arXiv research

New model simplifies symmetry handling in generative AI.

New equations for rigid body motion on infinite-dimensional spaces of operators.

Paper compares Lagrangian reduction methods for rigid body systems.

Paper provides closed-form time derivatives for rigid body systems.

Geometrically interpolates rigid body motions with initial and terminal twists.

Develops computational methods for simulating rigid body dynamics on SO(3).

We consider an SO(4) Euler rigid body with two 'inertia momenta' coinciding. We study it from the point of view of bihamiltonian geometry. We show how to algebraically integrate it by means of the method of separation of variables.

Study of rigid body displacements in a projective space over dual numbers with geometric interpretations.

The numerical integration plays a fundamental role in understanding the behaviour of many mechanical systems. In this paper some important aspects of the mechanical integrators on the dynamics of a mechanical system are studied. More specific, we have shown that if that the Lie-Trotter integrator is obtained, in case o…

A linkage mechanism consists of rigid bodies assembled by joints which can be used to translate and transfer motion from one form in one place to another. In this paper, we are particularly interested in a family of spacial linkage mechanisms which consist of $n$-copies of a rigid body joined together by hinges to form…

Study on symmetries and equilibria in Poisson manifolds, with applications to rigid body dynamics.

Paper derives and applies a parallel transport equation on Lie groups.

Extended Regge complex for linearized Riemann-Cartan geometry and cohomology.

New normalizing flows model molecular crystal structures.

Integrates magnetic geodesic and sub-Riemannian flows on Stefel variety, proving integrability and Lax presentations.

Suppose that the initial triangle formed by the three moving masses of the three-body problem is similar to the triangle formed at some later time. We derive a simple integral formula for the overall rotation relating the two triangles. The formula is based on the fact that the space of similarity classes of triangles …

Optimizes angular velocity transfers for rigid bodies under deadline constraints.

The aim of this note is to present simple proofs of the completeness of Manakov's integrals for a motion of a rigid body fixed at a point in $\mathbb R^n$, as well as for geodesic flows on a class of homogeneous spaces $SO(n)/SO(n_1)\times\dots\times SO(n_r)$.

Model learns Lagrangian dynamics from images for better prediction and control.

Real-life control tasks involve matters of various substances---rigid or soft bodies, liquid, gas---each with distinct physical behaviors. This poses challenges to traditional rigid-body physics engines. Particle-based simulators have been developed to model the dynamics of these complex scenes; however, relying on app…

Paper reduces movement primitive dimensionality in parameter space.

Infants' spontaneous and voluntary movements mirror developmental integrity of brain networks since they require coordinated activation of multiple sites in the central nervous system. Accordingly, early detection of infants with atypical motor development holds promise for recognizing those infants who are at risk for…

We recast the Calabi flow in DeGiorgi's language of minimizing movements. We establish the long time existence of minimizing movements for K-energy with arbitrary initial condition. Furthermore we establish some a priori regularity of these solutions, and that sufficiently regular minimizing movements are smooth soluti…

We give a criterion of (micro-)kroneckerity of the linear Poisson pencil on $\frak{g}^*$ related to an algebraic Nijenhuis operator $N:\frak{g}\to \frak{g}$ on a finite-dimensional Lie algebra $\frak{g}$. As an application we get a series of examples of completely integrable systems on semisimple Lie algebras related t…

Taureau uses Twitter sentiment analysis to predict stock market movement.

We propose a sliding surface for systems on the Lie group $SO(3)\times \mathbb{R}^3$ . The sliding surface is shown to be a Lie subgroup. The reduced-order dynamics along the sliding subgroup have an almost globally asymptotically stable equilibrium. The sliding surface is used to design a sliding-mode controller for t…

This paper presents a novel approach for incremental semiparametric inverse dynamics learning. In particular, we consider the mixture of two approaches: Parametric modeling based on rigid body dynamics equations and nonparametric modeling based on incremental kernel methods, with no prior information on the mechanical …

The study models market price movement based on investors' expectations.

Neural nets predict user attention from mouse movements.

Paper proves minimizing movements match smooth droplet flow in 3D.

MPANF improves naive forecast by incorporating directional information.

We study involuntary micro-movements of the eye for biometric identification. While prior studies extract lower-frequency macro-movements from the output of video-based eye-tracking systems and engineer explicit features of these macro-movements, we develop a deep convolutional architecture that processes the raw eye-t…

Framework infers coordination strategies from movement data.

Neuroscientific studies of drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole. This work is about empirically supported mathematical ideas behind splitting and merging…

The Hamilton-Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias of the existence of a natural symplectic structure on the cotangent bundle. First it is developed …

Study identifies key trades predicting market movements.

The study introduces a new stickiness parameter for stock prices using a non-linear model.

The rise of non-linear and interactive media such as video games has increased the need for automatic movement animation generation. In this survey, we review and analyze different aspects of building automatic movement generation systems using machine learning techniques and motion capture data. We cover topics such a…

Bayesian method infers local rules for collective animal movement.

NoTMF forecasts sparse urban road movement speeds with nonstationary temporal matrix factorization.

Optimizing data movement significantly improves transformer training efficiency.

This paper presents a semi-parametric algorithm for online learning of a robot inverse dynamics model. It combines the strength of the parametric and non-parametric modeling. The former exploits the rigid body dynamics equa- tion, while the latter exploits a suitable kernel function. We provide an extensive comparison …

Study on pseudo-Riemannian Bertrand manifolds finds no closed movement systems.

Study identifies personality traits from dance movements in music.

There is a well-known example of integrable conservative system on $S^2$, the case of Kovalevskaya in the dynamics of a rigid body, possessing an integral of fourth degree in momenta. Goryachev proposed a one-parameter family of examples of conservative systems on $S^2$ possessing an integral of fourth degree in moment…

New algorithm reduces dynamic regret in time-varying movement costs.

Generically learns movement control policies from exploration data.

In this paper we will discuss some new developments in the design of numerical methods for optimal control problems of Lagrangian systems on Lie groups. We will construct these geometric integrators using discrete variational calculus on Lie groups, deriving a discrete version of the second-order Euler-Lagrange equatio…