Trajectory Method Research Articles

Reconstruction of Single-Cell Trajectories Using Stochastic Tree Search.

The recent advancement in single-cell RNA sequencing technologies enables the understanding of dynamic cellular processes at the single-cell level. Using trajectory inference methods, pseudotimes can be estimated based on reconstructed single-cell trajectories which can be further used to gain biological knowledge. Existing methods for modeling cell trajectories, such as minimal spanning tree or k-nearest neighbor graph, often lead to locally optimal solutions. In this paper, we propose a penalized likelihood-based framework and introduce a stochastic tree search (STS) algorithm aiming at the global solution in a large and non-convex tree space. Both simulated and real data experiments show that our approach is more accurate and robust than other existing methods in terms of cell ordering and pseudotime estimation.

Third-Generation Dynamic Anterior Plate-Screw System for Quadrilateral Fractures: Digital Design Based on 834 Pelvic Measurements.

Background and Objectives: To investigate the digital measurement method for the plate trajectory of dynamic anterior plate-screw system for quadrilateral plate (DAPSQ), and then design a third-generation DAPSQ plate that conforms to the needs of the Chinese population through collating a large sample anatomical data. Materials and Methods: Firstly, the length of the pubic region, quadrilateral region, iliac region, and the total length of the DAPSQ trajectory were measured by a digital measurement approach in 22 complete pelvic specimens. Then, the results were compared with the direct measurement of pelvic specimens to verify the reliability of the digital measurement method. Secondly, 504 cases (834 hemilateral pelvis) of adult pelvic CT images were collected from four medical centers in China. The four DAPSQ trajectory parameters were obtained with the digital measurement method. Finally, the third-generation DAPSQ plate was designed, and its applicability was verified. Results: There was no statistically significant difference in the four trajectory parameters when comparing the direct measurement method with the digital measurement method (p > 0.05). The average lengths of the pubic region, quadrilateral region, iliac region, and the total length in Chinese population were (60.96 ± 5.39) mm, (69.11 ± 5.28) mm, (84.40 ± 6.41) mm, and (214.46 ± 10.15) mm, respectively. Based on the measurement results, six models of the DAPSQ plate including small size (A1,A2), medium size (B1,B2), and the large size (C1,C2) were designed. The verification experiment showed that all these six type plates could meet the requirement of 94.36% cases. Conclusions: A reliable computerized method for measuring irregular pelvic structure was proposed, which not only provided an anatomical basis for the design of the third-generation DAPSQ plate, but also provided a reference for the design of other pelvic fixation devices.

Pseudo-spectral optimization and model predictive control of vehicle shift process with dual clutch transmission

To improve the shift quality of dual clutch transmission (DCT) vehicles and reduce the jerk and sliding friction in the shift process, a real-time planning of clutch optimal engagement trajectory and control method in the shift process is proposed. This method combines pseudo-spectral optimization, machine learning, and model predictive control. First, considering the jerk, sliding friction work, and shift time as the optimization indices, the adaptive pseudo-spectral method is employed to optimize the engagement trajectory of the clutch during the shift process. Based on the optimal trajectory data set, a gradient boosting decision tree-based real-time planning method for the clutch target engagement trajectory is proposed. Second, a model predictive control strategy for the shift process is proposed based on the DCT system model to track the optimal target trajectory in real-time. Simulations and experiments reveal that the proposed target engagement trajectory planning method can plan the clutch target engagement trajectory for various accelerator pedal openings and initial clutch speed states in real-time, and the proposed model predictive control method can accurately track the target trajectory. Compared with the original vehicle strategy, under 35% and 65% accelerator pedal opening, the maximum absolute value of jerk produced by the proposed strategy was reduced by 31.06% and 31.46%, respectively, and the sliding friction work was reduced by 22.87% and 23.24%, respectively. The shift times of the proposed strategy under 35% and 65% accelerator pedal openings were 19.12% and 20.69% lower than that of the original vehicle strategy, respectively.

