Sampling Trajectories Research Articles

Route flow estimation based on the fusion of probe vehicle trajectory and automated vehicle identification data

Accurate estimation of route flow is crucial to traffic control optimization. Existing route flow estimation models are typically built upon strong assumptions on traveler route choice behavior or turn to data-driven approaches which heavily rely on prior OD estimation and high sensor coverage rate. This study proposes a route flow estimation framework by fusing the probe vehicle trajectory and automated vehicle identification (AVI) data. The notion of probe vehicle route penetration rate (RPR) is utilized for the construction of a novel data-driven objective function. Sensor-OD flow and observable route flow penetration are formulated as model constraints. The solution uniqueness is guaranteed though an iterative procedure under the principle of entropy maximization. Numerical studies are conducted based on pNEUMA, a large-scale full sample trajectory dataset. Results show that the proposed model performs better than the traditional path flow estimation model, especially when the prior flow information is not available. Sensitivity analysis on AVI sensor coverage rate, probe vehicle route coverage rate and RPR distribution demonstrates the proposed model’s applicability in practice.

A simplified weak simulation method for the probabilistic response analysis of nonlinear random vibration problems

Numerical simulation methods are among the most used techniques to evaluate the stochastic response of engineering systems subjected to random excitations. In many practical situations the system should be integrated over long time intervals and a large number of sample trajectories need to be generated to assess the quantities of interest. In this circumstance conventional methods usually show exploding behavior or their implementation is computationally very demanding. In this paper we propose a new numerical simulation method for the probabilistic response analysis of nonlinear random vibration problems. We devise a simplified weak method having the simplicity of basically needing only three-point distributed random variable per time step for its implementation. Also, we prove that it reproduces the same statistical properties that characterize the exact solution to the linearized equation corresponding to the underlying system. This makes the method an efficient tool for stable long term simulations. Numerical experiments are carry out to illustrate the practical performance of the method.

B-Spline Parameterized Joint Optimization of Reconstruction and K-Space Trajectories (BJORK) for Accelerated 2D MRI.

Optimizing k-space sampling trajectories is a promising yet challenging topic for fast magnetic resonance imaging (MRI). This work proposes to optimize a reconstruction method and sampling trajectories jointly concerning image reconstruction quality in a supervised learning manner. We parameterize trajectories with quadratic B-spline kernels to reduce the number of parameters and apply multi-scale optimization, which may help to avoid sub-optimal local minima. The algorithm includes an efficient non-Cartesian unrolled neural network-based reconstruction and an accurate approximation for backpropagation through the non-uniform fast Fourier transform (NUFFT) operator to accurately reconstruct and back-propagate multi-coil non-Cartesian data. Penalties on slew rate and gradient amplitude enforce hardware constraints. Sampling and reconstruction are trained jointly using large public datasets. To correct for possible eddy-current effects introduced by the curved trajectory, we use a pencil-beam trajectory mapping technique. In both simulations and in- vivo experiments, the learned trajectory demonstrates significantly improved image quality compared to previous model-based and learning-based trajectory optimization methods for 10× acceleration factors. Though trained with neural network-based reconstruction, the proposed trajectory also leads to improved image quality with compressed sensing-based reconstruction.

Symmetry-induced many-body quantum interference in chaotic bosonic systems: an augmented truncated Wigner method

