arXiv research

Classifies 3-braids from choreographic motions on Lissajous curves, linking them to mapping classes and geodesics.

Math and dance blend in choreographer's research.

Since the foundational work of Chenciner and Montgomery in 2000 there has been a great deal of interest in choreographic solutions of the n-body problem: periodic motions where the n bodies all follow one another at regular intervals along a closed path. The principal approach combines variational methods with symmetry…

Our team of dance artists, physicists, and machine learning researchers has collectively developed several original, configurable machine-learning tools to generate novel sequences of choreography as well as tunable variations on input choreographic sequences. We use recurrent neural network and autoencoder architectur…

Dance Dance Revolution (DDR) is a popular rhythm-based video game. Players perform steps on a dance platform in synchronization with music as directed by on-screen step charts. While many step charts are available in standardized packs, players may grow tired of existing charts, or wish to dance to a song for which no …

With the aim of creating virtual cloth deformations more similar to real world clothing, we propose a new computational framework that recasts three dimensional cloth deformation as an RGB image in a two dimensional pattern space. Then a three dimensional animation of cloth is equivalent to a sequence of two dimensiona…

New periodic solutions found in 2n-body problem, braids of pseudo-Anosov type with stretch factors as metallic ratios.

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.

New framework predicts diverse, contextually plausible 3D human motions.

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…

Neural network estimates rigid motion in stroke imaging to improve image quality.

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.

The paper presents a method to reduce arm motion complexity for prosthetics and robotics.

Researchers calculate the Laplace transform of a geometric Brownian motion integral.

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

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…

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.

A new model captures option price dynamics using sub-fractional Brownian motion.

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

Equations for minimal surfaces from rigid motions in high dimensions.

Proposes using Dynamic Mode Decomposition with delays for short-term human motion anticipation.

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.

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.

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

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

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…