A pattern accumulated compression method for trajectories constrained by urban road networks

In an edge computing framework, a moving object in an urban road network can collect both its own and others’ trajectories to answer spatial–temporal queries. How to store the ever increasing amount of trajectories with limited storage space is a great challenge. We observe that the traces of moving objects in urban road networks usually exhibit great repetition in terms of spatial and velocity distributions. So we propose two strategies, Pattern Accumulated Compression based on Average Velocity (PAC-AV) and Pattern Accumulated Compression based on Representative Velocity (PAC-RV), to compress trajectories online on the mobile devices. The former mainly exploits the path pattern to compress trajectories while the latter exploits both the path pattern and the velocity pattern to compress trajectories. Both PAC-AV and PAC-RV compress the trajectories by two stages. First, we extract the spatial as well as velocity components according to a velocity deviation threshold. Second, we compress the components into a series of identifiers leveraging a Path Pattern Dictionary (PPD) and a Velocity Pattern Dictionaries (VPD). Our method not only greatly cuts down the storage space but also directly supports the velocity-related queries on the compressed trajectories. Experimental results demonstrate the effectiveness and efficiency of our method.

Quasi-Classical Trajectory Dynamics Study of the Reaction OH + H2S→H2O + SH and Its Isotopic Variants: Comparison with Experiment

The hydrogen abstraction reaction OH + H2S→H2O + SH plays an important role in acid rain formation, air pollution and climate change. In this work, the product energy disposals of the reaction and its isotopic variants OD + H2S and OD + D2S are calculated on a new ab-initio-based ground electronic state potential energy surface (PES) using the quasi-classical trajectory method. The PES is developed by fitting a total of 72,113 points calculated at the level of UCCSD(T)-F12a/aug-cc-pVTZ and using the fundamental invariant-neural network method, resulting in a total RMSE of 4.14 meV. The product H2O formed in the OH + H2S reaction at 298 K is found to be largely populated in the first overtone states of its symmetric and asymmetric stretching modes, while the vibrational distributions of the products HOD and D2O in the isotopically substituted reactions are visibly different. The computed product vibrational state distributions agree reasonably well with experimental results and are rationalized by the sudden vector projection model.

Real-time trajectory position error compensation technology of industrial robot

In order to meet the requirements of high positioning accuracy and trajectory accuracy of industrial robots in the field of high-precision operation, this paper studied the real-time compensation method of the robot trajectory error used laser tracker to measure the end position of robot in real time. This real-time error calculation method of robot trajectory based on continuous dynamic time warping (CDTW), which was studied to determine the position error of robot trajectory at each moment. Moreover, this paper researched the PID parameter tuning technology of response surface model method based on gray analysis and got a real-time compensation method. The compensation value was fed back to the robot for motion compensation in real time through KUKA RSI. The last, the influence of compensation parameters and period was analyzed and the error compensation experiment of positioning, linear trajectory and arc trajectory were carried out. After compensation, the absolute positioning error of the robot was less than 0.06 mm and the trajectory position error was less than 0.15 mm, which greatly improved the position accuracy of the robot.

Ion-atom-atom three-body recombination: From the cold to the thermal regime.

We present a study on ion-atom-atom reaction A + A + B+ in a wide range of systems and collision energies ranging from 100 μK to 105 K, analyzing two possible products: molecules and molecular ions. The dynamics is performed via a direct three-body formalism based on a classical trajectory method in hyperspherical coordinates developed in Pérez-Ríos et al. [J. Chem. Phys. 140, 044307 (2014)]. Our chief finding is that the dissociation energy of the molecular ion product acts as a threshold energy, separating the low- and high-energy regimes. In the low-energy regime, the long-range tail of the three-body potential dictates the fate of the reaction and the main reaction product. On the contrary, in the high-energy regime, the short-range of atom-atom and atom-ion interaction potential dominate the dynamics, enhancing molecular formation.

MobCal-MPI 2.0: an accurate and parallelized package for calculating field-dependent collision cross sections and ion mobilities.

