Trajectory Perturbations Research Articles

COmoving Computer Acceleration (COCA): N-body simulations in an emulated frame of reference

N-body simulations are computationally expensive and machine learning (ML) based emulation techniques have thus emerged as a way to increase their speed. Surrogate models are indeed fast, however, they are limited in terms of their trustworthiness due to potentially substantial emulation errors that current approaches are not equipped to correct. To alleviate this problem, we have introduced COmoving Computer Acceleration (COCA), a hybrid framework interfacing ML algorithm with an N-body simulator. The correct physical equations of motion are solved in an emulated frame of reference, so that any emulation error is corrected by design. Thus, we are able to find a solution for the perturbation of particle trajectories around the ML solution. This approach is computationally cheaper than obtaining the full solution and it is guaranteed to converge to the truth as the number of force evaluations is increased. Even though it is applicable to any ML algorithm and N-body simulator, we assessed this approach in the particular case of particle-mesh (PM) cosmological simulations in a frame of reference predicted by a convolutional neural network. In such cases, the time dependence is encoded as an additional input parameter to the network. We find that COCA efficiently reduces emulation errors in particle trajectories, requiring far fewer force evaluations than running the corresponding simulation without ML. As a consequence, we were able to obtain accurate final density and velocity fields for a reduced computational budget. We demonstrate that this method exhibits robustness when applied to examples outside the range of the training data. When compared to the direct emulation of the Lagrangian displacement field using the same training resources, COCA's ability to correct emulation errors results in more accurate predictions. Therefore, COCA makes N-body simulations cheaper by skipping unnecessary force evaluations, while still solving the correct equations of motion and correcting for emulation errors made by ML.

Vector-Indistinguishability: Location Dependency Based Privacy Protection for Successive Location Data

With the wide use of GPS enabled devices and Location-Based Services, location privacy has become an increasingly worrying challenge to our community. Existing approaches provide solid bases for addressing this challenge. However, they mainly focus on independent location perturbation or whole trajectory perturbation with little attention to location dependency based perturbation between two successive locations. This may result in that perturbed successive locations lose mutual distance and direction dependency, which in turn can lead to significant data utility loss. To address this problem, we propose a new location dependency based privacy notion named as vector-indistinguishability (vector-ind). Vector-ind defines a vector to represent the dependency relationship between two successive locations. Correspondingly, it consists of distance-indistinguishability for distance dependency and direction-indistinguishability for direction dependency. Noise generation for applying Differential Privacy is based on the distance and direction, hence can reflect the location dependency to ensure data utility after perturbation. We also present four mechanisms to achieve vector-ind notion. Finally, we evaluate the empirical privacy and utility of vector-ind in real-world GPS data to demonstrate how our proposed mechanisms for vector-ind can protect location privacy with high data utility in successive location data.

Stochastic perturbations in the semi-Lagrangian advection algorithm of the SL-AV global atmosphere model

Abstract An algorithm for stochastic perturbation of the semi-Lagrangian trajectories is implemented in the ensemble weather prediction system based on the global atmosphere model SL-AV20 with a horizontal resolution of approximately 20 km, 51 vertical levels, and Local Ensemble Transform Kalman Filter (LETKF). The combined use of methods for stochastic perturbation of trajectories and the parameters and tendencies of subgrid-scale processes parameterizations allows to generate ensembles with a larger spread compared to ensembles without stochastic perturbations of trajectories. An improvement in probabilistic estimates of the ensemble forecasts for various variables is shown. The comparison of two versions of ensemble prediction system is presented.

Trajectory Data Collection with Local Differential Privacy

Trajectory data collection is a common task with many applications in our daily lives. Analyzing trajectory data enables service providers to enhance their services, which ultimately benefits users. However, directly collecting trajectory data may give rise to privacy-related issues that cannot be ignored. Local differential privacy (LDP), as the de facto privacy protection standard in a decentralized setting, enables users to perturb their trajectories locally and provides a provable privacy guarantee. Existing approaches to private trajectory data collection in a local setting typically use relaxed versions of LDP, which cannot provide a strict privacy guarantee, or require some external knowledge that is impractical to obtain and update in a timely manner. To tackle these problems, we propose a novel trajectory perturbation mechanism that relies solely on an underlying location set and satisfies pure ε-LDP to provide a stringent privacy guarantee. In the proposed mechanism, each point's adjacent direction information in the trajectory is used in its perturbation process. Such information serves as an effective clue to connect neighboring points and can be used to restrict the possible region of a perturbed point in order to enhance utility. To the best of our knowledge, our study is the first to use direction information for trajectory perturbation under LDP. Furthermore, based on this mechanism, we present an anchor-based method that adaptively restricts the region of each perturbed trajectory, thereby significantly boosting performance without violating the privacy constraint. Extensive experiments on both real-world and synthetic datasets demonstrate the effectiveness of the proposed mechanisms.

