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.

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.

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.

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.

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.

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.

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.

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.

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.

Particle trajectories under interactions between solitary waves and a linear shear current

This paper is concerned with particle trajectories beneath solitary waves when a linear shear current exists.The fluid is assumed to be incompressible and inviscid,lying on a flat bed.Classical asymptotic expansion is used to obtain a Korteweg-de Vries(Kd V)equation,then a forth-order Runge-Kutta method is applied to get the approximate particle trajectories.On the other hand,our particular attention is paid to the direct numerical simulation(DNS)to the original Euler equations.A conformal map is used to solve the nonlinear boundary value problem.Highaccuracy numerical solutions are then obtained through the fast Fourier transform(FFT)and compared with the asymptotic solutions,which shows a good agreement when wave amplitude is small.Further,it also yields that there are different types of particle trajectories.Most surprisingly,periodic motion of particles could exist under solitary waves,which is due to the wave-current interaction.

Symptom trajectories in patients with breast cancer:An integrative review

Objective This study aimed to synthesize the available knowledge of symptom trajectories in patients with breast cancer and identify predictors associated with these trajectories.Methods Whittemore and Knafl’s integrative review method was employed to guide a systematic search for literature in four databases(PubMed,Embase,Web of Science,and CINAHL).The retrieved articles’publication time was limited to 2010 to 2020,and only peer-reviewed English articles were included.Results Twenty-seven articles were included.The findings of the relevant studies were analyzed using thematic analysis.They were grouped into two themes:symptom trajectories of patients with breast cancer(symptom trajectories in patients with breast cancer,in patients who underwent surgery,and in patients who received cancer-related treatment)and associated factors(socioeconomic factors,health characteristics,cancer-related treatment characteristics).Newly diagnosed patients tended to report high trajectories of depression and persistent sleep disturbance.Most patients who underwent surgery reported significant sleep disturbance and anxiety shortly after surgery.For patients who received cancer-related treatment,only a small proportion had a high level of physical activity after cancer-related therapy over time.A high body mass index,a low relationship quality,parental responsibilities,insufficient social support,a low educational background,and an unhealthy lifestyle may increase the risk of negative symptom trajectories in patients with breast cancer.Additionally,old patients were more likely to report cognitive impairment after chemotherapy,while young patients tended to report trajectories of persistent sexual dysfunction.Concurring symptoms and poor health status also contributed to adverse symptom trajectories.Conclusion The findings of this review add to the body of knowledge of the interindividual variability of symptom trajectories in patients with breast cancer.Despite the overall similarity in appraisal at baseline,the patients reported varied symptom trajectories over time.It is recommended that nurses consider sociodemographic,clinical and cancer-related treatment characteristics and perform targeted early preventive interventions for patients with breast cancer.

Topset‑to‑forest rollover trajectories as reliable predictors of sediment‑volume partitioning into deep‑lake areas

