A CNN method reduces navigator slice acquisitions in 4D MR imaging.
problem Reduces navigator slice acquisitions without degrading image quality.
method Convolutional Neural Network (CNN) for motion field prediction.
result Halves the number of registrations required for 4D reconstruction.
New SDEs use G-Brownian motion, extending mean-field models.
problem Extending mean-field models to new types of stochastic processes.
method Introduced G-SDEs with coefficients dependent on current state and solution as random variable. result Validated new SDE framework for complex stochastic systems.
Deep neural nets predict vortex-induced vibrations from limited flow data.
problem Predicting lift and drag forces on structures from scattered velocity field data.
method Extended deep neural networks solving coupled Navier-Stokes and structural dynamics equations.
result Deep neural networks can accurately infer structural parameters, pressure field, and velocity field from limited flow data.
Improved vehicle motion prediction with uncertainty estimation.
problem Robust motion prediction for autonomous vehicles, especially under distributional shift.
method Presented an approach significantly improving the benchmark and taking 2nd place on the leaderboard.
result Significantly improved motion prediction and uncertainty measurement.
Neural network predicts vessel motions with high accuracy.
problem Real-time prediction of heave and surge motions for improved performance and safety.
method Developed an LSTM-based machine learning model trained on measured waves and motion data.
result The model predicts vessel motions up to 46.5 seconds into the future with an average accuracy of 90%.
Researchers define a limit for fractional Brownian motion as Hurst parameter approaches zero.
problem Defining a limit for fractional Brownian motion with zero Hurst parameter.
method Developed a Gaussian random distribution and log-correlated random field as limits.
result Fractional Brownian motion converges to a Gaussian random distribution when Hurst parameter approaches zero.
New findings on magnetic geodesic flows and periodic motions.
problem Characterizing superintegrable systems in magnetic geodesic flows.
method Analyzing rotationally symmetric magnetic geodesic flows.
result All sufficiently slow motions in a central magnetic field are periodic under specific curvature and homogeneity conditions.
Study of motion constraints and path-following on 3D space.
problem Path-following with non-holonomic constraints on R3. method Exploration of geometric structure and construction of guiding vector fields.
result General principles for constructing guiding vector fields for path-following.
Study shows non-integrability of magnetic billiards on curved surfaces.
problem Non-existence of polynomial integrals for magnetic billiards.
method Examined billiard motion on constant curvature surfaces with magnetic fields.
result For most magnetic field values, billiard motion lacks polynomial integrals.
New framework predicts diverse, contextually plausible 3D human motions.
problem Predicting multiple plausible future 3D poses given observed poses.
method Developed a new variational framework that conditions latent variable on past observation to encourage relevant information.
result Our approach generates motions of higher quality and preserves contextual information.
ANN models predict ground motion intensity measures for Texas, Oklahoma, and Kansas.
problem Inaccurate ground motion prediction models for low magnitude, short distance events in CENA.
method Artificial Neural Networks (ANNs) developed from ground motion recordings.
result ANN models provide more accurate predictions of ground motion intensity measures.
Cohomotopy theory predicts M-theory anomaly cancellation on 8-manifolds.
problem Anomaly cancellation in M-theory on 8-manifolds.
method Using J-twisted Cohomotopy theory, we prove anomaly cancellation conditions.
result Cohomotopy theory implies specific anomaly cancellation conditions in M-theory.
Paper introduces a new method for generating diverse human motion predictions.
problem Stochastic human motion prediction with limited flexibility.
method Stochastically combines root variations with previous pose information in a recurrent network.
result Model generates more diverse motion sequences than existing techniques.
In this paper we prove the existence of a periodic motion of a charge on a large class of manifolds under the action of the magnetic fields. Our methods also give a class of closed manifolds whose cotangent bundle contain no the closed exact Lagrangian submanifolds.
Modular method predicts motion in crowded scenes using learned environment models.
problem Predicting motion in dynamic, crowded environments.
method Modular model of spatial and dynamic aspects, unsupervised adaptation to new tasks.
result Comparable performance to state-of-the-art, transferable across tasks.
Paper compares stock price prediction models using Heston and Geometric Brownian Motion.
problem Predicting stock prices accurately.
method Developed Heston and Geometric Brownian Motion models using Ito's lemma and Euler-Maruyama methods.
result Models outperform statistical indicators in predicting stock prices.
