相关论文: Symmetric similarity 3D coordinate transformation …
We generalize the background gauge in the Matrix model to propose a new gauge which is useful for discussing the conformal symmetry. In this gauge, the special conformal transformation (SCT) as the isometry of the near-horizon geometry of…
Some new properties of symmetries that disappear as point symmetries after the first reduction of order of an ODE and reappear after the second are analyzed from the aspect of three-dimensional subalgebra of symmetries of differential…
The idea of style similarity metrics has been recently developed for various media types such as 2D clip art and 3D shapes. We explore this style metric problem and improve existing style similarity metrics of 3D shapes in four novel ways.…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
Navigating cluttered environments is a challenging task for any mobile system. Existing approaches for ground-based mobile systems primarily focus on small wheeled robots, which face minimal constraints with overhanging obstacles and cannot…
Geometric Deep Learning techniques have become a transformative force in the field of Computer-Aided Design (CAD), and have the potential to revolutionize how designers and engineers approach and enhance the design process. By harnessing…
While conformal transformations of the plane preserve Laplace's equation, Lorentz-conformal mappings preserve the wave equation. We discover how simple geometric objects, such as quadrilaterals and pairs of crossing curves, are transformed…
Applications of the three-dimensional transformation for rotating coordinate systems to quantum mechanics, general theory relativity and optics are considered.
Noncommutative geometry has seen remarkable applications for high energy physics, viz. the geometrical interpretation of the Standard Model. The question whether it also allows for supersymmetric theories has so far not been answered in a…
We study the problem of symmetry detection of 3D shapes from single-view RGB-D images, where severely missing data renders geometric detection approach infeasible. We propose an end-to-end deep neural network which is able to predict both…
State-of-the-art methods for driving-scene LiDAR-based perception (including point cloud semantic segmentation, panoptic segmentation and 3D detection, \etc) often project the point clouds to 2D space and then process them via 2D…
The laws of quantum-critical scaling theory of quantum fidelity, dependent on the underlying system dimensionality $D$, have so far been verified in exactly solvable $1D$ models, belonging to or equivalent to interacting, quadratic…
Surveying techniques such as Terrestrial Laser Scanner have recently been used to measure surface changes via 3D point cloud (PC) comparison. Two types of approaches have been pursued: 3D tracking of homologous parts of the surface to…
We propose a geometric numerical analysis of SDEs admitting Lie symmetries which allows us to individuate a symmetry adapted coordinates system where the given SDE has notable invariant properties. An approximation scheme preserving the…
We sketch a procedure to capture general non-invertible symmetries of a d-dimensional quantum field theory in the data of a higher-category, which captures the local properties of topological defects associated to the symmetries. We also…
Template matching is a basic method in image analysis to extract useful information from images. In this paper, we suggest a new method for pattern matching. Our method transform the template image from two dimensional image into one…
We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…
We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used,…
A manifestly Lorentz-covariant calculus based on two matrix-coordinates and their associated derivatives is introduced. It allows formulating relativistic field theories in any even-dimensional spacetime. The construction extends a…