Analysis of the correlation between the longitudinal trajectory of SOFA scores and prognosis in patients with sepsis at 72 hour after admission based on group trajectory modeling

Background:To identify the distinct trajectories of the Sequential Organ Failure Assessment(SOFA)scores at 72 h for patients with sepsis in the Medical Information Mart for Intensive Care(MIMIC)-IV database and determine their effects on mortality and adverse clinical outcomes.Methods:A retrospective cohort study was carried out involving patients with sepsis from the MIMIC-IV database.Group-based trajectory modeling(GBTM)was used to identify the distinct trajectory groups for the SOFA scores in patients with sepsis in the intensive care unit(ICU).The Cox proportional hazards regression model was used to investigate the relationship between the longitudinal change trajectory of the SOFA score and mortality and adverse clinical outcomes.Results:A total of 16,743 patients with sepsis were included in the cohort.The median survival age was 66 years(interquartile range:54-76 years).The 7-day and 28-day in-hospital mortality were 6.0%and 17.6%,respectively.Five different trajectories of SOFA scores according to the model fitting standard were determined:group 1(32.8%),group 2(30.0%),group 3(17.6%),group 4(14.0%)and group 5(5.7%).Univariate and multivariate Cox regression analyses showed that,for different clinical outcomes,trajectory group 1 was used as the reference,while trajectory groups 2-5 were all risk factors associated with the outcome(P<0.001).Subgroup analysis revealed an interaction between the two covariates of age and mechanical ventilation and the different trajectory groups of patients’SOFA scores(P<0.05).Conclusion:This approach may help identify various groups of patients with sepsis,who may be at different levels of risk for adverse health outcomes,and provide subgroups with clinical importance.

UTM:A trajectory privacy evaluating model for online health monitoring

A huge amount of sensitive personal data is being collected by various online health monitoring applications.Although the data is anonymous,the personal trajectories(e.g.,the chronological access records of small cells)could become the anchor of linkage attacks to re-identify the users.Focusing on trajectory privacy in online health monitoring,we propose the User Trajectory Model(UTM),a generic trajectory re-identification risk predicting model to reveal the underlying relationship between trajectory uniqueness and aggregated data(e.g.,number of individuals covered by each small cell),and using the parameter combination of aggregated data to further mathematically derive the statistical characteristics of uniqueness(i.e.,the expectation and the variance).Eventually,exhaustive simulations validate the effectiveness of the UTM in privacy risk evaluation,confirm our theoretical deductions and present counter-intuitive insights.

A study on continuous Chinese speech recognition based on stochastic trajectory models

After pointed the unreasonableness of the three basic assumptions contained in HMM, we introduce the theory and the advantage of Stochastic najectory Models (STMs) that possibly resolve these problems caused by HMM assumptions. In STM, the acoustic observations of an acoustic unit are represented as clusters of trajectories in a parameter space.The trajectories are modelled by mixture of probability density functions of random sequence of states. After analyzing the characteristics of Chinese speech, the acoustic units for continuous Chinese speech recognition based on STM are discussed and phone-like units are suggested. The performance of continuous Chinese speech recognition based on STM is studied on VINICS system. The experimental results prove the efficiency of STM and the consistency of phone-like units.

Application Study of Trajectory Plume Model in Atmospheric Environmental Impact Assessment

[ Objective] The research aimed to study application of the trajectory plume model in atmospheric environmental impact assessment. [ Method] Trajectory plume model was used to retrospectively evaluate regional atmospheric improvement degree by fuel gas desulfurization project in Mawan Power Plant of Shenzhen. On this basis, we analyzed applicability of the model in atmospheric prediction of the construction project. [- Re- sult~ Under the situation of complex flow field and variable weather condition, the trajectory plume model displayed good prediction accuracy, to- gether with the use of flow field diagnosis model. Under complex weather condition, this model could be complementary to atmospheric environmen- tal quality prediction model recommended by new atmosphere guidelines, which had the value of popularization in future atmospheric environmental evaluation and planning. [ Conduslon~ Trajectory plume model had broad application potential in atmospheric environmental impact assessment.