Topset-to-forest rollover trajectories and their relation to sediment-and sand-budget partitioning into deep-lake areas are far from being well understood,as compared with their marine counterparts of shelf edges.Two quantitatively distinctive topset-to-forest rollover trajectories and clinothem-stacking patterns were recognized in the Oligocene Qikou Sag of the Bohai Bay Basin and are quantifed in terms of trajectory angles(T_(se)),topset thickness(T_(t)),forest thickness(T_(f)),bottomset thickness(T_(b)),and clinothem-set relief(R_(c)).Rising topset-to-forest trajectories have positive T_(se) of 0.15°-0.51°(averaging 0.35°).Ranges in T_(t),T_(f),T_(b),and R_(c) of their associated progradational and aggradational clinothem sets are,respectively,32.4-58.7 m(averaging 42.7 m),76.9-176.2 m(averaging 148.3 m),0 m,and 167.8-320.8 m(averaging 272.9 m).Falling topset-to-forest rollover trajectories,in contrast,have negative T_(se) of−0.12°to−0.02°(averaging−0.06°).Ranges in T_(t),T_(f),T_(b),and R_(c) of their associated progradational and downstepping clinothem sets are,respectively,0 m,266.0-395.7 m(averaging 333.4 m),441.1-542.5 m(averaging 464.1),and 874.9-922.6 m(averaging 892.5 m).These two topset-to-forest rollover trajectories and clinothem-stacking patterns are closely linked to two distinctive patterns of sediment-and sandvolume partitioning into deep-lake areas,which are quantifed in terms of T_(t),T_(b),and diferential sediment aggradation of topset segments and forest-to-bottomset compartments(As/Ad).Rising topset-to-forest rollover trajectories and associated progradational and aggradational clinothem sets are characterized by aggradational topsets(reported as T_(t) of 32.4-58.7 m),a lack of time-equivalent bottomsets,and As/Ad of 0.22-0.87(averaging 0.33),and are fronted by mud-dominated depositional deposits,with sporadic occurrence of thinner and regionally localized forest sands.They are,therefore,inefcient at delivering terrestrial sediments or sands into deep-lake settings.Falling topset-to-forest rollover trajectories and associated progradational and downstepping clinothem sets,in contrast,are characterized by toplap,erosional terminations but aggradational bottomsets(reported as T_(b) of 266.0-473.4 m),and As/Ad of 0,and are fronted by sand-rich depositional deposits,with widespread occurrence of thicker and regionally extensive time-equivalent deep-lake bottomset sands.They are,thus,efcient at delivering terrestrial sediments or sands into deep-lake settings.Topset-to-forest rollover trajectories and associated clinothem-stacking patterns are thus reliable predictors of sediment-and sand-volume partitioning into deep-lake areas,assisting greatly in developing a more dynamic stratigraphy.

Clustered trajectories anonymity in wireless sensor networks

This paper proposes a clustered trajectories anonymity scheme （CTA） that enhances the kano nymity scheme to provide the intended level of source location privacy in mobile event monitoring when a global attacker is assumed. CTA applies isomorphic property of rotation to create traces of the fake sources distributions which are similar to those of the real sources. Thus anonymity of each trajectory and that of the clustered is achieved. In addition, location kdiversity is achieved by dis tributing fake sources around the base station. To reduce the time delay, tree rooted at the base sta tion is constructed to overlap part of the beacon interval of the nodes in the hierarchy. Both the ana lytical analysis and the simulation results prove that proved energy overhead and time delay. our scheme provides perfect anonymity with improved energy overhead and time delay.

An Analysis of the Air Parcel Trajectories of Long-Range Transport at Shanghai

1.INTRODUCTION Acid rain observations show that acid cloud water in Shanghai region appears not only

Quantum Interference by Entangled Trajectories

The quantum interference pattern in the double-slit experiment is qualitatively reproduced by using the entangled trajectory molecular dynamics method and compared with previous works. We compare entangled trajectory and classical trajectory with the same initial state in the phase space to show quantum effect in the evolution of trajectories. It is involved with breakdown in the statistical independence of the trajectories. Although our result does not agree well with exact quantum calculation in quantitatively with loss of part of interference pattern peaks, we can offer a reasonable explanation by analyzing quantum interference of two Gaussian wave packets in the phase space.

Which Proof We Have against Continuous Trajectories for Particles?

It is in general accepted that the concept of continuous trajectories for particles is at odds with the relativistic quantum mechanics. Namely, when examining the evolution of entangled quantum objects according to frames of coordinates in relative move-ment, one gets contradictory trajectories. Such a situation is typically derived from the famous “Hardy’s paradox”. However, it is argued here that if the rationale ignores the principle of quantum contextuality, as happens typically when using Hardy’s thought-experiment, the conclusion—rejection of the assumption of trajectories—is questionable. The issue is exemplified by an additional example: the 101 property of spin 1 bosons implies conflicting trajectories when the singlet state of two such bosons is examined according to frames in relative movement. It is concluded here that in the absence of a rationale which doesn’t violate the quantum contextuality, there are no sufficient arguments for refuting the possibility of a substructure of the quantum mechanics, consisting in particles following continuous trajectories.