Long-term human motion can be represented as a series of motion modes---motion sequences that capture short-term temporal dynamics---with transitions between them. We leverage this structure and present a novel Motion Transformation Variational Auto-Encoders (MT-VAE) for learning motion sequence generation. Our model j…
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48 results for “motion”
Introduces Motion Programs for better video analysis of human motion.
problem Current video analysis focuses on raw pixels or keypoints, missing higher-level motion primitives.
method Introduces Motion Programs as a neuro-symbolic representation of motions as a composition of high-level primitives.
result Motion Programs accurately describe diverse human motions and improve downstream tasks.
Study motion planning for points avoiding obstacles in a plane.
problem Avoiding collisions for multiple points in a plane with unknown obstacles.
method Algebraic and topological tools for motion planning.
result New topological complexity for planar motion planning.
Programmatic Motion Concepts learn human actions from paired videos.
problem Learning motion concepts from paired video and action sequences.
method Semi-supervised learning architecture for hierarchical motion representation.
result Outperforms established baselines, especially in small data settings.
Unified framework for human motion generation on Riemannian manifolds.
problem Learning valid human motion in Euclidean spaces.
method Riemannian Motion Generation (RMG) on product manifolds, Riemannian flow matching.
result Achieves state-of-the-art FID (0.043) on HumanML3D and surpasses strong baselines on MotionMillion.
Asymptotic windings of the block determinants of a unitary Brownian motion and related diffusionsmath.PR
Study on determinants of unitary Brownian motion and their asymptotic laws.
problem Understanding determinants of unitary Brownian motion and their behavior over time.
method Using Stiefel fibration and skew-product decomposition of the Stiefel Brownian motion.
result Prove asymptotic laws for determinants of block entries of unitary Brownian motion.
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.
Data-driven modelling and synthesis of motion is an active research area with applications that include animation, games, and social robotics. This paper introduces a new class of probabilistic, generative, and controllable motion-data models based on normalising flows. Models of this kind can describe highly complex d…
Study refracted skew Brownian motion, find densities and asymptotics.
problem Modeling and analyzing refracted skew Brownian motion.
method Perturbation approach to find potential densities, transition density, and asymptotic behaviors.
result Expressions and asymptotic behaviors of refracted skew Brownian motion.
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%.
Study fractal dimension for motion without crossing a subset.
problem Fractal dimension of a subset X in R^n for motion without crossing.
method Analyzes fractal dimension of subset X in R^n.
result Determines conditions for motion without crossing a subset.
Let be a closed set in the Riemann sphere . We consider a holomorphic motion of over a complex manifold , that is, a holomorphic family of injections on parametrized by . It is known that if is the unit disk in the complex plane, then any holomorphic motion of ove…
Neural network estimates rigid motion in stroke imaging to improve image quality.
problem Rigid patient motion during C-arm CBCT imaging reduces image quality.
method Neural network trained to regress reprojection error based on image information.
result Neural network outperforms entropy-based method in motion estimation.
Study cohomological equation for robotic screw motions on SE(3).
problem Understanding obstruction phenomena in robotic rigid-body motion.
method Combining Fourier analysis and Peter-Weyl theory, reduce to finite-dimensional linear transport systems.
result Explicit screw motion illustrates resonance conditions and finite-dimensional obstructions.
New approach for obstacle avoidance in robotics using learned representations.
problem Challenges in sensor-based motion planning for new and dynamic environments.
method Proposes a new obstacle representation using PointNet architecture trained jointly with policies for obstacle avoidance.
result Significant improvements in accuracy and efficiency compared to state of the art.
Paper defines multi-dimensional fractional Brownian motion under volatility uncertainty.
problem Volatility uncertainty in fractional Brownian motion.
method Definition and study of multi-dimensional fractional Brownian motion (G-fBm) with Hurst index.
result First results on stochastic calculus for G-fBm with Hurst index > 0.5.
The paper presents a method to reduce arm motion complexity for prosthetics and robotics.
problem Reducing the complexity of human arm motions for robotic and prosthetic control.
method Data-driven techniques including DTW, DBA, Ward's distance, batch-DTW, and fPCA.
result Representative motion clusters and averages for different arm DOF levels.
Researchers calculate the Laplace transform of a geometric Brownian motion integral.
problem Calculating the Laplace transform of a specific integral functional of geometric Brownian motion.
method Analytical calculation of the Laplace transform of the cumulative distribution and probability density functions.
result The Laplace transform of the integral functional of geometric Brownian motion is derived.
Researchers created a continuous Markov martingale that mimics Brownian motion but lacks the strong Markov property.
problem Constructing a continuous Markov martingale with Brownian marginals that misses the strong Markov property.
method Developed a new approach to create a continuous Markov martingale that differs from Brownian motion in terms of the strong Markov property.
result A continuous Markov martingale with Brownian marginals that lacks the strong Markov property was successfully constructed.
We consider -dimensional discrete motions such that any two neighbouring positions correspond in a pure rotation ("rotating motions"). In the Study quadric model of Euclidean displacements these motions correspond to quadrilateral nets with edges contained in the Study quadric ("rotation nets"). The main focus of ou…
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.
The paper explores representations of graph manifolds to Seifert motion groups.
problem Existence of faithful representations of graph manifolds to Seifert motion groups.
method Discussion and proof of non-existence of certain representations.
result Graph manifolds can have virtually no faithful representations to the Seifert motion group.
Geodesic walks converge to Brownian motion on Finsler manifolds.
problem Understanding random walks on Finsler manifolds.
method Analyzing convergence of geodesic random walks to diffusion processes.
result The Brownian motion on a Riemannian metric is a key result.