Although highly successful, the truncated Wigner approximation (TWA) does not account for genuine many-body (MB) quantum interference between different solutions of the mean-field equations of a bosonic MB system. This renders the TWA essentially classical, where a large number of particles formally takes the role of the inverse of Planck’s constant ℏ. The failure to describe genuine interference phenomena, such as localization and scarring in Fock space, can be seen as a virtue of this quasiclassical method, which thereby allows one to identify genuine quantum effects when being compared with ‘exact’ quantum calculations that do not involve any a priori approximation. A rather prominent cause for such quantum effects that are not accounted for by the TWA is the constructive interference between the contributions of symmetry-related trajectories, which would occur in the presence of discrete symmetries provided the phase-space distribution of the initial state and the observable to be evaluated feature a strong localization about the corresponding symmetry subspaces. Here we show how one can conceive an augmented version of the TWA which can account for this particular effect. This augmented TWA effectively amounts to complementing conventional TWA calculations by separate truncated Wigner simulations that are restricted to symmetric subspaces and involve weight factors that account for the dynamical stability of sampling trajectories with respect to perpendicular deviations from those subspaces. We illustrate the validity of this method at pre- as well as post-Ehrenfest time scales in prototypical Bose–Hubbard systems displaying chaotic classical dynamics, where it also reveals the existence of additional MB interference effects.

Optimizing Full 3D SPARKLING Trajectories for High-Resolution Magnetic Resonance Imaging.

The Spreading Projection Algorithm for Rapid K-space sampLING, or SPARKLING, is an optimization-driven method that has been recently introduced for accelerated 2D MRI using compressed sensing. It has then been extended to address 3D imaging using either stacks of 2D sampling patterns or a local 3D strategy that optimizes a single sampling trajectory at a time. 2D SPARKLING actually performs variable density sampling (VDS) along a prescribed target density while maximizing sampling efficiency and meeting the gradient-based hardware constraints. However, 3D SPARKLING has remained limited in terms of acceleration factors along the third dimension if one wants to preserve a peaky point spread function (PSF) and thus good image quality. In this paper, in order to achieve higher acceleration factors in 3D imaging while preserving image quality, we propose a new efficient algorithm that performs optimization on full 3D SPARKLING. The proposed implementation based on fast multipole methods (FMM) allows us to design sampling patterns with up to 107 k-space samples, thus opening the door to 3D VDS. We compare multi-CPU and GPU implementations and demonstrate that the latter is optimal for 3D imaging in the high-resolution acquisition regime ( 600μ m isotropic). Finally, we show that this novel optimization for full 3D SPARKLING outperforms stacking strategies or 3D twisted projection imaging through retrospective and prospective studies on NIST phantom and in vivo brain scans at 3 Tesla taking the particular case of T2 *-w imaging. Overall the proposed method allows for 2.5-3.75x shorter scan times compared to GRAPPA-4 parallel imaging acquisition at 3 Tesla without compromising image quality.

A behavior fusion method based on inverse reinforcement learning

Inverse reinforcement learning (IRL) is usually used in deep reinforcement learning systems for tasks that are difficult to design with manual reward functions. If the task is too complicated, the expert sample trajectories obtained artificially often have different preferences, resulting in a relatively large variance in the learned reward function. For this purpose, this study proposes a behavior fusion method based on adversarial IRL. We decompose complex tasks into several simple subtasks according to different preferences. After decoupling the tasks, we use the inherent relationship between IRL and generative adversarial network (GAN): the discriminator network fits the reward function and the generator network fits strategy, and the reward function and policy are learned respectively. Moreover, we improve the adversarial IRL model by using multiple discriminators to correspond to each subtask, and provide a more efficient update for the whole structure. The behavior fusion in this work acts a weighted network on the reward functions in different subtasks. The proposed method is evaluated on Atari enduro racing game with baseline methods, and we implement a wafer inspection experiment for further discussions. The experimental results show our method can learn more advanced policies in complicated tasks, and the training process is more stable.

Bayesian optimization of distributed neurodynamical controller models for spatial navigation.

