Entropy of deterministic trajectory via trajectories ensemble

We present a formulation of the single-trajectory entropy using the trajectories ensemble. The single-trajectory entropy is affected by its surrounding trajectories via the distribution function. The single-trajectory entropies are studied in two typical potentials, i.e., harmonic potential and double-well potential, and in viscous environment by interacting trajectory method. The results of the trajectory methods are in agreement well with the numerical methods(Monte Carlo simulation and difference equation). The single-trajectory entropies increasing(decreasing) could be caused by absorption(emission) heat from(to) the thermal environment. Also, some interesting trajectories, which correspond to the rare evens in the processes, are demonstrated.

Triceps skinfold thickness trajectories and the risk of all-cause mortality:A prospective cohort study

BACKGROUND The measurement of triceps skinfold(TSF)thickness serves as a noninvasive metric for evaluating subcutaneous fat distribution.Despite its clinical utility,the TSF thickness trajectories and their correlation with overall mortality have not been thoroughly investigated.AIM To explore TSF thickness trajectories of Chinese adults and to examine their associations with all-cause mortality.METHODS This study encompassed a cohort of 14747 adults sourced from the China Health and Nutrition Survey.Latent class trajectory modeling was employed to identify distinct trajectories of TSF thickness.Subjects were classified into subgroups reflective of their respective TSF thickness trajectory.We utilized multivariate Cox regression analyses and mediation examinations to explore the link between TSF thickness trajectory and overall mortality,including contributory factors.RESULTS Upon adjustment for multiple confounding factors,we discerned that males in the‘Class 2:Thin-stable’and‘Class 3:Thin-moderate’TSF thickness trajectories exhibited a markedly reduced risk of mortality from all causes in comparison to the‘Class 1:Extremely thin’subgroup.In the mediation analyses,the Geriatric Nutritional Risk Index was found to be a partial intermediary in the relationship between TSF thickness trajectories and mortality.For females,a lower TSF thickness pattern was significantly predictive of elevated all-cause mortality risk exclusively within the non-elderly cohort.CONCLUSION In males and non-elderly females,lower TSF thickness trajectories are significantly predictive of heightened mortality risk,independent of single-point TSF thickness,body mass index,and waist circumference.

A promising resilience parameter for breeding:the use of weight and feed trajectories in growing pigs

Background Increasing resilience is a priority in modern pig breeding.Recent research shows that general resilience can be quantified via variability in longitudinal data.The collection of such longitudinal data on weight,feed intake and feeding behaviour in pigs has been facilitated by the development of technologies such as automated feeding stations.The goal of this study was to investigate resilience traits,which were estimated as deviations from longitudinal weight,feed intake and feeding behaviour data during the finishing phase.A dataset with 324,207 records between the age of 95 and 155 days on 5,939 Pietrain pigs with known pedigree and genomic information was used.We provided guidelines for a rigid quality control of longitudinal body weight data,as we found that outliers can significantly affect results.Gompertz growth curve analysis,linear modelling and trajectory analyses were used for quantifying resilience traits.Results To our knowledge,this is the first study comparing resilience traits from longitudinal body weight,feed intake and feeding behaviour data in pigs.We demonstrated that the resilience traits are lowly to moderately heritable for deviations in body weight(h2=2.9%–20.2%),in feed intake(9.4%–23.3%)and in feeding behaviour(16.2%–28.3%).Additionally,these traits have good predictive abilities in cross-validation analyses.Deviations in individual body weight and feed intake trajectories are highly correlated(rg=0.78)with low to moderate favourable genetic correlations with feed conversion ratio(rg=0.39–0.49).Lastly,we showed that some resilience traits,such as the natural logarithm of variances of observed versus predicted body weights(lnvarweight),are more robust to lower observation frequencies and are repeatable over three different time periods of the finishing phase.Conclusions Our results will help future studies investigating resilience traits and resilience-related traits.Moreover,our study provides first results on standardization of quality control and efficient data sampling from automated feeding station data.Our findings will be valuable for breeding organizations as they offer evidence that pigs’general resilience can be selected on with good accuracy.Moreover,this methodology might be extended to other species to quantify resilience based on longitudinal data.