A framework for computing holonomy groups of hybrid systems to achieve forward motion.
problem Achieving forward motion from periodic leg motion.
method Developing a framework for computing holonomy groups of hybrid systems.
result Computing holonomy groups of hybrid systems to achieve non-zero net motion.
Study homotopy motions of surfaces in 3-manifolds.
problem Understanding the behavior of surfaces under continuous deformations in 3-manifolds.
method Introduce and study homotopy motions of surfaces in closed orientable 3-manifolds.
result Systematic study of homotopy motions of surfaces in 3-manifolds.
The paper proposes a model to forecast traffic motion from sensor data.
problem Accurately predicting traffic motion for safe vehicle maneuvers.
method Implicit latent variable model using interaction graphs and graph neural networks.
result Achieves state-of-the-art motion forecasting and interaction understanding.
New SDEs use -Brownian motion, extending mean-field models.
problem Extending mean-field models to new types of stochastic processes.
method Introduced -SDEs with coefficients dependent on current state and solution as random variable.
result Validated new SDE framework for complex stochastic systems.
The sub-fractional CEV modelq-fin.MF
A new model captures option price dynamics using sub-fractional Brownian motion.
problem Capturing the complex price dynamics of financial options.
method Developed a CEV model driven by a mixed sub-fractional Brownian motion.
result Empirical tests show the model effectively captures option price dynamics.
New model uses generalized fractional Brownian motion for stock price prediction.
problem Traditional models fail to accurately predict stock price fluctuations.
method Introduces generalized fractional Brownian motion as a new stochastic process for price modeling.
result Validates the new model for option pricing and risk assessment.
Equations for minimal surfaces from rigid motions in high dimensions.
problem Finding minimal surfaces from rigid motions in .
method Derives equations for minimal surfaces using rigid motions in .
result Equations for minimal surfaces in .
Proposes using Dynamic Mode Decomposition with delays for short-term human motion anticipation.
problem Lack of interpretability and explainability in neural network-based motion anticipation methods.
method Dynamic Mode Decomposition with delays for motion representation and prediction.
result Anticipation errors comparable or better than recurrent neural networks for very short times.
This paper derives the non-analytic solution to the Fokker-Planck equation of fractional Brownian motion using the method of Laplace transform. Sequentially, by considering the fundamental solution of the non-analytic solution, this paper obtains the transition probability density function of the random variable that i…
RFC enhances humanoid control to imitate complex human motions.
problem Dynamics mismatch between humanoid models and real humans.
method Residual Force Control (RFC) augments control policies with external forces.
result RFC outperforms state-of-the-art methods in convergence speed and motion quality.
A Gaussian Markov alternative to fractional Brownian motion for pricing financial derivativesq-fin.MF
Replacing Black-Scholes' driving process, Brownian motion, with fractional Brownian motion allows for incorporation of a past dependency of stock prices but faces a few major downfalls, including the occurrence of arbitrage when implemented in the financial market. We present the development, testing, and implementatio…
Selective relevance method improves motion explainability in 3D activity recognition models.
problem Models do not appropriately factor motion information into their decisions.
method Selective relevance method to adapt 2D explanation techniques for 3D inputs.
result Improves selectivity of motion explanations, revealing model's spatial bias.
Linking human whole-body motion and natural language is of great interest for the generation of semantic representations of observed human behaviors as well as for the generation of robot behaviors based on natural language input. While there has been a large body of research in this area, most approaches that exist to…
The discrete sum of geometric Brownian motions plays an important role in modeling stochastic annuities in insurance. It also plays a pivotal role in the pricing of Asian options in mathematical finance. In this paper, we study the probability distributions of the infinite sum of geometric Brownian motions, the sum of …
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.
New geometric approach controls motion of a spinning sphere on a plane.
problem Controlling the motion of a spinning sphere on a straight path.
method Geometric-based planning approach using Darboux frame kinematics.
result Iterative algorithm tunes inputs for desired configurations.
Perceive, Predict, and Plan: Safe Motion Planning Through Interpretable Semantic Representationscs.RO
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.
Abstract: Study motion of divisors on curves with topological constraints.
problem Topological restrictions on divisors' motion.
method Analysis of closed motion of simple real divisors on non-singular real algebraic projective curves.
result Found topological restrictions on divisors' motion.
The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and…
The book explores stochastic areas and heat kernels on manifolds.
problem Understanding stochastic area functionals and heat kernels on manifolds.
method Study of Brownian motions and heat kernels on Lie groups and Riemannian manifolds.
result Rich interactions between stochastic calculus, geometry, and random matrices.
Modeling a Financial System with Memory via Fractional Calculus and Fractional Brownian Motionq-fin.ST
Modeling financial markets with memory using fractional calculus and Brownian motion.
problem Capturing memory effects in financial markets using stochastic models.
method Fractional Langevin equation with colored noise generated by fractional Brownian motion.
result Anomalous marginal glass phase observed in some regions of the system.
We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional periodic environment by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuous analysis. The case of a homogeneous environment has been recently treated by Braides, Gelli and…
Spectral gap estimates for Brownian motion on domains with sticky-reflecting boundary diffusionmath.PR
Estimates spectral gap for Brownian motion on sticky-reflecting domains.
problem Estimating spectral gap for Brownian motion on sticky-reflecting domains.
method Interpolation method and novel applications of Reilly formula.
result Lower bounds for spectral gap derived for general domains.
Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curvesnlin.SI
We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete …
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.