Ion mobility spectrometry (IMS), which can be employed as either a stand-alone instrument or coupled to mass spectrometry, has become an important tool for analytical chemistry. Because of the direct relation between an ion's mobility and its structure, which is intrinsically related to its collision cross section (CCS), IMS techniques can be used in tandem with computational tools to elucidate ion geometric structure. Here, we present MobCal-MPI 2.0, a software package that demonstrates excellent accuracy (RMSE 2.16%) and efficiency in calculating low-field CCSs via the trajectory method (≤30 minutes on 8 cores for ions with ≤70 atoms). MobCal-MPI 2.0 expands on its predecessor by enabling the calculation of high-field mobilities through the implementation of the 2nd order approximation to two-temperature theory (2TT). By further introducing an empirical correction to account for deviations between 2TT and experiment, MobCal-MPI 2.0 can compute accurate high-field mobilities that exhibit a mean deviation of <4% from experimentally measured values. Moreover, the velocities used to sample ion-neutral collisions were updated from a weighted to a linear grid, enabling the near-instantaneous evaluation of mobility/CCS at any effective temperature from a single set of N2 scattering trajectories. Several enhancements made to the code are also discussed, including updates to the statistical analysis of collision event sampling and benchmarking of overall performance.

Lagrange tracking-based long-term drift trajectory prediction method for Autonomous Underwater Vehicle.

Autonomous Underwater Vehicle (AUV) works autonomously in complex marine environments. After a severe accident, an AUV will lose its power and rely on its small buoyancy to ascend at a slow speed. If the reserved buoyancy is insufficient, when reaching the thermocline, the buoyancy will rapidly decrease to zero. Consequently, the AUV will experience prolonged lateral drift within the thermocline. This study focuses on developing a prediction method for the drift trajectory of an AUV after a long-term power loss accident. The aim is to forecast the potential resurfacing location, providing technical support for surface search and salvage operations of the disabled AUV. To the best of our knowledge, currently, there is no mature and effective method for predicting long-term AUV underwater drift trajectories. In response to this issue, based on real AUV catastrophes, this paper studies the prediction of long-term AUV underwater drift trajectories in the cases of power loss. We propose a three-dimensional trajectory prediction method based on the Lagrange tracking approach. This method takes the AUV's longitudinal velocity, the time taken to reach different depths, and ocean current data at various depths into account. The reason for the AUV's failure to ascend to sea surface lies that the remaining buoyancy is too small to overcome the thermocline. As a result, AUV drifts long time within the thermocline. To address this issue, a method for estimating thermocline currents is proposed, which can be used to predict the lateral drift trajectory of the AUV within the thermocline. Simulation is conducted to compare the results obtained by the proposed method and that in a real accident. The results demonstrate that the proposed approach exhibits small directional and positional errors. This validates the effectiveness of the proposed method.

Low-lying doubly heavy baryons: Regge relation and mass scaling

In framework of heavy-diquark–light-quark endowed with heavy-pair binding, we explore excited baryons QQ^{prime }q containing two heavy quarks (QQ^{prime }=cc,bb,bc) by combining the method of Regge trajectory with the perturbative correction due to the heavy-pair interaction in baryons. Two Regge relations, one linear and the other nonlinear, are constructed semi-classically in the QCD string picture, and a mass scaling relation based on the heavy diquark–heavy antiquark symmetry are employed between the doubly heavy baryons and heavy mesons. We employ the ground-state mass estimates compatible with the observed doubly charmed baryon Xi _{cc} and spectra of the heavy quarkonia to determine the trajectory parameters and the binding energies of the heavy pair, and thereby compute the low-lying masses of the excited baryons Xi _{QQ^{prime }} and Omega _{QQ^{prime }} up to 2S and 1P excitations of the light quark and heavy diquark. The level spacings of heavy diquark excitations are found to be smaller generally than that of the light-quark excitations, in according with the nature of adiabatic expansion between the heavy and light-quark dynamics.

