The period of orbits in the restricted three-body problem depends on the enclosed region.
problem Understanding the period of orbits in the restricted three-body problem.
method Analyzing the relationship between the period and the enclosed region using the Jacobian integral.
result The period of a closed orbit is determined by the enclosed region and a function of the Jacobian integral.
Posing Kepler's problem of motion around a fixed "sun" requires the geometric mechanician to choose a metric and a Laplacian. The metric provides the kinetic energy. The fundamental solution to the Laplacian (with delta source at the "sun") provides the potential energy. Posing Kepler's three laws (with input from Gali…
Novel methods for splitting Gaussian mixtures improve uncertainty propagation in nonlinear systems.
problem Improving accuracy and efficiency in nonlinear uncertainty propagation.
method Preserving mean and covariance, novel heuristics for selecting splitting direction informed by initial uncertainty and nonlinear function properties.
result Improved accuracy and efficiency in uncertainty propagation compared to existing techniques.
Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a half-line drawn from the origin of V. The impulsion is a bivector whose support is …
MT-VAE learns motion transitions for generating diverse future motions.
problem Learning long-term human motion sequences with transitions.
method Jointly learns motion mode embeddings and transitions using Variational Auto-Encoders.
result Generates multiple plausible future motion sequences from input.
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.
Paper introduces new motion synthesis model using normalizing flows.
problem Data-driven motion synthesis with probabilistic and controllable models.
method Probabilistic, generative, autoregressive model using normalizing flows and LSTMs.
result Randomly sampled motion from the model outperforms task-agnostic baselines.
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.
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.
The paper extends holomorphic motions over non-simply connected Riemann surfaces.
problem Extending holomorphic motions over non-simply connected Riemann surfaces.
method Analyzing conditions for extending holomorphic motions over Riemann surfaces, focusing on the triviality of the monodromy.
result A topological condition, the triviality of the monodromy, is necessary and sufficient for extending a holomorphic motion of E E E over X X X to a holomorphic motion of C ^ \widehat{\mathbb{C}} C over X X X . Formula calculates optimal number of paths for correlated Brownian motions.
problem Determining the optimal number of paths for simulating correlated Brownian motions.
method Provides an explicit formula for the optimal number of paths.
result Optimal number of paths for simulating correlated Brownian motions is calculated.
Generative model learns motion to language and vice versa using deep RNNs.
problem Linking human motion and natural language for semantic representations and robot behaviors.
method Bidirectional mapping between motion and language using deep recurrent neural networks (RNNs) and sequence-to-sequence learning.
result Model generates realistic motions from natural language descriptions and vice versa.
Holomorphic motions can't map to complex domains.
problem Characterizing mappings between holomorphic motions and complex domains.
method Analyzing biholomorphic properties of graph mappings.
result Graphs of holomorphic motions cannot be biholomorphic to strongly pseudoconvex domains.
Paper solves fractional Brownian motion using Laplace transforms.
problem Fractional Brownian motion and its applications.
method Non-analytic solution via Laplace transform.
result Transition probability density function derived for fractional 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 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.
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.
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.
The paper studies discrete sums of geometric Brownian motions in finance.
problem Modeling stochastic annuities and pricing Asian options.
method Analyzes probability distributions and asymptotic behavior of discrete sums of geometric Brownian motions.
result Derives tail asymptotics and computes asymptotic distribution functions for discrete sums.
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.
New topological complexity considers efficient motion planners.
problem Existence of efficient motion planners.
method Introduced a variant of topological complexity for motion planners with shortest average path lengths.
result Topological complexity never differs by more than 1 from the new variant.
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.
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.
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.
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.
Derives financial models for markets with multidimensional Hermite motions.
problem Modeling financial markets with multidimensional Hermite motions.
method Derives conditions for no-arbitrage and market completeness, prices perpetual derivatives and forwards.
result Derives partial and partial-differential equations for pricing.
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 n n n -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…
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.
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.
MPNet uses neural networks for efficient motion planning.
problem Exponential increase in computational complexity with motion planning problem dimensionality.
method MPNet encodes workspaces from point cloud measurements and generates collision-free paths.
result MPNet is computationally efficient and generalizes to unseen environments.
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.
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.
Alternative model for financial derivatives pricing using Gaussian Markov process.
problem Inaccurate pricing of financial derivatives due to past dependency of stock prices.
method Developed a simplified Gaussian Markov process alternative to fractional Brownian motion.
result Improved accuracy in pricing derivatives by allowing past dependency.
New SDEs use G G G -Brownian motion, extending mean-field models.
problem Extending mean-field models to new types of stochastic processes.
method Introduced G G G -SDEs with coefficients dependent on current state and solution as random variable. result Validated new SDE framework for complex stochastic systems.
This paper shows that explicitly learning motion improves reinforcement learning in dynamic environments.
problem Learning controllers for dynamic environments without explicit motion representation.
method Explicitly learning motion representation using image difference or temporal stacks of frames.
result Explicit motion learning improves the quality of learned controllers in dynamic scenarios.
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.
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.
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.
Equations for minimal surfaces from rigid motions in high dimensions.
problem Finding minimal surfaces from rigid motions in R N \mathbb{R}^N R N . method Derives equations for minimal surfaces using rigid motions in R N \mathbb{R}^N R N . result Equations for minimal surfaces in R N \mathbb{R}^N R N .