Dynamical systems models for controlling multi-agent swarms have demonstrated advances toward resilient, decentralized navigation algorithms. We previously introduced the NeuroSwarms controller, in which agent-based interactions were modeled by analogy to neuronal network interactions, including attractor dynamics and phase synchrony, that have been theorized to operate within hippocampal place-cell circuits in navigating rodents. This complexity precludes linear analyses of stability, controllability, and performance typically used to study conventional swarm models. Further, tuning dynamical controllers by manual or grid-based search is often inadequate due to the complexity of objectives, dimensionality of model parameters, and computational costs of simulation-based sampling. Here, we present a framework for tuning dynamical controller models of autonomous multi-agent systems with Bayesian optimization. Our approach utilizes a task-dependent objective function to train Gaussian process surrogate models to achieve adaptive and efficient exploration of a dynamical controller model’s parameter space. We demonstrate this approach by studying an objective function selecting for NeuroSwarms behaviors that cooperatively localize and capture spatially distributed rewards under time pressure. We generalized task performance across environments by combining scores for simulations in multiple mazes with distinct geometries. To validate search performance, we compared high-dimensional clustering for high- vs. low-likelihood parameter points by visualizing sample trajectories in 2-dimensional embeddings. Our findings show that adaptive, sample-efficient evaluation of the self-organizing behavioral capacities of complex systems, including dynamical swarm controllers, can accelerate the translation of neuroscientific theory to applied domains.

Learning-based method for k-space trajectory design in MRI.

Variable density sampling of the k-space in MRI is an integral part of trajectory design. It has been observed that data-driven trajectory design methods provide a better image reconstruction as compared to trajectories obtained from a fixed or a parametric density function. In this paper, a data-driven strategy has been proposed to obtain non-Cartesian continuous k-space sampling trajectories for MRI under the compressed sensing framework (greedy non-Cartesian (GNC)). A stochas-tic version of the algorithm (stochastic greedy non-Cartesian (SGNC)) is also proposed that reduces the computation time. We compare the proposed trajectory with a traveling salesman problem (TSP)-based trajectory and an echo planar imaging-like trajectory obtained by a greedy method called stochastic greedy-Cartesian (SGC) algorithm. The training images are taken from knee images of the fastMRI dataset. It is observed that the proposed algorithms outperform the TSP-based and the SGC trajectories for similar read-out times.

Computational Proposal for Tracking Multiple Molecules in a Multifocus Confocal Setup.

Tracking single molecules continues to provide new insights into the fundamental rules governing biological function. Despite continued technical advances in fluorescent and non-fluorescent labeling as well as data analysis, direct observations of trajectories and interactions of multiple molecules in dense environments remain aspirational goals. While confocal methods provide a means to deduce dynamical parameters with high temporal resolution, such as diffusion coefficients, they do so at the expense of spatial resolution. Indeed, on account of a confocal volume’s symmetry, typically only distances from the center of the confocal spot can be deduced. Motivated by the need for true three dimensional high speed tracking in densely labeled environments, we propose a computational tool for tracking many fluorescent molecules traversing multiple, closely spaced, confocal measurement volumes providing independent observations. Various realizations of this multiple confocal volumes strategy have previously been used for long term, large area, tracking of one fluorescent molecule in three dimensions. What is more, we achieve tracking by directly using single photon arrival times to inform our likelihood and exploit Hamiltonian Monte Carlo to efficiently sample trajectories from our posterior within a Bayesian nonparametric paradigm. A nonparametric paradigm here is warranted as the number of molecules present are, themselves, a priori unknown. Taken together, we provide a computational framework to infer trajectories of multiple molecules at once, below the diffraction limit (the width of a confocal spot), in three dimensions at sub-millisecond or faster time scales.

Modelo con elasticidad constante de la varianza: Una aplicación en la Bolsa de Valores de Lima

The objective of this article is to present the constant elasticity of variance model, its main probabilistic aspects, and we implement the stochastic Runge Kutta method to simulate the sample trajectories based on the data of the CREDITC1 asset of the Bank of Credit from Perú taken from the Lima stock exchange.