Numerical study of the formation and stability of a pair of particles of different sizes in inertial microfluidics

The formation of pairs and trains of particles in inertial microfluidics is an important consideration for device design and applications, such as particle focusing and separation. We study the formation and stability of linear and staggered pairs of nearly rigid spherical particles of different sizes in a pressure-driven flow through a straight duct with a rectangular cross section under mild inertia. An in-house lattice-Boltzmann-immersed-boundary-finite-element code is used for three-dimensional simulations. We find that the stability and properties of pairs of heterogeneous particles strongly depend on particle sizes and their size ratio, while the formation of the pairs is also determined by the initial lateral position and the axial order of the particles. Our findings imply that perturbations of particle trajectories caused by other particles, as they are expected to happen even in dilute suspensions, can be important for the formation of stable pairs in inertial microfluidics.

Movement is governed by rotational neural dynamics in spinal motor networks.

Although the generation of movements is a fundamental function of the nervous system, the underlying neural principles remain unclear. As flexor and extensor muscleactivities alternate during rhythmic movements such as walking, it is often assumed that the responsible neural circuitry is similarly exhibiting alternating activity1. Here we present ensemble recordings of neurons in the lumbar spinal cord that indicate that, rather than alternating, the population is performing a low-dimensional 'rotation' in neural space, in which the neural activity is cycling through all phases continuously during the rhythmic behaviour. The radius of rotation correlates with the intended muscle force, and a perturbation of the low-dimensional trajectory can modify the motor behaviour. As existing models of spinal motor control do notoffer an adequate explanation of rotation1,2, we propose a theory of neural generation of movements from which this and other unresolved issues, such as speed regulation, force control and multifunctionalism, are readily explained.

Investigation of the Increment of Transverse Instability of a Kiloampere Electron Beam in a Linear Induction Accelerator for Its Use in a Terahertz FEL

The Institute of Nuclear Physics SB RAS in cooperation with the Russian Federal Nuclear Center VNIITF performs a series of researches aimed at acquiring a relative electron beam with energy up to 20 MeV, current up to 2 kA, and duration up to 200 ns at normalized emittance ca. 1000 π∙mm∙rad in a linear induction accelerator (LIA). In order to generate electron beams with such parameters we require thorough investigation of all main sources of perturbation of electron beam trajectory caused by different instabilities that occur during the transport and acceleration of a high currency beam in the accelerating structure of LIA. For the experimental series on measuring the dynamics of transverse oscillation of a beam, we applied a set of fast current transformers which are used for registration of beam current and mode fields caused by this beam in the structure. These measurements were performed for the electron beam with the energy of 8.5 MeV and current of 1 kA going through the structure at different modes of focusing magnetic fields size in LIA. As a result, we registered oscillation of the electromagnetic field of normal modes in the accelerating modules of LIA, as well as we determined the dependence of the oscillation amplitude of these modes’ EM field on the number of accelerating module. This dependence was compared with the result of modeling of development dynamics of transverse instability in LIA that was performed using the created program system. This allowed us to determine the size of the increment of transverse instability of a relativistic electron beam under the given experimental conditions. Based on the acquired results, we made the analysis of possibility to use the beam generated in ILA as a driver for the FEL generator of coherent impulses of THz radiation within the frequency range of 0.3–1.2 THz with a sub-gigawatt level of power.