A Three-Dimensional Model of Transport and Diffusion of Seeding Agents within Stratus

It is essential to learn the temporal and spatial concentration distributions and variations of seeding agents in cloud seeding of precipitation enhancement. A three-dimensional puff trajectory model incorporating a mesoscale nonhydrostatic model has been formulated, and is applied to simulating the transporting and diffusive characteristics of multiple line sources of seeding agents within super-cooled stratus. Several important factors are taken into consideration that affect the diffusion of seeding materials such as effects of topography and vertical wind shear, temporal and spatial variation of seeding parameters and wet deposition. The particles of seeding agents are assumed to be almost inert, they have no interaction with the particles of the cloud or precipitation except that they are washed out by precipitation. The model validity is demonstrated by the analyses and comparisons of model results, and checked by the sensitivity experiments of diffusive coefficients and atmospheric stratification. The advantage of this model includes not only its exact reflection of heterogeneity and unsteadiness of background fields, but also its good simulation of transport and diffusion of multiple line sources. The horizontal diffusion rate and the horizontal transport distance have been proposed that they usually were difficult to obtain in other models. In this simulation the horizontal diffusion rate is 0.82 m s(-1) for average of one hour, and the horizontal average transport distance reaches 65 km after 1 4 which are closely related to the background Fields.

Vehicle Motion Prediction at Intersections Based on the Turning Intention and Prior Trajectories Model

Intersections are quite important and complex traffic scenarios,where the future motion of surrounding vehicles is an indispensable reference factor for the decision-making or path planning of autonomous vehicles.Considering that the motion trajectory of a vehicle at an intersection partly obeys the statistical law of historical data once its driving intention is determined,this paper proposes a long short-term memory based(LSTM-based)framework that combines intention prediction and trajectory prediction together.First,we build an intersection prior trajectories model(IPTM)by clustering and statistically analyzing a large number of prior traffic flow trajectories.The prior trajectories model with fitted probabilistic density is used to approximate the distribution of the predicted trajectory,and also serves as a reference for credibility evaluation.Second,we conduct the intention prediction through another LSTM model and regard it as a crucial cue for a trajectory forecast at the early stage.Furthermore,the predicted intention is also a key that is associated with the prior trajectories model.The proposed framework is validated on two publically released datasets,next generation simulation(NGSIM)and INTERACTION.Compared with other prediction methods,our framework is able to sample a trajectory from the estimated distribution,with its accuracy improved by about 20%.Finally,the credibility evaluation,which is based on the prior trajectories model,makes the framework more practical in the real-world applications.

Association of fluid balance trajectories with clinical outcomes in patients with septic shock:A prospective multicenter cohort study

Background:Septic shock has a high incidence and mortality rate in Intensive Care Units(ICUs).Earlier intravenous fluid resuscitation can significantly improve outcomes in septic patients but easily leads to fluid overload(FO),which is associated with poor clinical outcomes.A single point value of fluid cannot provide enough fluid information.The aim of this study was to investigate the impact of fluid balance(FB)latent trajectories on clinical outcomes in septic patients.Methods:Patients were diagnosed with septic shock during the first 48 h,and sequential fluid data for the first 3 days of ICU admission were included.A group-based trajectory model(GBTM)which is designed to identify groups of individuals following similar developmental trajectories was used to identify latent subgroups of individuals following a similar progression of FB.The primary outcomes were hospital mortality,organ dysfunction,major adverse kidney events(MAKE)and severe respiratory adverse events(SRAE).We used multivariable Cox or logistic regression analysis to assess the association between FB trajectories and clinical outcomes.Results:Nine hundred eighty-six patients met the inclusion criteria and were assigned to GBTM analysis,and three latent FB trajectories were detected.64(6.5%),841(85.3%),and 81(8.2%)patients were identified to have decreased,low,and high FB,respectively.Compared with low FB,high FB was associated with increased hospital mortality[hazard ratio(HR)=1.63,95%CI 1.22–2.17],organ dysfunction[odds ratio(OR)=2.18,95%CI 1.22–3.42],MAKE(OR=1.80,95%CI 1.04–2.63)and SRAE(OR=2.33,95%CI 1.46–3.71),and decreasing FB was significantly associated with decreased MAKE(OR=0.46,95%CI 0.29–0.79)after adjustment for potential covariates.Conclusion:Latent subgroups of septic patients followed a similar FB progression.These latent fluid trajectories were associated with clinical outcomes.The decreasing FB trajectory was associated with a decreased risk of hospital mortality and MAKE.

