Entire Trajectories Research Articles

Trajectories of school absences across compulsory schooling and their impact on children's academic achievement: An analysis based on linked longitudinal survey and school administrative data.

Prior research has identified that school absences harm children's academic achievement. However, this literature is focused on brief periods or single school years and does not consistently account for the dynamic nature of absences across multiple school years. This study examined dynamic trajectories of children's authorised and unauthorised absences throughout their compulsory school career in England. It investigated the consequences of these absence trajectories for children's achievement at the end of compulsory schooling. We analyse linked administrative data on children's absences and achievement from the National Pupil Database and survey data from the Millennium Cohort Study for a representative sample of children born in 2000/2001 in England (N = 7218). We used k-means clustering for longitudinal data to identify joint authorised-unauthorised absence trajectories throughout compulsory schooling and a regression-with-residuals approach to examine the link between absence trajectories and achievement. We identified five distinct absence trajectories: (1) 'Consistently Low Absences', (2) 'Consistently Moderate Authorised Absences', (3) 'Moderately Increasing Unauthorised Absences', (4) 'Strongly Increasing Unauthorised Absences', and (5) 'Strongly Increasing Authorised Absences'. We found substantial differences between trajectory groups in GCSE achievement, even when accounting for significant risk factors of school absences. Compared to 'Consistently Low Absences', 'Strongly Increasing Unauthorised Absences' reduced achievement by -1.23 to -1.48 standard deviations, while 'Strongly Increasing Authorised Absences' reduced achievement by -0.72 to -1.00 SD for our continuous outcomes. 'Moderately Increasing Unauthorised Absences' (-0.61 to -0.70 SD) and 'Consistently Moderate Authorised Absences' (-0.13 to -0.21 SD) also negatively affected achievement compared to 'Consistently Low Absences'. Our research underscores the critical importance of examining entire trajectories of absenteeism and differentiating between types of absences to fully grasp their associations with academic outcomes and design targeted interventions accordingly.

On the deep superstring spectrum

We propose a covariant method of constructing entire trajectories of physical states in superstring theory in the critical dimension. It is inspired by a recently developed covariant technology of excavating bosonic string trajectories, that is facilitated by the observation that the Virasoro constraints can be written as linear combinations of lowering operators of a bigger algebra, namely a symplectic algebra, which is Howe dual to the spacetime Lorentz algebra. For superstrings, it is the orthosymplectic algebra that appears instead, with its lowest weight states forming the simplest class of physical trajectories in the NS sector. To construct the simplest class in the R sector, the lowest weight states need to be supplemented with other states, which we determine. Deeper trajectories are then constructed by acting with suitable combinations of the raising operators of the orthosymplectic algebra, which we illustrate with several examples.

Create your own path: social cerebellum in sequence-based self-guided navigation.

Spatial trajectory planning and execution in a social context play a vital role in our daily lives. To study this process, participants completed a goal-directed task involving either observing a sequence of preferred goals and self-planning a trajectory (Self Sequencing) or observing and reproducing the entire trajectory taken by others (Other Sequencing). The results indicated that in the observation phase, witnessing entire trajectories created by others (Other Sequencing) recruited cerebellar mentalizing areas (Crus 2 and 1) and cortical mentalizing areas in the precuneus, ventral and dorsal medial prefrontal cortex and temporo-parietal junction more than merely observing several goals (Self Sequencing). In the production phase, generating a trajectory by oneself (Self Sequencing) activated Crus 1 more than merely reproducing the observed trajectories from others (Other Sequencing). Additionally, self-guided observation and planning (Self Sequencing) activated the cerebellar lobules IV and VIII more than Other Sequencing. Control conditions involving non-social objects and non-sequential conditions where the trajectory did not have to be (re)produced revealed no differences with the main Self and Other Sequencing conditions, suggesting limited social and sequential specificity. These findings provide insights into the neural mechanisms underlying trajectory observation and production by the self or others during social navigation.

