相关论文: South Pointing Chariot: An Invitation to Different…

Although Bayesian methods are robust and principled, their application in practice could be limited since they typically rely on computationally intensive Markov Chain Monte Carlo algorithms for their implementation. One possible solution…

The eccentric pie chart, a generalization of the traditional pie chart is introduced. An arbitrary point is fixed within the circle and rays are drawn from it. A sector is bounded by a pair of neighboring rays and the arc between them, The…

In this text, we explore the tools that Projective Differential Geometry can provide for the asymptotic analysis of classical fields on projectively compact manifolds. We emphasise on the case of order 2-compactifications and develop, in…

Since the subject of noncommutative geometry is now entering maturity, we felt there is need for presentation of the material at an undergraduate course level. Our review is a zero order approximation to this project. Thus, the present…

Deviation equation: Second order differential equation for the 4-vector which measures the distance between reference points on neighboring world lines in spacetime manifolds. Relativistic geodesy: Science representing the Earth (or any…

To definite and compute differential invariants, like curvatures, for triangular meshes (or polyhedral surfaces) is a key problem in CAGD and the computer vision. The Gaussian curvature and the mean curvature are determined by the…

Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…

In this study, we investigate the problem of tracking objects with unknown shapes using three-dimensional (3D) point cloud data. We propose a Gaussian process-based model to jointly estimate object kinematics, including position,…

In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…

This book is a textbook for the basic course of differential geometry. It is recommended as an introductory material for this subject.

Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…

The Peirce quincuncial projection is a mapping of the surface of a sphere to the interior of a square. It is a conformal map except for four points on the equator. These points of non-conformality cause significant artifacts in photographic…

We develop a mathematical concept towards gauge field theories based upon a Hilbert space endowed with a representation of a skew-adjoint Lie algebra and an action of a generalized Dirac operator. This concept shares common features with…

We introduce the historical development and physical idea behind topological Yang-Mills theory and explain how a physical framework describing subatomic physics can be used as a tool to study differential geometry. Further, we emphasize…

For a geodesic ball with non-negative Ricci curvature and almost maximal volume, without using compactness argument, we construct an $\epsilon$-splitting map on a concentric geodesic ball with uniformly small radius. There are two new…

The Gaussian process is a powerful and flexible technique for interpolating spatiotemporal data, especially with its ability to capture complex trends and uncertainty from the input signal. This chapter describes Gaussian processes as an…

This is an elementary introduction to exterior differential systems motivated by two examples: minimal submanifolds and the isometric embedding problem. The two main goals of the lectures are: 1. To explain how to find an appropriate…

Certain wheeled mobile robots e.g., electric wheelchairs, can operate through indirect joystick controls from users. Correct steering angle becomes essential when the user should determine the vehicle direction and velocity, in particular…

The students build and use an old navigational tool from the Arab world of the 9th century, the kamal. After an introduction to historic seafaring and navigation, they build this simple tool and understand how it can be used to measure…

Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…