IMPACT OF CONVECTION OVER THE SOUTH CHINA SEA ON TROPICAL CYCLONE MOTION OVER THE WESTERN NORTH PACIFIC DURING SUMMER MONSOON

The intraseasonal oscillation(ISO) of the South China Sea(SCS, 105-120°E, 5-20°N) convection and its influences on the genesis and track of the western North Pacific(WNP) tropical cyclones(TCs) were explored, based on the daily average of NCEP/NCAR reanalysis data, the OLR data and the western North Pacific tropical cyclone best-track data from 1979 to 2008. The mechanism of the influences of ISO on TC movement and the corresponding large-scale circulation were discussed by a trajectory model. It was found as follows.(1) During the SCS summer monsoon, the SCS convection exhibits the ISO features with active phases alternating with inactive phases. The monsoon circulation patterns are significantly different during these two phases. When the SCS convection is active(inactive), the SCS-WNP monsoon trough stretches eastward(retreats westward) due to the activity(inactivity) of SCS monsoon, and the WNP subtropical high retreats eastward(stretches westward), which enhances(suppresses) the monsoon circulation.(2) The amount of TC genesis in the active phase is much more than that in the inactive phase. A majority of TCs form west of 135 °E during the active phases but east of 135 °E in the inactive phases.(3) The TCs entering the area west of 135 °E and south of 25 °N would move straight into the SCS in the active phase, or recurve northward in the inactive phase.(4) Simulation results show that the steering flow associated with the active(inactive)phases is in favor of straight-moving(recurving) TCs. Meanwhile, the impacts of the locations of TC genesis on the characteristics of TC track cannot be ignored. TCs that occurred father westward are more likely to move straight into the SCS region.

The Motion Trace of Particles in Classifying Flow Field

According to the theory of the stochastic trajectory model of particle in the gas-solid two-phase flows, the two-phase turbulence model between the blades in the inner cavity of the FW-Φ150 horizontal turbo classifier was established, and the commonly-used PHOENICS code was adopted to carried out the numerical simulation. It was achieved the flow characteristics under a certain condition as well as the motion trace of particles with different diameters entering from certain initial location and passing through the flow field between the blades under the correspondent condition. This research method quite directly demonstrates the motion of particles. An experiment was executed to prove the accuracy of the results of numerical simulation.

Ten-Year Climatological Features and Air Origin of Midlatitude Double Tropopauses

The 10-year climatological features related to midlatitude double tropopause events （DTs） are examined using ERA- Interim data from 2003 to 2012. The analysis is based on tropopauses defined by lapse rate. Results show that DTs are permanent or semi-permanent in the midlatitudes, and high DT frequency bands move poleward in winter and equatorward in summer, which is consistent with the seasonal movement of the subtropical jet. Based on our statistics, the second tropopause is found at about 100 hPa in the subtropics and at slightly lower altitudes in sub-polar regions. The thickness between the first and second tropopause is smaller in the subtropics and increases with latitude. Next, the origin of air sandwiched between the first and second tropopause of DTs is studied with a revised version of the UK Universities Global Atmospheric Modelling Programme Offline Trajectory Code （Version 3） diabatic trajectory model. The results show that, in the lower or middle troposphere, air is transported into the DTs from lower latitudes, mainly in the tropics. The dominant source regions are mainly areas of deep convection and steep orography, e.g., the western Pacific and Himalayan Mountains, and they show strong seasonality following the seasonal shift of these strong upwelling regions.

A numerical method for spherical particle motion in turbulent flow with large Reynolds number

A new mathematical model, fluctuation spectrum random trajectory model (FSRTM) for the particle motion in environmental fluid was developed using Lagrangian method, in which the time mean velocity of the fluid was calculated by a time mean velocity formula for two dimensional homogeneous shear turbulent flows in open channel, the velocity fluctuation of the fluid was determined by Fourier expansion and fluctuation spectrum, and the particle motion equation was solved using Ronge Kutta method. For comparison, the spherical cation exchange resins with a density of 1 44 g/cm\+3 and diameters ranging from 0 50—0 60 mm, 0 60—0 70 mm and 0 80—0 90 mm were selected as the experimental solid particles, and their moving velocities and trajectories in shear turbulent flows with the flow Reynolds number of 4710, 10240, 11900 and 20760 were investigated. The comparing analyses of the modeled results with the measured results have shown that the model developed in this paper can describe the motions of the particles in shear turbulent flow.