Effect of reactant’s rotational excitation on stereodynamic properties of C + SH($$v = 0, j =0{-}40$$) → H + CS reaction investigated with quasi-classical trajectory method

Effect of reactant’s rotational excitation on stereodynamic properties of C + SH($$v = 0, j =0{-}40$$) → H + CS reaction investigated with quasi-classical trajectory method

A method for detecting abnormal behavior of ships based on multi-dimensional density distance and an abnormal isolation mechanism.

Abnormal ship behavior detection is essential for maritime navigation safety. Most existing abnormal ship behavior detection methods only build A ship trajectory position outlier detection model; however, the construction of a ship speed outlier detection model is also significant for maritime navigation safety. In addition, in most existing methods for detecting a ship's abnormal behavior based on abnormal thresholds, one unsuitable threshold leads to the risk of the ship not being minimized as much as possible. In this paper, we proposed an abnormal ship behavior detection method based on distance measurement and an isolation mechanism. First, to address the problem of traditional trajectory compression methods and density clustering methods only using ship position information, the minimum description length principle based on acceleration (AMDL) algorithm and Multi-Dimensional Density Clustering (MDDBSCAN) algorithm is used in this study. These algorithms not only considered the position information of the ship, but also the speed information. Second, regarding the issue of the difficulty in determining the anomaly threshold, one method for determining the anomaly threshold based on the relationship between the velocity weights and noise points of the MDDBSCAN algorithm has been introduced. Finally, due to the randomness issue of the selected segmentation value in iForest, a strategy of selectively constructing isolated trees was proposed, thus further improving the efficiency of abnormal ship behavior detection. The experimental results on the historical automatic identification system data set of Xiamen port prove the practicality and effectiveness of our proposed method. Our experiment results show that the proposed method achieves an improvement of about 10% over the trajectory outlier detection based on the local outlier fraction method, about 14% over the isolation-based online anomalous trajectory method in terms of the accuracy of ship position information anomaly detection, and about 3% over the feature fusion method in terms of the accuracy of ship speed anomaly detection. This method improves algorithm efficiency by about 5% compared to the traditional isolation forest anomaly detection algorithm.

Full-dimensional potential energy surface for the photodissociation of HNCO via its S1 band.

A full-dimensional potential energy surface (PES) for the first excited state S1(1A'') of HNCO has been built up by the neural network method based on more than 36 000 ab initio points, which were calculated at the multireference configuration interaction level with Davidson correction using the augmented correlation consistent polarized valence triple zeta basis set. It was found that two minima, namely, trans and cis isomers of HNCO, and another seven stationary points exist on the S1 PES for the two dissociation pathways: HNCO(S1) → H + NCO/NH + CO. Particularly, a new out-of-plane transition state between the two minima was found in this work, thanks to including all the degree of freedoms for this system. The adiabatic excitation energy of the S1(1A'') ← S0(1A') transition and dissociation energies D0(HNCO → H + NCO) and D0((HNCO →NH(a1Δ) + CO) calculated on the PES are in good agreement with experimental results. In addition, based on the newly constructed S1 PES, the percentage of products H + NCO in the photodissociation of HNCO(S1) was obtained by a quasi-classical trajectory method at the photon wavelengths ranging from 190 to 225 nm, which is in reasonably good agreement with earlier theoretical and experimental results. For the dissociation lifetimes of the trajectories, they were calculated to be less than 5 ps, which is also consistent with experimental observations.