Computational exploration of FOXM1 inhibitors for glioblastoma: an integrated virtual screening and molecular dynamics simulation study

In this study, a comprehensive investigation of a set of phytochemicals to identify potential inhibitors for the Forkhead box protein M1 (FOXM1) was conducted. FOXM1 is overexpressed in glioblastoma (GBM) cells and plays a crucial role in cell cycle progression, proliferation, and invasion. FOXM1 inhibitors have shown promising results in preclinical studies, and ongoing clinical trials are assessing their efficacy in GBM patients. However, there are limited studies on the identification of novel compounds against this attractive therapeutic target. To address this, the NPACT database containing 1,574 phytochemicals was used, employing a hierarchical multistep docking approach, followed by an estimation of relative binding free energy. By fixing user-defined XP-dock and MM-GBSA cut-off scores of −6.096 and −37.881 kcal/mol, the chemical space was further narrowed. Through exhaustive analysis of molecular binding interactions and various pharmacokinetics profiles, we identified four compounds, namely NPACT00002, NPACT01454, NPACT00856, and NPACT01417, as potential FOXM1 inhibitors. To assess the stability of protein-ligand binding in dynamic conditions, 100 ns Molecular dynamics (MD) simulations studies were performed. Furthermore, Molecular mechanics with generalized Born and surface area solvation (MM-GBSA) based binding free energy estimations of the entire simulation trajectories revealed a strong binding affinity of all identified compounds towards FOXM1, surpassing that of the control drug Troglitazone. Based on extensively studied multistep docking approaches, we propose that these molecules hold promise as FOXM1 inhibitors for potential therapeutic applications in GBM. However, experimental validation will be necessary to confirm their efficacy as targeted therapies. Communicated by Ramaswamy H. Sarma

On Transforming Reinforcement Learning With Transformers: The Development Trajectory.

Transformers, originally devised for natural language processing (NLP), have also produced significant successes in computer vision (CV). Due to their strong expression power, researchers are investigating ways to deploy transformers for reinforcement learning (RL), and transformer-based models have manifested their potential in representative RL benchmarks. In this paper, we collect and dissect recent advances concerning the transformation of RL with transformers (transformer-based RL (TRL)) to explore the development trajectory and future trends of this field. We group the existing developments into two categories: architecture enhancements and trajectory optimizations, and examine the main applications of TRL in robotic manipulation, text-based games (TBGs), navigation, and autonomous driving. Architecture enhancement methods consider how to apply the powerful transformer structure to RL problems under the traditional RL framework, facilitating more precise modeling of agents and environments compared to traditional deep RL techniques. However, these methods are still limited by the inherent defects of traditional RL algorithms, such as bootstrapping and the "deadly triad". Trajectory optimization methods treat RL problems as sequence modeling problems and train a joint state-action model over entire trajectories under the behavior cloning framework; such approaches are able to extract policies from static datasets and fully use the long-sequence modeling capabilities of transformers. Given these advancements, the limitations and challenges in TRL are reviewed and proposals regarding future research directions are discussed. We hope that this survey can provide a detailed introduction to TRL and motivate future research in this rapidly developing field.

An excursion into the string spectrum

We propose a covariant technique to excavate physical bosonic string states by entire trajectories rather than individually. The approach is based on Howe duality: the string’s spacetime Lorentz algebra commutes with a certain inductive limit of sp(•), with the Virasoro constraints forming a subalgebra of the Howe dual algebra sp(•). There are then infinitely many simple trajectories of states, which are lowest-weight representations of sp(•) and hence of the Virasoro algebra. Deeper trajectories are recurrences of the simple ones and can be probed by suitable trajectory-shifting operators built out of the Howe dual algebra generators. We illustrate the formalism with a number of subleading trajectories and compute a sample of tree-level amplitudes.

Exploring the free-energy landscape of a rotating superfluid.

The equilibrium state of a superfluid in a rotating cylindrical vessel is a vortex crystal-an array of vortex lines, which is stationary in the rotating frame. Experimental realizations of this behavior typically show a sequence of transient states before the free-energy-minimizing configuration is reached. Motivated by these observations, we construct a new method for a systematic exploration of the free-energy landscape via gradient-based optimization of a scalar loss function. Our approach is inspired by the pioneering numerical work of Campbell and Ziff [Phys. Rev. B. 20, 1886 (1979)] and makes use of automatic differentiation, which crucially allows us to include entire solution trajectories in the loss. We first use the method to converge thousands of low free-energy relative equilibria in the unbounded domain for vortex numbers in the range 10≤N≤30, which reveals an extremely dense set of mostly saddle-like solutions. As part of this search, we discover new continuous families of relative equilibria, which are often global minimizers of free energy. These continuous families all consist of crystals arranged in a double-ring configuration, and we assess which state from the family is most likely to be observed experimentally by computing energy-minimizing pathways from nearby local minima-identifying a common entry point into the family. The continuous families become discrete sets of equal-energy solutions when the wall is introduced in the problem. Finally, we develop an approach to compute homoclinic orbits and use it to examine the dynamics in the vicinity of the minimizing state by converging connections for low-energy saddles.

