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We give an elementary derivation of the Montgomery phase formula for the motion of an Euler top, using only basic facts about the Euler equation and parallel transport on the 2-sphere (whose holonomy is seen to be responsible for the…
The paper proposes a technique to estimate the angular velocity of a rigid body from vector measurements. Compared to the approaches presented in the literature, it does not use attitude information nor rate gyros as inputs. Instead, vector…
The Euler-Maclaurin summation formula is generalized to a modified form by expanding the periodic Bernoulli polynomials as its Fourier series and taking cuts, which includes both the Euler-Maclaurin summation formula and the Poission…
We consider a parameter identification problem related to a quasi-linear elliptic Neumann boundary value problem involving a parameter function $a(\cdot)$ and the solution $u(\cdot)$, where the problem is to identify $a(\cdot)$ on an…
In this paper, the dynamic modeling of a seven linked humanoid robot, is accurately developed, in the three dimensional space using the Newton-Euler formalism. The aim of this study is to provide a clear and a systematic approach so that…
Robotics and computer vision problems commonly require handling rigid-body motions comprising translation and rotation - together referred to as pose. In some situations, a vectorial parameterization of pose can be useful, where elements of…
The paper discusses the improvement of the accuracy of an inertial navigation system created on the basis of MEMS sensors using machine learning (ML) methods. As input data for the classifier, we used infor-mation obtained from a developed…
Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter.…
We consider the problem of computing the Euler characteristic of an abstract simplicial complex given by its vertices and facets. We show that this problem is #P-complete and present two new practical algorithms for computing Euler…
Certain triangle inequalities involving the circumradius, inradius, and side lengths of a triangle are generalized to spherical and hyperbolic geometry. Examples include strengthenings of Euler's inequality, $R\geq2r$. An extension of…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from the symmetry argument for three kinds of variables. One is a…
This paper explores learning emulators for parameter estimation with uncertainty estimation of high-dimensional dynamical systems. We assume access to a computationally complex simulator that inputs a candidate parameter and outputs a…
Many existing translation averaging algorithms are either sensitive to disparate camera baselines and have to rely on extensive preprocessing to improve the observed Epipolar Geometry graph, or if they are robust against disparate camera…
We use some basic properties of binomial and Stirling numbers to prove that the Euler characteristic is, essentially, the unique numerical topological invariant for compact polyhedra which can be expressed as a linear combination of the…
The shape of a molecule determines its physicochemical and biological properties. However, it is often underrepresented in standard molecular representation learning approaches. Here, we propose using the Euler Characteristic Transform…
We address the problem of human motion tracking by registering a surface to 3-D data. We propose a method that iteratively computes two things: Maximum likelihood estimates for both the kinematic and free-motion parameters of a kinematic…
Previous work on predicting or generating 3D human pose sequences regresses either joint rotations or joint positions. The former strategy is prone to error accumulation along the kinematic chain, as well as discontinuities when using Euler…
We present a novel analysis method for measurements of polarization transferred in $A(\vec{e},e'\vec{N})$ experiments, which can be applied to other kinds of polarization measurements as well. In this method the polarization transfer…
More than 150 years after their invention by Hamilton, quaternions are now widely used in the aerospace and computer animation industries to track the paths of moving objects undergoing three-axis rotations. It is shown here that they…