajectories. Redundancy analysis (RDA) was employed to pinpoint the drivers of ESB formation and evolution. The results revealed that from 2000 to 2030, land use changes were primarily observed in cropland, forestland, and construction land. Between 2000 and 2020, 92.88% of the region did not experience shifts in ESB types. In UPS, the ESB pattern in the study area underwent significant changes, with only 76.68% of the region exhibiting stabilized trajectories, while the other two scenarios recorded percentages higher than 80%. Key drivers of ESB-type shifts included initial food provision services, elevation, slope, changes in the proportion of construction land, and population change. This multi-scenario simulation of ESB evolution due to land use changes aids in comprehending potential future development directions from diverse perspectives and serves as a valuable reference for formulating and changing ecological management policies and strategies.

With the growth of global trade, port shipping is becoming more and more important. In this paper, an analysis of a ship’s inbound and outbound track characteristics is conducted using the OD–Hausdorff distance. The accuracy and efficiency of trajectory data analysis have been enhanced through clustering analysis. Trajectories are arranged in a time sequence, and representative port segments are selected. An improved OD–Hausdorff distance method is employed to capture the dynamic characteristics of a ship’s movements, such as speed and heading. Additionally, the DBSCAN algorithm is utilized for clustering, allowing for the processing of multidimensional AIS data. Data cleaning and preprocessing have ensured the reliability of the AIS data, and the Douglas–Peucker algorithm is used for trajectory simplification. Significant improvements in the accuracy and efficiency of trajectory clustering have been observed. Therefore, the main channel of the Guan River and the right side of Yanwei Port are usually followed by ships greater than 60 m in length, with a lateral Relative Mean Deviation (RMD) of 7.06%. Vessels shorter than 60 m have been shown to have greater path variability, with a lateral RMD of 7.94%. Additionally, a crossing pattern at Xiangshui Port is exhibited by ships shorter than 60 m due to the extension of berths and their positions at turns. Enhanced clustering accuracy has provided more precise trajectory patterns, which aids in better channel management.

Unusual crowd analysis is an important problem in surveillance video due to their features cannot be extracted efficiently on the crowd scenes. To overcome this challenge, this paper introduced the appearance and motion based unusual events detection method by using multiple moving objects. This method includes appearance and motion based computation, and moving objects trajectory analysis. By using these all techniques, the unusual crowds and their activities can be obtained by analyzing moving objects size and the distance among multiple moving objects. Two benchmark datasets such as PETS 2009 and UMN are used for the experimental results. Also, several existing algorithms are compared with the proposed method to evaluate the effectiveness of the proposed work. The comparative analysis results proved that the proposed method achieved best accuracy for unusual crowd events.

We decomposed complex synthetic wavefields in an inhomogeneous sedimentary basin into P-, SV-, and SH-wavefields, and quantitatively evaluated the amplitude, propagation velocity, and propagation direction of coherent waves in each decomposed wavefield within the 0.125–1 Hz frequency band. In sedimentary basins with irregular subsurface structures, P-, SV-, and SH-waves can coexist at the same location and time, propagating as either body waves or surface waves, where SH-waves manifest as Love waves and P- and SV-waves combine to form Rayleigh waves. The relative amplitudes of these wave types depend on both the source radiation pattern and the subsurface geometry. To accurately evaluate the propagation characteristics, such as amplitude and directional variation, of each wave type, it is necessary to first decompose the wavefield by wave type. To date, no studies have addressed this issue from such a perspective. We fully decomposed the reproduced strong-motion waveforms from the 2018 Mw 5.6 earthquake beneath the margin of the Osaka sedimentary basin in Japan—the target event of this study—into P-, SV-, and SH‑wave components using Helmholtz decomposition. By applying semblance analysis to the decomposed wavefields, we quantitatively evaluated the propagation processes of each wave type in the three-dimensional sedimentary basin. Using the derived propagation characteristics, we conducted pseudo-trajectory analysis (PTA) to visualize wave propagation paths, analogous to streamlines in fluid dynamics. We noted spatial differences in the SH‑ and SV‑wavefields. For example, during an early time window, ground motions were oriented northwest–southeast on both sides of the north–south fault zone in the Osaka Plain. These motions result from southwestward-propagating SH-waves in the western region and southeastward-propagating SV-waves in the eastern region. Later, in the western region, Love waves dominated in the 0.125–0.25 Hz band, while Rayleigh waves dominated in the 0.25–0.5 Hz band. The spatiotemporal amplitude variations of these wave types depend on the combined effects of the source radiation pattern and the subsurface structure as noted above. The proposed method can also be applied to identify, where and what types of waves are likely to be generated. Graphical Abstract