Generative abstraction of Markov population processes

Markov population models are a widespread formalism used to model the dynamics of complex systems, with applications in systems biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by simulation, which can be costly for large or stiff systems, particularly when a massive number of simulations has to be performed, e.g. in a multi-scale model. A strategy to reduce computational load is to abstract the population model, replacing it with a simpler stochastic model, faster to simulate. Here we pursue this idea, exploring and comparing state-of-the-art generative models, which are flexible enough to automatically learn distributions over entire trajectories, rather than single simulation steps, from observed realizations of the system. In particular, we compare a Generative Adversarial setting with a Score-based Diffusion approach and show how the latter outperforms the former both in terms of accuracy and stability at the cost of slightly higher simulation times. To improve the accuracy of abstract samples, we develop an active learning framework to enrich our dataset with observations whose expected satisfaction of a temporal requirement differs significantly from the abstract one. We experimentally show how the proposed abstractions are well suited to work on multi-scale and data-driven scenarios, meaning that we can infer a (black-box) dynamical model from a pool of real data.

Therapeutic mobility and breast cancer in France: Experiences of African women

While breast cancer is the most common cancer globally, not all women have access to quality care. Long considered a disease of high-income countries, low- and middle-income countries are now facing a major public health issue regarding cancer. This is the case in sub-Saharan Africa, where access to quality breast cancer treatment is often lacking. This context leads some women to travel abroad, particularly to France, hoping to save their lives. This article aims to examine the experiences, the social cost and the perceptions associated with therapeutic mobility for breast cancer in France. To this end, this study uses a qualitative method based on nineteen biographical interviews with women from sub-Saharan Africa with breast cancer who have migrated to France seeking for treatment. It shows that these women often face significant difficulties throughout their care and life paths in France. Main issues lay in accessing care, housing insecurity, loneliness, and administrative instability. This reflects how the double biographical disruption, caused by cancer and migration, impact entire disease trajectories, from entry to care to post-breast cancer period. With this research, we suggest extending the concept of social death to the issue of women who have undergone therapeutic mobility for their breast cancer in France. Highlighting the experiences of women who remain almost invisible in the public arena, this article analyses poorly heard realities and shows how social inequalities in health can be found even in reconstructing oneself after breast cancer.

Flight Demonstration of High Altitude Aircraft Navigation With Cellular Signals

This article presents the first demonstration of navigation with cellular signals of opportunity (SOPs) on a high-altitude aircraft. An extensive flight campaign was conducted by the Autonomous Systems Perception, Intelligence, and Navigation Laboratory in collaboration with the U.S. Air Force to sample ambient downlink cellular SOPs in different regions in Southern California, USA. Carrier phase measurements were produced from these signals, which were subsequently fused in an extended Kalman filter along with altimeter measurements to estimate the aircraft’s state (position, velocity, and time). Three flights are performed in three different regions: 1) rural, 2) semiurban, and 3) urban. A multitude of flight trajectories and altitudes above ground level (AGL) was exercised in the three flights: 1) a 51-km trajectory of grid maneuvers with banking and straight segments at about 5,000 ft AGL, 2) a 57-km trajectory of a teardrop descent from 7,000 ft AGL down to touchdown at the runway, and 3) a 55-km trajectory of a holding pattern at about 15,000 ft AGL. The estimated aircraft trajectory is computed for each flight and compared with the trajectory from the aircraft’s onboard navigation system, which utilized a GPS receiver coupled with an inertial navigation system and an altimeter. The cellular SOPs produced remarkable sustained navigation accuracy over the entire flight trajectories in all three flights, achieving a 3D position root mean-squared error of 10.53 m, 4.96 m, and 15.44 m, respectively.