A Case Study of Typical Regional Pollution Transport in Fuzhou City

Based on data of PM2.5 hourly concentration and HYSPLIT model backward trajectory in coastal cities of Fujian Province during January 25 -26, 2014, a typical regional pollution process affecting Fujian from the north to the south and the east to the west on January 26 was investiga- ted. Taking Fuzhou as an example, based on weather situation on the ground and at high altitudes as well as corresponding meteorological data such as wind direction, wind velocity, and visibility, the changes of meteorological elements before, during and after the pollution were compared. Based on the V-3θ atmospheric vertical structure diagrams, the weather reasons for the generation, maintaining and dissipation of the pollution were discussed. The results indicated that the regional pollution was transported from the northeast to the southwest. The northeasterly air flow in front of the cold ridge strengthened and moved toward the east, so that the pollutant from the north affected Fujian form the north to the south and from the east to the west. As a result, there was a dramatic increase of pollutant concentration, rapid drop of visibility, and deterioration of air quality in the affected areas. The heavy pollution process featured high-speed transport and short-time generation. The air quality changed from good state to heavy pollution in just 3 -4 hours. The maximum of IAQIpM2.5 reached 280. The whole pollution process lasted for 14 hours. Solar radiation had been deeply affected by aerosol clouds, so that atmospheric stratification was extremely stable. Along with the eastward movement of cold high pressure into the sea, the dominant wind direction near the ground changed from the northeast to the east, so that the source of the pollutant was cut off , and air quality quickly turned well. The changes of atmospheric vertical structure indicated that the high inversion layer and clouds near 700 hPa kept lower air clean and blocked upper pollution transport. The later sudden increase of wind speed and strengthening of atmospheric mechanical turbu- lent destroyed inversion layer, so that the upper pollutants invaded air near the ground rapidly. During the period of high pollution, the isothermal layer （aerosol clouds） leaded to decrease of wind speed, and the atmosphere became more stable. The pollution ended until the wind field changed.

Analysis of Extreme Precipitation Events over Central Plateau of Iran

This paper describes the results of an analysis of extreme rainfall events in the central plateau of Iran. To study the extreme events, daily records of eighteen stations’ rainfalls in the region for different initial dates up to 2005 gathered from the bureau of meteorology. Then, the extreme rainfall threshold was calculated for each individual station using the statistical index of Gamble type I. Lastly, 22 mm was determined as the extreme rainfall value for the entire stations, and eventually 17 out of 169 extreme precipitation events were extracted in accordance with three factors including a) days with precipitation in not less than 50% of the stations, b) maximum rainfall is 22 mm or more in at least one of the stations, and c) mean precipitation of the basin is more than 3 mm. In the next step to analyze the synoptic features, the relevant meteorological data i.e. relative vorticity, geopotential height, sea level pressure, u and v wind components, relative humidity, vertical velocity, and precipitable water content at multiple levels of the atmosphere were examined from the NCEP/NCAR reanalysis dataset. The synoptic findings indicate that two patterns of deep trough and high ridge of the eastern Mediterranean were responsible for making the heavy precipitation events over the central plateau of Iran. The most and severest rainfall events occurred via deep tough pattern, which covered 76% of days with extreme precipitations during the examined period. Furthermore, the results suggest that the main moisture resources, which identified by HYSPLIT model’s outputs and moisture convergence/divergence zones for the rainy systems in the first pattern (deep trough) including Persian Gulf, Oman Sea, Indian Ocean, and Red Sea, while for the second pattern (high ridge) Persian Gulf and Red Sea play a significant role in feeding the storms in the central regions of Iran. Moreover, the southward movement of Polar Vortex is also considered as those important factors to produce extreme precipitation events over the central plateau of Iran. In general, the HYSPLIT trajectories model’s outputs confirmed the observed synoptic features in particular for the systems’ moisture feeding discussed in the patterns.

A drifting trajectory prediction model based on object shape and stochastic mo-tion features

There is a huge demand to develop a method for marine search and rescue（SAR） operators automatically predicting the most probable searching area of the drifting object. This paper presents a novel drifting prediction model to improve the accuracy of the drifting trajectory computation of the sea-surface objects. First, a new drifting kinetic model based on the geometry characteristics of the objects is proposed that involves the effects of the object shape and stochastic motion features in addition to the traditional factors of wind and currents. Then, a computer simulation-based method is employed to analyze the stochastic motion features of the drifting objects, which is applied to estimate the uncertainty parameters of the stochastic factors of the drifting objects. Finally, the accuracy of the model is evaluated by comparison with the flume experimental results. It is shown that the proposed method can be used for various shape objects in the drifting trajectory prediction and the maritime search and rescue decision-making system.

