A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study on rotating surfaces in 4D space with matrices.
A new transform links rotating calorons to solutions of a differential equation.
We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C. Moore in the Euclidean 4-space. We study Lorentz general rotational surfaces with plane meridian curves and give the complete classificat…
The paper defines and analyzes homotopic rotation sets for surfaces of higher genus.
Study of timelike surfaces in Minkowski space with specific geometric properties.
The study characterizes loxodromes on specific rotational surfaces in 3D space.
General rotational surfaces as a source of examples of surfaces in the four-dimensional Euclidean space have been introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the base of our invariant theory of spacelike surfaces we study general rotational surfaces with…
Rotation systems can't always be drawn in surfaces.
This paper proposes a set of rules to revise various neural networks for 3D point cloud processing to rotation-equivariant quaternion neural networks (REQNNs). We find that when a neural network uses quaternion features under certain conditions, the network feature naturally has the rotation-equivariance property. Rota…
RotEqNet preserves rotation symmetry in fluid systems using high-order tensors.
The rotation prediction (Rotation) is a simple pretext-task for self-supervised learning (SSL), where models learn useful representations for target vision tasks by solving pretext-tasks. Although Rotation captures information of object shapes, it hardly captures information of textures. To tackle this problem, we intr…
The paper applies Clairaut's theorem to rotational surfaces in pseudo-Euclidean 4-space.
Convolutional networks are successful due to their equivariance/invariance under translations. However, rotatable data such as images, volumes, shapes, or point clouds require processing with equivariance/invariance under rotations in cases where the rotational orientation of the coordinate system does not affect the m…
We consider -dimensional discrete motions such that any two neighbouring positions correspond in a pure rotation ("rotating motions"). In the Study quadric model of Euclidean displacements these motions correspond to quadrilateral nets with edges contained in the Study quadric ("rotation nets"). The main focus of ou…
Minimal sets of moves for rotational Reidemeister diagrams are identified.
New method studies moving points on curves using rotating frames.
Study on rotational hypersurfaces with constant Gauss-Kronecker curvature.
In-plane drill rotations are impossible for smooth shells.
Positive factorization found for a specific map on surfaces.
Study of rotation angles in a rotating disc model.
The study disproves rotating ancient flows in 4D space.
Study rotational surfaces with prescribed Gauss curvature in 3D space.
In this work, we study a class of rotational surfaces in the pseudo-Euclidean space whose profile curves lie in two-dimensional planes. We solve the differential equation that characterizes the rotational surfaces with zero mean curvature to determine the profile curves of such rotational surfaces. The…
The paper classifies CMC free boundary hypersurfaces in rotational domains.
We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis which give…
Helicoidal surfaces rotate and translate under mean curvature flow.
The study explores special surfaces in a normed space.
Extends Euler class result to symplectic group.
The study characterizes helices in Euclidean and hyperbolic spaces.
We study the problem of learning representations of entities and relations in knowledge graphs for predicting missing links. The success of such a task heavily relies on the ability of modeling and inferring the patterns of (or between) the relations. In this paper, we present a new approach for knowledge graph embeddi…
In this paper we study general rotational surfaces in the 4- dimensional Euclidean space E4 and give a characterization of flat general rotation surface with pointwise 1-type Gauss map. Also, we show that a non-planar flat general rotation surface with pointwise 1-type Gauss map is a Lie group if and only if it is a Cl…
In the four-dimensional pseudo-Euclidean space with neutral metric there are three types of rotational surfaces with two-dimensional axis - rotational surfaces of elliptic, hyperbolic or parabolic type. A surface whose mean curvature vector field is lightlike is said to be quasi-minimal. In this paper we classify all q…
New quadratic forms expand and rotate linear endomorphisms in geometric theory.
In neural networks, it is often desirable to work with various representations of the same space. For example, 3D rotations can be represented with quaternions or Euler angles. In this paper, we advance a definition of a continuous representation, which can be helpful for training deep neural networks. We relate this t…
Motivated by Wick-rotations of pseudo-Riemannian manifolds, we study real geometric invariant theory (GIT) and compatible representations. We extend some of the results from earlier works \cite{W2,W1}, in particular, we give some sufficient as well as necessary conditions for when pseudo-Riemannian manifolds are Wick-r…
In short, our experiments suggest that yes, on average, rotation forest is better than the most common alternatives when all the attributes are real-valued. Rotation forest is a tree based ensemble that performs transforms on subsets of attributes prior to constructing each tree. We present an empirical comparison of c…
RP-GFRFT unifies fractional order and rotation control for graph signals.
Characterizes rotational solitons for curve shortening flow on revolution surfaces.
Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map translations. This is not the case for rotations. Global rotation equivariance is typic…
Recent work (Cohen & Welling, 2016) has shown that generalizations of convolutions, based on group theory, provide powerful inductive biases for learning. In these generalizations, filters are not only translated but can also be rotated, flipped, etc. However, coming up with exact models of how to rotate a 3 x 3 filter…
The rotation angle of a rolling disc is shown to be a geometric phase related to the Hopf fibration.
New formula for rotation number without needing a base point.
New approach to rotational Weingarten surfaces using geometric momentum.
We investigate the duality between minimal surfaces in Euclidean space and maximal surfaces in Lorentz-Minkowski space in the family of rotational surfaces. We study if the dual surfaces of two congruent rotational minimal (or maximal) surfaces are congruent. We show that in the duality process by means of a one-parame…
Study on unique minimal hypersurfaces in rotational domains.
Study on rotational surfaces in de Sitter space with specific curvature conditions.
GCNNs gain rotation invariance with more training augmentation, making SVD-Universal more effective.
We study Wick-rotations of left-invariant metrics on Lie groups, using results from real GIT (\cite{1}, \cite{2}, \cite{3}). An invariant for Wick-rotation of Lie groups is given, and we describe when a pseudo-Riemannian Lie group can be Wick-rotated to a Riemannian Lie group. We also prove a general version (for gener…