Planning and Learning for Non-markovian Negative Side Effects Using Finite State Controllers

Autonomous systems are often deployed in the open world where it is hard to obtain complete specifications of objectives and constraints. Operating based on an incomplete model can produce negative side effects (NSEs), which affect the safety and reliability of the system. We focus on mitigating NSEs in environments modeled as Markov decision processes (MDPs). First, we learn a model of NSEs using observed data that contains state-action trajectories and severity of associated NSEs. Unlike previous works that associate NSEs with state-action pairs, our framework associates NSEs with entire trajectories, which is more general and captures non-Markovian dependence on states and actions. Second, we learn finite state controllers (FSCs) that predict NSE severity for a given trajectory and generalize well to unseen data. Finally, we develop a constrained MDP model that uses information from the underlying MDP and the learned FSC for planning while avoiding NSEs. Our empirical evaluation demonstrates the effectiveness of our approach in learning and mitigating Markovian and non-Markovian NSEs.

Learning disentangled skills for hierarchical reinforcement learning through trajectory autoencoder with weak labels

Typically, hierarchical reinforcement learning (RL) requires skills that are applicable to various downstream tasks. Although several recent studies have proposed the supervised and unsupervised learning of such skills, the learned skills are often entangled, which hinders their interpretation. To alleviate this, we propose a novel method to use weak labels for learning disentangled skills from the continuous latent representations of trajectories. To this end, we extended a trajectory variational autoencoder (VAE) to impose an inductive bias using weak labels, which explicitly enforces the disentangling of the trajectory representations into factors of interest intended for the model to learn. Using the latent representations as skills, a skill-based policy network is trained to generate trajectories similar to the learned decoder of the trajectory VAE. Furthermore, using the disentangled skill, we propose a skill repetition that can expand the entire trajectories generated by the policy at test time, resulting in an effective planning strategy. Experiments were performed on several challenging navigation tasks in mazes, and the results demonstrate the effectiveness of our method at solving hierarchical RL problems even with a long horizon and sparse rewards.

Comparison of Arrivals on Green Estimations from Vehicle Detection and Connected Vehicle Data

Many agencies use Automated Traffic Signal Performance Measures (ATSPMs), which require vehicle detection and communication equipment, to evaluate traffic signal efficiency. ATSPMs usually rely on projections based on spatially limited vehicle trajectory samples to estimate performance. Recently, connected vehicle (CV) data has become available that provides entire vehicle trajectories that can be used to generate accurate signal performance measures without the need for projections or infrastructure upgrades. This paper analyzes over 50 intersections in Utah to evaluate how traditional detector-based arrivals on green (AOG) calculations compare with their CV-based calculations. The effects that saturation and queue- lengths have on estimations are analyzed. In general, there is close correlation between computations when queues are short and undersaturated conditions exist. However, if queues extend past the advance detector, detector-based calculations tend to overestimate AOG since vehicles are detected during green but may stop before. This impact is particularly large when the approach is oversaturated, which led to overestimations of around 40% in this study. In addition, detector-based estimations can underestimate AOG in undersaturated scenarios with short queues if vehicles reach the advance detector on red but reduce their speed afterwards, allowing them to not stop. In some cases, the detector-based technique underestimated AOG by over 50%. The findings can help practitioners understand how detector-based estimations vary by traffic conditions. This is particularly important as the industry moves toward a hybrid blend of detector- and CV-based signal performance measures. It is recommended that CV trajectories be used to measure AOG during periods with long queues, oversaturated conditions, or both.

Abstract 6625: Mathematical modeling of single-cell data reveals the key role of stochasticity - not fitness - in determining the clonal origins of relapse in childhood leukemia