Classification of Hailstone Trajectories in a Hail Cloud over a Semi-Arid Region in China

The growth trajectory of hailstones in clouds determines the ground intensity and spatial distribution of hailfall.A systematic study of hail trajectories can help improve the current scientific understanding of the mechanisms by which hail forms in semi-arid regions of China and,in doing so,improve the quality of hail forecasts and warnings and help to prevent and mitigate disasters.In this study,the WRFv3.7.1 model was employed to provide the background field to drive the hailstone trajectory model.Cluster analysis was then used to classify hail trajectories to investigate the characteristics of different types of hail trajectories and the microphysical characteristics of hail formation.The differences in hail trajectories might be mainly due to differences in the background flow fields and microphysical fields of hail clouds in different regions.Comparative analysis revealed that as the maximum particle size of ground hailfall increased,the maximum supercooled cloud water content and the maximum updraft velocity for the formation and growth of hailstone increased.The larger the size when the hailstone reaches its maximum height,the larger the ground hailstone formed.Overall,the formation and growth of hailstone are caused by the joint action of the dynamical flow field and cloud microphysical processes.The physical processes of hailstone growth and main growth regions differ for different types of hail trajectories.Therefore,different catalytic schemes should be adopted in artificial hail prevention operations for different hail clouds and trajectories due to differences in hail formation processes and ground hailfall characteristics.

Forecasting Future Trajectories with an Improved Transformer Network

An increase in car ownership brings convenience to people’s life.However,it also leads to frequent traffic accidents.Precisely forecasting surrounding agents’future trajectories could effectively decrease vehicle-vehicle and vehicle-pedestrian collisions.Long-short-term memory(LSTM)network is often used for vehicle trajectory prediction,but it has some shortages such as gradient explosion and low efficiency.A trajectory prediction method based on an improved Transformer network is proposed to forecast agents’future trajectories in a complex traffic environment.It realizes the transformation from sequential step processing of LSTM to parallel processing of Transformer based on attentionmechanism.To performtrajectory predictionmore efficiently,a probabilistic sparse self-attention mechanism is introduced to reduce attention complexity by reducing the number of queried values in the attention mechanism.Activate or not(ACON)activation function is adopted to select whether to activate or not,hence improving model flexibility.The proposed method is evaluated on the publicly available benchmarks nextgeneration simulation(NGSIM)and ETH/UCY.The experimental results indicate that the proposed method can accurately and efficiently predict agents’trajectories.

Association between Occupational Change Trajectories and Mental Health: Results from the Korean Longitudinal Study of Aging

Objectives:This study was to longitudinally investigate the association between occupational change trajectories and mental health in the Korean population aged 45 years and older from the Korean Longitudinal Study of Aging(KLo-SA).Methods:After excluding missing values,the data of 6,224 participants from thefirst to eighth waves of the KLo-SA were analyzed using t-test,Analysis of variance(ANOVA),Group-based Trajectory Model(GBTM)from 1–5th KLoSA and Time-Lagged Generalized estimating equation(GEE)model from 5–8th KLoSA to analyze the association between occupational change trajectories and mental health in the Korean population aged 45 years and older.Results:An analysis of the association between occupational change trajectories and mental health demonstrated that,among all age group,the“sustained in unemployment”group had a worse MMSE and CESD score compared to“sustained WC”group.unlike the under-54 age group,those aged≥55 years demonstrated reductions in the MMSE and CESD scores in the sustained unemployment and the changed working condition from Standard BC to Unemployment groups,whereas those who underwent a change from the Standard WC to unemployment group only demonstrated a reduction in MMSE scores.Conclusions:There was a close relationship between occupational change trajectories and mental health.Therefore,this study can serve as the foundation for policies and institutional measures to manage the deteriorate mental health in the late middle-aged and older population.

Latent Growth Mixture Modeling to Estimate Differential PTSD Trajectories and Associated Risk Factors in Psychiatric Staff Following Workplace Violence

Background: Workplace violence (WV) towards psychiatric staff has commonly been associated with Posttraumatic Stress Disorder (PTSD). However, prospective studies have shown that not all psychiatric staff who experience workplace violence experience post-traumatic stress. Purpose: We want to examine the longitudinal trajectories of PTSD in this population to identify possible subgroups that might be more at risk. Furthermore, we need to investigate whether certain risk factors of PTSD might identify membership in the subgroups. Method: In a sample of psychiatric staff from 18 psychiatric wards in Denmark who had reported an incident of WV, we used Latent Growth Mixture Modelling (LGMM) and further logistic regression analysis to investigate this. Results: We found three separate PTSD trajectories: a recovering, a delayed-onset, and a moderate-stable trajectory. Higher social support and negative cognitive appraisals about oneself, the world and self-blame predicted membership in the delayed-onset trajectory, while higher social support and lower accept coping predicted membership in the delayed-onset trajectory. Conclusion: Although most psychiatric staff go through a natural recovery, it is important to be aware of and identify staff members who might be struggling long-term. More focus on the factors that might predict these groups should be an important task for psychiatric departments to prevent posttraumatic symptomatology from work.