Subspace Trajectory Piecewise-Linear Model Order Reduction for Nonlinear Circuits

Despite the efficiency of trajectory piecewise-linear(TPWL)model order re-duction(MOR)for nonlinear circuits,it needs large amount of expansion points forlarge-scale nonlinear circuits.This will inevitably increase the model size as well as the simulation time of the resulting reduced macromodels.In this paper,subspaceTPWL-MOR approach is developed for the model order reduction of nonlinear cir-cuits.By breaking the high-dimensional state space into several subspaces with much lower dimensions,the subspace TPWL-MOR has very promising advantages of re-ducing the number of expansion points as well as increasing the effective region of thereduced-order model in the state space.As a result,the model size and the accuracy of the TWPL model can be greatly improved.The numerical results have shown dra-matic reduction in the model size as well as the improvement in accuracy by using the subspace TPWL-MOR compared with the conventional TPWL-MOR approach.

A data-driven approach to modeling high-density terminal areas：A scenario analysis of the new Beijing,China airspace

Airports are being developed and expanded rapidly in China to accommodate and promote a growing aviation market.The future Beijing Daxing International Airport（DAX） will serve as the central airport of the JingJinJi megaregion,knitting the Beijing,Tianjin,and Hebei regions together.DAX will be a busy airport from its inception,relieving congestion and accommodating growth from Beijing Capital International Airport（PEK）,currently the second busiest airport in the world in passengers moved.We aim to model terminal airspace designs and possible conflicts in the future Beijing Multi-Airport System（MAS）.We investigate standard arrival procedures and mathematically model current and future arrival trajectories into PEK and DAX by collecting large quantities of publicly available track data from historical arrivals operating within the Beijing terminal airspace.We find that（1） trajectory models constructed from real data capture aberrations and deviations from standard arrival procedures,validating the need to incorporate data on historical trajectories with standard procedures when evaluating the airspace and（2） given all existing constraints,DAX may be restricted to using north and east arrival flows,constraining the capacity required to handle the increases in air traffic demand to Beijing.The results indicate that the terminal airspace above Beijing,and the future JingJinJi region,requires careful consideration if the full capacity benefits of the two major airports are to be realized.

Effect of Long-Term Systolic Blood Pressure Trajectory on Kidney Damage in the Diabetic Population： A Prospective Study in a Community-Based Chinese Cohort

Background：Previous studies have shown that hypertension is an important factor contributing to the occurrence and progression of diabetic kidney damage.However,the relationship between the patterns of blood pressure （BP） trajectory and kidney damage in the diabetic population remains unclear.This prospective study investigated the effect of long-term systolic BP （SBP） trajectory on kidney damage in the diabetic population based on an 8-year follow-up community-based cohort.Methods：This study included 4556 diabetic participants among 101,510 participants.BP,estimated glomerular filtration rate （eGFR）,and urinary protein were measured every 2 years from 2006 to 2014.SBP trajectory was identified by the censored normal modeling.Five discrete SBP trajectories were identified according to SBP range and the changing pattern over time.Kidney damage was evaluated through eGFR and urinary protein value.A multivariate logistic regression model was used to analyze the influence of different SBP trajectory groups on kidney damage.Results：We identified five discrete SBP trajectories：low-stable group （n =864）,moderate-stable group （n =1980）,moderate increasing group （n =609）,elevated decreasing group,（n =679）,and elevated stable group （n =424）.The detection rate of kidney damage in the low-stable group （SBP：118-124 mmHg） was the lowest among the five groups.The detection rate of each kidney damage index was higher in the elevated stable group （SBP：159-172 mmHg） compared with the low-stable group.For details,the gap was 4.14 （11.6% vs.2.8%） in eGFR 〈60 ml.min-1.1.73 m 2 and 3.66 （17.2% vs.4.7%）,3.38 （25.0% vs.7.4%）,and 1.8 （10.6% vs.5.9%） times in positive urinary protein,eGFR 〈60 ml.min-1.1.73 m 2 and/or positive urinary protein,and eGFR decline ≥30%,respectively （P 〈 0.01）.Conclusion：An elevated stable SBP trajectory is an independent risk factor for kidney damage in the diabetic population.