Abstract Acute lymphoblastic leukemia (cALL) is the most common pediatric cancer, and since up to 20% of children relapse after initially responding to chemotherapy treatment, the largest cause of cancer-related childhood deaths in the western world. With the idea that dissecting the evolutionary population dynamics leading to relapse would help explain treatment failure from a mechanistic standpoint, several studies have performed comparisons of genetic heterogeneity at diagnosis and relapse. These showed that as many as 70% of relapses are dominated by a single diagnostic subclone or one of its evolutionary progeny; leading to the prevailing view that treatment selection in cALL primarily operates at the genotype level. However, a crucial caveat of these studies is their reliance, due primarily to technical and economic constraints, on very limited data timepoints. While the dynamics linking said timepoints are often interpreted based on simple intuition. To overcome this sparse data challenge and reconstruct the entire spatial and temporal evolutionary trajectories of individual cALL cells from diagnosis to relapse, we have integrated experimental data with an in silico model. Single-cell WGS and RNAseq data were obtained from primary and xenografted leukemic cells before and after chemotherapy. These were then used to parameterize an agent-based mathematical model allowing tracking of the genotype and evolving phenotype of individual cells over time. When short treatment courses akin to those we delivered in vivo were used, the in silico model closely recapitulated the experimental results. Since cALL treatment lasts several years, it cannot be entirely modelled in vivo. Due to the rarity of post-treatment residual cells and the lack of universal cell surface markers to isolate them, direct analysis of clinical samples is also challenging. However, based on the initial treatment data, our calibrated model provided a unique opportunity to simulate longer remission-relapse dynamics of several leukemias. Mechanistic analysis of the collected data showed that, strikingly, in most cases, clonal dominance at relapse results from stochastic sweeps rather than deterministic differences in clonal fitness. Indeed, independent treatment of the same leukemia with an identical drug regimen more frequently ended with a considerably different clonal landscape (either polyclonal disease or a different dominant clone) than with the same outcome initially observed. Rather than genotype differences, the size of residual disease and a founder effect linked to the stochastic exit, post-treatment, of individual cells from quiescence were the key determinants of the relapse genetic landscape. Altogether, our data highlight the misinterpretation risk associated with snapshot analysis and might inform promising alternative treatment schedules. Citation Format: Virginia Turati, Javier Herrero, Mark Robertson-Tessi, Tariq Enver, Andriy Marusyk, Alexander RA Anderson. Mathematical modeling of single-cell data reveals the key role of stochasticity - not fitness - in determining the clonal origins of relapse in childhood leukemia [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 6625.

Computational analysis of interactions between AMPA receptor and con-ikot-ikot conotoxin.

Con-ikot-ikot (CII) is a toxin found in the venom of a marine snail Conus striatus, and the only conotoxin known so far to specifically target AMPA receptors (AMPAR) - a subtype of ionotropic glutamate receptors which are important for synaptic transmission and plasticity. It is small in size (∼20 kDa) and has a unique binding site, nestled between the layers of amino-terminal domains (ATDs) and ligand-binding domains (LBDs) of the receptor, which constitute its extracellular portion. Conotoxins and other animal-derived toxins have an established role as important molecular tools in studying various ion channels and some have already been repurposed as therapeutics, therefore we are interested in using CII to study AMPA receptors. In order to gain a better understanding of the interactions between con-ikot-ikot and AMPA receptors, we have performed all-atom molecular dynamics (MD) simulations of a complex of AMPAR extracellular domains (ATDs and LBDs) with glutamate and CII. Network analysis of the resulting MD simulation trajectories, performed using a residue interaction network (RIN)-based tool we are developing, recapitulates previously identified key residue interactions with ligand-binding domains (LBDs) of AMPARs, reveals novel interactions with the LBD layer and suggests interactions between CII and AMPAR amino-terminal domains (ATDs), making CII potentially the only known ligand to interact with AMPAR ATDs. Our new network analysis tool will allow the user to visualise and explore residue interaction networks of single frames, entire trajectories, or sets of trajectories. It will not only be a tool suitable for our needs in investigating the AMPAR/CII complex, but will also act as a general exploratory, hypothesis-generating tool that will be of interest for anyone looking to understand dynamic networks of protein-protein interactions.

Characterization of heterogeneous dimer and oligomer formation of amyloid-beta using single-molecule FRET.

Protein aggregation is implicated as the cause of pathology in various diseases. Polymorphism in the structure of fibrils formed by aggregation suggests the existence of many different assembly pathways and therefore a heterogeneous ensemble of soluble oligomers. Characterization of this heterogeneity is the key to understanding the aggregation mechanism and toxicity of specific oligomers, but in practice it is extremely difficult to probe individual aggregation pathways in a mixture. Using fluorescence lifetime imaging and deep learning, we have recently visualized the formation of highly diverse fibrils of amyloid-beta (Abeta) in real time (PNAS_2022_e2116736119). Here, we further characterize the heterogeneity in the early stages of aggregation, dimerization and oligomerization of 42-residue Abeta (Abeta42), using single-molecule FRET. We found the dimerization of Abeta is extremely rare. The dimer dissociation constant is unexpectedly high, >5 mM. In addition, the dimerization is highly heterogeneous in terms of the FRET efficiency and kinetics. At least 6 clusters of dimers were needed to fit the entire equilibrium dimerization trajectories. This structural and kinetic diversity suggests that the heterogeneous fibril formation starts from the beginning of the assembly, the dimerization step. Then, we sought the formation of larger stable oligomers of Abeta42 that appear during aggregation. Combination of peptide incubation in a plate reader, single-molecule free-diffusion FRET experiment, and a newly-developed maximum likelihood method based on the rigorous photon statistics and diffusion theory allows for the accurate characterization of stable oligomers appearing at various stages of aggregation. We found that the size of these oligomers ranges from 30- to 100-mer and their overall population is unexpectedly low, less than 1 nM, before and during aggregation of 1-µM Abeta42 peptide. The amounts of small oligomers such as dimers and tetramers are negligible.