This paper presents a fully remote approach for the assessment of rockfall incidents that is based on leveraging data that become available online with the goal to develop three dimensional (3D) models, document in detail the rockfall trajectory immediately following the incident and conduct rockfall analyses fully remotely. Such an approach can reduce the effort necessary to collect data and learn from incidents. The approach is well suited following natural disasters, where a wealth of field performance data may become available online through social media platforms and local news media. The steps to implement this approach involve: datamining the internet for crowdsourced data and particularly Unmanned Aerial Vehicle (UAV) footage of the incident, reconstructing the site morphology in the three-dimensional space by applying the Structure-from-Motion method, extracting insights from the crowdsourced data and conducting three-dimensional rockfall trajectory back-analysis. We demonstrate the approach through two incidents that occurred in Greece, where different amounts of crowdsourced data became available. We evaluate the proposed approach, discuss its limitations and benefits, and provide insights based on these two incidents. This paper shows that in both cases, the proposed approach enabled the rapid extraction of critical, perishable insights such as block detachment positions, block size, and fragment distribution. Also, the proposed approach allowed for the collection of all the input necessary to conduct detailed three-dimensional trajectory analyses. This supports the creation of high-precision inventories of both past and future incidents. Implementing this approach can enhance risk assessment accuracy, and inform mitigation strategies. The proposed approach allows the evaluation of geohazards globally fully remotely and possibly without the need for on-site visits. 

Parthenium hysterophorus (congress grass) is a harmful weed and its pollen grains are important allergens. Due to its minute size and allergenic activity, this particular type of pollen is selected for the study. The aeropalynological survey was conducted for the year 2019 at Chauras Campus, Hemvati Nandan Bahuguna Garhwal University, Srinagar, Uttarakhand. It is located on the right bank of the Alaknanda river (30°13’35.81”N & 78°48’11.05”E; 560 m amsl). A Rotarod sampler was used for air sampling. The maximum pollen count was observed in July. To evaluate the correlation matrix in R software, correlations (Pearson’s and Spearsman’s) between pollen count and meteorological parameters have been calculated. Back trajectory analysis has also been done using NOAA HYSPLIT MODEL.

Background Home-based palliative care (HPC) is considered to moderate the problem of rising healthcare utilization of cancer patients at end-of-life. Reports however suggest a proportion of HPC patients continue to experience high care intensity. Little is known about differential trajectories of healthcare utilization in patients on HPC. Thus, we aimed to uncover the heterogeneity of healthcare utilization trajectories in HPC patients and identify predictors of each utilization pattern. Methods This is a cohort study of adult cancer patients referred by Singapore Health Services to HCA Hospice Service who died between 1st January 2018 and 31st March 2020. We used patient-level data to capture predisposing, enabling, and need factors for healthcare utilization. Group-based multi-trajectory modelling was applied to identify trajectories for healthcare utilization based on the composite outcome of emergency department (ED) visits, hospitalization, and outpatient visits. Results A total of 1572 cancer patients received HPC (median age, 71 years; interquartile range, 62–80 years; 51.1% female). We found three distinct trajectory groups: group 1 (31.9% of cohort) with persistently low frequencies of healthcare utilization, group 2 (44.1%) with persistently high frequencies, and group 3 (24.0%) that begin with moderate frequencies, which dropped over the next 9 months before increasing in the last 3 months. Predisposing (age, advance care plan completion, and care preferences), enabling (no medical subsidy, primary decision maker), and need factors (cancer type, comorbidity burden and performance status) were significantly associated with group membership. High symptom needs increased ED visits and hospitalizations in all three groups (ED visits, group 1–3: incidence rate ratio [IRR] 1.74–6.85; hospitalizations, group 1–3: IRR 1.69–6.60). High home visit intensity reduced outpatient visits in all three groups (group 1–3 IRR 0.54–0.84), while it contributed to reduction of ED visits (IRR 0.40; 95% CI 0.25–0.62) and hospitalizations (IRR 0.37; 95% CI 0.24–0.58) in group 2. Conclusions This study on HPC patients highlights three healthcare utilization trajectories with implications for targeted interventions. Future efforts could include improving advance care plan completion, supporting care preferences in the community, proactive interventions among symptomatic high-risk patients, and stratification of home visit intensity.

Aim Understanding temporal changes in aquatic communities is essential to address the freshwater biodiversity crisis. In particular, it is important to understand the patterns and drivers of spatial variation in local community dynamics, generalizing temporal trends from discrete locations to entire landscapes that are the main focus of management. Here, we present a framework for producing spatially continuous views of community dynamics, focusing on stream fish affected by hydropower development. Location River Sabor, NE Portugal. Methods We sampled stream fish at thirty sites between 2012 and 2019. Community trajectory analysis was used to quantify the directionality and velocity of community change, and the geometric resemblance of community trajectories between sites. Geostatistical models for stream networks were used to relate metrics describing community dynamics to environmental variables, while controlling for Euclidean and hydrologic spatial dependencies, and to map spatial variation in community dynamics across the watershed. Results Trajectories in multivariate space underlined strong temporal dynamics, with local communities deviating and returning to previous states, but without evidence for directional changes. Accordingly, directionality values were low and not consistently affected by environmental variables. The velocity of community change varied markedly across the watershed and it was strongly affected by stream order and elevation, with faster changes observed in lowland streams draining into hydroelectric reservoirs and with a high proportion of exotic species. Pairwise distances between community trajectories were strongly related to hydrologic and environmental distances between sites. Main conclusions Local stream fish communities were in a loose equilibrium across the watershed, but they fluctuated at a faster rate closer to a hydroelectric reservoir. Integrating community trajectory analysis and geostatistical modelling provides a relatively simple framework to understand how, where and why temporal community dynamics vary across dendritic stream networks and to visualize spatial patterns of community change over time in relation to anthropogenic impacts.