Improved motion prediction for self-driving cars using trajectory sets and auxiliary losses.
problem Accurately predicting future vehicle motion for self-driving cars.
method Classification over trajectory sets with an auxiliary loss for off-road predictions and spatial-temporal relationships.
result Significant improvement in motion prediction performance on small datasets using map information.
We study the motion of a charge on a conformally flat Riemannian torus in the presence of magnetic field. We prove that for any non-zero magnetic field there always exist orbits of this motion which have conjugate points. We conjecture that the restriction of conformal flatness of the metric is not essential for this r…
Improved pedestrian motion prediction in urban intersections.
problem Accurate prediction of pedestrian trajectories in crowded urban environments.
method Incorporates semantic features from the environment into a Gaussian Process (GP) model for pedestrian motion prediction.
result 12.5% improvement in prediction accuracy and 2.65 times reduction in AUC.
Proposes a method to predict vehicle intentions and motion adaptively.
problem Accurately predicting vehicle behaviors in various traffic scenarios.
method Probabilistic framework based on deep neural network.
result Better long-term motion prediction performance.
Study improves vehicle motion prediction by incorporating traffic density.
problem Lack of contextual knowledge in predicting driving behavior.
method Categorize and define external conditions, evaluate motion prediction approach.
result Traffic density significantly improves motion prediction accuracy.
We consider a periodic problem for the motion of a charged particle in a magnetic field. Introducing a notion of Ricci curvature for such Lagrangian systems and using the methods of the calculus of variations in the large, we prove the existence of periodic motions for such particles under a condition of positivity of …
DMGNN predicts 3D human motions using adaptive multiscale graphs.
problem Predicting 3D skeleton-based human motions accurately.
method Dynamic multiscale graph neural networks (DMGNN) with adaptive multiscale graphs and MGCU.
result DMGNN outperforms state-of-the-art methods in short and long-term predictions.
Deep learning predicts human survival from cardiac MRI motion data.
problem Predicting human survival from cardiac MRI motion data.
method Fully convolutional network for dense motion modeling, autoencoder for latent code learning, Cox partial likelihood loss for right-censored data.
result Predictive accuracy (C-index) significantly higher (p < .0001) for deep learning model (C=0.73) than human benchmark (C=0.59).
Method learns attractive areas from agent motions to represent environments.
problem Representing environments based on moving agents' nonlinear motions.
method Switching model of velocity fields, parametric representation of attractive spots.
result Dynamic map of attractive areas for online learning.
End-to-end learnable network for safer self-driving with interpretable intermediate representations.
problem Safe motion planning for self-driving vehicles.
method Differentiable semantic occupancy representation for cost calculation in motion planning.
result Significantly outperforms state-of-the-art planners in imitating human behaviors and producing safer trajectories.
The paper studies how test particles' mass and charge vary in Kaluza-Klein models.
problem Understanding how test particles' mass and charge change in Kaluza-Klein models.
method Analyzes geodesic motion in a 5D Kaluza-Klein spacetime with background metrics encoding 4D gauge fields and Higgs-like scalars.
result The mass and charge of test particles become variable when traversing regions with massive gauge fields or non-constant Higgs scalars.
A new Fourier model improves ODE prediction.
problem Improving the accuracy of ODE solutions, especially for periodic functions.
method Constructing a Fourier state space model and a hybrid model combining Taylor and Fourier methods.
result The hybrid model can predict ODE solutions more accurately, especially for periodic functions.
A new model for predicting market order book dynamics using a buffer Hawkes process.
problem Predicting the evolution of limit order books in financial markets.
method Introducing a Markovian single point process with a buffer mechanism and self-exciting effect.
result The model accurately predicts market order book dynamics and converges to Brownian motion.
Flow of curves with curvature and forcing vector field exists.
problem Existence of a curve flow with curvature and forcing.
method Proved existence through Brakke motion law.
result Non-trivial flow of curves exists through singularities.
Proposes a hybrid deep learning network for better heart failure survival prediction.
problem Improving survival prediction in heart failure patients.
method Joint analysis of cardiac motion features and clinical risk factors using a hybrid deep learning network.
result Optimal integration of clinical risk factors into deep prediction networks.