FVID: Fishing Vessel Type Identification Based on VMS Trajectories

Vessel Monitoring System(VMS) provides a new opportunity for quantified fishing research. Many approaches have been proposed to recognize fishing activities with VMS trajectories based on the types of fishing vessels. However, one research problem is still calling for solutions, how to identify the fishing vessel type based on only VMS trajectories. This problem is important because it requires the fishing vessel type as a preliminary to recognize fishing activities from VMS trajectories. This paper proposes fishing vessel type identification scheme(FVID) based only on VMS trajectories. FVID exploits feature engineering and machine learning schemes of XGBoost as its two key blocks and classifies fishing vessels into nine types. The dataset contains all the fishing vessel trajectories in the East China Sea in March 2017, including 10031 pre-registered fishing vessels and 1350 unregistered vessels of unknown types. In order to verify type identification accuracy, we first conduct a 4-fold cross-validation on the trajectories of registered fishing vessels. The classification accuracy is 95.42%. We then apply FVID to the unregistered fishing vessels to identify their types. After classifying the unregistered fishing vessel types, their fishing activities are further recognized based upon their types. At last, we calculate and compare the fishing density distribution in the East China Sea before and after applying the unregistered fishing vessels, confirming the importance of type identification of unregistered fishing vessels.

Optimal design of near-Earth asteroid sample-return trajectories in the Sun–Earth–Moon system

In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun, Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-kin-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a 10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition. In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth-Moon system, and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.

Charging Pile Siting Recommendations via the Fusion of Points of Interest and Vehicle Trajectories

By mining of the requirements of lots of electric vehicle users for charging piles, this paper proposes the charging pile siting algorithm via the fusion of Points of Interest and vehicle trajectories. The proposed algorithm computes appropriate charging pile locations by: 1) mining user Points of Interest from social network; 2) mining parking sites of vehicle form GPS trajectories and 3) fusing the Points of Interest and parking sites together then clustering the fusions with our improved DBSCAN algorithm, whose clustering results indicates the final appropriate charging pile locations. Experimental results show that our proposed methods are more efficient than existing methods.

Effect of laser intensity on quantum trajectories in the macroscopic high-order harmonic generation

We macroscopically investigate the effect of the laser intensity and gas density on quantum trajectories in the highorder harmonic generation of Ne atoms irradiated by few-cycle, 800-nm laser pulses. The time–frequency profile of the harmonics shows that the long quantum trajectory is dominant at both lower and higher gas densities for a low laser intensity. At high laser intensities, the long quantum trajectory plays an important role for lower gas densities, while the short quantum trajectory is dominant at higher gas densities. An analysis of the phase mismatch for high-order harmonic generation shows that the primary emission of the quantum trajectories is determined by dynamic changes in the laser electric field during the propagation process.

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.

Achievement of chaotic synchronization trajectories of master-slave manipulators with feedback control strategy

This paper addresses a master-slave synchro- nization strategy for complex dynamic systems based on feedback control. This strategy is applied to 3-DOF pla- nar manipulators in order to obtain synchronization in such complicated as chaotic motions of end-effectors. A chaotic curve is selected from Duffing equation as the trajectory of master end-effector and a piecewise approximation method is proposed to accurately represent this chaotic trajectory of end-effectors. The dynamical equations of master-slave manipulators with synchronization controller are derived, and the Lyapunov stability theory is used to determine the stability of this controlled synchronization system. In numer- ical experiments, the synchronous motions of end-effectors as well as three joint angles and torques of master-slave manipulators are studied under the control of the proposed synchronization strategy. It is found that the positive gain matrix affects the implementation of synchronization con- trol strategy. This synchronization control strategy proves the synchronization＇s feasibility and controllability for com- plicated motions generated by master-slave manipulators.

Generalized flyby trajectories around elongated minor celestial bodies as a rotating mass dipole

The aim of this paper is to understand the common characteristics of the generalized flyby trajectory around natural elongated bodies. Such flyby trajectories provide a short-term mechanism to clear away vicinal objects or temporally capture ejecta into circling orbits. The gravitational potential of elongated bodies is described by a unified approximate model, i.e., the rotating mass dipole which is two point masses connected with a constant massless rod The energy power is used to illustrate the flyby effect in terms of the instantaneous orbital energy. The essential of the single flyby trajectory is studied analytically, and the relationship between the flyby trajectory and its Jacobi integral is also illustrated. Sample trajectories are given to show the variational trend of the energy increment with respect to differen orbital periapsides. The distribution of natural ejecting orbits is presented by varying the parameters of the approximate model.

Key techniques for predicting the uncertain trajectories of moving objects with dynamic environment awareness

Emerging technologies of wireless and mobile communication enable people to accumulate a large volume of time-stamped locations,which appear in the form of a continuous moving object trajectory.How to accurately predict the uncertain mobility of objects becomes an important and challenging problem.Existing algorithms for trajectory prediction in moving objects databases mainly focus on identifying frequent trajectory patterns,and do not take account of the effect of essential dynamic environmental factors.In this study,a general schema for predicting uncertain trajectories of moving objects with dynamic environment awareness is presented,and the key techniques in trajectory prediction arc addressed in detail.In order to accurately predict the trajectories,a trajectory prediction algorithm based on continuous time Bayesian networks（CTBNs） is improved and applied,which takes dynamic environmental factors into full consideration.Experiments conducted on synthetic trajectory data verify the effectiveness of the improved algorithm,which also guarantees the time performance as well.