Capturing of particles in suspension flow through a micro cross-shaped channel

Capturing of microscale particles through microfluidics has been a flourishing research area in chemical and biological engineering applications. This work follows our previous report (Zhang et al., AIChE J., vol. 66, 2019, e16822) by using micro plane laser-induced fluorescence (μPLIF) and high-speed photography technology to study the flow of a diluted suspension of buoyant particles in a micro cross-shaped channel at 30≤Re≤350. Particular attention is paid to particle accumulation behaviors caused by vortex breakdown within the steady engulfment flow and vortex shedding flow. Three particle capture modes are identified in accumulation regions including the particle chain mode, the steady and unsteady particle cluster mode at 100≤Re≤300. Multiple stable equilibrium orbits formed by captured particles in accumulation regions are attributed to the axial force balance. In addition, perturbations in particle trajectories induced by the vortex shedding flow or particle-particle interactions contribute to the particle release.

B-plane and Picard–Chebyshev integration method: Surfing complex orbital perturbations in interplanetary multi-flyby trajectories

Orbital resonances have been exploited in different contexts, with the latest interplanetary application being the ESA/NASA mission Solar Orbiter, which uses repeated flybys of Venus to change the ecliptic inclination with low fuel consumption. The b-plane formalism is a useful framework to represent close approaches at the boundaries of the sphere of influence of the flyby planet. In the presented work, this representation is exploited to prune the design of perturbed resonant interplanetary trajectories in a reverse cascade, replacing the patched conics approximation with a continuity link between flybys and interplanetary legs. The design strategy splits the flyby time and state variables in a two-layer optimization problem. Its core numerically integrates the perturbed orbital motion with the Picard–Chebyshev integration method. The analytical pruning provided by the b-plane formalism is also used as starting guess to ensure the fast convergence of both the numerical integration and the trajectory design algorithm. The proposed semi-analytical strategy allows to take advantage of complex gravitational perturbing effects optimizing artificial maneuvers in a computationally efficient way. The method is applied to the design of a Solar Orbiter-like quasi-ballistic first resonant phase with Venus.

Personalized trajectory privacy-preserving method based on sensitive attribute generalization and location perturbation

Trajectory data may include the user’s occupation, medical records, and other similar information. However, attackers can use specific background knowledge to analyze published trajectory data and access a user’s private information. Different users have different requirements regarding the anonymity of sensitive information. To satisfy personalized privacy protection requirements and minimize data loss, we propose a novel trajectory privacy preservation method based on sensitive attribute generalization and trajectory perturbation. The proposed method can prevent an attacker who has a large amount of background knowledge and has exchanged information with other attackers from stealing private user information. First, a trajectory dataset is clustered and frequent patterns are mined according to the clustering results. Thereafter, the sensitive attributes found within the frequent patterns are generalized according to the user requirements. Finally, the trajectory locations are perturbed to achieve trajectory privacy protection. The results of theoretical analyses and experimental evaluations demonstrate the effectiveness of the proposed method in preserving personalized privacy in published trajectory data.

Estimation of the thermospheric density using ephemerides of the CYGNSS and Swarm constellations

Modeling the neutral density in the upper atmosphere is a major challenge as it involves a comprehensive understanding of the complex coupling between the thermosphere and its environment. In addition, this system is strongly driven by solar activity, which is hardly predictable. This complexity limits the ability of thermospheric models to accurately estimate thermospheric characteristics, such as the neutral density. With the rapidly increasing number of satellites in orbit and the recent progress in tracking their trajectories, new techniques are being implemented to derive density estimates based on trajectory perturbations. However, most of these methods require the integration of complex and costly orbit determination algorithms, which greatly limit their applicability at a public level. The approach presented here provides density estimates along a spacecraft trajectory and only requires the implementation of an orbit propagator. More specifically, it corrects density predictions made by the NRLMSIS00e thermosphere model by optimizing the orbit fitting of modeled trajectories with observations under different thermospheric density conditions. The algorithm is applied to the Cyclone Global Navigation Satellite System and Swarm-B spacecraft trajectories during a period of varying geomagnetic activity. The study puts in evidence a bias in NRLMSIS00e estimates during moderate solar activity, corrected by the algorithm. In addition, the approach provides a better characterization of the rapid density enhancement resulting from a geomagnetic storm. Overall, the correlation with the Level 2 data is improved by 15% and the normalized root mean square error decreased by a factor ~2.3, compared to the estimations with NRLMSIS00e.

Approximate Representations of Shaped Pulses Using the Homotopy Analysis Method.