Policy Optimization with Stochastic Mirror Descent

Improving sample efficiency has been a longstanding goal in reinforcement learning. This paper proposes VRMPO algorithm: a sample efficient policy gradient method with stochastic mirror descent. In VRMPO, a novel variance-reduced policy gradient estimator is presented to improve sample efficiency. We prove that the proposed VRMPO needs only O(ε−3) sample trajectories to achieve an ε-approximate first-order stationary point, which matches the best sample complexity for policy optimization. Extensive empirical results demonstrate that VRMP outperforms the state-of-the-art policy gradient methods in various settings.

Long-range stray field mapping of statically magnetized nanoparticles using magnetoresistive sensor

Analyzing the spatial distribution of stray field from magnetic nanoparticles is a crucial step to design and optimize the magnetometric system for a clinical magnetic particle imaging (MPI) scanner. Here, we used a magnetoresistive (MR) sensor to probe the stray field directly from a commercial magnetic nanoparticle suspension conditioned under a static field. For a given 20 mT by a small permanent magnet, the stray field of a liquid sample with a 0.7 mgFe iron mass is in nanotesla order measured by the MR sensor at 50 mm apart from the sample, while the magnetization is comparable to several microtesla. This field decay demands picotesla sensitivity of the sensing system to record the stray field for a further distance or a smaller excitation field. Moreover, from a two-dimensional trajectory of sample and magnet movements relative to the sensor position, we confirmed that the spatial distribution of the stray field appeared to correlate with sample geometry. The distribution became broadening for low iron mass concentration of the sample. From this observation, an MR sensor proves its potential for locating the magnetic nanoparticles under a quasistatic field, which can be extensively implemented for a single-sided MPI scanner.

The Use of Digital Terrain Models for Natural Feature Tracking at Asteroid Bennu

The Origins, Spectral Interpretation, Resource Identification, and Security–Regolith Explorer (OSIRIS-REx) mission rendezvoused with asteroid (101955) Bennu in 2018 with the primary objective of collecting a sample of regolith from the surface. As the first NASA asteroid sample return mission, OSIRIS-REx deployed several new technologies to achieve program objectives. Here we present an overview of Natural Feature Tracking (NFT), a system developed to autonomously guide the spacecraft to the desired sampling site using optical navigation and the natural terrain on the surface of Bennu. NFT utilized a series of image-based digital terrain models (DTMs) constructed by means of stereophotoclinometry to represent patches on the surface of the asteroid. These DTMs were used to generate synthetic renderings of the terrain and identify features for use in navigating to the sampling location. In addition, high-resolution models of the sampling site constructed from scanning lidar data were used for predicting the time and location of contact with the surface. These models went through a series of validation tests to ensure the performance of the NFT system. When the spacecraft executed the sampling trajectory in 2020 October, NFT enabled real-time guidance updates that delivered it safely to the desired sampling location while also providing critical hazard avoidance capabilities in the rocky Bennu environment.

Golden-Angle Radial MRI: Basics, Advances, and Applications.

In recent years, golden‐angle radial sampling has received substantial attention and interest in the magnetic resonance imaging (MRI) community, and it has become a popular sampling trajectory for both research and clinical use. However, although the number of relevant techniques and publications has grown rapidly, there is still a lack of a review paper that provides a comprehensive overview and summary of the basics of golden‐angle rotation, the advantages and challenges/limitations of golden‐angle radial sampling, and recommendations in using different types of golden‐angle radial trajectories for MRI applications. Such a review paper is expected to be helpful both for clinicians who are interested in learning the potential benefits of golden‐angle radial sampling and for MRI physicists who are interested in exploring this research direction. The main purpose of this review paper is thus to present an overview and summary about golden‐angle radial MRI sampling. The review consists of three sections. The first section aims to answer basic questions such as: what is a golden angle; how is the golden angle calculated; why is golden‐angle radial sampling useful, and what are its limitations. The second section aims to review more advanced trajectories of golden‐angle radial sampling, including tiny golden‐angle rotation, stack‐of‐stars golden‐angle radial sampling, and three‐dimensional (3D) kooshball golden‐angle radial sampling. Their respective advantages and limitations and potential solutions to address these limitations are also discussed. Finally, the third section reviews MRI applications that can benefit from golden‐angle radial sampling and provides recommendations to readers who are interested in implementing golden‐angle radial trajectories in their MRI studies.Evidence Level5Technical EfficacyStage 1