Human Action Recognition Based on Dense Trajectories Analysis and Random Forest

This paper presents a human action recognition method. It analyzes the spatio-temporal grids along the dense trajectories and generates the histogram of oriented gradients （HOG） and histogram of optical flow （HOF） to describe the appearance and motion of the human object. Then, HOG combined with HOF is converted to bag-of-words （BoWs） by the vocabulary tree. Finally, it applies random forest to recognize the type of human action. In the experiments, KTH database and URADL database are tested for the performance evaluation. Comparing with the other approaches, we show that our approach has a better performance for the action videos with high inter-class and low inter-class variabilities.

Trajectories of response in schizophrenia-spectrum disorders: A one-year prospective cohort study of antipsychotic effectiveness

BACKGROUND Antipsychotic drugs remain the mainstay of schizophrenia treatment;however,their effectiveness has been questioned,and it is not possible to predict the response to a specific antipsychotic drug in an individual patient.Thus,it is important to compare the effectiveness of the various antipsychotics and search for possible response predictors.AIM To investigate the effectiveness of antipsychotic drugs,we examined response trajectories and predictors for belonging to different trajectory groups.METHODS The Bergen-Stavanger-Innsbruck-Trondheim(BeSt InTro)trial compared the effectiveness of three atypical antipsychotics-amisulpride,aripiprazole,and olanzapine-in a prospective,semirandomized,rater-blind,head-to-head design.Adult participants with a schizophrenia spectrum disorder diagnosis,according to international classification of diseases,Tenth Revision(ICD-10)F20–29,were included.Participants were followed for a period of 12 mo,with assessments at baseline;after one,three and six weeks;and after three,six,nine and 12 mo.A latent class mixed model was fitted to our data.The three-trajectory model based on the Positive and Negative Syndrome Scale(PANSS)total score reduction was found to have adequate fit,and the study drugs,as well as various demographic and clinical parameters,were tested as predictors for belonging to the different trajectory groups.RESULTS Overall,144 participants were included,and 41%completed the 12-mo study period.The largest trajectory group,consisting of 74%of participants,showed a PANSS total score reduction of 59%from baseline to 12 mo(Good response group).A trajectory group comprising 13%of participants had their PANSS total score reduced by 82.5%at 12 mo(Strong response group),while the last response trajectory group comprising 13%of the participants had a PANSS total score reduction of 13.6%(Slight response group).The largest part of the total reduction for the Good and Strong response groups occurred at six weeks of treatment,amounting to 45%and 48%reductions from baseline,respectively.The use of amisulpride predicted belonging to the Strong response group,while unemployment,depression,and negative psychotic symptoms at baseline increased the chance of belonging to the Slight response group,indicating a poor response to antipsychotic drug treatment.CONCLUSION Most of the participants(87%)had a good outcome after one year.Amisulpride users,more often than aripiprazole and olanzapine users,belonged to the response trajectory group with a strong response.

Critical Equatorial Trajectories of Massless Particles in a Kerr Spacetime

In the presented work a closed analytical expression is obtained that describes the critical photon orbits in the equatorial plane of a spinning Kerr black hole (BH). A significant difference in the behavior of photons with prograde and retrograde directions of rotation is shown. The photons with prograde rotation exhibit an exponential increase in the deflection angle together with the number of rotations around the BH as its spin parameter increases. The number of rotations exceeds 103 when spin parameter of the BH reaches 0.999. At the same time this value decreases insignificantly for reverse rotating photons and is less than that for the non-spinning Schwarzschild BH. The transition to a zero spin limit made it possible to determine the number of photon rotations along the critical trajectory for such BHs.

Nonadiabatic Effect on the Rescattering Trajectories of Electrons in Strong Laser Field Ionization Process

The important features of the rescattering trajectories in strong field ionization process such as the cutoff of the return energy at 3.17Up and that of the final energy at 10Up are obtained, based on the adiabatic approximation in which the initial momentum of the electron is assumed to be zero. We theoretically study the nonadiabatic effect by assuming a nonzero initial momentum on the rescattering trajectories based on the semiclassical simpleman model. We show that the nonzero initial momentum will modify both the maximal return energy at collision and the final energy after backward scattering, but in different ways for odd and even number of return trajectories. The energies are increased for even number of returns but are decreased for odd number of returns when the nonzero （positive or negative） initial momentum is applied.