The evolution of nuclear spin magnetization during a radiofrequency pulse in the absence of relaxation or coupling interactions can be described by three Euler angles. The Euler angles in turn can be obtained from the solution of a Riccati differential equation; however, analytic solutions exist only for rectangular and chirp pulses. The Homotopy Analysis Method is used to obtain new approximate solutions to the Riccati equation for shaped radiofrequency pulses in NMR spectroscopy. The results of even relatively low orders of approximation are highly accurate and can be calculated very efficiently. The results are extended in a second application of the Homotopy Analysis Method to represent relaxation as a perturbation of the magnetization trajectory calculated in the absence of relaxation. The Homotopy Analysis Method is powerful and flexible and is likely to have other applications in magnetic resonance.

О динамическом хаосе фазовых траекторий системы атомов кристалла

The molecular dynamics method is used to study the stability of phase trajectories of ions of a NaCl crystal to the perturbation of the initial data. It is shown that there is a local instability of perturbations of the phase trajectories of the system both in the configuration space and in the velocity space. At the initial stage, small perturbations grow exponentially, growth increments are the same in both cases, and they depend on the structure of the crystal and its temperature. With increasing the temperature, growth increments increase too. Further, the growth of perturbations slows down, and they reach a “plateau” value, the characteristic size of which in the configuration space is comparable with the size of the ion localization region, and in the velocity space with its maximum velocity. In addition, it was found that the velocity autocorrelation function of all ions decays to zero, i.e., their mixing takes place in the system in addition to the local instability of phase trajectories. Thus, a dynamic chaos takes place in the system of atoms of crystalline matter.

Trajectory Perturbation in Surrogate Safety Indicators

Traffic conflicts based surrogate safety indicators have been applied extensively on real trajectories and in simulation. Such indicators can be useful to assess the safety of a given scenario without the need to use real crash data (which in many cases may be unavailable). Unfortunately, all traffic conflict indicators that are commonly used have a structural limitation: they are not able to consider potential conflicts with roadside obstacles or barriers and conflicts between vehicles which are travelling on non-conflicting trajectories. This limitation is a serious limitation since crash data analy sis shows that at least 40% of fatal crashes are originated by single vehicle accidents against a fixed object or by vehicles travelling in opposite directions. This paper is intended as a concept paper that presents an alternative view on conflict safety indicators showing that new indicators can be generated by the perturbation of vehicle trajectories overcoming the above indicated limitations.

Second-Order Trajectory Sensitivity Analysis of Hybrid Systems

Hybrid dynamical systems are characterized by intrinsic coupling between continuous dynamics and discrete events. This paper has adopted a differential-algebraic impulsive switched (DAIS) model to capture such dynamic behavior. For such systems, trajectory sensitivity analysis provides a valuable approach for describing perturbations of system trajectories resulting from small variations in initial conditions and/or uncertain parameters. The first-order sensitivities have been fully described for hybrid system and used in a variety of applications. This paper formulates the differential-algebraic equations (DAE) that govern second-order sensitivities over regions where dynamics are smooth, i.e., away from events. It also establishes the jump conditions that describe the step change in second-order sensitivities at discrete (switching and state reset) events. These results together fully characterize second-order sensitivities for general hybrid dynamical system.

A prospective cohort for the investigation of alteration in temporal transcriptional and microbiome trajectories preceding preterm birth: a study protocol

IntroductionPreterm birth (PTB) results from heterogeneous influences and is a major contributor to neonatal mortality and morbidity that continues to have adverse effects on infants beyond the neonatal period. This...

Resolving range aliasing in Omega-K synthetic aperture beamforming

The Omega-K algorithm is a beamforming algorithm that exploits Stolt migration in the wavenumber domain to focus stripmap synthetic aperture data. Because of its efficiency and its inherently broad-band properties it has been a common solution for synthetic aperture beamforming problems, especially in situations where trajectory perturbations are small and computational resources are limited. The algorithm is commonly divided into two stages: a bulk compression stage leveraging a phase multiplication in the wavenumber domain (sometimes used in isolation for resonance and shadow enhancement), which focuses data at the scene center, and Stolt migration which brings the entire scene into focus. For systems with very broad beamwidth the bulk compression stage can lead to spatial aliasing for close range scatterers, causing a loss of spatial spectrum information and increased noise. The cause of this frequently overlooked aliasing problem, its manifestation in SAS images, and methods for its avoidance will be discussed and demonstrated using both simulations and ClutterEX17 sonar data.