Motion of Lee–Yang Zeros

We consider the zeros of the partition function of the Ising model with ferromagnetic pair interactions and complex external field. Under the assumption that the graph with strictly positive interactions is connected, we vary the interaction (denoted by t) at a fixed edge. It is already known that each zero is monotonic (either increasing or decreasing) in t; we prove that its motion is local: the entire trajectories of any two distinct zeros are disjoint. If the underlying graph is a complete graph and all interactions take the same value $$t\ge 0$$ (i.e., the Curie-Weiss model), we prove that all the principal zeros (those in $$i[0,\pi /2)$$ ) decrease strictly in t.

Long Duration Stochastic MPC With Mission-Wide Probabilistic Constraints Using Waysets

A stochastic Model Predictive Control (MPC) formulation is presented for systems operating for a finite time subject to constraints on the Mission-Wide Probability of Safety (MWPS). For linear discrete-time systems subject to unknown disturbances, the goal is to formulate an MPC controller to achieve a desired probability of mission success, where the entire closed-loop state and input trajectories stay within the state and input constraint sets and the final state reaches the desired terminal set. To enable longer missions under greater uncertainty, a wayset-based approach is proposed that allows for the prediction horizon of the MPC to be significantly shorter than the length of the mission. Using a scenario-based approach to stochastic MPC, the use of constrained zonotopes makes the computation of these waysets efficient and practical. Numerical results demonstrate the utility of the waysets for increasing the feasibility of MWPS constraints to longer missions and that the percentage of successful missions asymptotically converges above the desired probability.

A Posteriori Learning for Quasi‐Geostrophic Turbulence Parametrization

AbstractThe use of machine learning to build subgrid parametrizations for climate models is receiving growing attention. State‐of‐the‐art strategies address the problem as a supervised learning task and optimize algorithms that predict subgrid fluxes based on information from coarse resolution models. In practice, training data are generated from higher resolution numerical simulations transformed in order to mimic coarse resolution simulations. By essence, these strategies optimize subgrid parametrizations to meet so‐called a priori criteria. But the actual purpose of a subgrid parametrization is to obtain good performance in terms of a posteriori metrics which imply computing entire model trajectories. In this paper, we focus on the representation of energy backscatter in two‐dimensional quasi‐geostrophic turbulence and compare parametrizations obtained with different learning strategies at fixed computational complexity. We show that strategies based on a priori criteria yield parametrizations that tend to be unstable in direct simulations and describe how subgrid parametrizations can alternatively be trained end‐to‐end in order to meet a posteriori criteria. We illustrate that end‐to‐end learning strategies yield parametrizations that outperform known empirical and data‐driven schemes in terms of performance, stability, and ability to apply to different flow configurations. These results support the relevance of differentiable programming paradigms for climate models in the future.

Structure-Informed Graph Learning of Networked Dependencies for Online Prediction of Power System Transient Dynamics

Online transient analysis plays an increasingly important role in dynamic power grids as the renewable generation continues growing. Traditional numerical methods for transient analysis not only are computationally intensive but also require precise contingency information as input, and therefore, are not suitable for online applications. Existing online transient assessment studies focus on the determination of post-contingency system stability or stability margin. This paper develops a novel graph-learning framework, Deep-learning Neural Representation or DNR, for online prediction, of the time-series trajectories of the system states using initial system responses that can be measured by phasor measurement units (PMUs). The proposed DNR framework consists of two sequential modules: a Network Constructor that captures network dependencies among generators, and a Dynamics Predictor that predicts the system trajectories. The key to improved prediction performance is the introduction of the spatio-temporal message-passing operations into graph neural networks with structural knowledge. Its effectiveness and scalability are validated through comparative studies, demonstrating the prediction performance under different contingency scenarios for systems of different sizes. This framework provides a solution to online predicting post-fault system dynamics based on real-time PMU measurements. Additionally, it can also be applied to facilitate the offline transient simulation without simulating the entire trajectories.