In this article, we will formulate a mathematical framework that allows us to treat character animations as points on infinite dimensional Hilbert manifolds. Constructing geodesic paths between animations on those manifolds allows us to derive a distance function to measure similarities of different motions. This appro…
Study predicts Gaussian Volterra processes with noisy Brownian motion.
problem Predicting Gaussian Volterra processes with hidden Brownian motion.
method Regular conditional law analysis under model disturbances.
result Developed method for variance reduction in measurement errors.
We study the motion of charged particle under a natural choice of electromagnetic field in a general class of compact homogeneous spaces. As a special case we describe the motion in homogeneous Riemannian spaces (G/H,g), where g is any deformation of a normal metric along the fibers of a homogeneous fibration $K/H\…
Proposes a method to model multi-vehicle interactions using Gaussian processes.
problem Challenges in modeling correlations between multiple road users over time.
method Uses a stochastic vector field model and non-parametric Bayesian learning.
result Captures motion patterns from complex multi-vehicle interactions without heroic prior assumptions.
Model predicts Bitcoin prices using fractional Brownian motion.
problem Predicting Bitcoin prices with long-term dependence.
method Monte Carlo simulation with geometric fractional Brownian motion.
result Most probable Bitcoin price at the start of 2018 was 6358 USD.
Framework predicts interactions between multiple traffic participants.
problem Accurately predicting interactions between multiple traffic participants.
method Probabilistic framework with hierarchical modules forecasting intentions and motions.
result Framework predicts continuous motions and interaction durations for multiple interacting road participants.
We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process X(t) and a \emph{predictive mean-field} backward SDE (BSDE) in the unknowns Y(t),Z(t),K(t,⋅). The driver of …
Paper compares machine learning methods for predicting target motion.
problem Challenges in accurately modeling target dynamics due to mismatch between assumed and true motion.
method Three machine learning methods (GPs, IMM, LSTM) compared against EKF.
result LSTM network outperforms other methods in real-world scenarios.
Proposes a new model for predicting future motion of road actors in autonomous vehicles.
problem Forecasting the long-term future motion of road actors for safe autonomous driving.
method Recurrent graph-based attentional approach with interpretable geometric and social relationships.
result Can produce diverse predictions conditioned on hypothetical or 'what-if' scenarios.
Study on the geometric Dyson Brownian motion of non-square matrix products.
problem Understanding the spectrum of a product of non-square random matrices.
method Proportional depth-width limit followed by mean-field limit, solving Burgers equation.
result Free log-normal law is obtained in the identity-start case.
This paper learns motion primitives from driving data to improve vehicle path-tracking.
problem Improving vehicle path-tracking accuracy through learned motion primitives.
method Two-level structure with path segmentation and clustering; Gaussian Mixture Model (GMM) and Gaussian Mixture Regression (GMR).
result The model predicts future lateral control commands with high accuracy.
Recently, it has been shown that Absolute Parallelism (AP) geometry admits paths that are naturally quantized. These paths have been used to describe the motion of spinning particles in a background gravitational field. In case of a weak static gravitational field limits, the paths are applied successfully to interpret…
This paper studies the large time existence for the motion of closed hypersurfaces in a radially symmetric potential. In physical, this surface can be considered as an electrically charged membrane with a constant charge per area in a radially symmetric potential. The evolution of such surface has been investigated by …
A new neural network improves the accuracy of predicting constants of motion.
problem Discovering constants of motion in dynamical systems.
method A novel neural network architecture using SVD and a two-phase training algorithm.
result The new approach retains advantages of COMET and improves performance.
A model predicts visual motion by learning from natural videos.
problem Temporal prediction accuracy in visual perception.
method Self-supervised representation learning using Fourier shift theorem.
result Achieves better prediction performance than traditional methods.
Improved pedestrian crossing prediction for AVs using contextual factors.
problem Accurate prediction of pedestrian crossing behavior for autonomous vehicles.
method Factored Latent-Dynamic Conditional Random Fields (FLDCRF) for multi-label sequence prediction and joint interaction modeling.
result Achieved at least 0.9 seconds earlier prediction accuracy for pedestrian crossing behavior compared to existing methods.
Small bodies follow geodesics in general relativity.
problem Understanding the motion of small bodies in space-time.
method Analyzes the motion of small bodies as timelike geodesics or Lorentz-force curves in general relativity.
result Clarifies the relationship between modeling bodies as distributions or smooth fields.