arXiv research

Study reveals dynamics of neural networks with normalization, weight decay, and SGD.

The Bounded Spherical Functions are determined for a Cartan Motion Group

Study integral kernels on complex symmetric spaces and their Dyson Brownian Motion applications.

Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.

We study the motion of a particle in the hyperbolic plane (embedded in Minkowski space), under the action of a potential that depends only on one variable. This problem is the analogous to the spherical pendulum in a unidirectional force field. However, for the discussion of the hyperbolic plane one has to distinguish …

The paper examines curvature and stability in quasi-geostrophic motions using spherical harmonics.

Simple geodesics on spherical tetrahedra identified for specific angles.

Study characterizes bladder motion using dynamic MRI and statistical analysis.

Study on curve shortening flow in 3D space curves, showing convexity preservation and avoidance principle.

Dual spherical conchoidal motion has been defined by Yapar. In this work, we define this motion on a dual hyperbolic unit sphere in the dual Lorentzian space with dual signature, and the results carried to the Lorentzian lines space by means of the Study s mapping. We also obtain the study maps of the orbits drawn on t…

By further developing the generalized $Γ$-calculus for hypoelliptic operators, we prove hypocoercive estimates for a large class of Kolmogorov type operators which are defined on non necessarily totally geodesic Riemannian foliations. We study then in detail the example of the velocity spherical Brownian motion, whose …

Paper proposes SMFN for high-res spherical video super-resolution.

Simplified Ricci curvature for spherical fluid dynamics models.

A single-vertex origami is a piece of paper with straight-line rays called creases emanating from a fold vertex placed in its interior or on its boundary. The Single-Vertex Origami Flattening problem asks whether it is always possible to reconfigure the creased paper from any configuration compatible with the metric, t…

Paper studies generic dynamics of MCFs with spherical singularities.

Model financial dynamics using 2-manifold geometries, revealing the torus as best for cyclical data.

The behavior of geodesic curves on even seemingly simple surfaces can be surprisingly complex. In this paper we use the Hamiltonian formulation of the geodesic equations to analyze their integrability properties. In particular, we examine the behavior of geodesics on surfaces defined by the spherical harmonics. Using t…

The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equation relating the coefficients that dictate the frame motion. In this work, we extend these investigations to characterize curves that lie on a…

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…

Survey on manifold complexities and motion planning in robotics.

We prove that the cosine law for spherical triangles and spherical tetrahedra defines integrable systems, both in the sense of multidimensional consistency and in the sense of dynamical systems.

It is known that the so-called rotation minimizing (RM) frames allow for a simple and elegant characterization of geodesic spherical curves in Euclidean, hyperbolic, and spherical spaces through a certain linear equation involving the coefficients that dictate the RM frame motion (da Silva, da Silva in Mediterr J Math …

Understanding biological network dynamics is a fundamental issue in various scientific and engineering fields. Network theory is capable of revealing the relationship between elements and their propagation; however, for complex collective motions, the network properties often transiently and complexly change. A fundame…

In dynamic environments, learned controllers are supposed to take motion into account when selecting the action to be taken. However, in existing reinforcement learning works motion is rarely treated explicitly; it is rather assumed that the controller learns the necessary motion representation from temporal stacks of …

RFC enhances humanoid control to imitate complex human motions.

A new neural network improves the accuracy of predicting constants of motion.

Study timelike bounce in charged null dust collapse, identifying key surfaces.

New cutoff phenomenon found for geodesic paths on hyperbolic manifolds.

We solve the dynamics of large spherical Minority Games (MG) in the presence of non-negligible time dependent external contributions to the overall market bid. The latter represent the actions of market regulators, or other major natural or political events that impact on the market. In contrast to non-spherical MGs, t…

For every compact surface $S$ of finite type (possibly with boundary components but without punctures), we show that when $n$ is sufficiently large there is no lift $σ$ of the surface braid group $B_n(S)$ to $\operatorname{Diff}(S,n)$, the group of $C^1$ diffeomorphisms preserving $n$ marked points and restricting to t…

Modeling price dynamics in AMMs with fees using geometric Brownian motion.

This paper presents preliminary work on learning the search heuristic for the optimal motion planning for automated driving in urban traffic. Previous work considered search-based optimal motion planning framework (SBOMP) that utilized numerical or model-based heuristics that did not consider dynamic obstacles. Optimal…

Paper compares machine learning methods for predicting target motion.

DMGNN predicts 3D human motions using adaptive multiscale graphs.

Derives equations of motion for systems with angular momentum on Finsler geometries.

Experimental fractal landscape dynamics observed in emulsions.

Louis Poinsot has shown in 1854 that the motion of a rigid body, with one of its points fixed, can be described as the rolling without slipping of one cone, the 'body cone', along another, the 'space cone', with their common vertex at the fixed point. This description has been further refined by the second author in 19…

Using generating functional and replica techniques, respectively, we study the dynamics and statics of a spherical Minority Game (MG), which in contrast with a spherical MG previously presented in J.Phys A: Math. Gen. 36 11159 (2003) displays a phase with broken ergodicity and dependence of the macroscopic stationary s…

This paper explains how predictable order flow can lead to Brownian motion in financial prices.

In this paper, a machine learning-based simulation framework of general-purpose multibody dynamics is introduced. The aim of the framework is to generate a well-trained meta-model of multibody dynamics (MBD) systems. To this end, deep neural network (DNN) is employed to the framework so as to construct data-based meta-…

A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from m…

Motion Code models time series dynamics with sparse approximations.

We derive a semi-analytic formula for the transition probability of three-dimensional Brownian motion in the positive octant with absorption at the boundaries. Separation of variables in spherical coordinates leads to an eigenvalue problem for the resulting boundary value problem in the two angular components. The main…

New method separates market motion from stock correlations.

Study nonrigid dynamics of unitary groups on Lie groups via kinetic energy metrics.

Explains planetary motion in a sub-Riemannian setting.

Context plays a significant role in the generation of motion for dynamic agents in interactive environments. This work proposes a modular method that utilises a learned model of the environment for motion prediction. This modularity explicitly allows for unsupervised adaptation of trajectory prediction models to unseen…

Construct intrinsic Langevin dynamics for rigid inclusions on curved surfaces.