Learning Contraction Policies From Offline Data

This letter proposes a data-driven method for learning convergent control policies from offline data using Contraction theory. Contraction theory enables constructing a policy that makes the closed-loop system trajectories inherently convergent towards a unique trajectory. At the technical level, identifying the contraction metric, which is the distance metric with respect to which a robot’s trajectories exhibit contraction is often non-trivial. We propose to jointly learn the control policy and its corresponding contraction metric while enforcing contraction. To achieve this, we learn an implicit dynamics model of the robotic system from an offline data set consisting of the robot’s state and input trajectories. We propose a data augmentation algorithm for learning contraction policies using this learned dynamics model. We randomly generate samples in the state space and propagate them forward in time through the learned dynamics model to generate auxiliary sample trajectories. We then learn both the control policy and the contraction metric such that the distance between the trajectories from the offline data set and our generated auxiliary sample trajectories decreases over time. We evaluate the performance of our proposed framework on simulated robotic goal-reaching tasks and demonstrate that enforcing contraction results in faster convergence and greater robustness of the learned policy.

Bayesian Optimization of Distributed Neurodynamical Controller Models for Spatial Navigation

Dynamical systems models for controlling multi-agent swarms have demonstrated advances toward resilient, decentralized navigation algorithms. We previously introduced the NeuroSwarms controller, in which agent-based interactions were modeled by analogy to neuronal network interactions, including attractor dynamics and phase synchrony, that have been theorized to operate within hippocampal place-cell circuits in navigating rodents. This complexity precludes linear analyses of stability, controllability, and performance typically used to study conventional swarm models. Further, tuning dynamical controllers by hand or grid search is often inadequate due to the complexity of objectives, dimensionality of model parameters, and computational costs of simulation-based sampling. Here, we present a framework for tuning dynamical controller models of autonomous multi-agent systems based on Bayesian Optimization (BayesOpt). Our approach utilizes a task-dependent objective function to train Gaussian Processes (GPs) as surrogate models to achieve adaptive and efficient exploration of a dynamical controller model's parameter space. We demonstrate this approach by studying an objective function selecting for NeuroSwarms behaviors that cooperatively localize and capture spatially distributed rewards under time pressure. We generalized task performance across environments by combining scores for simulations in distinct geometries. To validate search performance, we compared high-dimensional clustering for high- vs. low-likelihood parameter points by visualizing sample trajectories in Uniform Manifold Approximation and Projection (UMAP) embeddings. Our findings show that adaptive, sample-efficient evaluation of the self-organizing behavioral capacities of complex systems, including dynamical swarm controllers, can accelerate the translation of neuroscientific theory to applied domains.

Interplay of structural and dynamical heterogeneity in the nucleation mechanism in nickel.

Gaining a fundamental understanding of crystal nucleation processes in metal alloys is crucial for the development and design of high-performance materials with targeted properties. Yet, crystallization is a complex non-equilibrium process and, despite having been studied for decades, the microscopic aspects that govern the crystallization mechanism of a material remain elusive to date. Recent evidence shows that the spatial heterogeneity in the supercooled liquid, characterised by extended regions with distinctive mobility and order, may be a key microscopic factor that determines the mechanism of crystal nucleation. These findings have advanced our view of the fundamental nature of crystallization, as most research has assumed that crystal clusters nucleate from random fluctuations in a 'homogeneous' liquid. Here, by analysing transition path sampling trajectories, we show that dynamical heterogeneity plays a key role in the mechanism of crystal nucleation in an elemental metal, nickel. Our results demonstrate that crystallization occurs preferentially in regions of low mobility in the supercooled liquid, evidencing the collective dynamical nature of crystal nucleation in Ni. In addition, our results show that low mobility regions form before and spatially overlap with pre-ordered domains that act as precursors to the crystal phase that subsequently emerges. Our results show a clear link between dynamical and structural heterogeneity in the supercooled liquid and its impact on the nucleation mechanism, revealing microscopic descriptors that could pave a novel way to control crystallization processes in metals.

