Related papers: Interpolating Rotations with Non-abelian Kuramoto …
In this paper we consider interpolation in model spaces, $H^2 \ominus B H^2$ with $B$ a Blaschke product. We study unions of interpolating sequences for two sequences that are far from each other in the pseudohyperbolic metric as well as…
We discuss how the kernel convolution approach can be used to accurately approximate the spatial covariance model on a sphere using spherical distances between points. A detailed derivation of the required formulas is provided. The proposed…
We show that the task of synthesizing human motion conditioned on a set of key frames can be solved more accurately and effectively if a deep learning based interpolator operates in the delta mode using the spherical linear interpolator as…
We provide an explicit geometric algorithm involving only ruler and compass constructions in order to specify the specular reflection point on the surface of a reflecting sphere of radius $r$ given two focal points $A$ and $B$ lying outside…
Imitation learning of robot policies from few demonstrations is crucial in open-ended applications. We propose a new method, Interaction Warping, for learning SE(3) robotic manipulation policies from a single demonstration. We infer the 3D…
A new algorithm is introduced to integrate the equations of rotational motion. The algorithm is derived within a leapfrog framework and the quantities involved into the integration are mid-step angular momenta and on-step orientational…
We present an improved and more accurate numerical scheme for a generalization of the Kuramoto model of coupled phase oscillators to the three-dimensional space. The present numerical scheme relies crucially on our observation that the…
AIMS: An alternative to the traditional method for modeling kinematics of the Earth's rotation is proposed. The purpose of developing the new approach is to provide a self-consistent and simple description of the Earth's rotation in a way…
Algebraic curve interpolation is described by specifying the location of N points in the plane and constructing an algebraic curve of a function f that should pass through them. In this paper, we propose a novel approach to construct the…
Based on the background of the 2021 Higher Education Club Cup National College Students Mathematical Contest in Modeling A, according to the relevant data of the China Sky Eye (FAST) radio telescope, the main cable nodes and actuators are…
We propose implicit integrators for solving stiff differential equations on unit spheres. Our approach extends the standard backward Euler and Crank-Nicolson methods in Cartesian space by incorporating the geometric constraint inherent to…
Video Frame Interpolation synthesizes non-existent images between adjacent frames, with the aim of providing a smooth and consistent visual experience. Two approaches for solving this challenging task are optical flow based and kernel-based…
Rotating wave approximation in a quantum spin system driven by a linearly polarized alternating magnetic field with quadrupole interaction presents is investigated in detail in this paper. The conventional way to employ the rotating wave…
In this paper a local approximation method on the sphere is presented. As interpolation scheme we consider a partition of unity method, such as the modified spherical Shepard's method, which uses zonal basis functions (ZBFs) plus spherical…
The one-dimensional Hatano-Nelson model with non-reciprocal hoppings is a prominent example of a relatively simple non-Hermitian quantum-mechanical system, which allows to study various phenomena in open quantum systems without adding extra…
In this work, we propose an approach to perform non-uniform image interpolation based on a Gaussian Mixture Model. Traditional image interpolation methods, like nearest neighbor, bilinear, Hamming, Lanczos, etc. assume that the coordinates…
We propose a new embedding method for a single vector and for a pair of vectors. This embedding method enables: a) efficient classification and regression of functions of single vectors; b) efficient approximation of distance functions; and…
We present the Hbot, a holonomic, singularity-free spherical robot designed for haptic simulations. The Hbot is made up of a caged sphere actuated by steered and driven non-holonomic wheels to produce continuous and unlimited spherical…
This article presents and compares four approaches for computing the rotation of a point about an axis by an angle in $\mathbb{R}^3$. We illustrate these methods by computing, by hand, the rotation of point $P=(1,0,1)^T$ about axis…
One of a classical synchronization model is the Kuramoto model. We propose both first and second order Kuramoto dynamical models on graphs using discrete optimal transport dynamics. We analyze the synchronization behaviors for some examples…