ANALISA KESTABILAN TRANSIEN MENGGUNAKAN METODE TRAJEKTORI KRITIS PADA SISTEM WILAYAH SUMBAR

This research is to examine the transient stability analysis using the critical trajectory method in the system of the West Sumatra region. Transient stability plays an important role for safety and reliability in the electric power system which aims to estimate the condition of the system when an outage occurs, either in the form of line discharge or generator discharge. This study discusses the stability of transients that occur due to disturbances in the system that affect the generator. When a disturbance occurs, the system will be in a transient state. In this condition, the safety relay will work to open the circuit breaker within a certain time. However, this does not guarantee that the system will return to steady state conditions. This study discusses the stability of transients that occur due to disturbances in the system that affect the generator. When a disturbance occurs, the system will be in a transient state. In this condition, the safety relay will work to open the circuit breaker within a certain time. However, this does not guarantee that the system will return to steady state conditions. After the disturbance the system will return to stability with a tcb open time of 0.300 second, while when the release of channel 10 between the Pauh Limo-Simpang Haru buses occurs with a tcb open time of 0.250 seconds, the critical clearing time value is 1.143 seconds, then the critical path that occurs in the simulation results the time of the loose line between the Pauh Limo-Simpang Haru bus is 1.143-1.144 second.

An observability and detectability analysis for non-linear uncertain CSTR model of biochemical processes

The problem of proving observability/detectability properties for selected non-linear uncertain model of biochemical processes has been addressed in this paper. In particular, the analysis of observability/detectability in the face of parametric and unstructured uncertainty in system dynamics transformed into unknown inputs, and unknown initial conditions has been performed. Various sets of system measured outputs were taken into account during the research. The considered biochemical processes were modelled as a continuous stirred tank reactor with the microbial growth reaction and microbial mortality with the aggregated substrate and biomass concentrations in aerobic phase. Classical tools based on differential geometry and the method of indistinguishable state trajectories (indistinguishable dynamics) were used to verify the properties of the system. The observability/detectability analysis was performed for nine cases covering a wide range of possible combinations of system measured outputs and unknown inputs. The obtained results of are crucial meaning for system state reconstruction (estimation), which involves the synthesis of state observers.

Trajectory analysis for low-order harmonic generation in two-color strong laser fields.

Focusing two-color laser fields in gas-phase medium produces ultrashort ultra-broadband low-order harmonics spanning from terahertz to extreme ultraviolet regime. The low-order harmonic generation can be explained by both macroscopic photocurrent model and microscopic strong field approximation theory. Here, we analytically build a bridge between the macroscopic and microscopic theories by means of the trajectory method, which manifests correspondences between macroscopic and microscopic theories. And we demonstrate the trajectory analysis to explain phase-dependent terahertz and third-harmonic generations, and contribute the phase-dependent yields and spectral shapes to the coherent superposition of electron trajectories released at distinct ionization instants, reflecting electron interfering with itself in radiation process. The trajectory method readily connects the low-order harmonics characteristics and behaviors of electron wavepacket, which has potential for reconstructing ultrafast electron dynamics by means of low-harmonics observations.

Quasiclassical approaches to the generalized quantum master equation.

The formalism of the generalized quantum master equation (GQME) is an effective tool to simultaneously increase the accuracy and the efficiency of quasiclassical trajectory methods in the simulation of nonadiabatic quantum dynamics. The GQME expresses correlation functions in terms of a non-Markovian equation of motion, involving memory kernels that are typically fast-decaying and can therefore be computed by short-time quasiclassical trajectories. In this paper, we study the approximate solution of the GQME, obtained by calculating the kernels with two methods: Ehrenfest mean-field theory and spin-mapping. We test the approaches on a range of spin-boson models with increasing energy bias between the two electronic levels and place a particular focus on the long-time limits of the populations. We find that the accuracy of the predictions of the GQME depends strongly on the specific technique used to calculate the kernels. In particular, spin-mapping outperforms Ehrenfest for all the systems studied. The problem of unphysical negative electronic populations affecting spin-mapping is resolved by coupling the method with the master equation. Conversely, Ehrenfest in conjunction with the GQME can predict negative populations, despite the fact that the populations calculated from direct dynamics are positive definite.

Biomechanical comparison of pedicle screw fixation strength among three different screw trajectories using single vertebrae and one-level functional spinal unit.