On the Nature of Caspian Clouds

Caspian clouds(CCs)are formed between the southern coast of the Caspian Sea and the Alborz Mountains.The purpose of this study is to identify characteristics of CCs using aerosol,cloud,and meteorological data from ModernEra Retrospective analysis for Research and Applications version 2(MERRA-2),Moderate Resolution Imaging Spectroradiometer(MODIS),and ECMWF Reanalysis version 5(ERA5)during 2000–2020.During this period,we identified and investigated 636 days with CCs.The results indicated that the frequency(%)of these clouds was higher in the summer than in other seasons because synoptic system activity varies between hot and cold periods.The hot season with the beginning of high-pressure subtropical Azores activity and the formation of a stable atmosphere in northern Iran leads to more frequent occurrence of CCs.These clouds are mainly the low-and middle-level clouds in the region,e.g.,stratus and altocumulus.CCs resulted in 13.9%of annual rainfall,and 55.9%and 18.7%of the summer and autumn rainfall,respectively,relative to total rainfall from all cloud types in the study region.In the multivariate regression analysis,CC precipitation exhibited a strong positive relationship with the cloud water path(CWP),cloud optical thickness(COT),and cloud effective radius(CER).A comparison of the mean and standard deviation of aerosol optical thickness(AOT)and aerosol index(AI)for CC and non-CC days did not show a significant difference.Examination of the synoptic patterns showed that the main factors in the formation of CCs are the specific environmental conditions of the region and the orographic lift of stable air masses.The Hybrid Single-Particle Lagrangian Integrated Trajectory(HYSPLIT)model indicated that the source of moisture for the formation of CCs was largely the Caspian Sea.

Design and simulation of an integrated end-effector for picking kiwifruit by robot

The harvesting of fresh kiwifruit is a labor-intensive operation that accounts for more than 25%of annual production costs.Mechanized harvesting technologies are thus being developed to reduce labor requirements for harvesting kiwifruit.To improve the efficiency of a harvesting robot for picking kiwifruit,we designed an end-effector,which we report herein along with the results of tests to verify its operation.By using the established method of automated picking discussed in the literature and which is based on the characteristics of kiwifruit,we propose an automated method to pick kiwifruit that consists of separating the fruit from its stem on the tree.This method is experimentally verified by using it to pick clustered kiwifruit in a scaffolding canopy cultivation.In the experiment,the end-effector approaches a fruit from below and then envelops and grabs it with two bionic fingers.The fingers are then bent to separate the fruit from its stem.The grabbing,picking,and unloading processes are integrated,with automated picking and unloading performed using a connecting rod linkage following a trajectory model.The trajectory was analyzed and validated by using a simulation implemented in the software Automatic Dynamic Analysis of Mechanical Systems(ADAMS).In addition,a prototype of an end-effector was constructed,and its bionic fingers were equipped with fiber sensors to detect the best position for grabbing the kiwifruit and pressure sensors to ensure that the damage threshold was respected while picking.Tolerances for size and shape were incorporated by following a trajectory groove from grabbing and picking to unloading.The end-effector separates clustered kiwifruit and automatically grabs individual fruits.It takes on average 4–5 s to pick a single fruit,with a successful picking rate of 94.2%in an orchard test featuring 240 samples.This study shows the grabbing–picking–unloading robotic end-effector has significant potential to facilitate the harvesting of kiwifruit.

Reframing the payments for ecosystem services framework in a coupled human and natural systems context:strengthening the integration between ecological and human dimensions

Introduction:As challenges to biodiversity mount,land-use policies have been implemented to balance human needs and the integrity of ecological systems.One such program,Payments for Ecosystem Services(PES),incentivizes resource users to protect ecosystem services and has been implemented around the world to reduce soil erosion,create or improve wildlife habitats,and improve water quality and other environmental goals.The PES policy,at its core,is a concept that aims to capture the reciprocal relationships between human systems and ecological function and process.As such,PES epistemologically embodies a coupled human and natural systems approach.Outcomes:Yet,despite this conceptual alignment,the on-the-ground implementation or evaluation of PES typically does not adopt this coupled approach and PES programs have little integration between socioeconomic,sociocultural,human demographic,and ecological elements.To advance the evolution of PES,we consider what and how socioeconomic and ecological factors have been incorporated into PES program implementation and evaluation.We also present a conceptual model to articulate how PES research can capture the reciprocal relationships among socioeconomics,demography,and ecology and discuss the quantitative modeling approaches that can support this conceptual development,i.e.,structural equation and agent-based modeling,and latent trajectory models.Conclusions:By strengthening the conceptual framework for PES within a coupled human and natural systems approach and identifyinganalytical approaches that can be used to quantify and characterize these complex cross-disciplinary relationships,we aim to support the evolution and advancement of PES,in service of more meaningful and positive outcomes for human well-being and ecological sustainability.