Stochastic Estimation of Ephemerides of Navigation Satellites in Perturbed Orbits

The errors of navigation satellite ephemerides are one of the key factors to determine the accuracy of satellite navigation. To improve the accuracy of ephemerides calculation, modern satellites are equipped with inter-satellite measurement equipment. However, random interference is inevitably present in the data transmission path and it is necessary to minimize its effect. To perform this task, it is proposed to use the stochastic estimation of ephemerides of navigation satellites that are moving along disturbed orbits in the form of a procedure of parametric optimization based on the minimization of the additive set of two functionals. The optimization of the first functional provides the minimum of uncertainty in the estimation of ephemerides. The optimization of the second functional provides the minimum of the norm of the vector of orbital parameters variations in the current time interval. To illustrate the effectiveness of the proposed approach, a numerical simulation of the satellite constellation’s ephemerides estimation was carried out for the corresponding trajectory perturbations. The simulation results illustrate the possibility to determine the ephemerides of navigation satellites with the accuracy within units of meters based on the approach considered that uses the noisy inter-satellite measurements.

Dynamics of rheological heterogeneities in mantle plumes

The geochemical record of Hawaiian basalts has been interpreted to reflect vertically stretched, partly filament-like heterogeneities in the Hawaiian plume, but one alternative interpretation has been that this record reflects intra-conduit mixing, caused by rheological contrasts across the conduit. Here we present numerical simulations of a mantle plume carrying rheological heterogeneities λ times more viscous than the surrounding fluid. Our first objective is to quantify how the heterogeneity deforms during upwelling. We find a full spectrum of shapes, from stretched filaments to nearly undeformed blobs, and we map the respective stability domain as a function of the viscosity ratio λ and of the flow characteristics, including the plume buoyancy flux. Our second objective is to test the hypothesis that a rheological heterogeneity can cause intra-conduit mixing. Although horizontal velocities do appear across the plume conduit, we have not found any toroidal “doughnut-shaped swirl” mode. Instead we show that perturbations of the flow trajectories are a local phenomenon, unable to cause permanent mixing. Our third objective is to determine over which time-scales a rheological heterogeneity crosses the magma capture zone (MCZ) beneath a hotspot volcano. For a blob-like heterogeneity of radius 30–40 km and viscosity ratio 15–20, the crossing time-scale is less than 1 Myr. Contrary to a stretched filament, a blob can entirely fill the MCZ, thereby representing the unique source rock of partial melts feeding a volcano. If the heterogeneity has a distinct isotopic fingerprint (or a distinct fertility), surface lavas will then record an isotopic fluctuation (or a fluctuation in melt productivity) lasting 0.5–0.8 Myr. Our simulations predict that such fluctuations should occur preferentially in low buoyancy flux hotspots, where blob-like rheological heterogeneities are more easily preserved than in the vigorous Hawaiian plume.

Reprojection Alignment for Trajectory Perturbation Estimation in Microtomography

For standard laboratory microtomography systems, acquired radiographs do not always adhere to the strict geometrical assumptions of the reconstruction algorithm. The consequence of this geometrical inconsistency is that the reconstructed tomogram contains motion artifacts, e.g., blurring, streaking, double-edges. To achieve a motion-artifact-free tomographic reconstruction, one must estimate, and subsequently correct for, the per-radiograph experimental geometry parameters. In this paper, we examine the use of re-projection alignment (RA) to estimate per-radiograph geometry. Our simulations evaluate how the convergence properties of RA vary with: motion-type (smooth versus random), trajectory (helical versus discrete-sampling ‘space-filling’ trajectories) and tomogram resolution. The idealized simulations demonstrate for the space-filling trajectory that RA convergence rate and accuracy is invariant with regard to the motion-type and that the per-projection motions can be estimated to less than 0.25 pixel mean absolute error by performing a single quarter-resolution RA iteration followed by a single half-resolution RA iteration. The direct impact is that, for the space-filling trajectory, one can incorporate RA in an iterative multi-grid reconstruction scheme with only a single RA iteration per multi-grid resolution step. We also find that for either trajectory, slowly varying vertical errors cannot be reliably estimated by employing the RA method alone; such errors are indistinguishable from a trajectory of different pitch. This has minimal effect in practice because RA can be combined with reference frame correction which is effective for correcting low-frequency errors.