arXiv research

Study characterizes bladder motion using dynamic MRI and statistical analysis.

Study compares LSTM, Transformer, and Mamba for bladder cancer recurrence analysis.

Proposes a two-stage method for testing variable interactions with FDR control.

New method provides reliable probabilistic bounds for VUR detection.

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…

Introduces Motion Programs for better video analysis of human motion.

Study motion planning for points avoiding obstacles in a plane.

Programmatic Motion Concepts learn human actions from paired videos.

Unified framework for human motion generation on Riemannian manifolds.

Study on determinants of unitary Brownian motion and their asymptotic laws.

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.

Neural network predicts vessel motions with high accuracy.

Study fractal dimension for motion without crossing a subset.

Let $E$ be a closed set in the Riemann sphere $\widehat{\mathbb{C}}$. We consider a holomorphic motion $φ$ of $E$ over a complex manifold $M$, that is, a holomorphic family of injections on $E$ parametrized by $M$. It is known that if $M$ is the unit disk $Δ$ in the complex plane, then any holomorphic motion of $E$ ove…

Study cohomological equation for robotic screw motions on SE(3).

New approach for obstacle avoidance in robotics using learned representations.

Paper defines multi-dimensional fractional Brownian motion under volatility uncertainty.

We consider $n$-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…

Researchers created a continuous Markov martingale that mimics Brownian motion but lacks the strong Markov property.

Improved vehicle motion prediction with uncertainty estimation.

The paper explores representations of graph manifolds to Seifert motion groups.

Geodesic walks converge to Brownian motion on Finsler manifolds.

A framework for computing holonomy groups of hybrid systems to achieve forward motion.

Study homotopy motions of surfaces in 3-manifolds.

The paper proposes a model to forecast traffic motion from sensor data.

New SDEs use $G$-Brownian motion, extending mean-field models.

The wide variety of motions performed by the human arm during daily tasks makes it desirable to find representative subsets to reduce the dimensionality of these movements for a variety of applications, including the design and control of robotic and prosthetic devices. This paper presents a novel method and the result…

Equations for minimal surfaces from rigid motions in high dimensions.

New model uses generalized fractional Brownian motion for stock price prediction.

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.

Diagnostic stroke imaging with C-arm cone-beam computed tomography (CBCT) enables reduction of time-to-therapy for endovascular procedures. However, the prolonged acquisition time compared to helical CT increases the likelihood of rigid patient motion. Rigid motion corrupts the geometry alignment assumed during reconst…

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.

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.

End-to-end learnable network for safer self-driving with interpretable intermediate representations.

New geometric approach controls motion of a spinning sphere on a plane.

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.

Modeling financial markets with memory using fractional calculus and Brownian motion.

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…

Estimates spectral gap for Brownian motion on sticky-reflecting domains.

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 $τ$ 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.

Affine deformations serve as basic examples in the continuum mechanics of deformable 3-dimensional bodies (referred as homogeneous deformations). They preserve parallelism and are often used as an approximation to general deformations. However, when the deformable body is a membrane, a shell or an interface modeled by …