Three key factors are responsible for the biomechanical performance of pedicle screw fixation: screw mechanical characteristics, bone quality and insertion techniques. To the best of the authors' knowledge, no study has directly compared the biomechanical performance among three trajectories, i.e., the traditional trajectory (TT), modified trajectory (MT) and cortical bone trajectory (CBT), in a porcine model. This study compared the pullout strength and insertion torque of three trajectory methods in single vertebrae, the pullout strength and fixation stiffness including flexion, extension, and lateral bending in a one-level instrumented functional spinal unit (FSU) that mimics the in vivo configuration were clarified. A total of 18 single vertebrae and 18 FSUs were randomly assigned into three screw insertion methods (n = 6 in each trajectory group). In the TT group, the screw converged from its entry point, passed completely inside the pedicle, was parallel to the superior endplate, was located in the superior third of the vertebral body and reached to at least the anterior third of the vertebral body. In the MT group, the convergent angle was similar to that of the TT method but directed caudally to the anterior inferior margin of the vertebral body. The results of insertion torque and pullout strength in single vertebrae were analyzed; in addition, the stiffness and pullout strength in the one-level FSU were also investigated. This study demonstrated that, in single vertebrae, the insertion torque was significantly higher in CBT groups than in TT and MT groups (p < 0.05). The maximal pullout strength was significantly higher in MT groups than in TT and CBT groups (p < 0.05). There was no significant difference in stiffness in the three motions among all groups. The maximal pullout strength in FSUs of MT and CBT groups were significantly higher than the TT groups (p < 0.05). We concluded that either MT or CBT provides better biomechanical performance than TT in single vertebrae or FSUs. The lack of significance of stiffness in FSUs among three methods suggested that MT or CBT could be a reasonable alternative to TT if the traditional trajectory was not feasible.

A Generalized Current Trajectory Based Fault Diagnostic Method for Three-Phase Two-Level Inverters

Inverters play a vital role in the distributed generated energy systems. Hence, the reliability of the entire distributed energy system depends on the consistent and continuous operation of the inverter. Consequently, to maintain a reliable operation, effective condition monitoring and fault diagnostic schemes have to be incorporated. In this paper, a method based on current trajectory is analyzed for the fault detection and diagnosis of open-switch faults in three-phase two-level voltage source inverters (VSI). The current trajectory-based method of fault diagnosis has been already presented literature for the identification and localization of open-switch fault in the three-phase two-level VSI. The main drawback of the existing current trajectory method is that the fault diagnosis and detection is dependent on the phase currents selected to plot the current trajectories. Therefore, in this paper, a generalization is proposed for the fault diagnosis and diagnosis based on the current trajectory, which make the method independent of the selection of the phase current used to plot the current trajectory. The validity and effectiveness of the proposed generalization is verified by simulation and experiments in a laboratory prototype of three-phase two-level VSI.

Staying the course: iteratively locating equilibria of dynamical systems on Riemannian manifolds defined by point-clouds

We introduce a method to successively locate equilibria (steady states) of dynamical systems on Riemannian manifolds. The manifolds need not be characterized by an a priori known atlas or by the zeros of a smooth map. Instead, they can be defined by point-clouds and sampled as needed through an iterative process. If the manifold is an Euclidean space, our method follows isoclines, curves along which the direction of the vector field $X$ is constant. For a generic vector field $X$, isoclines are smooth curves and every equilibrium lies on isoclines. We generalize the definition of isoclines to Riemannian manifolds through the use of parallel transport: generalized isoclines are curves along which the directions of $X$ are parallel transports of each other. As in the Euclidean case, generalized isoclines of generic vector fields $X$ are smooth curves that connect equilibria of $X$. Our algorithm can be regarded as an extension of the method of Newton trajectories to the manifold setting when the manifold is unknown. This work is motivated by computational statistical mechanics, specifically high dimensional (stochastic) differential equations that model the dynamics of molecular systems. Often, these dynamics concentrate near low-dimensional manifolds and have transitions (saddle points with a single unstable direction) between metastable equilibria. We employ iteratively sampled data and isoclines to locate these saddle points. Coupling a black-box sampling scheme (e.g., Markov chain Monte Carlo) with manifold learning techniques (diffusion maps in the case presented here), we show that our method reliably locates equilibria of $X$.