Energy-Efficient Local Path Planning of a Self-Guided Vehicle by Considering the Load Position

The local path planning, as one of the navigation stages, plays a significant role in the energy consumption of Self-Guided Vehicles (SGV). Since SGV must operate for several hours on a single battery charge to transport loads, its energy consumption is a critical issue. Therefore, this article puts forward an approach for boosting the energy efficiency of the local path planning stage using load position. Unlike other similar works which solely use robots’ kinematic and kinetic constraints to develop energy-efficient local path planners, this article considers the effect of load position on SGV’s dynamic. In this regard, first, the kinetic model of the differential drive SGV is developed to consider the change of SGV’s Center of Mass (CoM) affected by load properties. Second, machine learning methods are used to create two learning models for online estimation of the position of CoM (PoCoM) and prediction of required energy of sample trajectories. Hence, the generated SGV’s kinetic model is used to train the learning models. Finally, estimated parameters are employed to add a new constraint to extend the cost function of the local path planner. The outcomes of the study show that the proposed planner generates smoother and shorter paths to pass obstacles and corridors than a general one. Thus, SGV’s energy consumption decreases by considering the load effect.

Sample Complexity of Block-Sparse System Identification Problem

In this article, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state data samples. We characterize the properties of this estimator under high-dimensional scaling, where the growth rate of the system dimension is comparable to or even faster than that of the number of available sample trajectories. In particular, using contemporary results on high-dimensional statistics, we show that the proposed estimator results in a small elementwise error, provided that the number of sample trajectories is above a threshold. This threshold depends polynomially on the size of each block and the number of nonzero elements at different rows of input and state matrices, but only logarithmically on the system dimension. A by product of this result is that the number of sample trajectories required for sparse system identification is significantly smaller than the dimension of the system. Furthermore, we show that, unlike the recently celebrated least-squares estimators for system identification problems, the method developed in this work is capable of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">exact recovery</i> of the underlying sparsity structure of the system with the aforementioned number of data samples. Extensive case studies on switching networks and power systems are offered to demonstrate the effectiveness of the proposed method.

LAPNet: Non-Rigid Registration Derived in k-Space for Magnetic Resonance Imaging.

Physiological motion, such as cardiac and respiratory motion, during Magnetic Resonance (MR) image acquisition can cause image artifacts. Motion correction techniques have been proposed to compensate for these types of motion during thoracic scans, relying on accurate motion estimation from undersampled motion-resolved reconstruction. A particular interest and challenge lie in the derivation of reliable non-rigid motion fields from the undersampled motion-resolved data. Motion estimation is usually formulated in image space via diffusion, parametric-spline, or optical flow methods. However, image-based registration can be impaired by remaining aliasing artifacts due to the undersampled motion-resolved reconstruction. In this work, we describe a formalism to perform non-rigid registration directly in the sampled Fourier space, i.e. k-space. We propose a deep-learning based approach to perform fast and accurate non-rigid registration from the undersampled k-space data. The basic working principle originates from the Local All-Pass (LAP) technique, a recently introduced optical flow-based registration. The proposed LAPNet is compared against traditional and deep learning image-based registrations and tested on fully-sampled and highly-accelerated (with two undersampling strategies) 3D respiratory motion-resolved MR images in a cohort of 40 patients with suspected liver or lung metastases and 25 healthy subjects. The proposed LAPNet provided consistent and superior performance to image-based approaches throughout different sampling trajectories and acceleration factors.